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Formation and characterization of bulk metallic glasses
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Peker, Atakan
(1994)
Formation and characterization of bulk metallic glasses.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/KBSB-JM25.
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

After the discovery of solid state amorphization in early eighties, there were several years of paused research on metallic glass formation by melt quenching. At the end of the last decade, a Japanese group in Sendai discovered new metallic systems, which require substantially lower cooling rates for glass formation than previous systems and which have high thermal stability above their glass transition temperature.

As a major contribution to a new era of metallic glasses, this thesis extended the formation and the thermal stability of metallic glasses to the extent that many potential uses of metallic glasses have come to the brink of reality. For the first time, the art of metallic glass making has become as easy as a single step alloy preparation using conventional metallurgical processing. The production of the larger bulk metallic glass specimens is limited only by the scale of equipment in our laboratory and not by limitations arising from the glass forming ability of the particular alloy. These new developments presented throughout this thesis may not only extend the applications of metallic glasses but they also allow us to study the properties of highly undercooled metallic melts which are very important in phenomena such as nucleation and crystal growth.

The thesis starts with an introductory chapter describing the art and science of metallic glasses prior to this work. Then, a critical review of the current knowledge of thermodynamics and kinetics of glass formation is given in chapter 2. In chapter 3, an example of a highly processable metallic glass alloy, [...], is presented along with its preparation methods. Its general characteristics which distinguish it from conventional metallic glasses are emphasized. This particular glassy alloy, [...], belongs to an exceptionally large family of excellent glass forming metallic systems, which were developed in the course of this thesis research. In chapter 4, various forms of heterogeneous nucleation,--an important phenomena in glass formation--are discussed with reference to several glass forming alloys. Finally, conditions for bulk glass formation are proposed in view of our current theoretical knowledge and experimental observations. Difficulties in attaining these conditions are also discussed and suggestions are made for finding other bulk glass forming alloys.
Item Type:
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California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
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Research Advisor(s):
Johnson, William Lewis
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Defense Date:
14 March 1994
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CaltechETD:etd-10252005-074557
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FORMATION A N D CHARACTERIZATION
OF BULK METALLIC GLASSES

Thesis by
Ata kan Peker

In Partial Fulfillm.ent of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California

(March 14,1994)

01994
Atakan Peker

To 3ny family

Acknowledgements

I have found myself several times extremely fortunate being at the right time, at
the right place with the right person. This includes working on bulk metallic
glasses with Bill Johnson at Caltech. Having the most admirable history of
research on metallic glasses, Caltech provided me an excellent environment,
scientific and non-scientific, for a graduate study I have never thought of before.
This thesis has been possible not only because Bill acquired me to his group, but
also because he has an exemplary vision of research and teaching in this field -metallic glasses-- nobody can match. He has exceptional scientific intuition,
enthusiasm and enjoyment of science, and he has mastered in passing these to his
students. I have also found him as a great friend and am looking forward to long
years of collaboration and friendship..
Carol, our gifted microscopist, performed the exquisite TEM work on our
samples and provided invaluable TEIU pictures, which were impossible to obtain
without her incredible patience and talent.
I would like to appreciate Yoshi Abe, my former office-mate, for his kind
friendship and his patience in helping me in several stages of my learning how to
do research. He was the most helpful friend of mine during his stay at Caltech.
In the first three years of my graduate study, I have seen invaluable assistance,
help and friendship from the senior members of Johnson group and it is a

pleasure to thank them. My special thanks go to Dave Lee, Chuck Krill,
Zezhong Fu and Joe Holzer who provided my lab training which proved
extremely useful for my thesis. Also, I would like to thank Jurgen Eckart, Mo Li,
Rainer Birringer, Jorge Kittel and Phil Askenazy.
My acknowledgments cannot be complete without fellows with whom I had
friendship and cooperation in lab: Mohit Jain, Hugh Bruck, Marissa La Madrid,
my current office-mateEric Bakke, Xiang Lin, Jian Li, Z. Gao, L. Anthony, T.
Stephens and many others with whom I shared the lab.

