Emerging Evidence of a Second Glass Phase in Strong to Ultra-Fragile Bulk Metallic Glass-Forming Liquids - CaltechTHESIS

Emerging Evidence of a Second Glass Phase in Strong to Ultra-Fragile Bulk Metallic Glass-Forming Liquids - CaltechTHESIS
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Emerging Evidence of a Second Glass Phase in Strong to Ultra-Fragile Bulk Metallic Glass-Forming Liquids
Citation
Corona, Sydney Lea
(2022)
Emerging Evidence of a Second Glass Phase in Strong to Ultra-Fragile Bulk Metallic Glass-Forming Liquids.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/9bvb-2d78.
Abstract
This thesis compiles three experimental works that provide evidence for distinct bulk metallic glass (BMG) phases across a range of kinetic fragilities. Motivated by An et al.’s computational discovery of a secondary heterogeneous glass phase in pure Ag and binary AgCu and CuZr, the thesis reports the distinct glass phases in the high and ultra-high fragile regime with a tunable Pt
80-X
Cu
20
system, and the
kinetically strong Ni
71.4
Cr
5.64
Nb
3.46
16.5
(Ni208) BMG.
The high-fragility work utilizes direct measurement techniques for liquid configurational enthalpy as a function of temperature on anneal-equilibrated samples (Chapter 2). An apparent first-order glass-melting transition is revealed across kinetic fragilities ranging from m = 60 to over 90. The glass-melting temperature, T
gm
, traverses up the ∆T region with increasing Cu content, X. A further experimental study of PtCuP explored the traditional and second glass phases to determine if they are in fact equivalent to the two glasses of An et al. (Chapter 3). Hardness data reveal that while the high-fragility samples grow the second glass during anneal, it forms in the ultra-fragile samples on quenching. Further, this apparent glass-melting transition is visible via traditional thermodynamic methods in ultra-fragile samples. For X = 20, where T
gm
is in the inaccessible ∆T region, rapid capacitive discharge heating visualizes T
gm
as well.
Investigation of a kinetically stronger Ni-based BMG connects the presence of the secondary glass to the embrittlement transition in Ni208 (Chapter 4). Inclusions are only present in embrittled samples, and are suppressed to lower temperatures when the initial melt is overheated above a critical toughening temperature. The inclusions show a heterogeneous structure and 30% increased hardness, similar to the computational Ag secondary glass phase.
These works provide compelling evidence for the existence of a secondary glass phase across the spectrum from strong to ultra-fragile glasses, and validates the initial computational discovery. This proves to be a significant work, as it presents direct experimental evidence of a novel phenomenon in metallic liquids, and presents a new solid-like glass phase.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Bulk Metallic Glass; BMG; Angell Kinetic Fragility; Strong; Tough; Fragile; notch fracture toughness; indentation; Calorimetry; Mechanics; Secondary Glass Phase; G-Phase; L-Phase; Inclusions;
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Johnson, William Lewis (advisor)
Samwer, Konrad (co-advisor)
Thesis Committee:
Fultz, Brent T. (chair)
Johnson, William Lewis
Samwer, Konrad
Goddard, William A., III
Schwab, Keith C.
Defense Date:
28 April 2022
Funders:
Funding Agency
Grant Number
NSF Graduate Research Fellowship
UNSPECIFIED
NSF
UNSPECIFIED
Record Number:
CaltechTHESIS:04132022-221839497
Persistent URL:
DOI:
10.7907/9bvb-2d78
Related URLs:
URL
URL Type
Description
DOI
Article adapted for Chapter 2.
DOI
Figure adapted for Chapter 4.
Other
Figure adapted for Chapter 4.
ORCID:
Author
ORCID
Corona, Sydney Lea
0000-0002-4962-619X
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
14545
Collection:
CaltechTHESIS
Deposited By:
Sydney Corona
Deposited On:
02 Jun 2022 19:51
Last Modified:
08 May 2024 16:35
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Emerging Evidence of a Second Glass Phase in Strong to
Ultra-Fragile Bulk Metallic Glass-Forming Liquids

Thesis by

Sydney Lea Corona
they.them.theirs

In Partial Fulfillment of the Requirements for the
Degree of
Doctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2022
Defended 28 April 2022

ii

Sydney Lea Corona
they.them.theirs
ORCID: 0000-0002-4962-619X

To the part of me I lost
And all the parts I found

iv

ACKNOWLEDGEMENTS
Your PhD is a fight. On the third floor of Keck there is a story that describes
one’s thesis defense as fighting a snake (Appendix E). It describes that the
longer the time spent in your PhD, the smaller the snake you fight in your
defense. But what they don’t tell you is that some of us come in with a snake
we are already fighting. Sometimes these are small battles, sometimes they
are life or death. Mine were the latter. I entered Caltech with PTSD, anxiety,
and depression. Through my time here I found myself, my chosen family, refound my given family, and much more. Through communities of dance and
climbing I found self expression, strength, and encouragement. Through
my advisor’s field of researchers he nurtured himself, I found camaraderie
and family. Around the world in my research exchange in Finland I found
how small this place really is and how connected we can be. Through all of
it, I found a family, and that family saved my life.
First, I want to first thank my advisor, Bill Johnson, for both long discussions about
science and open conversations about the rigor and difficulty of graduate school.
I have always appreciated your honesty, and it has helped me find my way. The
group you fostered over your career is full of genuine, kind, and humble humans,
as well as impactful and impressive researchers. This unique combination of traits
comes directly from your humility, brilliance, and hard work, and drives me to raise
students and postdocs of the same quality of person hood. And finally, thank you
Bill for granting me the freedom to grow both personally and professionally, for the
second could not have happened without the first.
I would like to thank my co-advisor, Konrad Samwer. Your enthusiasm and support
for my degree has been continually validating. I appreciate so greatly your offering
to be my co-advisor "whether it can be done formally or not" simply because you
wanted to support me on my journey. Your guidance has helped me find a next job
that is supportive of my professional and personal journey, and your emphasis and
reminders to maintain myself and my values remain close to my heart.
I would like to thank Bill Goddard for your kindness and generosity. You offered
me a group to interact with in my last year — offering me the camaraderie I
had been missing. Thank you for making me a welcomed member of the group,
enthusiastically discussing my work at such dinners with anyone who would listen,

and for collaborating on our computational works. Your brilliance and guidance are
greatly appreciated.
Thank you Keith Schwab for our regular chats throughout my degree. We sometimes
discussed work, but most often we discussed the things we enjoy and keep us sane:
the outdoors. Thank you for encouraging me to always follow my passions and
to continue my hobbies no matter how hard work became, for that was when they
would be most important. I look forward to these chats through our futures as well.
Thank you Brent Fultz for supporting my accommodations during courses in my
first two years, and providing research group camaraderie in my third and fourth
years. Your group has been very supportive, a joyful home base at conferences, and
I am greatly appreciative for you all.
Thank you Kathy Faber for supporting my candidacy work and including me in your
group in my early Caltech years. Our passing conversations in the halls of Keck
gave wonderful support and guidance to new instruments and techniques.
I would like to thank my candidacy committee, Kathy Faber, Keith Schwab, and
Brent Fultz for their time in my candidacy exam, guidance throughout my degree,
and support as I finish.
Next I want to thank my therapists and my self for the work put in to better understand
myself and my needs throughout my career. I entered graduate school with PTSD
and the regular work independently and in therapy has helped me immensely with
maneuvering how I interact with the world. I write this for I believe it should not
be kept secret, for battles with mental health should be de-stigmatized. I started
therapy the year before graduate school, continued throughout, and will continue
through my career. I would also like to thank my therapy cat, Paisley, for she has
been so joyously supportive and silly every time I need it.
I want to thank my mentors turned friends that have supported me throughout
my career thus far — Emily Kinser, Jenna Balestrini, and Sam Johnson for being
unstoppable female forces. Michael Floyd and Andrew Hoff for their expertise in
maneuvering the graduate experience in Bill’s lab. Jose Lado and Bruno Amorim
for your advice and guidance on my first postdoc proposal — offering your time
to someone you did not know was incredibly validating and you have all of my
gratitude. And to all of you, I am continually grateful for your candid honesty about
your experience. It prepared me more than I could imagine. Thank you.
I would like to thank those I met in my hobbies of climbing and dancing over the

vi
last few years. Your encouragement and excitement have been a wonderful balance
to the stress of graduate school. Thank you for holding safe space for me and all
my parts. I loved sharing in these spaces. I could not possibly write a list in fear of
missing someone, so know I love you all dearly and hold you close in my heart.
I would like to thank my family for their unconditional love, support, and acceptance
of me and my self as I have grown into who I am as a person. This has been deeply
healing for me, and words cannot express how much your love in these recent years
has meant, and how foundational it has been in the development of my strengths.
Your love and acceptance of my non-binary self has been beautiful. Thank you, I
love you all. Mom and Dad, I love you so dearly. Thank you for being there to listen
and/or support me in whatever ways I’ve needed over my life. You both listen and
care so beautifully, and it means so much.
Paul Buerkner, thank you for always being yourself and showing me I can do the
same. You were the first person to give me the safe space to be fully myself outside
of gender, and you see me for all I am, always. I continually learn so much from you
and words cannot describe how wonderful you are. I love you deeply and I remain
excited for all of our adventures to come.
David Cutler-Creutz, your love and support have helped me find more love and
deeper acceptance for my self and my body. You help me relinquish insecurities
I no longer want to carry, showing me they were never mine to hold in the first
place. Thank you for sharing in this adventure with me, for our explorations and
silly adventures fill my joyous memories. I’m sure I’ll see you soon.
Éowyn Lucas, thank you for showing me how strong someone can be — in body,
mind, and heart — and for showing me I have that in myself too. Our friendship
is so deeply supportive of independence, autonomy, human connection, and safe
spaces. You are such a genuine, loving human. Let’s go cry on some big walls.
Thank you Katie Shanks, Claire Saunders, Daniel Mukasa, and Shaheed Qaasim
for being my homies and holding such safe spaces for me as I explore who I am
as a person. Your judgement-free accepting spaces have helped me grow so much.
Katie, it has been a joy exploring the non-binary space with you. You remind me of
all the ways I can be myself, and help me adventure thoroughly. Claire, #choochoo.
Love you dearly, ride or die. Thank you for trusting me with your self and your
being. I’m honored and I look forward to all our shenanigans to come. Daniel, it
has been an absolute gift getting to know you over quarantine and finding such a

vii
wonderful human to laugh with. I’ve loved every moment of or boba walks and
conversations. Cheers to never being burnt-out again. Shaheed, our long phone
calls are always a joy. I’ve appreciated our honest conversations exploring so many
topics that are easy, and others that are hard. Thank you for always being honestly
your self. You are an incredible human and I am so very grateful to call you my
friend.
I would like to thank my quarantine bubble: Éowyn Lucas, David Cutler-Kreutz,
and Logan Gloor. We made it through a wild year with an abundance of silliness
and adventures, and I am so grateful to have us all on the dream quaran-team.
Academically, I have many people to thank. I’d like to thank Joerg Loeffler and
Mihai Stoicha at ETH Zurich, and Jong Hyun Na at GMT for support on sample
casting, as well as Celia Chari for SEM and Seola Lee for nanoindentation help
during COVID. To the Johnson group alumni at Bill’s retirement party, thank you
for the many candid conversations about academia. This really helped me find that I
wanted to pursue academia and that my approach was feasible. Dale Conner, thank
you for reminding me to not make sure every box is checked before testing something,
but also showing me that some of them should definitely be checked before testing
something. Thank you to all the students I have mentored, for as I taught you,
you have helped me learn more about myself. TMS conference colleagues and
friends, our candid conversations have been brilliant. You are true wing-humans of
academia.
To my Finland family, thank you for being my home and family. You all know how
much my time in Finland meant to me, so you know I cannot possibly put it all into
words. But I found my self there. I accepted my self there. And I felt so loved for
being myself there. I miss you all so dearly and I’ll see you soon.
To my wild Taco Tuesday homies, thank you for a regular dose of bi-weekly shenanigans and spontaneity. The silliness is an absolute joy every time, and we never cease
to amaze me with the adventures we pursue.
The Caltech Y, to Greg and Agnes and JJ, thank you for hosting such a kind and
wonderful space to explore leadership and the outdoors. Our many trips kept me
grounded in my first few years and I will cary these memories with me as I continue
through life. Thank you.

viii

ABSTRACT

This thesis compiles three experimental works that provide evidence for distinct
bulk metallic glass (BMG) phases across a range of kinetic fragilities. Motivated
by An et al.’s computational discovery of a secondary heterogeneous glass phase in
pure Ag and binary AgCu and CuZr, the thesis reports the distinct glass phases in
the high and ultra-high fragile regime with a tunable Pt80−X Cu X P20 system, and the
kinetically strong Ni 71.4Cr5.64 N b3.46 P16.5 B3 (Ni208) BMG.
The high-fragility work utilizes direct measurement techniques for liquid configurational enthalpy as a function of temperature on anneal-equilibrated samples (Chapter
2). An apparent first-order glass-melting transition is revealed across kinetic fragilities ranging from m = 60 to over 90. The glass-melting temperature, Tgm , traverses
up the ∆T region with increasing Cu content, X. A further experimental study of
PtCuP explored the traditional and second glass phases to determine if they are in
fact equivalent to the two glasses of An et al. (Chapter 3). Hardness data reveal that
while the high-fragility samples grow the second glass during anneal, it forms in the
ultra-fragile samples on quenching. Further, this apparent glass-melting transition
is visible via traditional thermodynamic methods in ultra-fragile samples. For X =
20, where Tgm is in the inaccessible ∆T region, rapid capacitive discharge heating
visualizes Tgm as well.
Investigation of a kinetically stronger Ni-based BMG connects the presence of the
secondary glass to the embrittlement transition in Ni208 (Chapter 4). Inclusions
are only present in embrittled samples, and are suppressed to lower temperatures
when the initial melt is overheated above a critical toughening temperature. The
inclusions show a heterogeneous structure and 30% increased hardness, similar to
the computational Ag secondary glass phase.
These works provide compelling evidence for the existence of a secondary glass
phase across the spectrum from strong to ultra-fragile glasses, and validates the
initial computational discovery. This proves to be a significant work, as it presents
direct experimental evidence of a novel phenomenon in metallic liquids, and presents
a new solid-like glass phase.

ix

PUBLISHED CONTENT AND CONTRIBUTIONS

[1] Qi An et al. “The L–G phase transition in binary Cu–Zr metallic liquids”.
In: Physical Chemistry Chemical Physics 24.1 (2022), pp. 497–506. issn:
1463-9076, 1463-9084. doi: 10.1039/D1CP04157F. url: http://xlink.
rsc.org/?DOI=D1CP04157F (visited on 02/15/2022).
Sydney L. Corona contributed to the research discussions, conducted parallel
experimental tests (pending publication), and supported writing and editing
of the manuscript.
[2] Yidi Shen et al. “Shear Banding in Binary Cu-Zr Metallic Glass: Comparison
of the G-Phase With L-Phase”. In: Frontiers in Materials 9 (2022). issn:
2296-8016. url: https://www.frontiersin.org/article/10.3389/
fmats.2022.886788 (visited on 06/02/2022).
Sydney L. Corona contributed to the research discussions, conducted parallel
experimental tests (pending publication), and supported writing and editing
of the manuscript.
[3] Qi An et al. “The first order L-G phase transition in liquid Ag and AgCu alloys is driven by deviatoric strain”. In: Scripta Materialia 194 (Mar.
2021), p. 113695. issn: 13596462. doi: 10.1016/j.scriptamat.2020.
113695. url: https://linkinghub.elsevier.com/retrieve/pii/
S1359646220308174 (visited on 03/25/2021).
Sydney L. Corona contributed to the research discussions, conducted parallel
experimental tests (pending publication), and supported writing and editing
of the manuscript.
[4] Qi An et al. “First-Order Phase Transition in Liquid Ag to the Heterogeneous
G-Phase”. In: The Journal of Physical Chemistry Letters 11.3 (Feb. 6, 2020),
pp. 632–645. issn: 1948-7185, 1948-7185. doi: 10.1021/acs.jpclett.
9b03699. url: https://pubs.acs.org/doi/10.1021/acs.jpclett.
9b03699 (visited on 06/06/2020).
Sydney L. Corona contributed to the research discussions, conducted parallel
experimental tests (pending publication), and supported writing and editing
of the manuscript.
[5] Qi An et al. “Formation of two glass phases in binary Cu-Ag liquid”. In: Acta
Materialia 195 (Aug. 2020), pp. 274–281. issn: 13596454. doi: 10.1016/
j.actamat.2020.05.060. url: https://linkinghub.elsevier.com/
retrieve/pii/S1359645420304079 (visited on 07/13/2020).
Sydney L. Corona contributed to the research discussions, conducted parallel
experimental tests (pending publication), and supported writing and editing
of the manuscript.
[6] Jong H. Na et al. “Observation of an apparent first-order glass transition in
ultrafragile Pt–Cu–P bulk metallic glasses”. In: Proceedings of the National

Academy of Sciences 117.6 (Feb. 11, 2020), pp. 2779–2787. issn: 0027-8424,
1091-6490. doi: 10.1073/pnas.1916371117. url: http://www.pnas.
org/lookup/doi/10.1073/pnas.1916371117 (visited on 06/06/2020).
Sydney L. Corona contributed to the research discussions, manufactured
specimens for testing, conducted thermodynamic experiments, and helped
write and edit the manuscript and supplemental materials.

xi

TABLE OF CONTENTS

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Published Content and Contributions . . . . . . . . . . . . . . . . . . . . . . ix
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
List of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
Chapter I: The History and Evolution of the Field of Bulk Metallic Glass . . . 1
1.1 Metallic Glass and the Bulk Form . . . . . . . . . . . . . . . . . . . 1
1.2 Classical Theory for Bulk Metallic Glass . . . . . . . . . . . . . . . 6
1.3 Formation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4 Transition Types and Melting Criteria . . . . . . . . . . . . . . . . . 22
1.5 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Chapter II: The Emergent First-Order Phase Transition in Ultra-Fragile Pt80−x Cu x P20
Bulk Metallic Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . 50
Chapter III: Characterization of the Secondary Glass Phase in Ultra-Fragile
Pt80−x Cu x P20 Bulk Metallic Glass . . . . . . . . . . . . . . . . . . . . . 53
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 65
Chapter IV: Embrittlement Transition in a Ni-Based Bulk Metallic Glass as
Evidence of the G-Phase Glass . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 81
Chapter V: Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 Summary of Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

xii
Appendix A: Thermodynamic Derivations: A Gaussian Density of States in
PEL Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Appendix B: Supplemental Materials for Chapter 2 . . . . . . . . . . . . . . 99
B.1 Underlying Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 99
B.2 Entropy Derivation: Equivalence of Equation 2.1 and 2.2 . . . . . . 100
B.3 Sn Heating Rate Temperature Correction . . . . . . . . . . . . . . . 102
B.4 Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Appendix C: Supplemental Materials for Chapter 3 . . . . . . . . . . . . . . 104
C.1 Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Appendix D: Supplemental Materials for Chapter 4 . . . . . . . . . . . . . . 105
Appendix E: Resources for Surviving Graduate School . . . . . . . . . . . . 110
E.1 The "Snake Fight" Portion of Your Thesis Defense by Luke Burns . . 110

xiii

LIST OF ILLUSTRATIONS

Number
Page
1.1 Representative thermal scan depicting characteristic transitions in
BMGs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Visualization of ordered vs. disordered characteristics. a) Representative X-ray diffraction patterns for crystalline (top) and amorphous
(bottom) material. TEM image and electron diffraction for an ordered material (b) and a metallic glass (c). Reproduced from Wang
et al. (a) [6], and Jafary-Zadeh et al. (b,c) [7]. For b and c, copyright © 2018 by the authors. Licensee MDPI, Basel, Switzerland.
This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/) . . . . . . . . . . . . . 2
1.3 Visualization of select applications. a) A BMG-coated baseball bat
by LiquidMetal Technologies [5], b) a BMG disc on the Genesis
Mission as a solar wind collector [5], c) BMG flex splines for strain
wave gears [20], d) thermoplastic formed BMG nano-rod for a subcutaneous blood glucose sensor [21], and e) a BMG matrix composite
for increased toughness [22]. All images reproduced with permission. Image d: Reprinted with permission from [21]. Copyright
2017 American Chemical Society. . . . . . . . . . . . . . . . . . . . 5
1.4 Representative PEL. Reproduced with permission from [28]. . . . . . 7
1.5 Thermodynamic Functions via the Gaussian Landscape. Heat capacity, enthalpy, and entropy are plotted in the first, second, and third
components, respectively. Reprinted from [33] with the permission
of AIP Publishing. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Angell Plot: Log Viscosity vs. normalized temperature. The slope
as Tg is approached upon cooling indicates the Angell fragility parameter, m. Reprinted with permission from [40]. . . . . . . . . . . . 16
1.7 Representative Eutectic Diagram. . . . . . . . . . . . . . . . . . . . 18

xiv
1.8

1.9

2.1
2.2

2.3

2.4
2.5

2.6
2.7
2.8
2.9

2.10

Representative Temperature-Time-Transformation (TTT) diagram where
−TÛglass , −TÛc , and −TÛx are cooling rates achieving a glass, the critical
cooling rate, and a representative cooling rate where sample crystallizes, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Energetic coordinate diagram for the traditional BMG phase (L glass),
the secondary glass (G) phase, and the crystal of pure Ag. Figure
recreated from [62]. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Visualization of critical rod diameter variance with copper content,
X. Reproduced from Na et al.[68] . . . . . . . . . . . . . . . . . . . 32
Representative hC plot identifying hC (∞) and θ h terms, and depicting
n-dependent curvature. Methods and respective temperature ranges
are indicated by the data symbols; i.e., isothermal holds (triangle),
constant heating rate (square), rapid discharge heating (plus sign),
successive cyclic undercoolings (circle), melting of crystallized samples (diamond). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
t peak to τα = τM defined metastable liquid region (a), and normalized DTA scans displaying uniform peak shape (b). Reprinted with
permission from [68]. . . . . . . . . . . . . . . . . . . . . . . . . . 40
XRD post each thermodynamic step and transition for X = 23.
Reprinted with permission from [68]. . . . . . . . . . . . . . . . . . 41
Rapid heating profile of the X = 20 sample. a) Temperature vs. Time
profile shows rapid heating on recalescence. b) Ultrafast pyrometer
from t = 0.6 -– 0.85s. Reproduced with permission from [68]. . . . . 42
hC data plotted per method and composition. Method key matches
that of Figure 2.2. Reproduced with permission from [68]. . . . . . . 43
Fully normalized hC plot for composition and n comparison. Method
key matches that of Figure 2.2. Reproduced with permission from [68]. 44
Specific configurational entropy (a) and specific configurational Gibb’s
free energy for Pt57Cu23 P20 . Reprinted with permission from [68]. . 44
Variation of effective glass transition width, 1/n, with copper content
(atomic %) (a). XRD plots for X = 16 (b). Reprinted with permission
from [68]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Specific configurational enthalpy for X = 14 and 16. X = 14 an 16
data and limits plotted with dot-dash and solid lines, and dotted and
dashed lines, respectively. Reproduced with permission from [68]. . . 47