I have met with several world-class researches and extensively benefited from
them during my visit to Japan for RQ 8 conference. I would like to thank J.
Perepezko, B. Cantor, R. Bormann, R. Schwarz, U. Koster, H. Fecht, A. Inoue and
others which I may have forgotten to list. I would like to express my gratitude to
them for the valuable discussions and their friendship. Again, I like to thank my
advisor, Bill Johnson, for his encouragement to attend the conference and for his
friendship during this memorial visit. I would also like to thank my former
officemate, Yoshi Abe, for his kind hospitality in Japan.
Amorphous International Technologies, ATI, supported the first phase of bulk
metallic glass research of Bill Johnson's group. Later stages of research described
in this thesis are also supported by The United States Department of Energy.

I have seen great encouragement and help from my former professors: Dr. Sabri
Altintas, Dr. Can F. Delale, and Dr. Burak Erman. They prepared me for
graduate study and their help proved extremely useful. I also like to thank my
friend Hakan N. Ersoy who helped me in several respects to my academic life.
His help in my applications to graduate school was crucial.

vi
I can hardly express my gratitude to ]Dr. Talip Alp and Dr. Korkut Ozal who
provided me wise advice and inspirat~ionfor hard work before and throughout
my graduate study.
Finally, I would like to express my deepest gratitude to my family, who most
supported (and also most suffered) from my whole academic life. I tried my best
to deserve their support and right now I have the peace of mind to accomplish
that. My wife Hulya, my life-long friend in this world and hereafter, has always
been supportive of my graduate study. I can hardly pay off her sacrifice. My
very active son has been very generous to share his energy with me by keeping
me awake day and night so that I can finish my thesis as soon as possible.

Abstract

Since the discovery of metallic glass formation by ultra-rapid melt quenching at
Caltech in 1959, it was thought that metallic glasses can be processed only as very
thin ribbons or fine powders, due to the required high cooling rate, and that they
are not stable above the glass transition temperature. This has severely limited
the technological applications of metallic glasses which combine unique and
desirable properties. Also, bulk glass forming metallic alloys have long been
desired to improve our scientific knowledge of nucleation, crystal growth and
other properties of undercooled metallic melts.
After the discovery of solid state amorphization in early eighties, there were
several years of paused research on metallic glass formation by melt quenching.
At the end of the last decade, a Japanese group in Sendai discovered new metallic
systems, which require substantially lower cooling rates for glass formation than
previous systems and which have high thermal stability above their glass
transition temperature.
As a major contribution to a new era of metallic glasses, this thesis extended the
formation and the thermal stability of metallic glasses to the extent that many
potential uses of metallic glasses have come to the brink of reality. For the first
time, the art of metallic glass making has become as easy as a single step alloy
preparation using conventional metallurgical processing. The production of the

larger bulk metallic glass specimens is limited only by the scale of equipment in
our laboratory and not by limitations arising from the glass forming ability of the
particular alloy. These new developments presented throughout this thesis may
not only extend the applications of metallic glasses but they also allow us to
study the properties of highly undercooled metallic melts which are very
important in phenomena such as nucleation and crystal growth.
The thesis starts with an introductory chapter describing the art and science of
metallic glasses prior to this work. Then, a critical review of the current
knowledge of thermodynamics and kinetics of glass formation is given in chapter
2. In chapter 3, an example of a highly processable metallic glass alloy,
Zr41.2Til3.8C~12.5Ni10.0Be22.5
,is presented along with its preparation methods.

Its general characteristics which distinguish it from conventional metallic glasses

are emphasized. This particular glassy alloy, Zr41.2Til3.8Cul2.5Ni1o.oBe22.5
belongs to an exceptionally large family of excellent glass forming metallic
systems, which were developed in the course of this thesis research. In chapter 4,
various forms of heterogeneous nucleation, --an important phenomena in glass
formation-- are discussed with reference to several glass forming alloys. Finally,
conditions for bulk glass formation are proposed in view of our current
theoretical knowledge and experimental observations. Difficulties in attaining
these conditions are also discussed and suggestions are made for finding other
bulk glass forming alloys.

Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 What is glass? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The glass transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 A brief history of metallic glasses . . . . . . . . . . . . . . . . . . . 4
1.4 Previous work on bulk metallic glass . . . . . . . . . . . . . . . . . 11
1.5 Bulk metallic glass work at Tohoku University . . . . . . . . . . . 13
1.5.1La-base alloys . . . . . . . . . . . . . . . . . . . . . . 14
1.5.1 Mg-base alloys . . . . . . . . . . . . . . . . . . . . . . 15
1.5.1 Zr-base alloys . . . . . . . . . . . . . . . . . . . . . . 16
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Thermodynamics and kinetics of glass formation . . . . . . . 23
2.1 Classical theory of homoger~ousnucleation in undercooled
liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 The effect of thermodynamic parameters on the rate of
homogenous nucleation . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Davies .Uhlmann kinetic analysis . . . . . . . . . . . . . . . . . . 37
2.4 Limitations of Davies-Uhlm.annkinetic analysis . . . . . . . . . . 43
2.5 To criterion of glass formation . . . . . . . . . . . . . . . . . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Zr41.2Ti13.sCu12.5Ni10.0Be22.5: An example of bulk metallic

glass forming alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Mechanical properties . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.3 Thermal analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4 The critical cooling rate . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.5 TTT diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.6 Origins of exceptional glass forming ability . . . . . . . . . . . . . 84
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Heterogeneous nucleation and glass formation . . . . . . . . 92

xi
4.1 Origins of heterogeneous nucleation . . . . . . . . .
4.2 Examples of heterogeneous nucleation in preparation of
Zr-Ti-Cu-Ni-Be bulk glass forming system due to container
walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3 Heterogeneous nucleation from foreign particles and its effect
on bulk glass formation . . . . . . . . . . . . . . . . . . . . . . . .

111

4.3 Heterogeneous nucleation and thermal stability of metallic
glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

119

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Conclusion: How to find bulk metallic glasses . . . . . . . . . 130
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Appendix I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

List of Figures

Chapter 1:
1.1

Temperature dependence of the viscosity and heat capacity of an
undercooled melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Chapter 2:
2.1

Temperature dependence of the Gibb's free energy of liquid and
corresponding crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2

Gibb's Free energy change of nucleation of a crystalline embryo as a
function of its radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3

Variation of the logarithm of the frequency of homogenous
nucleation of crystals in undercooled liquid with reduced
temperature for various assignments of alp1/3 . . . . . . . . . . . . . . 33

2.4

Variation of the logarithm of the frequency of homogenous
nucleation of crystals in undercooled liquid with reduced
temperature for various assignments of reduced glass transition . . . . 35

2.5

Calculated critical cooling rates for glass formation plotted against
reduced glass transition temperature for a representative range of
elements and alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

xiii
2.6

Construction of the To(c)curve from the free energy curves of the
crystalline and liquid phase . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.7

The possibility of partitionless solidification of an undercooled liquid
at two different compositions . . . . . . . . . . . . . . . . . . . . . . . . 48

2.8

Three possible arraignments of To curves for simple eutectic systems . 52

Chapter 3:
3.1

Schematic picture of metallic mold casting unit . . . . . . . . . . . . . . 62

3.2

Samples of glassy alloy prepared by various processes . . . . . . . . . . 63

3.3

X-ray diffraction pattern (Co Kcx radiation) taken from the crosssectional surface of 12.6 mm diameter rod obtained by water
quenching in a silica tube. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.4

TEM micrographs of Zr41.2Ti13.1~Cu12.5Ni10.0Be22.5
alloy taken from
a glassy ingot of 6 grams: (a) bright field and (b) dark field . . . . . . . 66

3.5

The electron diffraction pattern of Zr41.2Til3.8Cul2.5Ni10.oBe22.5alloy
taken from a glassy ingot of 6 grams . . . . . . . . . . . . . . . . . . . . 67

3.6

The high resolution transmission electron image of
Zr41.2Ti13.8Cu12.5Ni1~.~Be22.5
al1.oy taken from a glassy ingot of 6

grams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.7

Samples of cold-rolled Zr41.2Til3.8Cul2.5Ni10.0Be22.5glassy alloy. . . . 69

3.8

Deformation of glassy alloy witlh aspect ratios . . . . . . . . . . . . . . 72

xiv
3.9

DSC scans of Zr41~2Ti13.8Cu1~.~Ni~oOoBe~~.~
glassy alloy . . . . . . . .