xv
2.11

2.12

3.1

3.2
3.3
3.4

3.5

3.6

3.7
4.1

4.2

An emerging trend with the glass-melting transition. As fragility
increases (decreasing X), Tgm decreases and ∆hC increases (filled
and unfilled circles, respectively). This reveals a larger glass-melting
transition in ultra-fragile metallic glasses. . . . . . . . . . . . . . . . 48
Specific configurational entropy for X = 14 and 16. X = 14 and 16
data and limits plotted with dot-dash and solid lines, and dotted and
dashed lines, respectively. Reproduced with permission from [68]. . . 49
Vicker’s Hardness data varying with composition and heat treatment.
Solid and dotted error bars are for as-cast samples and annealed
samples, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . 56
As-cast X-Ray diffraction scans for X = 14 – 23. Samples increase
in X from top to bottom. . . . . . . . . . . . . . . . . . . . . . . . . 58
Annealed X-Ray diffraction scans for X = 14 – 23. Samples increase
in X from top to bottom. . . . . . . . . . . . . . . . . . . . . . . . . 59
Thermal (DSC) scans for X = 18 at 20K/min. Scan of as-cast sample
(a) and annealed sample (b). The glass transition peak in the anneal
sample is enlarged (c). Transition temperatures are printed in Table
3.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Thermal (DSC) scans for X = 14 at 20K/min. Scan of as-cast sample (a) and annealed sample (b). The glass transition peak and
glass-melting transition are enlarged (c). Transition temperatures
are printed in Table 3.3. . . . . . . . . . . . . . . . . . . . . . . . . 62
Ohmic heating via rapid capacitive discharge. Temperature traces
versus time across various energy releases (a) and the accompanying
ultrafast thermal camera images from t = 0.1 - 0.6s for the purple trace. 64
Peculiar topography for X = 18 annealed for 24 hours. . . . . . . . . 65
Superimposed dashed and color contours of GFA and Notch Fracture
Toughness (KQ ), respectively, on the Ni alloy composition landscape.
Figure D.1 in Appendix D visualizes a color contour for GFA for
additional clarity. Please see the electronic version for assured visual
clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Visual representation of the two casting methods. Direct casting from
casting temperature Tcast (a), versus overheating to the toughening
temperature Ttough before cooling to and quenching from the casting
temperature Tcast (b). . . . . . . . . . . . . . . . . . . . . . . . . . . 69

xvi
4.3
4.4
4.5

4.6
4.7

4.8

4.9

4.10
B.1
C.1

D.1
D.2
D.3

D.4

Notch fracture toughness KQ and critical rod diameter dcr under the
direct casting method.[10] . . . . . . . . . . . . . . . . . . . . . . . 70
Notch fracture toughness KQ and critical rod diameter dcr under the
overheating casting method.[10] . . . . . . . . . . . . . . . . . . . . 70
Visualized inclusions on 1200-grit polished cross-sections of directcast samples. Please see the electronic version for assured visual
clarity. Inclusion area percentages for a-f: 4.05, 11.90, 5.74, 34.87,
0.12, and 0.00%, respectively. Note: there are three artifactual repeated smudges in each image. . . . . . . . . . . . . . . . . . . . . . 74
Vickers hardness micro indentations (∼ 50µm) across the heat treatmentinduced surfaces of Tcast = 1150°C Ni208. . . . . . . . . . . . . . . 75
SEM EDS across the matrix and inclusion. The bright central dot
is artifactual at the indentation location. Displayed sideways for
sufficient resolution. Please see the electronic version for assured
visual clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Bright-field TEM image of the matrix-inclusion interface (a) with
labeled locations (i - iv) for diffraction patterns. EDS completed on
locations (i-iv) reported the composition % calculated via eV counts
in b. Please see the electronic version for assured visual clarity. . . . 78
XRD for samples cast utilizing the direct casting method. Labels
are adjacent to their respective scans and labels a-f correlate to the
labeled cast temperature surfaces in Figure 4.5. . . . . . . . . . . . . 79
Hardness across inclusion, matrix, and bulk samples for Tcast = 1150°C. 80
Sn heat flow responses with respect to heating rate. . . . . . . . . . . 102
Cover slip location for carbon-puck masking method. Central cover
slip with hole highlighted with white borders on free edges. Full
cover slips outlined by grey dashed lines. . . . . . . . . . . . . . . . 104
The color contour plot equivalent to the dashed contour in Figure 4.1.
Included for visual clarity.REF . . . . . . . . . . . . . . . . . . . . . 106
Inclusion sizes across the direct cast samples’ casting temperatures. . 106
Two lighting approaches for inclusion visualization on the same sample area. Nanoindentations utilized for sample location identification
in SEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Top (a): SEM image depicting lack of visibility of the inclusions
relative to the 10x optical image (bottom, b). . . . . . . . . . . . . . 108

xvii
D.5

TEM 64k zoom on Ni208 inclusion-matrix interface. Enlarged here
for clarity. The reader is advised to view the image in the electronic
version. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

xviii

LIST OF TABLES
Number
Page
1.1 Summary of method cooling rates and respective practical geometries
and dimensions.[47, 48, 49, 50] . . . . . . . . . . . . . . . . . . . . 21
2.1 Pt80−X Cu X P20 glass system property variances with composition.[68]
Heating rates utilized are noted in parenthesis in K/min. . . . . . . . 32
2.2 Fitting parameters for configurational enthalpy (Equation 2.1) curves
in Figure 2.6a-d. Reproduced with permission from [68]. . . . . . . . 43
3.1 Vicker’s Hardness (average and standard deviations) with nearrest
neighbor (nn) distance in Angstroms for Pt90−X Cu X P20 compositions. Column headers are abbreviated with Cu X values. . . . . . . 57
3.2 Vicker’s Hardness (average and standard deviations) with nearrest
neighbor (nnd) distance in Angstroms for Pt80−X Cu X P20 compositions. Column headers are abbreviated with Cu X values. . . . . . . 60
3.3 Temperatures and enthalpy values for X = 14 and 18 thermodynamic
scans. Temperatures before correction by -11K from Table B.1. . . . 63
B.1 Peak offset correction values from Figure B.1. . . . . . . . . . . . . 103
B.2 Raw data accompanying Figure 2.11 identifying the trend of fragility,
copper content, glass-melting temperature, and latent heat of glassmelting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
D.1 Ni210 Properties. These properties were assumed equivalent to
Ni208 within error given sample properties were not able to be confirmed due to non-functional measurement apparatuses.[8] . . . . . . 105

Chapter 1

THE HISTORY AND EVOLUTION OF BULK METALLIC
GLASS
1.1

Metallic Glass and the Bulk Form

Traditionally, metals are ordered and crystalline, while disordered glasses are polymeric, molecular, or inorganic compounds such as oxides, chalcogenides, etc. Bulk
metallic glasses (BMGs), however, are amorphous metal alloys, and were the first
materials to bridge this gap. They extend metallic alloys to the amorphous state, and
emerge with beneficial properties from each. The first metallic glass was achieved
in 1960, when Duwez reported a Au-Si alloy that was splat quenched at 105 - 108
K/s, yielding an amorphous foil ∼10-µm thick.[1, 2, 3, 4] This first amorphous
metallic alloy would begin a new field of research; Metallic Glass (MG), and later,
with slower cooled samples on the millimeter scale, Bulk Metallic Glass (BMG).
To achieve a successful BMG, relatively rapid quenching of the molten alloy is
utilized to circumvent its natural tendency toward rapid crystallization. During
quenching, the molten alloy must pass rapidly through a thermodynamic regime
(Figure 1.1) where the liquid is metastable.[5] The sample must be undercooled
below its equilibrium melting temperature or liquidus temperature, Tl , in the case
of an alloy, while remaining in the liquid phase. This regime is termed the SuperCooled Liquid (SCL). The SCL alloy is then cooled until atomic motion is arrested,
and a configurationally frozen liquid or amorphous phase is achieved below the
glass transition (Tg ). Through the SCL, crystallization must be bypassed prior to

Figure 1.1: Representative thermal scan depicting characteristic transitions in
BMGs.

Figure 1.2: Visualization of ordered vs. disordered characteristics. a) Representative X-ray diffraction patterns for crystalline (top) and amorphous (bottom)
material. TEM image and electron diffraction for an ordered material (b) and
a metallic glass (c). Reproduced from Wang et al. (a) [6], and Jafary-Zadeh
et al. (b,c) [7]. For b and c, copyright © 2018 by the authors. Licensee
MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/)

arriving at the glass transition.
Once cast to below Tg , the sample requires verification of its amorphous structure
and lack of long-range order. This is most commonly displayed in X-Ray Diffractometer (XRD) scans and diffraction patterns by a broad diffraction band in place of
crystalline peaks. High resolution Transmission Electron Microscopy (TEM) images are often used to visualize the presence or absence of atomic order. Figure 1.2a
displays representative crystalline (top) and amorphous (bottom) XRD scans, while
Figures 1.2b and 1.2c show typical TEM and electron diffraction for ordered and
amorphous materials, respectively.[6, 7] From diffraction patterns, one can compute
Radial Distribution Functions (RDFs) that report the distribution of atomic neighbor
distances between pairs of atoms. The absence of periodicity (peaks) implies a lack
of long range atomic order.
Metallic Glass Characteristics: Thermal and Mechanical Properties
Once quenched to ambient temperature, BMGs display characteristic thermal events
on subsequent reheating from the glassy state (Figure 1.1).
In typical glasses, on passing through the Glass Transition Temperature, Tg , there is
an endothermic increase in heat capacity accompanied by a change in the volume
thermal expansion coefficient. Tg is traditionally defined as the temperature where
the observed viscosity reaches 1012 Pa-s or 1013 Poise during cooling (or heating).
Above Tg , atoms (or molecules) display increased mobility and the liquid exhibits the
ability to "flow" under stress. It transitions from solid-like to fluid-like behavior.[8]

Above Tg , liquid fluidity increases rapidly (by orders of magnitude) over a narrow
range of temperature. This temperature regime is utilized to reshape the material
and produce net-shape parts as is done in glass blowing, blow molding, or injection
molding.[5] The viscosity of 1012 Pa-s (often taken to define Tg ) corresponds to
the typical softening point of silicate glasses above which glass blowing can be
implemented.[8]
Similar to other glass systems, BMGs can be formed and reshaped as temperature
increases above the glass transition. However, given their metallic nature, there
are marked differences. First, the glass transition of MGs occurs over a wide
range of temperatures; Tg ranges from room temperature (e.g., for the Duwez Au-Si
metallic glass) to as high as ∼800 K for MGs based on refractory metals.[9, 10] This
compares, for example, to a lower and smaller range of 60 - 500 K for traditional
molecular and polymeric glasses.[11, 12] Second, while the glass transition is
present across all glass systems, BMGs tend to crystallize more readily and undergo
an accompanying distinct thermal event before melting; recalescence. Recalescence
is an exothermic heat release from the relatively sudden atomic rearrangement from
the liquid to crystalline phase transition. This occurs at a temperature designated as
Tx .
Many traditional glasses exhibit very sluggish crystallization kinetics and display
no distinct exothermic event or well-defined Tx . The region of liquid metastability
during heating, ∆T = Tx − Tg , thus tends to be smaller for BMGs than for many
polymer, molecular, or silicate glasses, where crystallization often does not occur on
any practical laboratory time scale between Tg and Tm . The relevant transitions and
temperature regimes are illustrated by a representative BMG Differential Scanning
Calorimeter (DSC) trace as shown in Figure 1.1.
Metallic Glasses exhibit certain unusual mechanical properties compared with traditional glasses and crystalline metals. For example, they have typical tensile strength
several times greater than steel and other crystalline engineering metals. This is
presumed to be due to the absence of dislocations and other extended defects that
are responsible for plastic yielding and deformation in the case of crystalline metals.
Metallic glasses deform by stress-induced activation of nano-meter scale local soft
regions called shear transformation zones.[13, 14] Below Tg , deformation tends to
become spatially localized and concentrated into bands called shear bands. The
formation and operation of these shear bands under stress is the primary mechanism
of plastic deformation in MGs. Unlike molecular and oxide glasses, MGs may ex-

hibit significant ductility under certain loading conditions such as compression and
bending. In this case, one observes formation and operation of many shear bands
throughout a macroscopic sample. In contrast, MGs exhibit little or no ductility
in unconfined loading conditions such as pure tension. In a tensile test, metallic
glasses tend to fail along a single narrow shear band inclined at an angle of 45
degrees with respect to the tensile axis. The fracture toughness (KC ) of metallic
glasses is reported to vary over an extremely wide range from that of very brittle
silicate glasses (KC ∼ 1 M Pa − m1/2 ) to as high as that of tough steels (KC ∼ 100
M Pa − m1/2 ).[15] Above Tg , flow becomes delocalized and homogeneous much
like flow in an ordinary liquid, albeit with a high viscosity. In this regime above Tg ,
metallic glasses can be shaped and formed in the same manner as thermoplastics.[2,
16, 17, 18]
In summary, while MGs offer distinct improvements over traditional metals such
as very high strength, they may also exhibit limited toughness and ductility, and
ultimately experience catastrophic brittle failure; e.g., in tension. The tendency to
crystallize easily in the supercooled liquid region means that relatively high cooling
rates from the molten state are required to produced BMGs. The requirement for
rapid cooling in turn limits the maximum dimensions of BMGs due to ability to
extract heat on quenching. In practice, BMGs are limited to cast rods of diameter
in the mm to cm range, or thin plates of similar thicknesses (Section 1.3). So
similar to traditional metallurgy, much research in the field of BMGs is directed to
addressing these limitations. Alloy development pursued the discovery of alloys that
have greater resistance to crystallization, and that exhibit enhanced toughness and
ductility, or other desirable attributes. Other areas of active study include oxidation
resistance, magnetism, and ferromagnetism. Further, studies of BMG composites
address brittle failure by utilizing crystalline dendrites in an amorphous matrix to
arrest crack growth. This has resulted in increasing fracture toughness ten-fold.[19]
This unusual combination of properties motivated research to investigate their fundamental origins. The remaining sections of this chapter outline the applications,
underlying physics, formation criteria, and casting methods that took BMGs from
microns thick to the bulk scale as Bulk Metallic Glass (BMG).
Applications
Following BMG discovery, many applications were explored. These applications
span commercial and research sectors. Examples are included in Figure 1.3.

Figure 1.3: Visualization of select applications. a) A BMG-coated baseball bat by
LiquidMetal Technologies [5], b) a BMG disc on the Genesis Mission as a solar wind
collector [5], c) BMG flex splines for strain wave gears [20], d) thermoplastic formed
BMG nano-rod for a subcutaneous blood glucose sensor [21], and e) a BMG matrix
composite for increased toughness [22]. All images reproduced with permission.
Image d: Reprinted with permission from [21]. Copyright 2017 American Chemical
Society.

In the commercial sector, applications have been explored in sporting goods, consumer electronics, and medical applications.[5] Sporting equipment has included
golf clubs, baseball bats, and tennis rackets with BMG coatings or frames. Consumer electronics applications have included injection molded and die-cast phone
frames and casings for increased scratch, water, and dent resistance. In orthodontics,
fabrication of dental brackets and appliances is being explored.
In the research sector, a Zr-based BMG was used as a collection device for the solar
wind on the 2001 NASA Genesis Discovery mission.[23] The "flow" characteristics
of BMGs have led to its use in additive manufacturing. NASA JPL has used cast netshaped BMG strain wave gears for precision robotics on rovers for improved wear
resistance.[20] Metallic glasses are an improved material for gearbox flexsplines
due to BMG embrittlement resistance at the low temperatures encountered in space
applications.[20]
When BMGs first emerged, it was hypothesized that a stronger, tougher, general-

use glassy “steel” was possible. But as time progressed and research developed,
the most successful pursuits arose when BMG compositions and properties were
tuned and selected specifically to meet particular goals and specifications in “niche”
applications. For example, the most common and processable BMG alloys to date
are the Zr-, Fe-, and Pt-based alloy families. Zr-BMGs (e.g., Vitreloy alloys) are
the most widely studied BMG system and have the most widespread structural
applications, while ferromagnetic Fe-base BMGs have been adopted in widespread
use as soft magnetic materials in inductors and transformer cores, and Pt-based
amorphous alloys have been used as a catalyst site for subcutaneous blood glucose
sensors, to name a few niche applications.[24, 25, 21]
Since fine tuning of properties of BMGs is where they provide the greatest benefits,
Section 1.3 describes how fundamental research developed standardized rules and
procedures for achieving and identifying good metallic glass formers with desirable
properties. These approaches, similar to applications, were informed by combining
theories and methods of both crystalline metals and traditional amorphous materials.
But to fully understand BMG casting, these theories and methods are first described
in Section 1.2 below.
1.2

Classical Theory for Bulk Metallic Glass

Periodicity in ordered materials permits simplifying models and assumptions in
theory development. These theories have underlain the advancement of our understanding of periodic crystalline materials in a broad range of fields; e.g., semiconductors, structural materials, Bloch’s theorem, etc.[26] Glasses in general and
BMGs in particular — without long-range atomic order — do not lend themselves
to such simplifications. A microscopic theory of the statistical mechanics of glasses
has been developed based on the concept of potential energy landscapes (PELs).
The PEL theory provides a microscopic basis for understanding the thermodynamic,
kinetic, and physical properties of glasses. The basic results of PEL theory provide
the basis for much of the work on metallic glasses in the present thesis. As such, it
is important to provide an outline of the basic theory.
Potential Energy Landscape Description of Bulk Metallic Glass
Metallic glasses are described energetically by a Potential Energy Landscape (PEL).
A PEL provides a topographic view of all the accessible potential energy states across
a system of interacting particles (Figure 1.4). This potential energy is a function

Figure 1.4: Representative PEL. Reproduced with permission from [28].

of the 3N atomic coordinates of all the atoms that comprise the system. These
energies arise from pair interactions (or more generally, many-body interactions)
between atoms, where the total potential energy is the sum of these interactions
across all atomic pairs. Varied local environments and configurations yield different
potential energies. A stable atomic arrangement corresponds to a local minimum
in the overall potential energy whereby the force on each atom is zero. Such a
local potential energy minimum is referred to as an inherent state (i.e., a state of
energy in a 3N particle system) of the liquid/glass. Therefore, specific stable atomic
configurations described by these minima are referred to as the inherent states of
the PEL; where crystal atomic configurations have deeper wells and greater stability
compared to typical amorphous inherent state structures.[27]
Movement around the PEL can be described as a sequence of transitions from
one inherent state to another; excitations.[27, 29, 28] Elementary excitations over
potential energy barriers move a system between its inherent state energy wells in
the PEL. They allow for inter-basin hopping between the local minima, but are not
energetic enough to move the system from a liquid inherent state to a crystalline
state; relaxations discussed further in Section 1.2: Kinetic Behavior in the PEL,
Relaxations. Glasses and liquids utilize this inter-basin hopping to achieve their
characteristic configurational changes associated with flow. Upon heating above
Tg , enough thermal energy is available to allow inter-basin hopping and internal
movement between amorphous/liquid inherent states, but not enough to access a
crystalline state or to access the higher energy states of a liquid above its melting

points (melting basin depth not shown in Figure 1.4).
In addition to PEL theory’s effective description of the energetics of atomic configurations, it can be combined with statistical mechanics to determine thermodynamic
state variables such as energy. It can be further refined by assuming separability of vibrational and configurational components for a more specific analysis, as
discussed below.
Thermodynamic Application of PEL: Separable Configurational and
Vibrational Components via the Canonical Ensemble
A key feature of PEL theory is that it allows for separation of configurational
and vibrational components in thermodynamic functions. This occurs through a
number of steps. First, with a PEL, a distribution of occupied inherent energy states
is required to describe a system. A statistical distribution is chosen to describe
the density of states (DOS); e.g., Gaussian, exponential, etc. Second, a partition
function (Z/ ) is required. Z/ is a function of temperature and microstate energies as
a model of microscopic constituents of a system; i.e., number of particles, volume,
particle mass. It relates these microscopic details to thermal quantities through its
logarithmic derivatives. Third, the partition function type is selected. For this work,
a canonical partition function is of practical use. The canonical partition function
comes from the canonical ensemble that allows environmental heat exchange at fixed
number of particles, volume, and temperature (the NVT ensemble). This applies to
equilibrium conditions of BMGs at fixed T and is therefore useful here.
Combining these criteria, a distribution-defined DOS and the Canonical Z/ , the
resultant separation is described through an example derivation of free energy, F.
Separability is achieved via the canonical approach to the partition function —
where taking the log of the partition function for the Helmholtz free energy yields
a sum of the exponential components (the log of factors is a sum); demonstrated
below.
Separability arises from the derivative of
F = −kT ln (Z/ ),

(1.1)

where Z/ is the canonical partition function with a DOS coefficient;
Z/ =

−E
dE.
D(E) exp
kT

(1.2)

with E the energy of the system. When E is represented by a sum of its configurational and vibrational parts, the following results:
E = ECon f ig + Evib,har + Evib,anh,

(1.3)

where vibrational energies are further divided into harmonic and non-harmonic
components.
When combining equations 1.1 - 1.3,
F = −kTln

∫

 
−(ECon f ig + Evib,har + Evib,anh )
D(E) exp
dE
kT

(1.4)

and using exponential and log manipulations
e x+y = e x · e y

(1.5)

ln(e x+y ) = ln(e x · e y )

(1.6)

ln(a · b) = ln(a) + ln(b)

(1.7)

ln(e x · e y ) = ln(e x ) + ln(e y ) = x + y

(1.8)

the thermodynamic functions emerge with distinguishable contributions from configurational and vibrational parts, and can be treated individually;

F = −kTln

∫

 
−ECon f ig
−Evib,har
−Evib,anh
D(E) exp
exp
exp
dE .
kT
kT
kT
(1.9)

While possible in this mathematical example, this separability is backed by theory
and experimental evidence as well.
For the separable behavior, a key underlying assumption is that the average vibrational DOS does not depend on the energy of an inherent state minima. Thereby
anharmonicity is avoided and the anharmonic approximation is not needed. This
separation of vibrations from energy dependence allows for the decoupling of the
vibrational and configurational parts from the canonical partition function, and full
separation is possible come manipulation for the Helmholtz free energy.
For experimental evidence, Smith et al. reported direct in-situ measurements of the
vibrational spectra of strong and fragile metallic glasses in the amorphous, liquid,

10
and crystalline phases in the vicinity of Tg . For both strong and fragile glasses, less
than 5% of the total excess vibrational entropy was found in the glass and liquid
phases over the crystal.[30] This provides experimental evidence that the excess
entropy of metallic glasses is almost entirely configurational in origin, validating
early theories that the glass transition is purely configurational.[31]
Through PEL assumptions, once separated, these components can be treated and
analyzed independently.
Vibrational Component
The vibrational component is characterized by phonon frequencies and the phonon
density of states. In the PEL, phonon frequencies arise from the curvature in the
landscape along the various directions of the configuration space surrounding the
local potential energy minimum. For 3N particles, there are 3N-6 independent
configurational coordinates (the 6 degrees of freedom associated with center of
mass motion and system rotation are not vibrational degrees of freedom). This
curvature matrix is the second derivatives of the PE with respect to the coordinates
(xi , yi , zi where “i” labels particles) and can be described as a dynamic matrix.
Through analysis of this matrix via diagonalization and eigenvalue determination,
one attains the normal modes and phonon DOS, respectively. In effect, the phonon
frequencies go to zero when the curvature of the PEL goes to zero (an inflection
point).[28] From the phonon DOS, the phonon free energy and vibrational entropy
are defined as seen in Smith et al.[30]
With the vibrational component separated and a focus drawn to phonons, this can
be used, for example, to deduce the sound velocity in a material. The sound
velocity of long wavelength phonons is determined by elastic constants. Sound
velocities can be measured using ultrasonic transducers where the long wavelength
vibrational modes are sampled, and elastic constants calculated. Elastic constants
are represented by phonons that collectively move large groups of atoms in phase
space. While useful, the separated vibrational component will not be addressed in
this work. In effect, the configurational component takes focus, and experiments to
determine the configurational contribution to the free energy are explored in Chapter
2 of the thesis.
Configurational Component
In the PEL, the configurational part of the partition function is a sum of configurational energies over all minima. When separable from vibrations, and as seen in

11
work by Smith et al., the glass transition at Tg is described as a purely configurational
event. Thus, if heated from a relaxed glass state, the resulting enthalpy associated
with the glass transition is purely configurational.
When isolated from the vibrational component, the configurational enthalpy is
actually representative of the potential energy of the system. This is achieved since
all of the experiments are done at ambient pressure. Strictly speaking, specific
enthalpy h = e + pv, and changes in specific enthalpy (with respect to a reference
state) can be expressed as ∆h = ∆e + p∆v.[32] In our experiments at ambient p,
the p∆v term can be shown to be very small compared with ∆e. As such, ∆h ∼ ∆e
can be shown to be an excellent approximation (i.e., p∆v is on the order of 10−3
compared to measured d∆h values (Chapter 2). So p∆v is neglectable to an accuracy
of 0.1% or better. Assuming using all of v, where ∆v is actually 10−2 of v.) In
equilibrium at fixed T, kinetic energy is simply 1/2kT per degree of freedom. It
follows that changes in configurational enthalpy (with respect to a reference state at
fixed T) are equivalent to changes in the specific configurational potential energy of
the system. This equivalence will be important throughout the discussion presented
in Chapter 2 and is described in further detail in Appendix B.1.
A Gaussian Landscape and Thermodynamic Functions
The PEL is particularly useful for defining thermodynamic functions of amorphous
materials. A widely used approach assumes a lack of energetic preference for atomic
interactions or configurations. This results in a random spatial distribution of atomic
configurations and random atomic interactions. Basically, the energy of inherent
states is assumed to arise from a sum of random variables. This naturally gives rise
to a Gaussian density of states (DOS) to represent the distribution of energies for the
inherent state minima.[27, 28] When applied to the canonical partition function, this
yields an integral over a Gaussian distribution. The derivation from the Gaussian
DOS in the canonical partition function to the Helmholtz free energy (F), entropy
(S), internal energy (U), enthalpy (H), and heat capacity (CP ) are carried out and
described in Appendix A, and are summarized below.