3.10 High temperature DSC scans of Zr41.2Til3.gCul2.5Ni10.0Be22.5
crystalline alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.11 The free energy difference between undercooled liquid and
corresponding crystal for Zr41.2~;Ti13.8Cu12.5Ni1000Be22.5. . . . . . . . 78
3.12 Calculated TTT and CHT curves for Zr41.2Til3.gCul2.5Ni10.0Be22.5 . . . 82
3.13 Schematic TTT diagrams for three different metallic glass formers . . . 85

Chapter 4:
4.1

Heterogeneous nucleation of crystalline embryo having a shape of
spherical cap on a flat container (or foreign particle such as oxide) wall 95

4.2

The value of the expression S(0)= (2 + CosO)(l- ~ o s 0 ) ~ /as
4a
function of wetting angle 0 . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.3

The total Gibbs' free energy change of a crystalline embryo for
heterogeneous and homogenous nucleation as a function of its radius

4.4

The formation of a crystalline ernbryo at the crack tip on a container
wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.5

X-ray diffraction patterns taken from the surface of 3.0 rnm thick
Zr41.2Til3.gCul2.5Ni10.0Be22.5alloy obtained by rnetallic mold casting

4.6

. 101

X-ray diffraction patterns with different radiation taken from the
as-cast surface of 1.0 mm thick Zr~oBe22.5Ni7.~
alloy obtained by
metallic mold casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.7

X-ray diffraction pattern taken from the polished surface (by -100
microns) of 1.0 mm thick Zr~~B~e22.5Ni7.5
alloy obtained by metallic
mold casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.8

X-ray diffraction patterns taken. from various parts of 6 grams ingot
of Zr41.2Ti13.sCu12.5Ni1~.~Be22.5
alloy . . . . . . . . . . . . . . . . . . . . 106

4.9

The high resolution transmission electron image of metastable
interface of Zr41.2Til3.8C~12.5Ni~~~~Be22.5
glassy alloy with
elemental Zr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.10 The transmission electron image of metastable interface of

Zr41.2Ti13.8C~12.5Ni10.~Be22.5
glassy alloy withelemental Ti . . . . . . 110
4.11 Construction of metastable liquidus line of Zr02 in a Zr alloy . . . . . . 114
4.12 Construction of metastable liquidus line of NbO in a Nb alloy . . . . . 117
4.13 DSC scans of two Zr41.2Ti13.sCu12.5Ni1~.oBe22.5
glassy alloys . . . . . . 121
4.14 DSC scans of three bulk glassy alloys . . . . . . . . . . . . . . . . . . . . 126
Chapter 5:

5.1

Phase Diagram of the Ti-Ni system . . . . . . . . . . . . . . . . . . . . . 138

5.2

Phase Diagram of the Zr-Cu system . . . . . . . . . . . . . . . . . . . .

5.3

Phase Diagram of the Zr-Ni system . . . . . . . . . . . . . . . . . . . . . 139

5.4

Hypothetical phase diagram of the Zr-Ni system . . . . . . . . . . . . . 139

5.5

Phase Diagram of the Ti-Cu system . . . . . . . . . . . . . . . . . . . . . 140

138

xvi
5.6

Hypothetical phase diagram of the Ti-Cu system . . . . . . . . . . . . . 140

5.7

Phase Diagram of the Zr-Be system . . . . . . . . . . . . . . . . . . . . . 141

5.8

Phase Diagram of the Ti-Be system . . . . . . . . . . . . . . . . . . . . . 141

5.9

High temperature DSC scans of the melting endotherms for a series of
ternary Zr-Cu-Be alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.10 Schematic ternary phase diagram showing the region in which bulk glass
forming alloys were found in ETM-LTM-Be alloys . . . . . . . . . . . . 145
5.11 Metallic radii of selected elements . . . . . . . . . . . . . . . . . . . . . . 146
5.12 Phase Diagram of the Zr-Si system . . . . . . . . . . . . . . . . . . . . . 147
5.13 Phase Diagram of the Ti-C system . . . . . . . . . . . . . . . . . . . . . . 147
5.14 Phase Diagram of the Ti-B system . . . . . . . . . . . . . . . . . . . . . . 148
5.15 Phase Diagram of the Zr-B system . . . . . . . . . . . . . . . . . . . . .