σ4
F = +kT ln 2σ −
kT
√  σ 4
S = −k ln 2σ − 2
kT

(1.10)
(1.11)

12

U=γ−

2σ 4
kT

2σ 4
kT
dU
2σ 2
CP =
=γ+
dT
kT 2
H =U =γ−

(1.12)
(1.13)
(1.14)

When applying the Gaussian DOS for the configurational contribution, the resulting
equations for the total crystal and liquid heat capacities (configurational + vibrational
contributions) are:
CP,x (T) = 3R + aT + bT 2

(1.15)

CP,l (T) = 3R + cT + dT −2

(1.16)

where 3R is the Dulong-Petit heat capacity, and the components with a, b, and c
coefficients are anharmonic contributions. Within the liquid heat capacity equation
there is a liquid-specific configurational term, "dT −2 ," that arises from the Gaussian
density of states assumption in the Gaussian Landscape Model; the last term of
Equation 1.14.
Figure 1.5a fits experimental heat capacity with Equations 1.15 and 1.16. Assuming
sufficient fit, enthalpy (Equation 1.13) and entropy (Equation 1.11 ) are plotted
in Figure 1.5b and c, respectively. When inspecting the total entropy curve, an
interesting phenomena appears; the Kauzmann Paradox. The Kauzmann Paradox
arises in thermodynamic glass physics when comparing the total entropy of a liquid
and crystal. At absolute zero, T = 0 K, the entropy of a solid phase should approach
zero (Third Law of Thermodynamics). However, as seen in Figure 1.5c, when
projected to 0 K, the SCL entropy extends below zero to negative values. Ostensibly,
the liquid entropy would become negative and non-physical. But experimentally,
the system arrests to a glass before this occurs. To this end, it is hypothesized the
glass transition exists to circumvent this thermodynamic paradox. We discuss this
apparent paradox in Chapter 2.
PEL theory provides a helpful picture to understand energetic states of glasses. But
while providing a classical and fundamental approach to BMG thermodynamics,
the Gaussian assumption leads to compounding problems as will be seen below.

13

Figure 1.5: Thermodynamic Functions via the Gaussian Landscape. Heat capacity, enthalpy, and entropy are plotted in the first, second, and third components,
respectively. Reprinted from [33] with the permission of AIP Publishing.
Issues Arise with the Gaussian Landscape
Upon greater inspection, the assumed Gaussian distribution of filled energy states is
not representative of a glass system. This simplification describes the local potential
energy distribution about each atom by assuming both a random spatial distribution
and random interactions around the given atom. The resulting summation over
multiple random atomic interactions leads to an assumption that the distribution is
Gaussian at all energies. However, with these assumptions, multiple issues arise. In
reality, a preferred and known absolute minimum is introduced at low temperatures;
the crystalline state. Therefore, the potential energy of a configurational state must
be bounded below, whereas a Gaussian distribution has no absolute lower bound.
And while Equation 1.15 fits the glass and crystal heat capacity data (at temperatures
where data are available) in Figure 1.5a, the SCL data varies widely from Equation
1.16 at low temperatures. The resultant T −2 dependence from a Gaussian DOS heat
capacity induces a sharp upward curvature at low temperatures that does not well
describe the SCL data.
Further compounding this issue of an approximate model, are inaccurate data. This
data inaccuracy is three-fold. First, given BMGs have higher transition temperatures than traditional glasses, a Differential Thermal Analyzer (DTA) with a higher
temperature range is necessary for measuring heat capacity, enthalpy, and related
variables. Traditional glasses use a Differential Scanning Calorimeter (DSC), and
this instrument reports high-quality heat capacity data which are then used to calculate further thermodynamic functions. This approach has been taken with BMGs
using a DTA, but the different measurement method makes this more difficult and
less accurate near Tg (Step Calorimetry). Choosing to measure heat capacity with
a DTA leads to error, whereas directly reporting enthalpy is more accurate for this

14
apparatus. Thus, direct reporting enthalpy and calculating to heat capacity (by
differentiation) is a necessary adjustment with a DTA.
Second, with the configurational dependence of glasses more recently established
in 2017, the data in Figure 1.5 did not prioritize achieving a well-defined reference
state. Without this reference state prior to measurement, each data point had a
different energetic baseline value — leading to the wide vertical spread of SCL data
in Figure 1.5a. Utilizing annealing for configurational and energy equilibration will
lead to more consistent and precise measurements.
Third, for metallic glasses, there are limited data in the mid-range SCL due to the
intervention by rapid crystallization. Additional data in this region could inform the
proper curvature of the heat capacity equation. This region is particularly elusive
to data measurement due to the center of the SCL having limited access from both
above (under cooling below Tl ), and from below (heating above Tg ). Moving too
far into this region for long times yields crystallization. Thus, a new method was
required with heating rate, data sampling rate, and accuracy capable of acquiring
data in this inaccessible region; to heat/cool and measure the material response
before crystallization. In 2011, Rapid Capacitive Discharge Heating (RDH) was
developed for this purpose. Since its inception, RDH has informed this data region
for a number of alloys, and contributes to Chapter 2.[34, 35, 36]
These three shortcomings compound and create challenges when attempting to
validate a Gaussian landscape model. There is the potential that the Gaussian DOS
assumption leads to an apparent Kauzmann paradox as either an artifact of the failed
Gaussian landscape model or from insufficient data to assess the model. As such,
an improved experimental approach is required to properly assess the theory. The
acquisition of better experimental data along with a test of the theory are explored
in Chapter 2.
Kinetic Behavior in the PEL, Relaxations
Recalling the initial introduction of the PEL model, the energetics of atomic configurations were discussed, and the transitions between inherent states through excitations and relaxations were first introduced. This section will elaborate on these
relaxations as how they enable sample equilibration.
In glass physics, atomic rearrangement has different features over key temperature
regimes; the super cooled liquid and solidified glass. As determined by Johari
and Goldstein, there are two distinguishable types of relaxations deemed α- and

15
β-relaxations.[37] α-relaxations (Maxwell relaxations) are primary relaxations associated with the irreversible rearrangement of atomic clusters. They describe
atomic motion at higher temperatures, are non-Arrhenius, and describe vitrification
and atomic motion arrest at Tg . α-relaxations are frozen-out below Tg , while βrelaxations remain operative. β-relaxations are secondary relaxations that describe
more limited atomic motion that persists at lower temperatures. Such limited motion is often described as the rattling of the “cage” or “cage rattling” of neighboring
atoms surrounding a given atom.[38] These β-relaxations tend to be more Arrhenius
in character. With respect to the PEL, α- and β-relaxations both relate to movement
between energy wells. Movements energetic enough to produce permutations of
neighboring atom pairs are referred to as inter-basin hopping and are α-relaxations,
while lower-energy intra-basin hopping between shallower local minima within a
larger megabasin are β-relaxations. A series of β-relaxations may lead to less
frequent α-relaxations.[39]
Both α- and β-relaxations are important to this discussion of structure and configuration because they enable structural rearrangements occurring at different temperatures. Annealing at or below Tg allows β-relaxations to occur without crystallizing.
The active β-relaxations allow the glass to sample local regions of its state space to
find a low-energy minima amongst the amorphous inherent structures. For anneals
above Tg , α-relaxations take over and the material will ultimately crystallize given
sufficient time dependent on the degree of atomic motion in the system. This time
duration describes the metastability of the glass state. Metastability is relative to
the relaxation time for configurational degrees of freedom. It can be quantified by
the ratio of the time to crystallization to the Maxwell (configurational) α-relaxation
time, τα = τM . This ratio quantifies the ability of the glass sample to achieve
configurational equilibrium prior to crystallization. It characterizes configurational
equilibration of the glassy state, and therefore describes the applicability of thermodynamics. The Maxwell relaxation time near Tg is typically ∼10 - 100 s and
decreases rapidly with temperature above Tg .
The accessibility of both relaxations determines atomic mobility in the glassy/liquid
states.[27] This in turn is related to Angell’s Kinetic Fragility of the liquid, and is
discussed below.

16

Figure 1.6: Angell Plot: Log Viscosity vs. normalized temperature. The slope as Tg
is approached upon cooling indicates the Angell fragility parameter, m. Reprinted
with permission from [40].
Kinetic (Angell) Fragility and Glass Quality
Kinetic (Angell) Fragility describes the rate of increase of atomic mobility as temperature increases above the glass transition temperature. It is closely correlated
with the deviation of viscosity from simple thermally activated Arrhenius behavior.
Arrhenius behavior (of atomic mobility or atomic diffusion) is characterized by a
single activation energy:

−Ea
k(T) = A exp
RT

(1.17)

and viscosity, η:

Ea
η = A exp
k BT

(1.18)

where k, R, A, Ea , k B , and T are respectively the rate constant, universal gas constant, pre-exponential factor, activation energy, Boltzmann constant, and absolute
temperature in Kelvin.[1, 41] In Figure 1.6, Arrhenius behavior corresponds to a
straight line, whereas actual liquid viscosities exhibit an increasing curvature and
deviation from an Arrhenius law. The Angell fragility parameter, m, quantifies
this deviation and is defined as the slope of each curve as the glass transition is
approached from above (Figure 1.6). Angell defined m as:

17
δ log10 η
m=
δ(Tg /T) T−Tg

(1.19)

and describes the extent of atomic diffusion near the glass transition via the derivative
of the logarithm of viscosity with respect to (Tg /T).[2, 1]
Liquid fragility m plays a critical role in successful vitrification of a liquid.[8]
“Strong” liquids with typical m < 50 have limited atomic mobility in the SCL region,
and therefore often readily freeze into an amorphous phase. Their sluggish kinetics
tend to yield lower critical cooling rates for glass formation that are advantageous
for casting bulk samples, millimeters or centimeters in dimension. Most early BMG
research focused on strong glass-forming liquids, and data for such systems dominate
the metallic glass literature. However, "fragile" glass-forming liquids with typical
m > 60 tend to crystallize more rapidly in the SCL region and therefore tend to be
poor glass formers. They generally require higher critical cooling rates than can be
achieved by common quenching methods, and therefore sample dimensions tend to
be limited. Fragile glasses tend to crystallize more readily on reheating above Tg
and thus require additional care in casting and testing. As such, published physical
property data on fragile liquid glass formers are limited and such liquids have thus
far been poorly characterized.[19]
Classical Theory Summary
The combination of metal and glass physics creates a multifaceted and interdisciplinary foundation. The PEL informs thermodynamic models, albeit with some
drawbacks. There remain possible improvements in thermodynamic models and
data collection, potentially in the elusive high-fragility regime. Even so, these
foundations inform casting requirements and parameters such as composition and
chemistry, thermodynamic and kinetic quenching conditions, methods, and more as
described in the next section.
1.3

Formation Criteria

Casting a successful BMG requires fine chemical, thermodynamic, and kinetic
control. This combines the traditional metallurgy and traditional glass physics
established above. These controls summarized succinctly, BMGs are metal alloys
that are quenched from the melt such that crystallization is avoided and the product
is retained in the meta-stable amorphous state.

18

Figure 1.7: Representative Eutectic Diagram.
Chemistry Controls
In 2000, three factors were identified that inhibit crystallization for BMG formation;
1) multicomponent alloys of at least three elements, 2) atomic size mismatch of over
12% in the constituent atoms, and 3) negative heats of mixing between the three
primary elements.[42, 43, 44] These factors stem from the “confusion” principle,
preventing ease of atomic ordering, and energetic favoring of the liquid over the
crystalline state, respectively. To promote application-specific properties in the cast
glass, these factors prove useful. For example, one might emphasize an element, say
Fe, for its magnetic properties. From there, adding two or more metallic elements
or nonmetals with features that promote glass formation (e.g., useful atomic size
mismatch or negative heats of mixing with Fe) provides a practical basis. However,
while these rules are a useful starting point, many additional considerations are
necessary for developing promising alloys for BMG formation.
Thermodynamic Factors — Eutectics
From a thermodynamic point of view, vitrification requires a quench of the overheated alloy melt. The melt must be cooled through the supercooled region below
the liquidus/solidus temperature, and down to the glass transition temperature before crystallization can occur, effectively freezing the atomic liquid in place as a
glassy solid. Essentially, the undercooled liquid must be frozen while avoiding the
nucleation and growth of crystalline phases.

19
In a typical phase diagram, this quench follows a vertical downward path from the
equilibrium liquid to the low-temperature amorphous solid.[45] Below the liquidus
curve, (Tl ), the driving force for crystallization increases monotonically with undercooling Tl − T. Crystallization results in a drop in free energy which increases
with the degree of undercooling Tl − T until one reaches an undercooling Tl − Tg
at the glass transition. In a eutectic phase diagram, the eutectic composition has a
characteristically depressed liquidus temperature compared to the melting points of
the atomic constituents (Figure 1.7). Turnbull first pointed out the importance of
the ratio Tg /Tl in achieving glass formation. In the literature, this ratio is referred to
as the reduced glass transition temperature or Turnbull’s parameter, trg . He noted
that at a eutectic composition, this ratio tends to display a maximum (versus composition). Further, he pointed out that when this ratio reaches a critical value of
∼2/3, easy glass formation is to be expected. This is now referred to as Turnbull’s
criterion.[8]
It is now well established that vitrification of metallic alloys is most easily achieved in
multicomponent alloys with compositions located near deep eutectic features in the
alloy phase diagrams. When choosing between eutectic systems, deeper eutectics
where Tg /Tl exceeds ∼0.6 have been found to allow for more stable undercooling
of the liquid and easy formation of BMGs. Although not a strict rule, the Turnbull
criterion is generally a useful and simple predictor of glass forming ability in metallic
systems. The alloys discussed in this thesis are excellent examples of deep eutectic
alloys where tr ∼ 0.6 or greater.
Kinetic Controls
When quenching an alloy from temperatures above melting, a crystal forms if the
material is not cooled at a sufficient rate to beat crystallization. The kinetic aspects
of glass formation are described by a Temperature-Time-Transformation (TTT)
diagram. TTT diagrams show the kinetics of crystallization in a 2-dimensional
space of temperature and log time (Figure 1.8). With respect to temperature, the
resultant phases are broken into four zones — Liquid, Supercooled Liquid (SCL),
and Glass, with Crystals grown in the SCL given sufficient time. The curved border
between the SCL and crystal is referred to as the "crystallization nose" or "nose."[34]
At time zero, at the top left of Figure 1.8, two overall behaviors emerge, i) the melt
is quenched fast enough such that crystallization is fully avoided and the sample is
successfully vitrified (Figure 1.8; −TÛglass ), or ii) any quench rate eclipsed by the

20

Figure 1.8: Representative Temperature-Time-Transformation (TTT) diagram where
−TÛglass , −TÛc , and −TÛx are cooling rates achieving a glass, the critical cooling rate,
and a representative cooling rate where sample crystallizes, respectively.

crystallization nose is interrupted by nucleation given too long of a cooling time,
and crystallization occurs within the sample (Figure 1.8; −TÛx ). The cooling rate
separating these two behaviors is defined as the critical cooling rate −TÛcrit . In order
to successfully vitrify the quenched melt, the crystallization kinetics of the sample
need to be sufficiently sluggish or the casting method be sufficiently fast (i.e., quench
rate faster than −TÛcrit ). Additionally, dependent on the regime of fragility, strong vs.
fragile, the casting method and or sample dimensions must be selected accordingly.
Pre-Quench Controls
Additional factors that influence successful glass formation are overheating and
fluxing. Overheated samples, samples taken at least 100°C over the liquidus temperature before quench, are found to exhibit better glass forming ability than those
taken only slightly over their melting point.[5] This is presumably a result of melting
any foreign particles such as oxides, etc.[8] Also, fluxing with boron oxide for long
times increases glass-forming ability.[25] Both details are currently correlated with
reduction of oxide-induced crystal nucleation sites. The former is believed to melt
the oxides before quenching, and the latter to remove the oxides during alloying.[46]
While the underlying physics behind the benefit of overheating is not fully understood, Chapter 4 on a Ni-glass will address the effect of overheating on BMG
embrittlement and its origin.

21
Method
Splat Quenching
Quartz Tube/Water
Injection Molding
Counter Gravity
Arc Melt/Suction
Air Quench

Cooling Rate (K/s)
105 − 106
14
102
101 − 102
101 − 102
1 - 10

Sample Geometry
Circular foil
Rod or capillary
Die cut
Die cut
Rounded
Any

Sample Dimension
2-cm x 10-µm
mm to needle
mm
cm
cm
Any

Table 1.1: Summary of method cooling rates and respective practical geometries
and dimensions.[47, 48, 49, 50]
Methods Addressing Kinetic Quench Requirements
When selecting a quenching method, multiple parameters must be discussed; the
cooling rate must be sufficiently fast (> −TÛc ), and the required sample geometry and
dimensions must be specified.
Cooling rates range from 105 − 106 K/s for splat quenching, down to 1 − 10 for
air quenching. Table 1.1 column 2 summarizes common casting methods and
their achievable cooling rates. For geometry, while fastest, splat quenching only
yields 2-cm x ~10-µm thick foils; only practical for select uses. Common practical
geometries include rods and capillaries through water-quenching in quartz tubes,
and injection casting achieves cylinders, plates, bars, wedges, etc. via die-cut copper
molds. Table 1.1 column 3 summarizes the geometries capable per casting method.
To achieve greater sample dimensions, stronger glasses with high Turnbull parameter
(trg ) and associated slower critical cooling rates make more methods accessible.
However, when sample kinetics are sufficiently fragile, atomic diffusion must be
suppressed at deep undercooling. The required faster critical cooling rate can be
accommodated by employing smaller sample dimensions. Essentially, the rate of
heat removable typically scales with the inverse square of sample thickness/diameter
according to the solutions of the transient Fourier heat flow equation. Quartz-drawn
capillaries are frequently used to achieve the smallest possible sample rod diameter
for quenching ultra-fragile glasses. Table 1.1 column 4 summarizes the dimensions
possible per casting method.
All these details work in concert to predict and achieve successful vitrification of
a quenched melt. It is also noteworthy that more intricate net shaped samples are
possible by use of post-casting methods that exploit the glass transition and BMG
formability. These include thermoplastic forming (TPF) and additive manufacturing
(3D printing) to build up more complex shapes.[51, 52] Thermoplastic forming takes

22
a pre-cast BMG rod, heated above Tg , and a force applied to induce flow into a mold.
This method was used, for instance, to cast nanopatterned BMGs for a subcutaneous
blood glucose biosensor.[21] A single BMG rod formed both the substrate and
nonopillars ∼200-nm in diameter.[21] 3D printing of BMG material deposits the
molten alloy in sequential layers to form a 3D structure, where the cooling rate of
individual layers is determined by the layer thickness. In both cases, the sample
cools before crystallization intervenes and remains amorphous.
Description for Glass Quality — Glass Forming Ability
The natural interplay between heat removal rate and sample dimension gives rise
to the synonymous metrics of critical casting thickness, critical rod diameter, and
glass-forming ability (GFA). GFA is reported in terms of the maximum achievable
fully amorphous rod diameter (or plate thickness). This is determined in practice
by identifying amorphous characteristics (by XRD, DSC, electron microscopy, etc.)
at increasing rod diameters until a detectable level of crystallinity is present (i.e.,
XRD peaks appear or a calorimetric Tg or Tx disappear).
Formation Summary — Taking Metallic Glass to the Bulk Form
Due to the collaborative nature of these factors, some alloy systems and compositions
form glasses more readily than others. Tuning the aforementioned formation controls
led early research to increase glass quality, qualified by max achievable sample
thickness. These methods resulted in the growth from the first AuSi 10-µm foil to
Bulk Metallic Glass, millimeters in dimension.
1.4

Transition Types and Melting Criteria

While initial descriptions of BMG transitions (Tg, Tx, Tm, Tl, Ts ) in Section 1.1 are
useful, further discussion is necessary to better support Chapters 2 and 3.
Transition Types — Thermodynamic Classifications
In 1933, Paul Ehrenfest proposed a classification system for phase transitions. Based
on the thermodynamic free energy and other state variables, transitions are labeled
by the lowest derivative for which the free energy exhibits a discontinuity at the
transition (phase boundary); where the Gibb’s free energy is a function of independent thermodynamic variables (T, P, H, c, etc.).[53] A transition that shows a
discontinuity in the first derivative of the free energy is labeled a first-order phase
transition, and similarly for a discontinuity in the second derivative; a second- or-

23
der phase transition.[54] In Ehrenfest’s classifications, there could theoretically be
third, fourth, and higher-order phase transitions, but only first- and second-order
transitions are discussed here.
These discontinuities in free energy derivatives have physical meaning. Typical
first-order transitions between solid, liquid, and gas have a discontinuity in the first
derivative of free energy with respect to pressure. This translates to a discontinuous
change in molar volume or density at the transition.[54] An example of a secondorder transition is the ferromagnetic phase transition in iron and other metals where
the derivatives are taken with respect to applied magnetic field strength, H. This
transition shows a continuous change in magnetization across the phase boundary
(first derivative), but reveals a discontinuity in magnetic susceptibility (second
derivative).[45]
While useful, not all transitions fit into Ehrenfest’s classification. For example,
the superfluid transition in liquid He and other transitions are characterized by
power law or logarithmic singularities in the second derivatives of the free energy
(e.g., heat capacity, sususceptibility, etc.) at the critical temperature, as opposed
to simple discontinuities.[45] These are often referred to as Lamda-transitions.
Such transitions are unclassifiable by Erhenfest’s classification scheme. Thus, these
classifications were replaced by a similar but simplified naming convention that does
account for these transitions.
Modern classifications use the same names as Erhenfest’s historical convention,
but with updated definitions. First-order transitions are now described as having a
latent heat — energy per volume is either absorbed or released at a fixed temperature. Transitions between solid, liquid, and gas phases remain first-order in this
classification. Second-order transitions are also called continuous or order-disorder
transitions, and exhibit a decay in a correlation length across the critical point.[45]
Examples include ferromagnetic, superconducting, and superfluid transitions.
But when compared mathematically, both naming schemes describe various phenomena in similar ways:
For first-order transitions, when G(T, P) is continuous and S = −(δG/δT)P or
V = −(δG/δP)T are discontinuous, there is a latent heat and/or density change,
respectively. For a second-order transition, when G(T, P) is continuous as well as
S(T, P) and V(T, P), discontinuities in the second derivatives of G(T, P, N) describe
discontinuities in the response functions for heat capacity, isothermal compressibil-

24
ity κ, and the thermal expansion coefficient, α:[45]