148

Appendix I:
A.l Glass forming range for (Zro.75Tio.25)100-b-~(Cul-~Ni~)bBe~
alloys for two
different cooling rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

List of Tables

Chapter 3:
3.1 The purity, form and suppliers of raw elements used in
characterization of glassy alloy . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2 The purity, form and suppliers of raw elements used in production
of bulky glassy alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Chapter 4:
4.1 Various properties of three highly processable metallic glasses . . . . . 125

Chapter 5:
5.1 Some bulk and thick glass forming alloy compositions, their reduced glass
transition temperature TW and critical cooling rates T , . . . . . . . . .

133

Appendix I:
A.l Readily glass forming (T< 104-106 K/s) Zr-Ti-Ni-Cu-Be alloys . . . . . 156
A.2 Thick glass forming (T< 102-103K/s) Zr-Ti-Ni-Cu-Be alloys . . . . . . . 157
A.3 Bulk glass forming (T< 10 K/s) Zr-Ti-Ni-Cu-Be alloys . . . . . . . . . . 158
A.4 Thermal properties of iT;rlOO-b-cCubNil~Bec
glassy alloys prepared

in the form of 1.0 rnrn strips . . . . . . . . . . . . . . . . . . . . . . . . .

160

A.5 Bulk glass forming

(T<10 K/s) ETM-LTM-Be type alloys . . . . . . . . 161

A.6 Thick glass forming (T< 102-103 K/s) ETM-LTM-Be type alloys . . . . . 161
A.7 Readily glass forming ( T< 104-106 K/s) ETM-LTM-Be type alloys

. . . 161

A.8 Thick glass forming ( k < 102-103K/s) Zr-Ti-Ni-Cu-Be-M type alloys . . 161

Chapter 1:

Introduction

In this chapter I will introduce and define some of the terminology used in this
thesis. After introducing glass and the glass transition, I will present a brief
history of metallic glasses and their characteristics. The early work on bulk
metallic glasses will then be reviewed. Finally, I will summarize the recent work
on bulk metallic glasses carried out at Tohoku University, which inspired this
thesis.

1.1 What is glass?
For the purpose of this thesis, I will use the original and the more specific
definition of glass. A glass is an amorphous solid, lacking any long range order,
formed by continuous hardening of a cooled liquid. The hardening is
determined quantitatively by viscosity and it is common to take a viscosity of
1013poise1 to distinguish fluid from solid behavior. The amorphous structure
can be determined by X-ray diffractio:n and transmission electron microscopy
(TEM). However, the difference between an amorphous and nanocrystalline
structure becomes vague when long range translational order is limited to a few
nanometers. A solid will be called amorphous, when no long range order can be

1 1poise = 10-1Ns m-2

detected down to -2 nm. Further, we can supplement X-ray and TEM by
calorimetry, which utilizes the thermtalmanifestations of the glass transition and
the crystallization of a glassy phase.

1.2 The glass transition
The glass transition can be defined as a transition during which undercooled
liquid configurationally freezes into a solid in a rather well defined temperature
range during continuous cooling. Alternatively, an undercooled liquid
transforms into a glass during the glass transition. This transition is roughly
reversible (ignoring irreversible relaxation effects in the glass), unless
crystallization intervenes, and transforms the glass into a highly undercooled
liquid state during continuous heating. During glass transition the atomic
mobility, which is correlated to the viscosity, changes by several orders of
magnitude. In figure 1.1(a) the temperature dependence of the viscosity of an
undercooled liquid is shown schematically. Usually the glass transition occurs in
a relatively small temperature interval though it is somewhat dependent on the
rate of heating and cooling. The glass transition temperature Tg has been arbitrarily
defined as the temperature at which viscosity has a value of 1013 poise. The

reduced glass transition temperature Trg, a crucial factor for glass formation, is
defined as TTg= 'Tg/Tm,where Tmis the thermodynamic freezing temperature of
liquid (where the liquid freezes to the equilibrium crystalline phase(s)).
It has been empirically observed that the heat capacity of undercooled liquid
increases with decreasing temperature below Tmand frequently exceeds the heat
capacity of the corresponding crystalline phase. Thus dCp =c; - C; ,defined as
the difference of heat capacity between liquid and crystal, increases with falling