δS
CP = T
δT P
 
1 δV
κT = −
V δP T
 
1 δV
α=
V δT

 2 
δ G
= −T 2
δ T
 2 P
1 δ G
=−
V δ 2T T
1 δ2 G
=−
V δT δP

The liquid/glass transition as observed experimentally displays a continuous change
in viscosity at Tg , an apparent jump in the volume thermal expansion coefficient and
heat capacity.[55] These sudden observed changes at Tg are what make detection
of the glass transition possible in a DSC or Thermomechanical analyzer (TMA).
However, these changes are also observed to depend on heat/cooling rates. There
has been an ongoing debate in the literature over whether the glass transition is a
purely kinetic transition or whether there exists an underlying thermodynamic phase
transition. Further, it is also known that the presence of disorder can broaden a firstor second-order phase transition. As a result, there has been further debate as to
whether the glass transition might be viewed as a broadened first-order transition
or how it might be described. The question of whether the glass transition is
characterized by an underlying thermodynamic transition is explored in Chapter
2. Further context on identifying this transition as a type of melting transition is
discussed there.
Additional Melting Criteria
In addition to the thermodynamic description of melting (a latent heat), two more
criteria have been developed and described in the literature. The Lindemann and
Born melting criteria focus on different aspects of melting — Lindemann on vibrational instability and Born on elastic rigidity loss. The Lindemann melting criterion
indicates that melting occurs via a vibrational instability — such that a material will
melt when the average amplitude of thermal vibrations exceeds some critical fraction of the interatomic distances.[56] Essentially the vibrations will cause motion
greater than intermolecular interactions will support. The Born melting criterion
focuses on the loss of elastic rigidity upon melting as quantified by the loss of a

25
finite shear modulus. Upon heating, a solid can no longer support shear stress; it
has lost rigidity. In this approach, melting is viewed as a "rigidity catastrophe."[57]
Liquid/Liquid Transitions in Experiment and Computer Simulation
While common phase transitions occur between the three states of matter — solid,
liquid, and gas — there also exist transitions within these states of matter, i.e.,
Intra-phase transitions. Such transitions may involve both ordered and disordered
materials and occur when a solid-solid or liquid-liquid transition phase boundary
is crossed within a phase diagram. An ordered solid can have various crystal or
amorphous structures (polymorphism), an amorphous material can have multiple
disordered structures (polyamorphism), and a liquid may exist in two distinct phases
(liquid polyamorphism). Such transitions are identified by changes in thermodynamic or structural characteristics as one crosses the phase boundary. Primary
polymorphism identifying tools include DSC and X-ray diffractometry, while Raman spectroscopy, thermomicroscopy, and other methods are used depending on the
material.[58]
These transitions occur in solids and liquids. Notable examples are as follows. For
solid-solid transitions, ice has 19 polymorphs, with three different amorphous structures.[59] The structures, identified via calorimetry and neutron powder diffraction,
were formed using varying pressure and other techniques, and the phases have
distinct structures and densities.[59] Liquid-liquid transitions are also observed,
but lack distinct structural differences as found in solids. These transitions occur
between states of disorder within the liquid phase and are often observed using
thermal DSC scans. Recent research has established a liquid-liquid polymorphism
as a key component in the pharmaceutical industry. Mannitol, a diuretic to reduce
pressure inside the eye or around the brain, is the first pharmaceutical that utilizes a
lower-energy polyamorph for increased aqueous solubility for drug delivery.[60]
While the phrase "liquid-liquid" transition is generally limited to the liquid phase,
polyamorphs may exist for any non-crystalline material; i.e., glasses, other amorphous solids, super-cooled liquids, as well as typical conventional liquids or fluids.
So within the liquid-like amorphous-structured solid phase, glass-glass transitions
are possible. While glass-glass transitions are often difficult to identify, discontinuous property changes are a strong indicator of a phase transition. For example, work
by Ketkaew and Schroers et al. observed an abrupt mechanical glass-glass toughening transition. They saw notch fracture toughness displaying an abrupt change as

26
a function of a well-controlled fictive temperature (describing average glass structure).[61] Through this, they identified how to achieve the two glass states with
different properties. The distinct ductility and hardness across the phase boundary
were tied to control of the fictive temperature by annealing. This transition potentially underlies the relatively abrupt embrittlement observed during processing of
BMGs.[61] Once discontinuous properties are identified, annealing, deformation,
or other processing may be used to reproducibly create the two different phases.
This method of discontinuous properties correlated with phase transition will be
used in Chapter 4 to explore the underlying case of the embrittlement transition in
Ni-based BMGs.
While discontinuous properties provide evidence of an intra-glass transition, the
thermodynamics are particularly difficult to identify due to the metastability of the
supercooled region. While experiments allow up to 20% undercooling of a BMG,
the metastable samples crystallize rapidly the deeper the undercooling.[62] Thus,
direct observation of evidence for a thermodynamic transition requires high-speed
techniques such as Flash DSC (FDSC) or, alternatively, computational methods
wherein much shorter time scales can be probed.
Experimental work has used FDSC to probe glass-glass transitions in the SCL.
Schawe and Loeffler et al. identified two monolithic polyamorphs in Au-based
quintary and quaternary BMGs.[63, 64] They used FDSC to access the heating rates
necessary to melt the intermediate metastable phases within the SCL. They termed
the two glass states a self-doped glass (SDG) and a chemical homogeneous glass
(CHG), each with their own crystallization nose in a TTT diagram.[63] Shen et
al. describes a secondary Metallic Glacial Glass (MGG) arising from a first-order
transition in the SCL.[65] They probed a quaternary La-glass and report the MGG
forming below the crystallization nose through FDSC.[65] It is important to note that
generally, as the number of elements in a BMG decreases, the fragility increases. The
FDSC works explored five- and four-element BMGs and found secondary glasses
by utilizing high heating rates. However, it is hypothesized that within the elusive
high-fragility regime, there may exist polyamorphs as secondary glass phases. To
achieve successful analysis of high and ultra-high fragility samples, the sample
kinetics require even faster methods than FDSC. In a collaboration with the author,
An et al. used molecular dynamics to probe this metastable deep-undercooling
regime for secondary glass phases in binary and single-element BMGs.
An et al. investigated pure Ag, and binary AgCu, and CuZr using Molecular

27

Figure 1.9: Energetic coordinate diagram for the traditional BMG phase (L glass),
the secondary glass (G) phase, and the crystal of pure Ag. Figure recreated from
[62].

Dynamics Simulations. They were the first to report and identify the heterogeneous
G-phase, and define its first-order liquid-liquid transition to the traditional liquidlike L-phase metallic glass. This secondary glass phase, termed the G-phase, is a
heterogeneous energetic metastable intermediate phase that lies thermodynamically
between the traditional homogeneous SCL (L) glass and the equilibrium crystalline
phase (Figure 1.9). It forms via a first-order freezing transition from the L-phase
liquid with a latent heat and discontinuous entropy change. The transition was
shown to be reversible, with the G-phase “melting” along a coexistence curve to
the L-phase liquid. The heterogenous G-phase structure is composed of ordered
core regions surrounded by disordered liquid-like regions with consistently higher
configurational enthalpy (Figure 1.9). The core regions exhibit local short-range
order on a scale of ∼1-nm resembling nanocrystals, but with distinct curvature in
the atomic planes along with stacking faults and point defects. The apparent size of
the ordered cores varied with temperature and composition (in the case of alloys).
The L-G transition is suppressed by the binary alloy systems with a reduced-ordered
core size and heterogeneity length scale, along with a smaller latent heat for the
L-G transition. The heterogeneity length scales were 4, 2, 1.8, and 1.5-nm for
pure Ag, AgCu, Cu7 Zr3 , and Cu2 Zr, respectively. Core regions exhibit fcc/hcp and
icosahedral short-range order for Ag and AgCu (fcc/hcp) versus CuZr (icosahedral)
cases, respectively. The G-phase is predominantly disordered, where ordered cores

28
contribute only 25% to overall local structure. The more-ordered solid-like Gglass exhibits persistent long-range elastic rigidity with a finite shear modulus as
compared with the more fluid-like L-phase. Compositionally, the G-phase shows
the structural heterogeneity as independent of chemistry or chemical separation in
pure Ag.[62] In the binary alloys, AgCu revealed similar average composition across
the heterogeneous G-phase structure, but wider variance from the L-phase.[66] The
CuZr alloys identified that chemistry is not correlated with the L-G transition, though
there is some spatial heterogeneity over the whole sample.[67]
These secondary glass works provide an important broader context for the findings
throughout this thesis. The details of the L-G transition as revealed in the simulation
work are related to the experimental results of Chapters 2 - 4, and will be expanded
on further there. The results of this thesis are compared back to the G-phase and
MGG to represent the simulation and experimental works, respectively. These are
described together, as it is hypothesized that the SDG of Schawe and Loeffler’s work
and the metallic glacial glass (MGG phase) of Shen’s work are essentially equivalent
to the An et al.’s G-phase. Throughout the thesis, the primary and secondary glasses
will be referenced by the terms L-, traditional-, and liquid-like glass/phase, and G-,
ordered-, or solid-like glass/phase, respectively.
1.5

Motivation

This introduction has provided a summary of the important theoretical concepts
and experimental background related to the nature of the glass transition in general
and metallic glasses in particular. In addition, each section outlined particular
shortcomings, inaccuracies, or a lack of sufficient understanding. These now become
the motivations for this thesis:
1. Insufficient data both at high fragility and in the SCL yield a limited understanding of metallic glasses;
2. Current thermodynamic methods collect data from a non-equilibrium state,
yielding erroneous data;
3. Inaccuracies of the Gaussian Landscape model in PEL theory require a new
DOS representation to accurately describe data;
4. Incomplete understanding of BMG embrittlement;

29
5. Uncertainty of how the secondary G-phase glass manifests across experimental glass fragility.
Chapter 2 addresses motivations 1 - 3 with analysis of ultra-high fragility Pt80−X Cu X P20
in a well-established ground state. The work presents a systematic experimental investigation of the configurational thermodynamics of the undercooled liquid as one
approaches the glass transition. By accurate direct measurements of the liquid
configurational enthalpy as a function of temperature, we are able to accurately
determine the thermodynamic state functions of the undercooled liquid as the glass
transition is approached. We find that the traditional Gaussian PEL model fails to
describe the configurational thermodynamics of these ultra-fragile liquids. With increasing fragility, the glass transition becomes progressively sharper and remarkably
evolves into an apparent discontinuous first-order phase transition with a latent heat
and discontinuous change in configurational entropy. In this high-fragility limit, the
glassy phase appears to display first-order “melting” in much the same manner as
crystals melt.
Chapter 3 addresses motivation 5 by investigating the mechanics, structure, and thermodynamics on either side of the anneal-induced transition proposed in Pt80−X Cu X P20
(Chapter 2). Hardness data reveal the G-phase grows on quenching in ultra-fragile
glasses, but on annealing in high-fragility glasses. X-ray diffraction report amorphous behavior across both phases (as-cast and anneal samples) in all compositions.
Thermodynamically, the onset of the glass-melting transition is observed in 20
K/min room temperature to melt DSC scans in the most ultra-fragile sample, X =
14. This is further supported by high-speed infrared imaging of rapid capacitive
heating, where a melting (cooling) front is observed before interruption by recalescence. These show Chapter 2’s configurational enthalpy glass-melting transition in
traditional thermodynamic scans, further supporting this glass-melting transition.
Chapter 4 addresses motivations 4 and 5 with a kinetically stronger glass system,
Ni 71.4Cr5.64 N b3.46 P16.5 B3 (Ni208) with m ∼ 54, and its observed embrittlement
transition. This work identifies previously unreported round inclusions that share
properties with the secondary glass in works by An et al. and Shen et al.; inclusions
maintain the same composition but are 25 - 28% harder than matrix, and highresolution TEM identifies a heterogeneous structure in the inclusions with SAED.
The inclusions are correlated with the embrittlement transition and suppression via
overheating, for they are only present in embrittled samples across multiple heat

30
treatment types. In effect, this chapter explores how the second glass phase in
high-fragility PtCuP may extend to a stronger glass system.

31
Chapter 2

THE EMERGENT FIRST-ORDER PHASE TRANSITION IN
ULTRA-FRAGILE Pt80−X Cu X P20 BULK METALLIC GLASS
2.1

Abstract

The following chapter reports the experimental configurational thermodynamics of
a highly-fragile near-eutectic Pt80−X Cu X P20 BMG system. When X is decreased
from 27 to 14, samples maintain bulk glass-forming ability, display increasing
fragility to the ultra-fragile regime (X < 17), and show an increasingly sharp glass
transition. A generalized equation is proposed and utilized for configurational
thermodynamic data fitting and analysis. At X < 17, evidence of a first-order melting
transition is observed. The specific configurational enthalpy versus temperature
curve displays a sudden discontinuous increase or latent heat at a well-defined glassmelting temperature, Tgm across the Pt80−X Cu X P20 composition landscape. When
analyzing configurational entropy, at low X, the Kauzmann temperature merges
with the glass transition temperature. Below Tgm , ultra-fragile samples comply
with the third law of thermodynamics; i.e., entropy falls and approaches that of the
crystalline eutectic solid at the low-temperature limit, thereby averting the Kauzmann
paradox. Configurational enthalpies of the equilibrated liquid are measured directly
and relative to well-defined crystalline reference state. The Pt80−X Cu X P20 alloy
system displays a first-order melting transition from a low-temperature solid-like
glass to a liquid-like phase as one progresses from a strong to a fragile metallic glass
system.
2.2

Introduction

As described in the overall introduction to this thesis, there are a number of shortcomings in existing metallic glass thermodynamic theory. This chapter aims to
address these shortcomings by focusing on the high- and ultra-high-fragility regime,
providing an accurate thermodynamic description with a well-established reference
state, proposing and utilizing a new, non-Gaussian approach to thermodynamic data
fitting, and utilizing methods that provide more accurate data in the ∆T data gap of
the liquid. Together, this work aims to discover what lies beneath when accurate
thermodynamics are utilized.
First, a high kinetically fragile metallic glass system that retains bulk glass-forming

32
Pt80−X Cu X P20
(at. %)
Pt66 Cu14 P20
Pt64 Cu16 P20
Pt62 Cu18 P20
Pt60 Cu20 P20
Pt57 Cu23 P20
Pt53 Cu27 P20

Fragility, m Tg (K)
TS (K)
TL (K)
>90
504
828.9 (1.0) 879.4 (1.0)
>90
504
827.8 (1.0) 877.5 (1.0)
>90
505
816.9 (0.5) 864.1 (0.5)
85
505
825.6 (1.0) 833.7 (1.0)
73
505
823.8 (0.2) 827.9 (0.2)
60
506
819.5 (0.1) 840.1 (0.1)

hm
(J/g)
67.7
68.7
71.8
67.8
68.5
67.5

GFA
(mm)
1.5-2
6-7
15
27

Table 2.1: Pt80−X Cu X P20 glass system property variances with composition.[68]
Heating rates utilized are noted in parenthesis in K/min.

Figure 2.1: Visualization of critical rod diameter variance with copper content, X.
Reproduced from Na et al.[68]

ability at high fragility is required. This maintained bulk glass formability will
allow the application of traditional equilibrium thermodynamics and testing while
supporting the high-fragility regime.

P t80−X CuX P20 ; A Tune-able High-Fragility Bulk Glass
Due to the difficulty in casting bulk high-fragility glasses, their properties have
remained predominantly unmeasured. However, in 2015, Na et al. at Glassimetal
Technologies discovered a bulk glass-forming high-fragility BMG system. This
Pt80−X Cu X P20 system displays widely varying and tunable fragility with alloy composition while maintaining bulk glass-forming ability. The already high-fragility
eutectic composition (m = 73 for X = 23) increases in fragility as the Cu content

33
of the alloy decreases.[10] The m reported for ultra-fragile compositions is in fact
a lower bound, as the viscosity becomes highly non-Newtonian and crystallization
becomes strain-rate sensitive. This makes the measurement of viscosity inaccessible at the lower Cu content when using traditional rheometric methods (TMA etc.).
Table 2.1 denotes how composition adjustment dramatically alters Angell fragility,
heat of fusion, and GFA with little to no change in the glass transition temperature,
Tg , or melting temperatures. When X < 17, fragility apparently extends into the
ultra-fragile m > 90 regime, and remarkably, GFA remains at the bulk scale (rods
of several mm diameter) as visualized in Figure 2.1. This allows for use of traditional bulk calorimetric methods and traditional testing (ultrasonic testing, viscosity
measurement, etc.).
Experimental Configurational Thermodynamics
The thermodynamic models and treatments described in Section 1.2 will be applied
here. Combined with further underlying assumptions described in Appendix B.1,
this chapter uses PEL separability to focus on configurational thermodynamics of a
fragile metallic glass system.
When studying configurational components of thermodynamic functions, wellequilibrated crystal and glass states are imperative. In the PtCuP system, glass
reference states are achieved through extended annealing at times several orders of
magnitude greater than the α (Maxwell) configurational relaxation time; annealing
of 15 hours for X = 18 - 27, and 3 hours for X < 17 due to their ultra-high fragility.
These give the PtCuP alloys sufficient time to configurationally relax, thereby establishing an equilibrium distribution of inherent state configurations. This in turn
justifies the application of thermodynamic relations between state variables (specific
heat, entropy, enathalpy, etc.)
Establishing a well-defined crystalline reference state at fixed T is essential, for
configurational enthalpies are measured as heats of crystallization and heats of
fusion relative to this crystalline reference state. This method used here describes
the evolution of structure energies at varying temperatures. In the PtCuP system, the
crystalline eutectic solid contains three crystalline phases (Pt7Cu, Pt5 P2 , Cu3 P),
each with distinct compositions from the liquid. This multi-phase eutectic solid
acts as the well-defined thermodynamic configurational ground state in the present
work.
This present work assures high-quality thermodynamic data by modifying a tradi-

34
tional approach. In place of commonly reported heat capacity measurements and
subsequent integration to obtain enthalpy, h(T), liquid enthalpy is directly measured
using the crystalline reference-state approach. In traditional glass calorimetry, heat
capacity is assumed to be an equilibrium property of the liquid in the absence of
crystallization, but BMG heat capacities are typically measured relative to the crystal. Utilizing the present approach, liquid configurational enthalpy is reported as the
heat of crystallization of the supercooled liquid state at a given temperature. This
assumes that the vibrational contributions to the enthalpy of the liquid and crystal
are approximately equal, and thus cancel in the vicinity of the glass transition temperature as has been experimentally demonstrated by Smith et al. and discussed in
Chapter 1.
Appendix B.1 describes the underlying assumptions and approximations used in
this work. In effect, the reported enthalpy is a direct measure of the difference in
potential energy across the liquid-crystal transformation at a given T. This difference
is then assumed to be purely configurational, so h L X (T) = hC (T). Thus through
direct measure of h L X , hc is determined. The reader is directed to Appendix B.1 for
a detailed summary of how these assumptions are used to arrive at these simplifying
conclusions.
Thermodynamic Theory and Analysis
Given the shortcomings of the Gaussian PEL DOS, this present work uses a more
generalized approach. Equation 2.1 is introduced to describe the configurational
enthalpy of the liquid. Introducing an alloy-dependent "isenthalpic" temperature,
θ h , a high-temperature enthalpy limit, h L X (∞) = hC (∞), and an exponent n as a
generalized thermodynamic fragility index:
θh
hc (T) = hc (∞) 1 −

 n

n+1
sc (φ) ∝ sc (φ0 ) − C(φ0 − φ)( n ),

(2.1)

(2.2)

here C is a normalization constant and φ0 is the limiting value of potential energy in
the high temperature limit, T → ∞. Also, in this case, n = 1 describes the Gaussian
distribution. The subsequent analysis will describe how this equation provides a
new view of the Kauzmann paradox at high n (or equivalently, high m).

35

Figure 2.2: Representative hC plot identifying hC (∞) and θ h terms, and depicting
n-dependent curvature. Methods and respective temperature ranges are indicated
by the data symbols; i.e., isothermal holds (triangle), constant heating rate (square),
rapid discharge heating (plus sign), successive cyclic undercoolings (circle), melting
of crystallized samples (diamond).

In effect, the experimental results of this chapter on a high-fragility BMG system
demonstrate that the glass transition becomes increasingly sharper and apparently
evolves toward a first-order “melting transition” in the limit of an ultra-fragile liquid.
In this limit, a glass melts in much the same manner as crystals melt — with an
accompanying latent heat, entropy of fusion, etc.
2.3

Methods

The overall approach records the configurational enthalpy via the heat of crystallization at various temperatures in the glass system. In order to measure the
configurational enthalpy about the glass transition, methods with various thermal
histories are required. Isotherms and low heating rate scans were used to measure
the low-temperature heat of crystallization in the low ∆T region, and fast scans via
rapid capacitive discharge heating yield mid-∆T crystallization data. Undercoolings
report high-temperature heat of crystallization, and hC is reported at decreasing
temperatures with successive undercooling cycles. All samples are reheated to the
equilibrium melt following crystallization and the enthalpy of fusion is reported.
These data regions are depicted in Figure 2.2 and a detailed description of each
method is outlined below. Together, these methods yield the configurational enthalpy curve of the liquid relative to the enthalpy of the crystallized eutectic sample.

36
Sample Preparation
Samples were cast by water quenching the molten alloys in quartz tubes. The alloys
are initially melted and equilibrated in a furnace at 900°C, well above the melting
temperature. The sample is then quickly transferred from the furnace and quenched
into a water bath. For compositions X = 18 - 23, rod samples were cast in 3-mm
fixed-diameter quartz tubes. For X = 14 and 16, samples were quenched in long,
tapered, drawn quartz capillaries up to 1-mm in diameter. Fluxing was not required
to obtain fully amorphous samples in the PtCuP system. For all DTA runs, the end
of a sample rod was made flat for good thermal contact. Each sample was cut to 30
- 60 mg for optimal signal-to-noise ratio. Samples were cleaned with 3 rinses and
1 ten-minute sonicated bath each of acetone and ethanol. Once dried, the samples
were weighed and placed flat-side down in a lidded alumina pan in the DTA.
Differential Scanning Calorimetry; hC T Measurement Methods
The calorimetry work reported here was done using a calibrated Netzsch 404C F3
DTA with separate calibrations for each constant heating rate reported. A sapphire
standard was used for calibration. All samples were annealed at Tg as the first step to
establish a well-defined thermal history and initial sample equilibrium state. Anneal
duration was dependent on fragility; 18 < X < 27 for 15 hours, and 3 hours for X <
17. The error in the measured enthalpy changes for the runs was established through
the measured variation of the enthalpy of fusion. Each DTA run melted the sample,
and the standard deviation across these runs was determined as the instrumental
error at ± 1.5 J/g.
Isothermal Holds
After annealing at Tg , samples were heated at 2 K/min to a range of temperatures
above Tg in the ∆T region and held isothermally at a fixed T until crystallization
occurred. Post crystallization, the samples were subsequently heated at 10 K/m
through the melting transition. Isothermal hold temperatures ranged 232 to 252°C
or 505 to 525K. Specific enthalpies of crystallization and fusion were recorded
and added to the hC (T) plots. Isothermal runs minimize thermal lag effects in the
calorimeter, allowing the instrument to reach stable steady-state conditions with a
well-defined signal baseline. In turn, this permits a very consistent and most accurate
determination of the heat of crystallization. However, due to the slow heating rate
to approach the isothermal hold temperatures and the finite time required to achieve

37
steady-state, accurate heat of crystallization data above 252°C or 525K could not be
obtained since crystallization intervenes before steady-state is achieved in the DTA.
Thus, to measure the heat of crystallization further into the ∆T region, one must
switch from the isothermal protocol to a constant heating rate protocol following
initial annealing at Tg .
Constant Heating Rate
After the annealing step, samples are heated at a constant heating rate through
crystallization and melting using a large range of rates, including 0.1, 0.5, 1.5, 3, 5,
8, 10, 15, and 20 K/min. This broad range assured the transition from isothermal
crystallization conditions to constant heating conditions was well explored, and the
heat of crystallization (or equivalently the configurational enthalpies) across a range
of temperatures was recorded. The shift in crystallization onset with temperature
is in part due to the instrumental lag (transient instrumental response) at higher
heating rates. Heating rates at and below 5 K/min are preferred for better sample
equilibration and reduced thermal lag within each run. The lower the heating
rate, the sharper the DTA time and temperature resolution achieved for the heat of
crystallization. Calibration runs of the melting transition of Sn at various heating
rates were used to correct for instrumental thermal lag effects. Tin’s melting point at
231.9°C is optimally located very near the PtCuP Tg of ∼ 230°C, thereby providing
an optimal correction for transient instrumental effects. The correction runs are
included in Appendix B.3. In general, 20 K/min heating rates are commonly
used in DSC and DTA studies reported in literature, but thermal lag effects are
seldom accounted for. By directly accounting for transient instrumental broadening
and temperature shift of the exothermic crystallization DTA signal, we are able to
improve the temperature resolution in our h L X (T) measurements. Basically, we more
precisely determine the sample temperature during the liquid-crystal transformation.
Cyclic Undercooling
As- cast samples are cycled repeatedly (heating and cooling) from below Tg through
crystallization and melting (Tm + 150K) at 5 K/min in the DTA. The number of cycle
steps is limited only by the number of programmable steps in the DTA. This method
allows for the collection of crystallization data over a wide range of temperatures in
the undercooled region. Successive undercoolings yield the crystallization event at
progressively lower and lower temperatures, thereby enabling collection of heat of

38
crystallization data in the upper range of the ∆T region of the hC curve.
Melting
Heating through melting of the crystallized sample was carried out after each crystallization run to assure a complete liquid-crystal transformation had occurred. Any
additional heat release events were investigated for structural differences via XRD.
The heat of fusion was determined for each sample following each crystallization
transformation.
Rapid Capacitive Discharge Heating
Rapid capacitive discharge heating (RDH) was used to measure data in the mid∆T region. The system uses ohmic dissipation with 15-kJ capacitive discharge
heating on rod samples 3-cm in length and ranging from 3 to 5-mm in diameter.
Samples were uniformly heated at heating rates up to ∼ 105 K/s by fully discharging
a capacitor bank from various charging voltages to vary the energy deposited in the
sample rod. The sample is clamped between two copper electrodes. Temperature
was measured with the Impac series 5 non-contact high-speed pyrometer with a 5
µs time resolution. A FLIR SC-4000 infrared camera was combined with the RDH
system for infrared images of coupled eutectic growth (see Figure 2.5). The infrared
camera functions with 256,000 pixels and frame rates up 1,300 frames/s.
Data Analysis; h(T)
For each of the methods listed above, the heat flow signal is recorded as a function
of temperature and or time (for isothermal segments). Configurational enthalpy is
calculated as the area beneath the exothermic crystallization curve and the enthalpy
of melting is calculated as area under the endothermic melting transition.
Additional Methods
Additional methods that provided supporting information for the thermal analysis
are included here. Viscosity was measured via Beam Bending in a Perkin-Elmer
Thermo Mechanical Analyzer. X-ray diffraction scans were completed with a Bruker
D2 Phaser diffractometer. The shear modulus was measured using ultrasonic transducers in the pulse-echo configuration. 25-MHz quartz transducers were used to
determine the shear sound velocities on 3-mm diameter rods. Density was measured
via wet/dry mass measurement in the Archimedes method.

39
2.4

Results and Discussion

While many properties of the PtCuP alloy family are detailed in Table 2.1, the
supercooled liquid must first be verified to be in metastable configurational equilibrium in order to apply equilibrium thermodynamic relationships in the analysis of
data. Configurational relaxation takes place with a characteristic time scale given
by the Maxwell relaxation time of the liquid. In turn, this can be determined from
the viscosity of the liquid along with knowledge of the liquid high-frequency shear
modulus. For X = 23, at Tg , time to crystallization onset is observed as t L X > 106 s (∼
1 wk). This establishes the samples as metastable liquids, where the initial anneal
times are sufficiently short to avoid nucleation and growth of crystalline phases.
Before subjecting samples to thermal analysis, the achieved metastable equilibrium
state must be verified further. Viscosity data are used to assess the extent of liquid
configurational relaxation prior to crystallization. These data, in combination with
the shear modulus, were used to estimate the Maxwell configurational relaxation
time for the undercooled liquid, τα = τM = η(T)/G, with G ∼ 32 GPa measured
ultrasonically. Initial isothermal holds reported crystallization peak times, t peak .
The X = 23 data for t peak and τα are illustrated in Figure 2.3a, where they are the top
and bottom curves, respectively. When compared, the ratio of t peak and τα quantifies
the extent of liquid relaxation toward metastable configurational equilibrium prior
to crystallization. With this ratio ranging from 103 to 106 for X = 23 and 20, it
indicates that h L X is representative of a configurationally relaxed undercooled liquid
in metastable equilibrium prior to the onset of crystallization. It follows that the
measured heat of crystallization is characteristic of the transformation of an equilibrium liquid to an equilibrium crystalline sample. This knowledge is applied to the
remainder of the PtCuP glass system.
Along with an established metastable configurational equilibrium, the crystallization
behavior of this system is important to defining a reference state for configurational
thermodynamics. Initial observation of crystallization in the PtCuP system reports
a sharp exothermic peak with rapid onset and decay. The peak shape is uniform
across isothermal runs as plotted on a logarithmic time scale when normalized to
peak height and peak time (Figure 2.3b). The crystallization event completes in
a time, ∆t L X , much shorter than the preceding incubation period; ∆t L X << t L X .
The peak and transformation times follow simple scaling behavior, which implies
a single crystallization event/mechanism. This is further verified by a pyrometer
visualization of Rapid Capacitive Discharge where a single crystallization front is
recorded. See the discussion accompanying Figure 2.5.

40

Figure 2.3: t peak to τα = τM defined metastable liquid region (a), and normalized
DTA scans displaying uniform peak shape (b). Reprinted with permission from
[68].

Further evidence of a single sharp crystallization event comes from XRD analysis.
As described in the Methods section, each run underwent multi-hour anneals, crystallization (isothermally or under constant heating rates), and then reheating and
melting. XRD scans were carried out on the samples after each thermodynamic
step and thermodynamic event. At slower heating rates, some samples expressed a
second but smaller exothermic peak during reheating between the initial large crystallization event and melting. XRD results indicated a fully amorphous sample up
to the initial crystallization event, and revealed no new crystalline diffraction peaks
after the smaller second event (Figure 2.4). Thus the crystallization event at 240°C
describes full crystallization. Further, with XRD showing no change in structure
after the smaller second exothermic peak, it is believed that this excess heat release
is due to coarsening of the microstructure produced by the primary/initial event.
Now that the equilibrium nature of the metastable liquid is validated and crystallization behavior understood, the enthalpy measurements from each method take
focus. First, particular notes on data collection are described before greater trends
are discussed across compositions and fragility. As discussed above, the isothermal
holds have a clean sharp peak, but present a secondary peak between 320 – 340°C.
This second peak is also observed in slow constant heating rate scans. However, this
second peak merged with the primary peak for heating rates above 1 K/min. When
present, the excess heat release peak is assumed due to relaxation or coarsening as
was done for the isotherms. And in both cases, the second ∆hC was added to the first
to equal the reported hC . The h L X onset temperature data are adjusted according
to the Sn melting corrections in Appendix B.3 and the raw data are included in

41

Figure 2.4: XRD post each thermodynamic step and transition for X = 23. Reprinted
with permission from [68].

Appendix B.4. No other heat release events are detected in other scan segments.
The isothermal scan and constant heating rate data compose the lower-temperature
data within the ∆T region just above the glass transition.
A third set of DTA scans include cyclic undercooling data. Here, the as-cast
samples underwent forty heating/cooling cycles from 200 to 900°C at 10 K/min.
Undercooling increased with successive cool-reheat cycles. This deepening of
undercooling is assumed due to the dissolution of heterogeneous crystal nucleants
through cycled overheating of the melt. Maximum undercooling was achieved to
365°C, which is ∼180°C below the eutectic temperature, TE , taken as the average
between the solidus and liquidus temperatures. The undercooling data fill in the hC
curve from just above the nucleation nose to ∼50°C below TE .
Melting data were collected for every scan during reheating, and describe the configurational enthalpy at the melting point, hC (TE ). These are the highest-temperature
data on the hC plots.
Measurements via rapid capacitive discharge contribute h L X (T) data to the mid-∆T
region. Figure 2.5a plots the T vs. t data. It visualizes the ultrafast heating to 350°C,
configurational relaxation and stabilization at ∼312°C, and rapid recalescence. Recalescence achieves 505°C which is below but near TE . The ultrafast pyrometer
data (Figure 2.5b) reveal a single crystallization event via coupled eutectic growth.
The singular growth front proceeds at ∼1.5-cm/s. This very high growth rate
suggests short-range chemical order for the crystal phases may already present in the
liquid, therefore mitigating the need for chemical partitioning along the advancing

42

Figure 2.5: Rapid heating profile of the X = 20 sample. a) Temperature vs. Time
profile shows rapid heating on recalescence. b) Ultrafast pyrometer from t = 0.6 -–
0.85s. Reproduced with permission from [68].
crystallization front, and further explains the small ∆t L X . The temperature increase
on recalescence was used to estimate the heat release as 52 J/g and was reported on
the hC plot along with the other calorimetric data.
With the data collected from the aforementioned methods, hC (T) plots are constructed first for 18 < X < 27, while a further discussion will be made for X < 17.
Figure 2.6a-d compiles the configurational enthalpy data for these compositions.
These data are fit with Equation 2.1 (99.4% correlation) with fitting parameters
listed in Table 2.2. From Figure 2.6a-d, the curvature of hC increases from the
fragility index, n, rising along with increasing Angell fragility, m. In X = 18,
the isotherm and constant heating rate data report different behaviors in the lowtemperature region of the hC curve. The two data sets have different slopes, but are
more vertical than that for the stronger, higher X glasses. In fact, the temperaturecorrected constant heating rate data suggest a vertical jump at 551K, indicative of a
potential latent heat. This separation from the low T hC data in X = 20 - 27 marks
the higher fragility samples as worth greater inquiry. This will be included in the
discussion on X = 14 and 16 samples.
For better comparison, the 18 < X < 27 data were plotted on axes normalized
by the isenthalpic temperature (θ h ) and the high temperature limit of enthalpy
(hC (∞)). Figure 2.7 collects the Pt alloy data on one plot and highlights the

43

Figure 2.6: hC data plotted per method and composition. Method key matches that
of Figure 2.2. Reproduced with permission from [68].
Pt80−X Cu X P20
(at. %)
Pt66 Cu14 P20
Pt64 Cu16 P20
Pt62 Cu18 P20
Pt60 Cu20 P20
Pt57 Cu23 P20
Pt53 Cu27 P20

Hc (∞)
(J/g) θ h (K)
67.9 561.1*
68.5 560.5*
72.4
508.3
68.3
492.2
70.2
484.8
69.9
433.6

-19.2*
-28.3*
25.7
13.3
8.36
4.3

>90
>90
>90
85
73
60

TK (∗)
(K)
562.1*
560.7*
517.4
511.4
505.5
472 ± 10

hR
hC (∞)

0.383
0.360
0.360
0.341
0.334
0.266

Table 2.2: Fitting parameters for configurational enthalpy (Equation 2.1) curves in
Figure 2.6a-d. Reproduced with permission from [68].

44

Figure 2.7: Fully normalized hC plot for composition and n comparison. Method
key matches that of Figure 2.2. Reproduced with permission from [68].

Figure 2.8: Specific configurational entropy (a) and specific configurational Gibb’s
free energy for Pt57Cu23 P20 . Reprinted with permission from [68].
increase in curvature from n, with increasing fragility, m. The plotted n’s for
PtCuP system increase from n = 4.3 and are included in the figure key. Projected
at higher fragilities is the fragile limit; the case in which n goes to infinity. In
this case, the configurational enthalpy approaches a heavy-side step function and
implies possible first-order transition behavior. For context, recall the Gaussian PEL
enthalpy Equation 2.1 is described by n = 1. The Gaussian enthalpy is superimposed
on Figure 2.7 and demonstrates, as expected, that the experimental data deviate
greatly from this model. This further demonstrates the Gaussian model inaccuracy
and the need for an accurate equation to describe the measured thermodynamics.
With 99.8% correlation, Equation 2.1 is a prominent contender.

45
With the now complete specific configurational enthalpy curves and the excellent
analytic fits provided by Equation 2.1, the enthalpy can be integrated to achieve
configurational entropy and free energy. The fit of Equation 2.1 to the thermodynamic data was used to analytically compute the specific configurational entropy,
sC (T), and specific configurational Gibb’s free energy gC (T). By integration, the
expression of sC (T) is:

T
nhC (∞)θ nh
hC (∞) n
n+2
sC (T) = ∆sF (TE ) +
θ h dTT
= ∆sF (TE ) −
(2.3)
n+1
T n+1
TE
∫ T

TE

where the integration constant is the measured entropy of fusion ∆sF (TE ) at the
eutectic temperature, TE . From the configurational entropy, the Kauzmann temperature, TK , is determined using sC (TK ) = 0 where ∆sF is reported in normalized
dimensionless units of hC (∞)/θ h . Figure 2.8a reports the specific configurational
entropy for X = 23.
TK = 

TE
  n+1  n+1
TE
1 + n+1
n ∆sF θ h

(2.4)

For X = 23, TK = 505.5K, very close to the calorimetric onset Tg of 505K. Further,
it is close to the rheologic Tg onset of 501.5K. To this end, the experimentally
defined TK is effectively indistinguishable from the thermodynamic and rheological
glass transition temperatures. The remaining Kauzmann temperatures for the other
compositions are listed in Table 2.2 and can be compared with the calorimetric glass
transition temperatures reported in Table 2.1.
To attain the Gibb’s free energy, we recall that at ambient pressures, the "Pv" term
can be ignored (compared with hC and Ts terms). Therefore gC (T) ∼ hC (T) −
T sC (T). We assume at TK the glass configurationally freezes, where below TK ,
sC (T) = 0, and gC (T) = hC (TK ). From these fits, below TK , entropy becomes
negative (subensemble), suggesting the system runs out of configurational states
when frozen at TK . In Figure 2.8b, gC (T) remains linear with respect to T down
to deep undercooling. This suggests configurational freezing sets in only at very
deep liquid undercooling and agrees with the Turnbull approximation for modest
undercooling.[8, 69]

46

Figure 2.9: Variation of effective glass transition width, 1/n, with copper content
(atomic %) (a). XRD plots for X = 16 (b). Reprinted with permission from [68].
At TK , the entropy and enthalpy have different behaviors. While the configurational
entropy reaches zero at TK , the configurational enthalpy remains finite. This leaves
a residual enthalpy, h R = hC (TK ), above that of the crystallized eutectic reference
state. This residual enthalpy is calculated relative to the high temperature limit
of enthalpy and reported in Table 2.2 under h R /hC (∞). h R represents the heat of
crystallization of a fully ordered ideal glass at TK , where the configurational enthalpy
of the ideal glass lies TR above that of the crystalline state.
The analysis for 18 < X < 27 has revealed promising results for configurational
freezing and a residual enthalpy, but when comparing the fitting parameters in Table
2.2 to copper content, X, a separation of character occurs at X ∼ 17. With n as
the thermodynamic fragility parameter of Equation 2.1, 1/n represents the relative
glass transition (half) width. When 1/n is plotted against copper content, X, Figure
2.9a uses a simple linear fit that suggest that n diverges at X ∼ 17. This divergence
implies the glass transition passes through a critical point and becomes a first-order
freezing transition at X = 17, and thus makes the lower copper content samples of
particular interest.
When compiling the configurational enthalpy data, the Sn heating-rate onset temperature corrections were utilized. The data for X = 14, 16 from the various methods
are summarized in Figure 2.10. When TC is temperature corrected for the heating
rate shift for X = 14 and 16, a clear vertical step emerges. This discontinuous
step is a latent heat and indicative of a first-order glass-melting transition. The
onset temperature is defined as Tgm , effectively the melting temperature of the lowtemperature “solid like” glass. For X = 14, Tgm = 533K, ∼30 K above the nominal
calorimetric onset Tg , and the latent heat of the transition is determined to be ∼27

47

Figure 2.10: Specific configurational enthalpy for X = 14 and 16. X = 14 an 16
data and limits plotted with dot-dash and solid lines, and dotted and dashed lines,
respectively. Reproduced with permission from [68].
J/g. For composition X = 16, a slightly smaller step discontinuity of ∼20 J/g occurs
at a somewhat higher Tgm = 548K. Both curves display behavior of a latent heat and
a first-order glass-liquid melting transition.
These latent heats of ∼20 - 30 J/g combine with the data in Figure 2.6a-d to reveal an
impressive trend. Between X = 14 and 16, a trend is observed that with increasing X
comes an increase in Tgm and a decrease in ∆hC . This trend continues into X = 18 as
mentioned briefly earlier, and even further in X = 27. Where Figure 2.6a displays a
previously overlooked but apparent small vertical jump in configurational enthalpy
at 651K. These data and trends are visualized in Figure 2.11. As X traverses the
composition range through 14, 16, 18, and 27, Tgm and ∆hC are 533, 548, 551, and
651K, and 27, 20, 23.7, and 15.7 J/g, respectively. The absence of the glass-melting
transition from X = 20 and 23 samples is attributed to the lack of available data in
the mid-∆T region where the suggested discontinuity would occur. For if the trend
is forecast to X = 20 and 23, Tgm is anticipated where only RDH measurements can
be captured.
Returning to focus on X = 14 and 16, in addition to the enthalpy jump at Tgm , Figure
2.10 shows the opposite curvature at low temperatures compared to the 18 < X <
27 compositions. This curvature change makes the current form of Equation 2.1
no longer appropriate. Fortunately, Equation 2.1 can be modified with the gained

48

Figure 2.11: An emerging trend with the glass-melting transition. As fragility
increases (decreasing X), Tgm decreases and ∆hC increases (filled and unfilled circles,
respectively). This reveals a larger glass-melting transition in ultra-fragile metallic
glasses.

knowledge of the additive residual enthalpy and put into a power law form;
 n
(hC (T) − h R )
(hC (∞) − h R )
θh

(2.5)

This new equation describes the approach to melting of the glass from below the
first-order transition and intersects with the enthalpy of fusion at Tgm . With this
modified equation, the fitting parameters have shifted as well. θ h now represents the
temperature where the low-temperature hC (T) curve crosses hC (∞), or equivalently
(when n is very large) where hC (T) for the low-temperature solid-like glass crosses
the enthalpy of fusion of the eutectic crystalline solid. The n parameter now has a
negative sign, which describes the glass freezing. Finally, hC (T) uses the ideal glass
h R as the natural zero for this adjusted glass enthalpy. With increasing n, Equation
2.5 approaches a heaviside step function from below θ h . In Figure 2.10, X = 14 and
16 are fitted with the results n = -19.2 and -29.2, respectively. The fitting parameters
are included in Table 2.2.
The curves in Figure 2.10 predominantly fit isothermal scan data for the ultra-fragile
samples below Tgm . For X = 14 and 16, the residual glass enthalpies approach h R
of ∼26.0 J/g and 24.5 J/g, respectively. The temperature dependence of hC below
Tgm suggests that the equilibrium solid-like glass is a configurationally excited state.
However, the potential of slow kinetics limiting relaxation and equilibration of

49

Figure 2.12: Specific configurational entropy for X = 14 and 16. X = 14 and 16
data and limits plotted with dot-dash and solid lines, and dotted and dashed lines,
respectively. Reproduced with permission from [68].
the glass below Tgm is unlikely. Particularly since the data were collected under
isothermal conditions with anneal times exceeding the Maxwell relaxation time by
orders of magnitude. Therefore, with assuming the data represent a well-equilibrated
glass, Equation 2.5 can be used to compute the configurational entropy.
Using the fits of Equation 2.5, the entropy is calculated by integration of ∆h/T
from low-temperature where sC = 0 to temperature TK∗ . TK∗ describes an "inverse"
Kauzmann temperature. In effect, this temperature is where the glass configurational
entropy extrapolates to the entropy of fusion of the crystalline eutectic alloy, i.e.,
where sC (TK∗ ) = ∆sF . The configurational entropy for X = 14 and 16 is plotted in
Figure 2.12. The equation for TK∗ is summarized as follows:
TK∗ = θ h

(n − 1)(hC (∞) − h R )θ h
nhC (∞)TE

 1/(n−1)

(2.6)

TK∗ functions as an upper bound for the glass-melting temperature and is slightly
lower for X = 14 than for X = 16, implying a more restrictive upper bound on the
highest fragility sample tested.
For the overall specific configurational entropy as a function of T, a piece-wise
continuous function is constructed as shown in Figure 2.12. The piece-wise plot
combines the fits of measured latent heat of glass-melting at Tgm and the entropy of

50
fusion of the crystalline eutectic. The figure shows sC (T) in units of the gas constant,
R, for X = 14 and 16. Within the above assumptions, for X = 14, the configurational
entropy at Tgm is 0.0308 J/gK or 0.533 R. Equation 2.5 provides a description of
glass entropy from T = 0K to Tgm . With the curvature present in the ultra-fragile X
= 14 and 16 samples, the equilibrium glass configurational entropy never becomes
negative, but rapidly approaches that of the crystallized eutectic solid as T falls
below Tgm . For the solid-like glass, the configurational entropy, sC (T), at T = 0K
vanishes within uncertainty of ∼ ± 0.03R. Thus, within the stated uncertainties, the
Kauzmann paradox is resolved where sC (T) obeys the third law of thermodynamics
for the solid-like glass phase. Effectively, the solid-like glass behaves much like a
crystalline solid but with a smaller heat of formation for configurational excitations
per Equation 2.5.
It is important to recall that phonon/vibrational contributions to the total entropy have
been excluded from this analysis (as these are assumed to be roughly equal for both
the glass and crystalline states in the temperature range of interest). While crystallization data technically include contributions arising from anharmonic differences
between the glass and crystalline states, they are apparently small by comparison
to configurational differences. This is understood because anharmonicity displays
a "T 2 " contribution to the enthalpy of crystallization, but the high n values are in
stark contrast to this potential contribution. Therefore, Equation 2.5 and high n
values strongly suggest that these anharmonic contributions are relatively small and
realistic to exclude. Therefore configurational degrees of freedom are expected to
dominate the temperature dependence of specific enthalpy below Tgm .
In effect, the ordered glass can be viewed as a configurationally ordered solid, but
with an infinite unit cell. It makes sense that this configurationally ordered glass
has a distinct configurational ground state enthalpy, h R , differing from that of the
eutectic crystalline solid. As discussed in Section 1.4, allotropes and polymorphic
crystals have ordered phases with phase-specific ground state energies. This is a
reasonable extension to a fully ordered solid-like ideal glass state as well.
2.5

Summary and Conclusion

The Pt80−X Cu X P20 system was a key part of this thesis research, and demonstrates
several prominent results. The homogeneous liquid exerts a single sharp crystallization event following coupled eutectic growth. This crystallization produces a welldefined crystalline reference state and allows for a direct and accurate measure of

51
the liquid enthalpy relative to that reference state. Before testing, the Pt80−X Cu X P20
system achieves a verified configurationally relaxed metastable state. The incubation time before crystallization, t L X , exceeds the Maxwell relaxation time, τα = τM
by several orders of magnitude, thus indicating the required metastable equilibrium
of the liquid is achieved before crystallization onset. Together, these features allow
an accurate assessment of the metastable equilibrium configurational enthalpy of
the liquid in reference to the crystalline eutectic solid. These features justify the
application of classical thermodynamics to compute the state functions of the liquid
phase.
The thermodynamic functions obtained from this work revealed the specific configurational enthalpy departs drastically from the 1/T temperature dependence expected
in the PEL Gaussian model. In actuality, n = 1 represents the Gaussian Landscape
model in Equation 2.1, but the magnitude of n is much larger for the reported
high-fragility and ultra-high fragility PtCuP samples. With Equation 2.1 and its
modification to Equation 2.5, this implies the density of inherent states approaches a
simple exponential behavior for W(φ) and is not Gaussian (see discussion in Chapter
1). With Equation 2.1, with increasing n, we see a divergence in heat capacity at
T = θ h . Similarly, the glass transition approaches first-order melting behavior as 1/n
approaches zero. For X = 14 and 16, one observes clear evidence of a latent heat and
first-order melting behavior of a solid-like glass to a fluid-like state. Equation 2.5
accounts for the residual enthalpy as one approaches the melt transition at Tgm from
below. Within measurement error and the assumptions of this work, a discontinuous
enthalpy (latent heat) is observed at a well-defined temperature Tgm for X = 14 and
16 compositions. This provides distinct evidence of a first-order melt transition of
this ordered ideal glass to a disordered liquid state where the liquid appears to be in
its high-temperature limit just above Tgm . For configurational entropy, the solid-like
glass follows a power law up to Tgm , but approaches zero (within error) as temperature approaches zero. Thus, within the error and the assumptions of this work,
the ultra-fragile liquid averts the Kauzmann paradox through a first-order freezing
transition, and the configurational entropy obeys the third law of thermodynamics
below the glass freezing temperature.
Ultra-fragile glasses demonstrate a distinct latent heat and glass-melting transition
temperature where a solid-like glass melts to a liquid-like phase. It is important
to note that both of these phases are non-crystalline (Figure 2.4). As X increases,
however, the latent heat decreases while the melting temperature increases. The

52
first transition is most clearly established for the X = 14 and 16 samples, but further
inspection of X = 18 and 27 reveal a possible continuation of the trend seen at
lower X. While Tgm continues to increase, the latent heat gets smaller, making
the transition more difficult to discern for the stronger, higher Cu-content glasses.
Furthermore, Tgm moves into the ∆T data gap, where existing methods either do not
allow measurements, or data are very difficult to collect (requiring RDH), and so
limited data exist. This explains why this possible transition is not identifiable in
higher Cu X = 20 and 23. In effect, these data identify the glass-melting transition
across the Pt80−X Cu X P20 composition landscape, and provide evidence that this
transition may exist in both stronger and highly fragile glasses.
These claims of a configurationally ordered glass are supported by Molecular Dynamics (MD) results by Berthier et al. and An et al. Berthier et al. have reported
ultrastable (configurationally relaxed) atomic glasses that exhibit first-order melting
on rapid heating through Tg .[70, 71, 72]These glasses are prepared by simulation
of layered atomic deposition onto heated substrates (near Tg ). This allows for a
degree of configurational relaxation not thought possible on cooling of a monolithic liquid.[70, 71] Bethier’s MD simulations showed a first-order melting front
propagation similar to direct melting of crystals and similar to the results reported
here for the PtCuP system. The MD analysis concluded the first-order melting
arose from the highly-ordered low configurational enthalpy ultrastable glass. It is
believed that the present work observes a similar highly-ordered low configurational
enthalpy/entropy ultrastable glass in the ultra-fragile Pt80−X Cu X P20 samples.
Further, the findings in this work are connected to the metastable structural and
energetic intermediate G-phase glass state in An et al.’s works described in Section
1.4. It is believed the PtCuP metastable configurational equilibrium solid-like glass
state is equivalent to the G-glass phase glass state reported from the MD simulations,
while the fluid-like phase in the X = 14, 16 case is equivalent to the L-phase
glass/liquid identified by An et al. The presence of the glass-melting transition
provides a natural starting point to explore mechanical and other characteristic
properties on either side of the first-order glass-melting transition. Attempts to
follow this line of investigation are reported in the next chapter where the possible
connection to the G-glass (and L-glass) is further strengthened.