Tg
Temperature

Figure 1.1:(a) Temperature dependence of the viscosity of an undercooled melt.

(b) Heat capacity of an undercooled melt as a function of temperature. Also
shown is the typical heat capacity of the corresponding crystalline solid at the
same composition.

temperature as shown in figure 1.1 (b). Alternatively, liquid loses entropy faster
relative to the corresponding crystal with decreasing temperature. According to
the "Kauzmann Paradox," this cannot continue indefinitely as entropy of melting
would fall to zero with decreasing temperature and become negative at some
temperature below the thermodynamic melting point [I]. This trend must
therefore be terminated at some low temperature by a solidification process. The
solidification can be either crystallization or the formation of an amorphous
solid, glass. When the crystallization is suppressed by the kinetic constraints, the
formation of an amorphous solid is realized through the glass transition. Figure
2 shows the heat capacity of undercooled liquid decreasing abruptly during the
glass transition thus avoiding the "Kauzmann Paradox." This abrupt change in
heat capacity has been traditionally exploited to determine the glass transition
temperature of undercooled liquids by the calorimetric techniques.

1.3 A brief history of metallic glasses
The history of metallic glasses formed by melt quenching starts in 1959, here at
Caltech, with an unexpected result of an experimental search for extended solid
solubility in the immiscible Au-Si binary system by very rapid quenching from
the molten state [2]. The very rapid quenching of liquid was achieved by a gun
quenching technique which can give exceptionally high cooling rates of 107 K/s
for samples having a thickness of a few microns or less [2,3]. Previously it had
been shown that extended solid solutions and new crystalline metastable phases
can form in binary systems having solid immiscibility upon rapid quenching
from the molten state using the same technique. For example, extended solid
solutions were found in Ag-Cu and Ag-Ge systems, and a new metastable
hexagonal phase was found in Ag-Ge system [2,3]. As the Au-Si system

resembles the Ag-Ge system in several respects, extended solid solutions and
new metastable crystalline phases weire expected in the Au-Si system upon very
rapid quenching of the liquid alloy. However, at the composition of Au75Si25, a
new metastable glassy phase was found which was called "non-crystalline phase"
at that time [4]. The main difference between Au-Si and Ag-Ge is that Au-Si has
a much deeper eutectic, at 18 atom percent Si, where metallic glass formation was
observed. This was quickly pointed out by Cohen and Turnbull [5] and they
proposed subsequently that glass formation is favored near deep eutectics.
Later, Turnbull used the classical theory of nucleation and growth of crystalline
phases in undercooled liquids to account for the glass forming ability of
materials [6]. He concluded that glass formation is favored at high reduced glass
transition temperatures, Typ defined as TygI TX/T,. As glass transition
temperature slowly varies with composition, deep eutectic compositions have
higher reduced glass transition temperature, hence better glass forming ability.
Since then, this has become a very popular guide to finding new metallic glass
forming systems.
However, metallic glasses didn't attract the attention of the scientific community
for a decade and were even referred to as "Pol Duwez' s stupid alloys" by one
visiting professor 171. After the discovery of strong ferromagnetism in Fe- base
metallic glasses [B], the level of research in this new field accelerated due, not
only to scientific interest in ferromagnetism, but also to possible exploitation in
industrial applications. Since then, numerous new metallic glass forming
systems have been studied and glass transition has been found in a large number
of binary systems. Initially, it was thought that glass formation was unique to
late transition metal-metalloid type eutectic systems such as Au-Si, Pd-Si, Fe-B,
etc. Here, the composition of metalloid element is typically found to be near 20