53
Chapter 3

CHARACTERIZATION OF THE SECONDARY GLASS PHASE
IN ULTRA-FRAGILE Pt80−X Cu X P20 BULK METALLIC GLASS
3.1

Abstract

Work in Chapter 2 and Shen et al. describe a secondary G-phase glass-forming
on annealing.[68, 65] The results discussed in this chapter pinpoint a divergence in
formation mechanism at ultra-high fragility, uncaptured by these previous works,
while showing additional evidence for the glass-melting transition.
After the discovery of the first-order glass-melting temperature Tgm as discussed in
Chapter 2, characterization between the as-cast and configurationally relaxed and
equilibrated reference glass state (annealed) were completed. Evidence suggests a
divergence of formation criteria for the secondary glass phase at ultra-high fragility.
This evidence arises from a hardness cusp and cusp shift at X = 18. The hardness
jump in high X but not low X indicates different structures from annealing in high
X, but consistent structures at low X. As such, ultra-fragile samples achieve the
secondary glass on quenching, but less fragile samples see the secondary glass
forming with annealing. When samples were explored for amorphous behavior,
both as-cast and annealed samples showed no crystallinity. However, while all
samples suggest ordering via a reduced FWHM of the amorphous band, highX samples tend to order more. This is consistent with high-X samples growing
the secondary phase on annealing and low-X samples quenching in the secondary
phase for a smaller ordering effect. Finally, multifaceted evidence of a glass-melting
transition is collected across multiple works. Chapter 2 introduced the glass-melting
transition at Tgm as manifested in configurational enthalpy. The current work uses
DSC scans at 20K/min to reveal the onset of glass-melting in the ∆T region. While
the transition does not complete in the allotted time before crystallization intervenes,
rapid capacitive discharge studies allow visualization of the same effect, collecting
further evidence for a glass-melting transition of the secondary glass phase.
3.2

Introduction

This work serves as an extension to a key finding of the previous chapter; annealed
ultra-fragile Pt80−X Cu X P20 displays an emergent latent heat as a glass-melting
transition of a secondary glass phase. Both Chapter 2 and work by Shen et al.

54
characterized a secondary glass as grown and present in annealed samples.[68,
65] However, An et al.’s work on ultra-fragile pure Ag revealed the secondary
glass (G-phase) forms on quenching or isothermal evolution in the moderately
undercooled melt. This suggests a transition point in the fragility landscape, across
which the secondary glass forms via different mechanisms. The present work
explores properties across this potential fragility-dependent formation mechanism.
Properties are explored as a function of fragility to determine if heat treatments lead
to different behavior.
This work will use the Pt80−X Cu X P20 system to characterize the difference between
the as-cast and configurationally relaxed and equilibrated reference glass state (annealed). All measurements are completed across the fragility range available to the
Pt80−X Cu X P20 system. In this study, X includes 14, 18, 20, 21.5, and 23. Given
this is the same alloy system as in Chapter 2, readers are referred to Section 2.2 for
the advantages of using the Pt80−X Cu X P20 high-fragility BMG system.
The existing reports of secondary glass formation include a number of marked
differences between the two glass phases. Particularly, while both glass phases
are amorphous or non-crystalline, the works by Shen and An report a 20 and 30%
increase in hardness on transforming from the typical L-glass to the MGG or G
phases, respectively.[65, 62] Shen also describes the Tg of their MGG as 18K higher
than the traditional (L-phase) as-cast glass Tg .[65] As such, these properties will be
explored via Vicker’s indentations, X-ray diffraction, and DSC thermal scans across
the sample processing conditions and fragility landscape.
3.3

Methods

Sample Preparation
Samples were cast by water quenching in quartz tubes. Compositions X = 18 – 23
were produced in 3-mm fixed-diameter tubes. The X = 14 sample was quenched in
quartz-drawn capillaries up to 1mm in diameter. Fluxing is not necessary to produce
the glass for these samples. Samples were sectioned from the cast rods to 4 and 8-mm
lengths for the 3-mm diameter and capillary pieces, respectively. The samples were
then cleaned before the next sample preparation steps. Sample cleaning procedure
included 10 minute sonication in baths of acetone and ethanol with three rinses
with the respective solvent before each sonication. Half the specimens were then
annealed at Tg for 15 hours in a horizontal tube furnace (X = 18 – 23) or 3 hours in a
Perkin Elmer DSC 7 (X = 14). The ultra-fragile X = 14 was annealed in the DSC due

55
to higher available temperature control. Once cleaned, all samples were embedded
in epoxy pucks where the puck height is < 9mm to enable mounting in the XRD
sample holder. The pucks were ground at 400 grit until flat. Subsequent polishing
went from 400-grit to 1 µm grain size. Grinding and polishing were completed with
a Buehler autopolisher (ecomet 3 variable speed grinder-polisher equipped with an
automet 2 power head). X = 18 – 23 samples were stood on end for a 3-mm diameter
exposed polished surface. X = 14 samples were laid on their side for a 1 x 8-mm
exposed cross section along the length of the rod. This provides sufficient surface
area for X-ray scans and indentations. Once polished, the surface was wiped with
isopropyl alcohol using a kim wipe to assure no debris was present.
X-Ray Diffraction
A Panalytical X’Pert Pro was utilized for all XRD scans. X = 18 – 23 samples
underwent 1-hour scans, and X = 14 samples 7-hour scans. The longer scan time
was utilized to achieve better signal to noise ratio due to the smaller sample size.
Given XRD samples were cast in carbon-based epoxy pucks, once mounted with
putty, the puck was masked-off with corning glass coverslips (thickness 2 18x18,
cat no. 2855-18) to block the carbon puck diffraction maxima at 26, 42–45, 50 and
54 °(2θ). Figures 3.2 and 3.3 show no carbon puck background peaks. A figure of
this layout is included in Appendix Figure C.1.
Vicker’s Hardness and Optical Imaging
Hardness indentations were completed in a LECO LV810AT Oprical Scope and
Hardness Tester using a 4.903N force and 5s dwell time. Indentations averaged
around 50-µm across. Indentations were completed with the sample embedded in
the epoxy puck to assure a level surface for accurate indentations. General surface
images were captured before indentation at 10x magnification. Apparent topography
contrast was most visible, if not only visible, at 10x magnification.
Differential Scanning Calorimetry
A Perkin Elmer DSC 4 was utilized for all thermal scans. Summary scans are
displayed from 100°C through melting. This starting point is chosen to remove the
consistent errors at temperatures < 100°C arising from transient effects on heating to
remove any confusion for the reader. Scans from room temperature through melting
(600-700°C) at a 20 K/min constant heating rate were utilized. A background scan
was conducted with a sapphire reference immediately before the test run. This

56

Figure 3.1: Vicker’s Hardness data varying with composition and heat treatment.
Solid and dotted error bars are for as-cast samples and annealed samples, respectively.

background scan was taken as the baseline and removed. Analysis utilized the Sn
onset temperature corrections from Table B.1. These corrections were carried out
on a Netzsch DTA 404C, and are assumed to approximate corrections at 20 K/min
for the Perkin Elmer DSC 4 data.
Rapid Capacitive Discharge Heating
Rapid capacitive discharge heating (RDH) was used to measure data in the mid∆T region. The system uses ohmic dissipation with 15-kJ capacitive discharge
heating on rod samples 3-cm in length and ranging from 3 to 5-mm in diameter.
Samples were uniformly heated at heating rates up to ∼ 105 K/s by fully discharging
a capacitor bank from various charging voltages to vary the energy deposited in the
sample rod. The sample is clamped between two copper electrodes. Temperature
was measured with the Impac series 5 non-contact high-speed pyrometer with a 5
µs time resolution. A FLIR SC-4000 infrared camera was combined with the RDH
system for infrared images of coupled eutectic growth (see Figure 2.5). The infrared
camera functions with 256,000 pixels and frame rates up 1,300 frames/s.
3.4

Results and Discussion

The as-cast and annealed samples were first explored using hardness measurements.
Vicker’s hardness measurements in Figure 3.1 suggest an apparent annealing effect

57
As
HV Ave
Cast
HV Stdev
Anneal HV Ave
at Tg
HV Stdev
%∆HV

Cu14
Cu18
368.27 398.58
18.13
12.11
376.21 393.59
22.5
20.65
2.16% -1.25%

Cu20
385.80
17.02
404.23
13.33
4.78%

Cu21.5
378.10
8.83
398.58
12.11
5.42%

Cu23
378.92
19.39
385.80
17.02
1.81%

Table 3.1: Vicker’s Hardness (average and standard deviations) with nearrest neighbor (nn) distance in Angstroms for Pt90−X Cu X P20 compositions. Column headers
are abbreviated with Cu X values.

at high X (lower fragility “m”), but, within standard error, there is no discernible
effect at low X (ultra-fragile). The standard error is taken as the standard deviation
from 25 independent indentations. For X = 20, 21.5, and 23, average hardness values
increase from 385.80, 378.10, and 378.92 HV to 404.23, 398.58, and 385.80 HV,
respectively. These samples experience, on average, a ∼4% increase in hardness.
This increase is not as great as that reported in other multi-phase glass works that
report an ∼20 - 25% jump from the computational L-glass to the G-glass by An
et al., and 20% for the as-cast to MGG phase by Shen et al.[62, 66, 67, 65] But
interestingly, the ultra-fragile samples that exhibited the first-order glass-melting
transition in Chapter 2 do not show any significant increase in hardness (any variance
is well within experimental error). Where the glass-melting transition occurs in the
X < 18 samples in the configurational thermodynamics study, a cusp is observed in
hardness at X = 18 for as-cast samples. This cusp persists in the annealed samples,
but appears to shift from X = 18 to 20. This cusp shift suggests X = 18 is some sort
of structural transition point, where the annealed structure is quenched-in on casting
for the ultra-fragile low-X compositions. This similar transition point (composition
and fragility (m > 90) suggests the low-X as-cast samples undergo the same annealinduced transition as the high-X samples, but transform instead during the quench.
This suggests the as-cast and anneal states at low X are both in the same glass state.
Indentation data are summarized in Table 3.1.
To investigate this behavior and potential evolution during annealing, X-ray diffraction scans were conducted on both the as-cast and annealed samples. XRD scans
report amorphous behavior across composition in both sample systems; the as-cast
and annealed scans are displayed in Figures 3.2 and 3.3, respectively. The full
width at half maximum (FWHM) of the amorphous band is utilized to determine if
ordering/structural change of the glass occurs during annealing. A narrowing of the

58

Figure 3.2: As-cast X-Ray diffraction scans for X = 14 – 23. Samples increase in X
from top to bottom.

59

Figure 3.3: Annealed X-Ray diffraction scans for X = 14 – 23. Samples increase in
X from top to bottom.

60
Peak (°2θ)
FWHM
d (Å)
nnd (Å)
Peak (°2θ)
Anneal FWHM
at Tg
d (Å)
nnd (Å)
∆Peak (°2θ)
∆FWHM
Change ∆d
∆nnd
As
Cast

Cu14
40.771
7.459
2.213
2.722
40.827
7.143
2.210
2.728
0.139%
-4.234%
-0.133%
-0.133%

Cu18
40.448
5.417
2.228
2.740
40.548
5.243
2.225
2.736
0.148%
-3.198%
-0.142%
-0.142%

Cu20
40.558
5.522
2.223
2.734
40.622
5.238
2.221
2.732
0.084%
-5.140%
-0.081%
-0.081%

Cu21.5
40.548
5.471
2.225
2.736
40.721
5.175
2.216
2.725
0.427%
-5.418%
-0.407%
-0.407%

Cu23
40.727
5.623
2.150
2.725
40.747
5.047
2.214
2.723
0.049%
-10.237%
-0.047%
-0.047%

Table 3.2: Vicker’s Hardness (average and standard deviations) with nearrest neighbor (nnd) distance in Angstroms for Pt80−X Cu X P20 compositions. Column headers
are abbreviated with Cu X values.

amorphous band and therefore a decrease in FWHM suggest ordering of the amorphous system, in analogy to how crystal grain growth yields narrower peaks. The
high-X compositions show a 5 - 10% decrease on annealing, while the low-X (X
≤ 18) samples show a 3 - 4% decrease (Table 3.2). This suggests that the high-X
samples undergo a greater ordering effect with annealing that could contribute to
their observed larger hardness increase. This further supports the idea that the low-X
samples are already predominantly in the G-phase solid-like glass following initial
casting.
In continued analysis of the XRD data, the estimated nearest neighbor distance
(nnd) and its relative change are quantified to determine if the atomic environment
changes on annealing over the range of X. These changes are reported in Table
3.2. To calculate an “effective” nearest neighbor distance, the d-spacing of the
first diffraction maxima is calculated from the peak angle by rearranging the Bragg
equation from
nλ = 2d sin θ,

(3.1)

nλ
2 sin (θ/2)

(3.2)

to
d=

61
Where d is the plane spacing, n the diffraction order, λ the radiation wavelength, and
θ/2 the angle from the surface normal.[3] The nearest neighbor distances, nnd, may
then be estimated using the “Debye” formula where nnd = 1.23d and are reported in
Table 3.2.[73] The estimated nearest neighbor distances all decrease on annealing,
but do not show an obvious trend between the low- and high-X compositions.
Given the ultra-fragile samples display a different hardness response to annealing,
thermodynamic scans via Perkin Elmer DSC 4 were utilized to investigate their
thermal response. It is important to note that the thermal scans in this chapter follow
a different protocol than those in the previous chapter. All samples in Chapter 2 were
annealed at Tg then immediately heated. Since those samples were not returned to
room temperature before heating, the thermal trace was not captured near Tg , and the
normal heating response associated with the ∆T region was not observed. Figures
3.4 and 3.5 show the 20 K/min thermal scans from 100°C through melting at ∼600°C.
The inset (c) of each figure highlights the ∆T region and its peculiarities arising
in the case of the annealed samples, and in particular, in the ultra-fragile X = 14
sample.
In Figure 3.4, the as-cast X = 18 sample shows a typical jump in apparent heat
capacity beginning at ∼230°C and ending at ∼250°C. This is the normal thermal
signature of the glass transition generally seen in an as-cast metallic glass. The
annealed sample, however, shows a sharper glass transition accompanied with an
enthalpy recovery peak.[74, 75] Enthalpy recovery is typical of a glass relaxed near
Tg then reheated as discussed by Busch et al. In the case of X = 14 in Figure
3.5, similar to X = 18, one observes a typical rise in heat capacity at Tg for the
as-cast sample. The annealed sample also shows an enthalpy recovery peak as in
the X = 18 case. For the annealed sample, however, a second new peak emerges
beyond the enthalpy recovery peak in the ∆T region. The inset (c) highlights this
region and not only shows the Tg heat capacity rise and enthalpy recovery, but also
shows a well-defined second endothermic peak before the onset of crystallization.
The author proposes this endothermic peak arises from the onset of the first-order
glass-melting transition equivalent to the transition at Tgm described in Chapter 2
(see Figure 2.10). The onset of melting during the scan is apparently interrupted by
crystallization of the melting solid-like glass, which causes the overall DSC signal to
turn sharply exothermic. Since crystallization interrupts this melting transition, the
true size of the apparent melting peak is much larger than visualized in the figure,
and the t peak temperature would be shifted higher. Even so, the unusual endothermic

62

Figure 3.4: Thermal (DSC) scans for X = 18 at 20K/min. Scan of as-cast sample (a)
and annealed sample (b). The glass transition peak in the anneal sample is enlarged
(c). Transition temperatures are printed in Table 3.3.

Figure 3.5: Thermal (DSC) scans for X = 14 at 20K/min. Scan of as-cast sample
(a) and annealed sample (b). The glass transition peak and glass-melting transition
are enlarged (c). Transition temperatures are printed in Table 3.3.

63

Cu14
Cu18

As-Cast
Anneal
As-Cast
Anneal

Tg
(K)
241.04
250.53
239.24
249.49

Tgm
(K)
270.60

Tx
(K)
282.81
285.68
302.39
302.17

Table 3.3: Temperatures and enthalpy values for X = 14 and 18 thermodynamic
scans. Temperatures before correction by -11K from Table B.1.

behavior is a strong indicator of the onset of the glass-melting transition. When this
representative Tgm is compared to that from Chapter 2’s ultra-fragile configurational
enthalpy plots (Figure 2.10), a similar temperature emerges. Chapter 2 reports Tgm
at 533K = 260°C for X = 14. Figure 3.5c indicates the approximate Tgm peak at
270°C, but corrects to 259°C utilizing the transient correction for the 20 K/min
heating rate (Table B.1). This suggests promising evidence that these DSC scans
capture at least the onset of configurational melting in the ultra-fragile glass.
Further investigation of this phenomenon requires suppressing crystallization so
that the apparent melting transition can be observed separately. Based on the work
in Chapter 2, one would expect that using a higher heating rate for the annealed
X = 14 sample could prove useful. As such, the RDH method was employed
to heat the annealed sample at very high rates. Such RDH data were displayed
earlier in 2.5. Figure 2.5 highlighted crystallization by coupled eutectic growth
present from t = 0.60 - 0.85s. However, a previously overlooked phenomenon
from t = 0.10 - 0.60s is related to the melting onset in Figure 3.5c. Given that
melting is an endothermic phenomenon, one expects a cooling behavior on melting
when the solid-like low-temperature glass phase is rapidly heated above its glassmelting point, Tgm . Under such conditions, the overheated solid-like phase will
absorb heat as it melts, thereby cooling until the temperature reaches Tgm . In the
overheated solid-like phase, the melting front would appear as a cooling front as it
traverses the sample. In fact, snapshots of such a cooling front were captured via
high-speed pyrometer and are compiled with the temperature-time trace (purple) in
Figure 3.6ab. When these snapshots are compared with the thermal trace and glassmelting behavior as discussed in Chapter 2, consistent behavior is observed. That
is, following rapid heating of the solid-like phase far above its Tgm , a spontaneous
cooling front propagates across the sample prior to the onset of crystallization. This
is immediately followed by crystallization at 0.60s just as melting (the cooling front)

64

Figure 3.6: Ohmic heating via rapid capacitive discharge. Temperature traces versus
time across various energy releases (a) and the accompanying ultrafast thermal
camera images from t = 0.1 - 0.6s for the purple trace.

completes. At t = 0.60s crystallization by coupled eutectic growth takes over and
the behavior follows that already displayed Figure 2.5b. Multiple RDH thermal
traces were collected using the pyrometer at higher RDH energy inputs. At the
higher energy inputs (see yellow curve in Figure 3.6a), a Tgm peak behavior emerges
followed by further overheating of the X = 20 annealed sample (solid-like phase)
to 410°C. This overheated solid-like phase then melts and cools back toward Tgm
as the sample absorbs the latent heat of fusion on melting. The initial heating
peak reaches ∼400°C, cools to 385°C due to enthalpy recovery, then finally heats
to 410°C as the RDH energy discharge is completed. This is followed by dramatic
cooling to ∼335°C as the overheated solid-like phase melts. Cooling by ∼75°C of
the overheated solid-like phase corresponds to excess heat absorption of ∼3 kJ/mole
(assuming an average estimated heat capacity of the overheated solid-like phase is
∼40 J/mole-K as suggested by the results of Chapter 2), or roughly 20 J/g in the
case of PtCuP at X = 20. With the latent heat only 2.7 kJ/mol, the excess 3 kJ/mol
is sufficient to adiabatically melt the entire solid-like glass phase. This peak pattern
also mirrors that observed by DSC in Figure 3.5c. Due to the much lower heating
rate, the annealed sample is far less overheated in the case of the DSC work, so the
melting rate is much lower and thus interruption by crystallization is observed.
One additional observation worth noting is that a peculiar topography arises when

65

Figure 3.7: Peculiar topography for X = 18 annealed for 24 hours.

the X = 18 is annealed for longer time; i.e., 24 hours, but still within the incubation crystallization time t L X and several orders of magnitude above the Maxwell
relaxation time τα . Pictured in Figure 3.7ab, this topography shows a structural
heterogeneity on the order of 10’s of microns compared to the typical surface highlighted in 3.7c. This heterogeneous topography covers roughly half the sample
and spreads from the center toward one edge. The scale of this heterogeneous pattern is significantly smaller than the Vicker’s diamond (50-µm across), so accurate
hardness measurements of the lighter and darker regions were not possible at this
indent resolution. However, it is hypothesized that the lighting contrast is from a
minor hardness-induced height difference revealed on polishing. This topography is
visible at 10x magnification through a single wavelength (green) optical scope. The
topography is not readily visible at 20 or 40x. While of a greater length scale, the
author believes it is worth noting that this heterogeneity bears a similar resemblance
to the G-phase structure in An et al.’s Ag, CuAg, and CuZr works.[62, 66, 67] This
topography is distinct from typical crystalline dendritic growth.
3.5

Summary and Conclusions

Existing published works describe a secondary glass phase that forms during annealing.[68, 62, 65] The present work investigates the properties on either side of the
believed heat treatment-induced transition for as-cast and annealed Pt80−X Cu X P20
samples. Vicker’s hardness presents an annealing effect at high X as a ∼ 4% hardness increase, but shows no discernible difference on low-X (ultra-fragile) samples

66
on annealing. When observing the hardness data over the composition range, a
cusp in hardness is present at X = 18 for as-cast samples, but shifts to X = 20
once annealed. This shift on annealing and the accompanying HV annealing effect
indicate X = 18 as an apparent transition point. Prior work on the same alloy system
reported a distinct latent heat present at compositions with X < 18.[68] This marks
this composition range as where the glass transition evolves toward a discontinuous
melting transition.
X-ray diffraction reveals fully amorphous character in both as-cast and annealed
samples across all compositions. In all cases, the glass appears to order during
annealing resulting in a narrower and sharper primary amorphous band. This effect
is more noticeable at high X with a 5 – 10% decrease, while low X samples see
only a 3 – 4% decrease (FWHM). This smaller change combined with the hardness
data suggest that, at low-X, the solid-like low-temperature glass phase is quenched
in during casting and further orders on annealing. Where, for high X, the traditional
glass phase is quenched, and annealing yields a more ordered glass phase.
Thermodynamically, both ultra-fragile X = 18 and 14 present the glass transition’s
characteristic rise in heat capacity, and the annealed samples display a recovery
enthalpy. X = 14 shows an unusual additional endothermic peak above the glass
transition that is interrupted by the rapid onset of crystallization. This is attributed
to the onset of a melting transition of the solid-like phase. This interpretation
is consistent with the results of Chapter 2, where a discontinuous configurational
enthalpy jump (latent heat) is observed for X < 18. Further, an apparent solidlike phase melting front is captured with high-speed pyrometer video during rapid
capacitive discharge heating measurements.[68] Through multiple methods and the
results presented in Chapter 2, the case for a first-order glass-melting transition
appears to be well established in the ultra-fragile metallic glass PtCuP system.

67
Chapter 4

EMBRITTLEMENT TRANSITION IN NI-BASED BULK
METALLIC GLASS AS EVIDENCE OF THE G-PHASE GLASS

The author recommends the figures of this chapter be viewed electronically for
assured visual clarity.
4.1

Abstract

Ni 80−X−Y Cr X N bY P16.5 B3 alloys report an embrittlement transition that has historically been related to composition.[76] More recent works identified overheating as
a mechanism to suppress the embrittlement transition in Ni 71.4Cr5.64 N b3.46 P16.5 B3
(Ni208). After a wide range of fragile-regime glasses in Pt80−X Cu X P20 revealed a
secondary glass phase and its glass-melting transition, the author explores Ni208
for the secondary glass phase in this stronger glass. This work connects the secondary glass phase to sample embrittlement in m ∼ 54 Ni208 via secondary glass
inclusions.
Cross sections of notch fracture toughness samples reveal inclusions present only in
embrittled samples, suggesting the overheating treatments suppressed embrittlement
by suppressing inclusion growth. Hardness reports a 25 - 28% increase from the
matrix to inclusion, similar to previously reported hardness jumps from the primary
to secondary glass.[65, 62, 66, 67] EDS in SEM and TEM revealed compositional
equivalence between the matrix and inclusions. Structural analysis via TEM, SAED,
and XRD reveal and explore a "cloudy" heterogeneous structure similar to what is
seen in computational reports on the secondary glass, albeit at a larger scale.[62,
66, 67] SAED reveals the inclusion as a mixed ordered-disordered phase, but XRD
clarify the inclusions as predominantly amorphous. This sheds light on how the
secondary glass may present in stronger glasses while informing the long-lasting
question on how overheating suppresses sample embrittlement — by suppressing
inclusion growth. Further explorations are necessary into this sample system for the
secondary glass, but these results provide a prominent foundation.
4.2

Introduction

The preceding chapters revealed a glass-melting transition in the full range of fragilities accessible to the Pt80−X Cu X P20 glass family. Identified via configurational en-

68

Figure 4.1: Superimposed dashed and color contours of GFA and Notch Fracture
Toughness (KQ ), respectively, on the Ni alloy composition landscape. Figure D.1
in Appendix D visualizes a color contour for GFA for additional clarity. Please see
the electronic version for assured visual clarity.
thalpy and traditional heating scans, fragilities of m = 60 to over 90 were explored.
While informative of the elusive fragile regime, the author now investigates whether
this second phase is present in stronger glasses and how it presents.
In determining a strong glass worth study, an odd phenomenon in a Ni-based BMG
system piqued the author’s interest. Ni 80−X−Y Cr X N bY P16.5 B3 exhibits an embrittlement transition with m ranging from 54 to 77. Numerous studies have explored
potential underlying factors to this embrittlement, but this author hypothesizes the
presence of the secondary glass and its increased hardness could play a critical role.
This introduction will briefly summarize the current understanding of the embrittlement transition in the Ni 80−X−Y Cr X N bY P16.5 B3 glass family and will serve as context behind this work’s search for the secondary glass in Ni 71.4Cr5.64 N b3.46 P16.5 B3
(Ni208).
Multiple studies investigated the underlying factors behind the embrittlement transition. First, a composition map along the Ni 80−X−Y Cr X N bY P16.5 B3 landscape was
probed for notch fracture toughness (KQ ) and glass forming ability (GFA). Figure

69

Figure 4.2: Visual representation of the two casting methods. Direct casting from
casting temperature Tcast (a), versus overheating to the toughening temperature
Ttough before cooling to and quenching from the casting temperature Tcast (b).

4.1 summarizes these findings with a color contour for KQ and a dashed contour for
GFA. These properties display overlapping maxima and minima across the composition landscape. A steep drop off is observed, where traversing the compositional
landscape reduces both GFA and KQ , switching the sample from tough and ductile
to brittle. This sudden change in properties makes this a composition region of
interest. In the desire to probe stronger glasses for the second glass phase, the
strongest glass in the NiCrNbPB system, Ni208, is a worthy pursuit. In addition to
its fragility of m ∼ 54, its location in the GFA vs. KQ vs. composition landscape
is promising for transitionary properties. Ni208 is marked by the star in Figure 4.1
near peaks in both GFA and KQ . Further, this composition is uniquely placed near
the transition between high and low GFA and KQ , such that small variances lead to
large property changes. So while this first work correlated embrittlement to GFA
and composition, a second study explored a more direct link to embrittlement in
Ni208.
A patent by Na et al. with Glassimetal Technologies compared thermal treatments
to probe the embrittlement transition in Ni208.[10] The samples were subjected
to two thermal treatments: direct casting and overheating before casting. In both
cases, the casting temperature, Tcast , describes the temperature of the sample just
before quenching to room temperature. The two pathways are visualized in Figure
4.2. Path (a) indicates the direct casting method. The sample is heated above
the liquidus to Tcast . Path (b) heats the sample above the liquidus and casting
temperature to an overheating temperature of 1250°C and held to attain equilibrium.

70

Figure 4.3: Notch fracture toughness KQ and critical rod diameter dcr under the
direct casting method.[10]

Figure 4.4: Notch fracture toughness KQ and critical rod diameter dcr under the
overheating casting method.[10]

71
Post equilibration, the sample is cooled slightly to the casting temperature before
quenching. Throughout the text, these methods are referred to as "cast T" or "directcast," and "overheating," respectively.
KQ and critical rod diameter dcr (mm) were measured on as-cast samples for each
casting condition. Figures 4.3 and 4.4 summarize these data. The respective thermal
treatment pathway is bolded in the inset. All samples are 3-mm diameter rods as
required for the ASTM standard for notch fracture toughness. When focusing on the
direct casting method, Figure 4.3 reveals a 65% drop in KQ from 1250 to 1200°C,
and a 55% decrease in dcr from 11 to 5mm across 1250 to 1100°C. These data
describe 1250°C as a critical toughening temperature, Ttough . When Tcast > Ttough
the sample exhibits tough behavior. The overheat method for Figure 4.4 utilizes
Ttough as an overheating temperature. This determined if overheating above Ttough
would have an effect on KQ and dcr . While the overheated samples saw similar
63% and 36% drops in KQ and dcr , they occurred at lower temperatures of 1050
and 900°C, respectively. The GFA minimum from overheated samples only fell to
7mm, maintaining a higher GFA across all casting temperatures compared to the
direct-cast samples.
The thermal treatment effect on KQ is visualized by direct comparison of Figures
4.3 and 4.4. The overheated samples in Figure 4.3 display embrittlement suppressed
to lower temperatures. This shifts the embrittlement transition by 150°C from 1200
(Figure 4.3) to 1050°C (Figure 4.4). As for the underlying cause, it is important to
note that in both cases, this embrittlement is not related to crystal formation; dcr
remains well above the 3-mm sample diameter for all KQ . In search of the embrittlement cause, the work of this chapter probes cross sections of the exact KQ samples
from Figure 4.3 and 4.4 for evidence of a second glass phase. With previous chapters indicating heat treatments (as-cast versus anneal) yielding different properties
related to the secondary glass, the Ni208 casting condition-related embrittlement is
a promising space to investigate the possible secondary glass phase.
4.3

Methods

Sample Preparation and Ni208 Caveat
The samples utilized in this work are the exact samples tested in Figure 4.3. Cross
sections were taken off the non-fractured ends of the rods to avoid potential phase
separation resultant from the fracture energy. Samples were cleaned before subsequent steps. Sample cleaning procedure included 10 minute sonication baths each

72
of acetone and ethanol with three rinses with the respective solvent before each sonication. Once cleaned, all samples were embedded in epoxy pucks such that the puck
height is < 9mm to fit in the XRD sample holder. The pucks were ground at 400 grit
until flat. Polishing stopped when inclusions were visible at 1200-grit. Grinding
and polishing were completed with a Buehler autopolisher (ecomet 3 variable speed
grinder-polisher equipped with an automet 2 power head). Samples were stood on
end for a 3-mm diameter exposed polished surface. Once polished, the surface was
wiped with isopropyl alcohol on a kim wipe to assure no debris was present.
Sample Caveat: Properties of Ni 71.4Cr5.64 N b3.46 P16.5 B3 (Ni208) are assumed similar enough to the those of Ni 70.4Cr5.64 N b4.46 P16.5 B3 (Ni210) given their almost
equivalent compositions. Tg , Tm , and m were not measured directly for Ni208 due to
defunct equipment by the time of sample study. Ni210 properties are summarized
in Table D.1.[8]
Vicker’s Hardness and Optical Imaging
Hardness indentations were completed in a LECO LV810AT Oprical Scope and
Hardness Tester using 4.903N force and a 5s dwell time. Indentations averaged
around 50-µm across. Indentations were completed in the epoxy puck to assure a
level surface for accurate indentations. General surface images were captured at 10x
magnification. The topography contrast is most-visible, if not only visible, at 10x
magnification.
Inclusion Area Percent Calculation
Two methods were employed for establishing the analysis surface. For Tcast = 1100,
1125, and 1150°C, the respective images in Figure 4.5 capture areas representative
of each sample’s overall inclusion prevalence. These images were then used to
calculate a representative percent. For samples where inclusions were more sparse
(Tcast = 950 and 1200°C), optical images were taken in a raster pattern across the
full sample surface and compiled into a mosaic in Adobe Photoshop. The full image
of the 3-mm cross-section surface was calculated over. With the analysis surface
established, a stark contrast was achieved between the inclusion and matrix areas.
ImageJ was then utilized to count the respective dark (inclusions) and light (matrix)
areas, and a percent over the full analysis area was calculated.

73
Scanning Electron Microscopy and Energy-Dispersive X-ray Spectroscopy
Samples were examined on a ZEISS 1550VP field-emission scanning electron microscope (SEM, Carl Zeiss Microscopy GmbH, Jena, Germany) equipped with an
Oxford X-Max Si-drift-detector energy dispersive X-ray spectrometer (EDS) system. SmartSEM and AZtec software packages were used for imaging, mapping,
and EDS analysis. Analysis used a 5-kV accelerating potential, operating at a magnification of 10kx. Given the inclusions are not discernible in SEM, indentations
were used to assure SEM imagaing and EDS analysis were completed in the correct
locations. Due to Covid-19 restrictions, SEM was conducted by Celia Chari, and
nano-indentations for inclusion mapping were conducted by Seola Lee.
High-Resolution Transmission Electron Microscopy for Energy-Dispersive XRay Spectroscopy and Selected Area Electron Diffraction
Samples were marked by arrays of nanoindentations, imaged optically at 10x, and
maps were composed to assure TEM samples were cut at the correct location
(matrix-inclusion interface). The lamellae were prepared using the ex-situ FIB liftout technique on an FEI Dual Beam FIB/SEM. The samples were capped e-CPt/I-C
prior to milling. The TEM lamella thickness was <100-nm. The samples were
then imaged with a FEI Tecnai Osiris FEG/TEM operated at 200kV in bright-field
(BF) TEM mode followed by composition analysis via energy dispersive X-ray
spectroscopy (EDS) and selected area electron diffraction (SAED). Due to COVID19 constraints, samples were sent out to EAG Laboratories for TEM analysis and its
sample preparations.
X-Ray Diffraction (XRD) and Crystallinity Calculation
XRD analysis was completed with 1 hour scans on a Panalytical X’Pert Pro. Given
the samples are cast in carbon-based epoxy pucks, once mounted with putty, the
puck was masked-off with corning glass cover slips (thickness 2 18x18, cat no.
2855-18) to remove the carbon peaks at 26, 42-45, 50 and 54 °(2θ). To assure all
puck peaks were removed, a 3-mm hole was drilled through a cover slip and aligned
with the sample. A figure of this layout is included in Appendix Figure C.1.
The crystallinity percentages were calculated from relative peak area over total
area under the XRD scan between 35 and 55 °(2θ). The calculation baseline was
established as the minima of each scan.

74

Figure 4.5: Visualized inclusions on 1200-grit polished cross-sections of direct-cast
samples. Please see the electronic version for assured visual clarity. Inclusion area
percentages for a-f: 4.05, 11.90, 5.74, 34.87, 0.12, and 0.00%, respectively. Note:
there are three artifactual repeated smudges in each image.
4.4

Results and Analysis

Cross sections were prepared from the exact direct-cast samples from Figure 4.3.
Post-polish, inclusions were visible of varying size and prevalence across each sample surface. These inclusions are visualized in Figure 4.5a-f, ordered by increasing
casting temperature. Inclusions are only present in brittle samples, with no inclusions visible in the tough samples. Relative coverage areas were calculated across
each sample surface. Inclusion area percentages report 4.05, 11.90, 5.74, 34.87, and
0.12% for 950, 1100, 1125, 1150, and 1200°C, respectively. The 1300°C sample
has no visible inclusions given the limits of the visualization method; i.e., inclusions
are discernible down to ∼ 5-µm. Thus 0.00% inclusion area is reported within this
limitation. The overheated samples of Figure 4.4 also only saw inclusions in the
brittle samples, but these samples are not further included in this discussion. In
addition to dcr sustaining well above the sample size, these inclusions are anticipated to be amorphous due to the inclusion shape. The inclusion-matrix interface is
distinctly rounded and not angular or dendritic, like would be observed for crystal
growth. The inclusions appear to grow radially and merge together, best highlighted
in Figure 4.5d. It is believed these inclusions could be related to the second glass

75

Figure 4.6: Vickers hardness micro indentations (∼ 50µm) across the heat treatmentinduced surfaces of Tcast = 1150°C Ni208.

phase, as they require the same unique lighting conditions as the peculiar surface
topography in the long-annealed Pt62Cu18 P20 sample in Figure 3.7. This marks
these inclusions as worth further exploration — starting with comparison to known
properties of the second glass phase.
The most established property difference between the two glass phases is hardness.
Previous works report a 20 – 30% increase in hardness from the primary to a
secondary glass. For the present work, micro-scale Vicker’s Hardness diamonds
were indented into three sample types/locations: the inclusion, matrix, and bulk.
The inclusion region is indeed the notable inclusions visualized in Figure 4.5. The
"matrix" refers to the sample surface outside of the inclusion area in brittle samples,
and the "bulk" refers to the tough samples were there are no visible inclusions. The
matrix and bulk are probed to determine if the matrix is a different glass than the
bulk. In choosing a sample, the inclusion and matrix regions must be of sufficient
size to support multiple 50 micron indentations in each, as well as a bulk sample. The
mid-range 1150°C samples achieve all criteria when both aforementioned casting
methods are utilized. The direct-cast method has sufficiently-sized inclusions in
the matrix (Figure 4.5d), and the overheated sample has no inclusions and exists
with only the "bulk." The data are plotted in Figure 4.6 where the matrix and

76
bulk samples report averages of 632.99 and 619.16 HV, respectively, but overlap
within error. However, the inclusions report an average of 793.38 HV; a 25.34 and
28.14% increase from the matrix and bulk, respectively. These data suggest the
matrix and bulk are equivalent glasses, and that the inclusions grow within the bulk
glass. Further, these inclusions show strong similarities with the reported character
difference between the two glass phases, showing promising early evidence of the
inclusions as a second glass phase.
Next, composition analysis on the matrix and inclusion was completed with an Energy Dispersive X-ray Spectroscopy (EDS)-equipped Scanning Electron Microscope
(SEM). With the inclusions not visible in SEM (see Figure D.4a), indentations were
utilized to validate the analysis location in the sample. Figure 4.7 depicts the matrix
and inclusion composition maps across the NiCrNbPB composition with inset percent prevalence (by eV counts). The central bright/dark spot is the indentation and
any color variance is assumed erroneous. The composition variance between the
matrix and inclusion is negligible at this resolution, varying a maximum of 0.28%
in Cr. Thus the Ni208 matrix and inclusions are compositionally equivalent, as
described across the other secondary glass works.[62]
Given the computational work of An et al. observed a structural difference between
the two glasses (L and G), with the secondary glass as a heterogeneous form,
high-resolution transmission electron microscopy (TEM) was utilized for improved
visualization, composition analysis, and diffraction of the Ni208 matrix-inclusion
interface. Figure 4.8 summarizes these results. Since inclusions are only visible
under optical microscopy and not discernible in SEM, the inclusion-matrix interface
locations were mapped against nano-indentation arrays to assure locations were
probed accurately (see Figure D.4).
The high-resolution TEM image in Figure 4.8a visualizes the matrix-inclusion interface, with the matrix on the top left and the inclusion on the bottom right. The
interface runs across the image from the bottom left to the top right. The inclusion
presents as a "cloudy" region with varied contrast. The darker regions between the
"clouds" appear equivalent to the matrix, and the "clouds" present brighter. With
the interface not angular as would be expected in traditional crystals, a connection
is drawn to the heterogeneous G phase of An et al.[62, 66, 67] Composition was
then probed across various regimes to add a higher-resolution analysis than that
provided by SEM. EDS was completed on the areas marked i-iv on Figure 4.8a and
are reported graphically in Figure 4.8b. While the averages vary slightly between

77

Figure 4.7: SEM EDS across the matrix and inclusion. The bright central dot is
artifactual at the indentation location. Displayed sideways for sufficient resolution.
Please see the electronic version for assured visual clarity.

78

Figure 4.8: Bright-field TEM image of the matrix-inclusion interface (a) with
labeled locations (i - iv) for diffraction patterns. EDS completed on locations (i-iv)
reported the composition % calculated via eV counts in b. Please see the electronic
version for assured visual clarity.

sections, all variance is within error. Thus the compositions are equivalent, and
TEM provides additional high-resolution verification of computational equivalence
as seen in the An et al. G-phase. However, the selected area electron diffraction
(SAED) patterns in Figure4.8i-iv — labeled with respect to the SAED location —
reveal an interesting structural story. The matrix acts as expected, revealing amorphous bands in i. However, the remaining locations in the general inclusion (ii), as
well as specifically in a "cloud" (iii) and between "clouds" (iv), reveal mixed order
and disorder. While the ordered regions of An et al.’s G-phase report curved planes
in fcc/hcp or icosahedral environments, it is not clearly discernible that this is the
cause of the diffraction patterns of ii-iv.[62, 66, 67] There is some concern about
whether the samples were altered by the energy of the focused ion beam (FIB) used
to prepare the TEM cross sections. With the hypothesis that this secondary phase
more readily crystallizes, this could potentially be a snapshot as it moves toward
crystallization.
To better understand if the sample preparation for TEM altered the samples, X-ray
Diffraction via a Panalytical X’Pert Pro was conducted on all cross sections of the
direct-cast samples (from Figure 4.5). These samples experienced the same sample
preparation as the optical imaging and HV indentation samples. Figure 4.9 visualizes

79

Figure 4.9: XRD for samples cast utilizing the direct casting method. Labels
are adjacent to their respective scans and labels a-f correlate to the labeled cast
temperature surfaces in Figure 4.5.
the hour-long XRD scans from 35 < 2θ < 55. This region was chosen to focus on the
amorphous band. No peaks appear in the tough 1300°C scan (f), nor in two of the
five brittle scans (950 and 1200°C for a and e, respectively). However, three minor
peaks arise at 44, 46.5, and 48 ° (2θ) in the brittle 1100, 1125, and 1150°C samples
(Figure 4.9b-d). These peaks are relatively minor, however, such that a dominant
amorphous band remains clearly visible for all samples. This raises a question on
whether the diffraction peaks arise from the inclusions, and if the inclusions are
partially or entirely crystalline. The degree of crystallinity, or crystallinity percent,
was calculated from the scans to compare with the aforementioned inclusion area
percentages. Taken as the percentage of area under the peaks relative to that under
the overall amorphous band, these data are reported along side KQ and inclusion area
percent in Figure 4.10. The crystallinity percentages are 0.00, 2.74, 2.74, 6.41, 0.00,
and 0.00% for Tcast = 950, 1100, 1125, 1150, 1200, and 1300°C direct cast samples,
respectively. When compared to the inclusion area, while the crystallinity does
increase with inclusion percent, the crystallinity is distinctly lower in all cases. This
informs that the inclusions are not fully crystalline, but do have some relationship
to crystallization. However, further analysis is required to determine the type of
crystalline ordering, to what extent, and how it may relate to a possible heterogeneous
G-phase glass.
Importantly, the relation of inclusion area percent to KQ is worth note. When even

80

Figure 4.10: Hardness across inclusion, matrix, and bulk samples for Tcast = 1150°C.

a small 0.12% of inclusions are present (but 0.00% diffraction peaks), the Ni208
system embrittles. This brittle behavior persists for all samples hosting inclusions.
So, as the inclusions are further investigated for their structure, it is clear they play
a key role in the embrittlement transition. The author hypothesizes the inclusions
have harder, lower toughness regions that lead to lower global toughness values.
Discussions and analysis on critical defect size have been implemented, but are
limited due to the lack of KC data. Assumptions were possible, but were too
extensive to justify defense of the conclusions. However, while the detailed origins
of global embrittlement have been explored here, no clear conclusions have been
drawn, leaving open questions for future works.
While there is promising HV and composition data, the microscopic structure of
the inclusions needs greater understanding. While the inclusions are apparently at
least partially amorphous, they also appear to contain nanocrystals as well. It is not
clear, for example, whether the inclusion is initially fully amorphous on formation
then subsequently partially crystallizes during its growth, if partial crystallization
occurs at the outset of inclusion formation, or whether TEM sample preparation
altered the inclusion structure. These efforts provide a promising starting point for
future investigations on formation of the second glass phase in strong metallic glass
systems, like the present Ni-based alloys.