atom percent. The first counter example was reported by Giessen and coworkers in 1967 [9]. Nb-Ni and Ta-Ni binary alloys with 60 atom percent Ni
were quenched into the glassy phase by splat-quenching. Later they reported
glass formation in Zr-TM (TM=Ni, Co, Cu, Pd) with late transition metal
concentration ranging from 25 atom percent to 60 atom percent [lo]. By the mid
eighties, several different types of glass forming metallic systems had been
discovered by rapid quenching techniques. These included metallic systems
containing up to 50 atom percent metalloid atoms, e.g., X U ~ ~ Z Y[Ill,
~ B metallic
~O
systems with no transition metal or metalloid, e.g., Mg70Zn30 [12], and transition
metal-simple metal systems, e.g., Ti50Be40Zr10 [13].
In the late sixties Chen and Turnbull successfully carried out the first
experimental studies of the glass transition in metallic glasses. This was a very
difficult task for metallic systems, as c:rystallization kinetics in metallic systems
are much faster than in oxide glasses such as fused silica. Crystallization
generally intercedes and precludes the glass transition in the time scale of
laboratory measurements. In the first system they studied, Au~1.4Si18.6,they
were not able to observe the glass transition calorimetrically (i.e., abrupt change
in heat capacity of glass) as crystalliza.tion intervened [14]. However, they found
that at the melting point, the liquid has a higher heat capacity than the crystal,
and dCp increases further with increasing liquid undercooling, whereas the heat
capacity difference between the glass and the crystalline phases from room
temperature up to the crystallization temperature is less than the heat capacity
difference of liquid and crystalline phases below the melting point. They
concluded that there should be a glass transition temperature, between the
crystallization temperature and melting point of the crystalline alloy, where the
trend of increasing ACp with falling temperature terminates. This was an indirect

proof for the existence of a glass transition in metallic glasses. Later, they
obtained direct thermal evidence that a glassy Au77Gel3.6Si9.4 alloy --a better
glass former-- exhibits a transition from the glass to a metastable supercooled
liquid state highlighted by the abrupt change in heat capacity as predicted [15].
They further confirmed their thermal results by viscosity measurements around
the glass transition [16]. In summary, they observed that upon continuous
heating, metallic glasses go through a glass transition, becoming a highly
undercooled liquid in a short temperature interval. When the transition is
complete, the typical force needed to sustain deformation of the undercooled
liquid is many orders of magnitude less than for the glass. This may have
practical applications such as easy fabrication of glassy alloys at temperatures far
below the melting temperature of crystalline alloy. However, the utilization of
the glass transition in fabrication of m.etallic glasses has never been realized,
since metallic glasses have not been stable enough against crystallization above
the glass transition. Since these early experiments, relatively very little
experimental work has been done on glass transition and related phenomena
such as viscosity change at the glass transition in metallic glass systems.
Until the early seventies, the reported studies of metallic glasses have
concentrated on measurement of physical properties which do not depend on
sample geometry such as electrical, magnetic, thermodynamic and structural
properties. At that time, the available rapid quenching techniques could not
produce metallic glass samples with suitable geometry for large scale mechanical
testing. Masumoto and Maddin were the first to report on the comprehensive
mechanical properties of metallic glasses 1171. They adapted the rotating crucible
technique, which was originally developed for the production of the crystalline
metal filaments from the melt [I$], to produce uniform and long enough Pd-Si

glassy ribbons to carry out mechanical tests. They found that metallic glasses
have exceptional high strength and show limited ductility in tension. However,
this apparent "brittleness" was completely different from that of oxide glasses as
there was evidence of plastic flow at failure surfaces. Deformation markings -shear bands-- were observed on the yield surfaces of metallic glass ribbons which
were pulled above the yield point. The first experiment to show the intrinsic
ductility of metallic glasses was actually carried out by Pol Duwez et al., though
not reported [19]. They were able to cold roll 40 micron thick glassy foil down to
13 micron without any cracking. Another good example of ductility in metallic
glasses was given by Chen and Polk [20]. They bent a Ni- base metallic glassy
ribbon around a radius of the order of magnitude of its thickness without any
breaking and crack formation. However, the ductility of metallic glasses
depends on the preparation method als well as on the composition. For example,
alloy [21].
no sign of ductility was observed in bending C ~ 6 0 Z ~ 4glassy