81
4.5

Summary and Conclusions

Previous works report an embrittlement transition in the Ni 80−X−Y Cr X N bY P16.5 B3
BMG system. The most recent study ties this embrittlement to the pre-casting thermal history of the metallic glass samples, specifically in the Ni 71.4Cr5.64 N b3.46 P16.5 B3
alloy (Ni208). When overheating above a critical toughening temperature, Ttough ,
during processing, embrittlement is suppressed even at lower subsequent casting
temperatures. Based on the observations in this chapter, the author hypothesizes
this embrittlement is due to the presence of harder secondary glass phase inclusions,
and that the presence or absence of the inclusions is related to the liquid thermal
history prior to casting of the glassy sample.
This work explored the cross sections of the Ni208 study samples. Inclusions are
found present only in the brittle samples, and are believed to be a secondary glass
phase. Visible in green-light optical imaging at 10x magnification, these inclusions
vary in size, prevalence, and location across the reported casting temperatures.
Inclusions display a 25 - 28% hardness increase from the surrounding glassy matrix,
similar to that reported for multiple secondary glasses.[65, 62, 66, 67] The matrix
around the inclusions and the bulk (when no inclusions are present) report equivalent
hardness, which suggests they are the same glassy phase. Thus, it is assumed
the inclusions form and grow from the undercooled liquid during the casting and
quenching process.
The structure and composition were explored via SEM with EDS, TEM with EDS
and SAED, and XRD. SEM EDS reports compositional equivalence between the
inclusion and matrix, where analysis was focused on one region at a time. Highresolution TEM on the interface revealed a "cloud-like" structure reminiscent of the
G-phase in Qiet al.’s work on pure Ag, albeit at a significantly larger scale (tens or
hundreds of nanometers). Composition analysis via EDS across numerous regions
reports equivalent averages within error. SAED revealed the expected amorphous
behavior in the matrix, but a mixed amorphous-partially crystallized behavior in the
inclusion. The curved planes in fcc/hcp- and icosahedral- like stacking in the Ag and
AgCu versus CuZr compositions reported by An et al. could be the cause of these
mixed results, but the nanocrystals observed in the Ni-alloy are at a significantly
larger length scale than the heterogeneities reported in the MD work. In fact, there
is possible concern that the FIB lift-out technique for the TEM lamellae sample
preparation may have altered the secondary glass phase and induced nanocrystal
formation. To address this concern, XRD was completed on the polished 3-mm

82
sample cross sections. XRD scans reported three relatively minor diffraction peaks
in three of the investigated brittle samples. Assessing the crystallinity using area
percentages based on X-ray, the crystalline regions are believed to be at most a small
portion of the overall inclusions. Thus, the inclusions are primarily amorphous.
Further, when only 0.12% inclusions (and 0.00% crystallinity) were present, the
sample embrittles by a 65% reduction in apparent fracture toughness. This verifies
the effect of inclusion presence on embrittlement, and that overheating samples prior
to casting suppresses embrittlement by suppressing inclusion formation and growth.
While further study is required to verify if these inclusions as initially formed are in
fact a fully amorphous secondary glass for this Ni-BMG system, the present work
provides a promising starting point from which to continue the study.

83
Chapter 5

CONCLUDING REMARKS
5.1

Conclusions

The three final chapters presented in the thesis draw direct links to the second
glass phase described in Chapter 1, Section 1.4. The combined works establish
experimental evidence for two distinct glassy phases across the spectrum of strong
to high- and ultra-high fragility metallic glass forming liquids.
Given that the secondary glass was first identified computationally in ultra-high
fragility Ag and binary AgCu and CuZr, experiments initially pursued the same high
fragility regime. Configurational thermodynamics on the Pt80−X Cu X P20 system
(Chapter 2) employs accurate direct measurements of the anneal-equilibrated liquid
configurational enthalpy as a function of temperature. This reveals an apparent firstorder glass-melting transition with discontinuous enthalpy and entropy changes
at the phase boundary, Tgm . The glass-melting transition is discernible across
X = 14 - 27, except for those compositions where Tgm is in the inaccessible ∆T
region (X = 20, 23). However, apparent melting is observed in X = 20 when the
heating rate is sufficiently high (via rapid capacitive discharge heating imaged via
ultra-fast pyrometer tracking and infra-red video as in Figure 3.6). Further, the
utilization of a new DOS approach to describe configurational entropy and accurate
data accumulation methods present a configurational entropy that vanishes in the
low-temperature limit, averting the Kauzmann paradox.
With the configurational thermodynamics approach employed in Chapter 2 revealing
the second glass phase behavior in annealed samples, mechanical, structure, and
thermodynamic approaches were utilized to reveal distinct physical characteristics
between the primary and secondary glasses (Chapter 3). The thermal treatments to
achieve each phase were proposed as follows: as-cast samples produce the primary
glass phase, whereas anneals achieve the secondary glass phase. However, HV data
suggest that the secondary glass phase grows on annealing in highly fragile glasses,
but is actually achieved on quenching for the ultra-fragile glasses. Structural data
via XRD report similar findings, where FWHM of the amorphous band describes
increased atomic ordering across all samples on going from as-cast to annealed, but
to different extents. The high-fragility samples show a markedly greater ordering

84
effect compared to the ultra-fragile samples, further suggesting the secondary glass
phase grows on annealing in the former samples, but is already present in the latter.
Heating the sample at 20 K/min from room temperature through the melt verified that
this melting transition is also visible using classical thermodynamic methods. The
ultra-fragile annealed X = 14 sample shows an onset melting transition after Tg that
is interrupted by crystallization. This Tgm is equivalent, within error, to that found
for X = 14 in Chapter 2. These two studies on the high-fragility to ultra-fragile
PtCuP alloys provide a promising multi-faceted foundation for the experimental
observation of two distinct glass phases.
Finally, the Ni208 study on a hypothesized second glass phase-induced embrittlement transition extends the discussion to the kinetically strong glass forming liquid
regime (Chapter 4). The work identifies roughly spherical, heterogeneously structured inclusions only present in brittle samples. These inclusions are ∼30% harder
than the glassy matrix phase, similar to the hardness jump reported between the
computational L and G glasses.[62, 66, 67] The inclusions are connected to results
of work presented in a prior patent that show that overheating the melt prior to casting a glassy sample suppresses the embrittlement transition. This work reveals that
overheating apparently suppresses embrittlement by suppressing the formation and
growth of inclusions. The heterogeneous inclusions are predominantly amorphous
but also show formation of nanocrystals within the inclusion. It is unclear if the
inclusions are entirely glassy upon initial formation and later partially crystallize,
or contain some amount of crystallinity from the outset of formation. As such, it
remains unclear if the inclusions can be identified with the G-phase observed in the
MD simulation work of An et al.[62]
The thesis presents direct experimental evidence of a novel glass-melting transition,
and presents a new solid-like glass phase. The evidence of the second glass phase
extends from strong to ultra-fragile glasses, and validates the initial computational
discovery. Paired with further computational and experimental studies, the second
glass phase is further predicted across traditional glass systems.
5.2

Summary of Outcomes

These results were achieved following the motivations outlined in Section 1.5 (indicated by the numbers in parentheses). The PtCuP system of Chapters 2 and
3 provided a high-fragility and ultra-fragile glass system for the previously unexplored regime (1). A direct calorimetry study of configurational thermodynamics

85
was applied with a well-equilibrated glassy state (2), a new analytic expression to
better represent the configurational enthalpy data was introduced (3), and an apparent glass-melting transition was revealed through improved accuracy of calorimetric
data. This melting transition occurs across a range of fragilities and shows an apparent glass-melting temperature Tgm spanning the ∆T undercooled liquid region.
This demonstrates that the inaccessible SCL regime requires further probing by
RDH or FDSC. These motivations yielded both the glass-melting transition and a
resolution to the Kauzmann paradox at ultra-high fragility. For stronger glasses, the
embrittlement transition is connected to the secondary glass via grown inclusions in
Chapter 4 (Figure 4.5). While these motivations proved very fruitful for this work,
there remain further questions to address.
5.3

Future Work

The combined works of this thesis provide experimental evidence and support for
the secondary glass phase. Specific details of An et al. and Shen et al. were
emphasized and verified in these studies (i.e., hardness, latent heat and melting
transition, heterogeneous structure, and composition equivalence). But in addition
to these addressed and verified G-phase characteristics, An et al. also investigated
the L-G transition through the lens of rigidity. They demonstrate that the L-G
transition corresponds to the emergence of elastic rigidity from determining the
shear modulus and the persistence of stress fields of each phase.[77] With an onset
of rigidity from the L to G phase, the melting transition (G to L) is described as a
loss of elastic rigidity. This is related to rigidity catastrophe described by the Born
melting criterion as discussed in Section 1.4.
A future study is proposed to probe the rigidity loss on G-phase melting. The shear
modulus can be measured with respect to temperature using ultrasonic methods
and in-situ transducers. Following the methods utilized by Mary-Laura Lind in
her 2008 Ph.D. dissertation, the shear modulus can be mapped versus temperature
and time. With increasing temperature on as-cast and annealed samples, the decay
of the shear modulus can be investigated. Further, observation of the evolution of
the heterogeneous G-phase structure over temperature in high-resolution TEM, or
using high-speed synchrotron X-ray methods would likewise shed valuable light on
the structure and structural transformation that accompanies the G-glass-melting
transition.
Additional pursuits could include a study on what underlies G-phase inclusion

86
formation and growth in strong metallic glasses. The images in Figure 4.5 visualize
inclusion size, prevalence, and location. Inclusions predominantly present internal
to the sample, but lie on the sample perimeter or container wall for others. In
particular, the low cast temperature 950°C sample has most inclusions on the crosssection perimeter, with only a few internal. This suggests that the rigid container
wall might be a preferred site for inclusion nucleation. This could be related to
elastic rigidity. The rigid quartz wall present during quenching could serve as a
rigidity-template for the the G phase per An et al.’s work. Internally nucleated
inclusions might relate to slower cooling of the melt where the secondary glass
forms just before the crystallization nose as per Shen et al.’s metallic glacial glass.

87

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96
Appendix A

THERMODYNAMIC DERIVATIONS: A GAUSSIAN DENSITY
OF STATES IN PEL THEORY
The included derivations correspond to Equations 1.10 - 1.14 in Chapter 1.2.
Starting with the equation for a Gaussian density of states to describe the inherent
energy states available to a glass system, with Φ the potential energy of an inherent
state,
−(Φ − Φ̄)2 1state
D(Φ) = √ exp
atom
2σ 2
σ 2π

(A.1)

one can then define a general equation for the partition function:
Z/ =

−Φ
D(Φ) exp
dΦ.
kT

(A.2)

Substituting in D(Φ) gives

Z/ =

σ 2π

0 
 −(Φ − Φ̄)
72
−Φ
 
dΦ,
exp 
 exp
 2σ 2 
kT

(A.3)

where Φ̄ goes to zero with Gaussian center set at zero.
Simplifying the exponential terms,
Z/ = √
σ 2π

  2

exp −
dΦ.
2σ 2 kT

(A.4)

Complete the square of bracketed exponential term in A.4 to define a new Gaussian
as Φ0 by first rearranging to
Φ2 +
One can then complete the square

2σ 2
Φ.
kT

(A.5)

97
"

σ2
Φ+
kT

2

σ2
kT

2#

(A.6)

and set
σ2
Φ = Φ+
kT

(A.7)

to substitute back into the exponential and distributing the negative sign.
Z/ = √
σ 2π

" 
2  2 2#
σ2
dΦ.
exp − Φ +
kT
kT

(A.8)

Z/ = √ exp
(A.9)
kT
σ 2π
The integral expression in A.9 becomes π due to the Gaussian integral relationship
∫∞
pπ
2 dx =
exp
−a(x
b)
a where a > 0.
−∞
Where the π cancels with the denominator to form the partition function with a
Gaussian configurational density of states,

 2∫
σ2

2
0)
exp
dΦ.
(−Φ


 2 2
Z/ (Φ, T) = √ exp
kT
σ 2

(A.10)

Utilizing this partition function, the thermodynamic state functions can be defined,
i.e., Helmholtz free energy (F), entropy (S), internal energy (U), enthalpy (H), and
heat capacity (Cp ).
Starting with the Helmholtz free energy (F), the derivations are carried out below
utilizing relationships defined in Morse.[32]
F = −kT ln (Z/ )
 2 2#
= −kT ln √ exp
kT
σ 2
 2 2
= −kT ln √ − kT
kT
σ 2
= +kT ln σ 2 −
kT

98
Then for Entropy,
S=−

dF
dT

 √  σ4
= −k ln σ 2 − 2
kT
For internal energy,
U = F + TS
 √  σ 4 −σ 4
= kT ln σ 2 −
kT
kT 2
2σ 4
=γ−
kT
 √ 
where γ = kT ln σ 2 .
Enthalpy (H) can be simplified with a simple observation: dH = dU + V dP, where
V dP is negligible due to the constant ambient pressure in standard DSC experiments.
Thus,
2σ 4
(A.11)
H =U =γ−
kT
Through the PEL and corresponding assumptions leading to a Gaussian distributionbased partition function outlined above, enthalpy has a T −1 dependence (correlated
with the n=1 dependence in Chapter 2).
Finally, through the above assumptions, the Gaussian landscape constant pressure
heat capacity (Cp ) has a T −2 dependence;
Cp =

dU
2σ 2
=γ+
dT
kT 2

(A.12)

99
Appendix B

SUPPLEMENTAL MATERIALS FOR CHAPTER 2
B.1

Underlying Assumptions

There are some fundamental assumptions made in this work that streamline the
mathematics. Starting from first principles and the First Law of Thermodynamics,
we derive our mathematical representation for configurational enthalpy and its underlying concepts. Through fundamental expansions and indexed steps, the enthalpy
is described as a function of the potential energy with the kinetic energy scaling
only with temperature.
From the First Law, U = T S − PV, its perfect differential dU = T dS − PdV, and
the fundamental expression for enthalpy, H = U + PV, the enthalpic differential
is determined as dH = dU + V dP.[32] Under the conditions of this work V =
10−5 m3 mol −1 , and P = 1 atm = 10+5 Pa. Thus, V dP = 1Jmol −1 and is negligible
compared to the experimental hCon f ig of 10k Jmol −1 . This simplification yields
enthalpy as a strict function of internal energy, U. Expanding this energy, however,
reveals U = PE + K E with the potential energy (PE) represented now as φ, and
the kinetic energy is known as 3k2B T from the equipartition theorem (equipartition
theorem of ideal gas states each degree of freedom of kinetic energy is k B2T . In three
dimensions this yields 3k2B T ).[32]
Probing deeper into the potential energy description, φ can be expanded; φ =
φl − φ x , with φl and φ x the potential energy of the liquid and crystalline components,
respectively. Each can then be expanded further into configurational and vibrational
terms:
φl = φCon
f ig + φvib = φCon f ig + φvib,har + φvib,anh
φ x = φCon
f ig + φvib = φCon f ig + φvib,har + φvib,anh

where the vibrational term contains separable harmonic and anharmonic components.
Substituting terms,
φ = φl − φ x
= φCon
f ig − φCon f ig + φvib,har − φvib,har + φvib,anh − φvib,anh

100
can be simplified via two approximations. The harmonic approximation utilizes
the Dulong-Petit heat capacity of 3R as a description of the harmonic component
of the potential energy. With CP,har = 3R = φl + φ x , the two terms split evenly
yielding φl = φ x = 3R
2 . The anharmonic approximation emphasizes the DebyeGrüneisen anharmonic heat capacity, CP − CV = α2 BvT with α the coefficient of
thermal expansion, B the isothermal bulk modulus, v the molar volume, and T
the temperature in Kelvin. When calculated, the φlvib,anh and φvib,anh
values are
negligible compared to the Dulong-Petit (25Jmol −1 ) and experimental enthalpy
measurements (10k Jmol −1 ). These components are thus neglected.
The equations for potential energy and enthalpy simplify to a configurational de3k B T
lx
pendence, φ = φl − φ x = φCon
2 +φ
f ig − φCon f ig = φC on f ig, and H = U =
with a standardized kinetic energy term. From this, the enthalpy is termed the
configurational energy in this work:
lx
H = HC = φCon
f ig +

3k BT

lx
where H can be offset by the kinetic energy term, H − 3k2B T = φCon
f ig , thus the
configurational enthalpy is truly a measure of the change in potential energy between the liquid and crystal through various phase transformations (glass transition,
crystallization, and melt).

Given configurational enthalpy is reported in units of J/g, the various thermodynamic
variables discussed here are all specific values. Thus, HC = hC ; SC = sC ; CV =
cV . Further, while here configurational components are denoted by the subscript
"Con f ig" for clarify, the text utilises the subscript "c" for concision.
B.2

Entropy Derivation: Equivalence of Equation 2.1 and 2.2

In the text, Equation 2.2 is derived from 2.2. Below is an outline of the steps.
Starting with Equation 2.1,
  n
θh
hC (T) = hC (∞) 1 −

101
the specific heat capacity becomes
hC (∞)θ nh
∂Q(T) ∂U(T) ∂hC (T)
cV =
hC (∞) −
∂T
∂T
∂T
∂T
Tn
∂ hC (∞)θ h
(hC (T))T=∞ −
δT
∂T
Tn
 n
θh
nhC (∞)θ nh
= cV,∞ − n cV (T)
Tn
T=∞
nhC (∞)θ nh
= cV,∞ +
T n+1
When ignoring the pressure dependence of hC (∞) and θ h at ambient pressure; i.e.,
ignoring the PV term in the free energy, cC is obtained:
cC =

nhC (∞)θ nh
T n+1

For the entropy, toward the high-temperature limit,
∫ ∞
∫ ∞
n
cV , ∞ nhC (∞)θ h
cV
dT =
sC =
T n+2
nhC (∞)θ h 1
= sC,∞ +
n + 1 T n+1
Now change the above expression for configurational entropy to the familiar microcanonical form. Multiply the second term of the configurational enthalpy by
  n+1
nhc (∞) θ h
sC = sC,∞ +
θ h (n + 1) T
From equation "1",

 n
hC (∞) − hC (T))
θh
hC (∞)

or

1  
hC (∞) − hC (T) n
θh
hC (∞)

So

θh

 n+1

1 
 
 n+1
hC (∞) − hC (T) n hC (∞) − hC (T)
hC (∞) − hC (T) n
hC (∞)
hC (∞)
hC (∞)

where
 n+1
 n+1
nhc (∞) hC (∞) − hC (T) n
hC (∞) − hC (T) n
sC = sC,∞ −
= sC,∞ − C
θ h (n + 1)
hC (∞)
hC (∞)

102
With Equation 2.2 in Chapter 2 written in terms of configurational potential energies φ and φ0 , these are equivalent to hC and h∞ , respectively ,given the prior
assumptions, with C a constant. The above equation generalizes to Equation 2.2.
So the above exhibits the derivation from Equation 2.1 to 2.2,
n+1

sc (φ) ∝ sC (φ0 ) − C(φ0 − φ) n
B.3

Sn Heating Rate Temperature Correction

DTA runs were completed on pure Sn (99.999%) at incremental heating rates from
0.5 to 20 K/min. These heat flow curves are plotted in Figure B.1 and increased
peak broadening and peak shift are observed at higher heating rates. This peak
broadening and shift effect are the results of thermal lag in the system, where
the sample has not yet caught up to the temperature at the thermocouple. These
peak shift corrections (Table B.1) are utilized in calculating accurate enthalpy peak
temperatures as discussed in Section 2.4.

Figure B.1: Sn heat flow responses with respect to heating rate.
The correction values utilized are as follows:

103
Heating Rate (K/min)
0.1
0.2
0.5
1.5
10
15
20

Temperature Correction (K)
-0.8
-1
-1.5
-2
-4.2
-5.2
-6.5
-9
-11

Table B.1: Peak offset correction values from Figure B.1.

Tgm (K)
∆hC (J/g)

Cu14
533
27

Cu16
548
20

Cu18
551
23.7

Cu20

Cu23

Cu27
651
15.7

Table B.2: Raw data accompanying Figure 2.11 identifying the trend of fragility,
copper content, glass-melting temperature, and latent heat of glass-melting.
B.4

Raw Data

Raw data are included in the supplemental material excel file included in the CaltechThesis archive.

104
Appendix C

SUPPLEMENTAL MATERIALS FOR CHAPTER 3
C.1

Raw Data

Raw data are included in the supplemental material excel file included in the CaltechThesis archive.

Figure C.1: Cover slip location for carbon-puck masking method. Central cover slip
with hole highlighted with white borders on free edges. Full cover slips outlined by
grey dashed lines.

105
Appendix D

SUPPLEMENTAL MATERIALS FOR CHAPTER 4

Compiled supporting materials for Chapter 4.

Ni 70.4Cr5.64 N b4.46 P16.5 B3

Tg (K) TL (K) m
671
1243 54

Table D.1: Ni210 Properties. These properties were assumed equivalent to Ni208
within error given sample properties were not able to be confirmed due to nonfunctional measurement apparatuses.[8]

106

Figure D.1: The color contour plot equivalent to the dashed contour in Figure 4.1.
Included for visual clarity.REF

Figure D.2: Inclusion sizes across the direct cast samples’ casting temperatures.

107

Figure D.3: Two lighting approaches for inclusion visualization on the same sample
area. Nanoindentations utilized for sample location identification in SEM.

108

Figure D.4: Top (a): SEM image depicting lack of visibility of the inclusions relative
to the 10x optical image (bottom, b).

109

Figure D.5: TEM 64k zoom on Ni208 inclusion-matrix interface. Enlarged here for
clarity. The reader is advised to view the image in the electronic version.

110
Appendix E

RESOURCES FOR SURVIVING GRADUATE SCHOOL
E.1

The "Snake Fight" Portion of Your Thesis Defense by Luke Burns

FAQ:
Q: Do I have to kill the snake?
A: University guidelines state that you have to “defeat” the snake. There are many
ways to accomplish this. Lots of students choose to wrestle the snake. Some
construct decoys and elaborate traps to confuse and then ensnare the snake. One
student brought a flute and played a song to lull the snake to sleep. Then he threw
the snake out a window.

Q: Does everyone fight the same snake?
A: No. You will fight one of the many snakes that are kept on campus by the facilities
department.

Q: Are the snakes big?
A: We have lots of different snakes. The quality of your work determines which
snake you will fight. The better your thesis is, the smaller the snake will be.

Q: Does my thesis adviser pick the snake?
A: No. Your adviser just tells the guy who picks the snakes how good your thesis
was.

Q: What does it mean if I get a small snake that is also very strong?
A: Snake-picking is not an exact science. The size of the snake is the main factor.
The snake may be very strong, or it may be very weak. It may be of Asian, African,
or South American origin. It may constrict its victims and then swallow them whole,
or it may use venom to blind and/or paralyze its prey. You shouldn’t read too much
into these other characteristics. Although if you get a poisonous snake, it often
means that there was a problem with the formatting of your bibliography.

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Q: When and where do I fight the snake? Does the school have some kind of pit or
arena for snake fights?
A: You fight the snake in the room you have reserved for your defense. The
fight generally starts after you have finished answering questions about your thesis.
However, the snake will be lurking in the room the whole time and it can strike at
any point. If the snake attacks prematurely it’s obviously better to defeat it and get
back to the rest of your defense as quickly as possible.

Q: Would someone who wrote a bad thesis and defeated a large snake get the same
grade as someone who wrote a good thesis and defeated a small snake?
A: Yes.

Q: So then couldn’t you just fight a snake in lieu of actually writing a thesis?
A: Technically, yes. But in that case the snake would be very big. Very big, indeed.

Q: Could the snake kill me?
A: That almost never happens. But if you’re worried, just make sure that you write
a good thesis.

Q: Why do I have to do this?
A: Snake fighting is one of the great traditions of higher education. It may seem
somewhat antiquated and silly, like the robes we wear at graduation, but fighting a
snake is an important part of the history and culture of every reputable university.
Almost everyone with an advanced degree has gone through this process. Notable
figures such as John Foster Dulles, Philip Roth, and Doris Kearns Goodwin (to name
but a few) have all had to defeat at least one snake in single combat.

Q: This whole snake thing is just a metaphor, right?
A: I assure you, the snakes are very real.