As the properties of metallic glasses have been measured and sorted out, it has
been found that these new glassy alloys have unique features and combine
several desirable properties which do not exist in their crystalline counterparts.
For example, metallic glassy alloys have very high elastic limit, high hardness,
very high strength --close to the theoretical limit--, good bend ductility, better
soft magnetic properties, increased corrosion resistance, low coefficient of friction
and other useful properties [22]. Although metallic glasses have very useful
properties for many technological applications, they were largely ignored by
industrial researchers for some time. Clearly, the single most important reason
was the difficulty in production of metallic glasses which requires very high
cooling rates. Since heat had to be extracted in at least one direction at 105-107

K/s, metallic glasses should have a thickness of less than 100 micron at least in

one direction. The early rapid quenching techniques were not convenient for the
large scale production of metallic glasses. By the mid seventies, the development
of new rapid quenching techniques for industrial production, such as single
roller chill-block casting 1231, opened the way for the applications of metallic
glasses 1247. The first applications utilized the unusual soft magnetic properties
of Fe-base metallic glasses to produce transformer cores which could be wound
from thin sheets. This also permitted the researchers to obtain better samples in
the form of uniform foils for more cornprehensive testing and characterization of
metallic glasses. The absence of bulk specimens nevertheless continued to hinder
use in structural applications.
In the first three decades of metallic glass research, the common wisdom has
been that metallic glass formation is generally limited to high cooling rates of 105
K/s or more. In turn, this cannot give glassy samples having a minimum
dimension greater than a few hundreds microns. There were a few exceptions.
For example, certain noble metal based alloy systems were found to exhibit glass
formation at somewhat lower cooling rates. To obtain bulk samples in more
practical alloys, several methods have been tried to consolidate metallic glasses;
however, most of them either failed or achieved moderate success at enormous
effort and cost 1251. One method used by Shingu deserves particular attention
[26]. This method exploits the homogenous deformation of metallic glasses
above the glass transition and requires relatively much smaller consolidation
pressures due to very low viscosity. However, known metallic glasses at the
time of this work were generally prone to crystallization above the glass
transition. In fact, most of them were observed to crystallize below the glass
transition temperature making the Shingu process very tricky and difficult to
implement and control. Another method which worked well in consolidation of

metallic glasses is shock wave consolidation [27,28]. However, this method is
very expensive and its practical applications are very limited. Ironically, until
the 1990's research efforts to find metallic glasses which do not require high
cooling rates (thus making bulk glass formation easier), or efforts to find metallic
glasses with better thermal stability above the glass transition, were relatively
rare compared to efforts on consolida-tionof metallic glasses.
The interest in metallic glass formation from the melt diminished quickly with
the discovery of solid state amorphization by R. B. Schwarz and W. L. Johnson (a
Ph.D. student of Pol Duwez) in 1983 1291. There has been little work reported on
melt quenched metallic glasses due to increased research interest in solid state
amorphization since then.
Starting in 1989, the group of Masumoto and Inoue, at Tohoku University,
discovered several novel metallic glass forming systems, which were all reported
in the journal of "JIM Materials Transactions." These systems are especially
distinguished from earlier ones by much lower critical cooling rates required to
produce glass. This enables glass forrnation in thicker samples and better
thermal stability above the glass transition. Moreover, these systems do not
contain expensive noble metals unlike earlier "thick glass formers. It is also
obvious that these alloys are better suited for scientific work, such as viscosity
and heat capacity measurements, and for possible technological applications.
Interestingly, there was little response in the scientific community to this
breakthrough work until 1993 [30].

1.4 Previous work on bulk metallic glasses
For the purpose of this thesis, I will define the terms of "thick glass" and "bulk
glass." The term "thick glass" refers to glassy samples having a minimum
dimension of one mm or more, whereas "bulk glass" will refer to glassy samples
having a minimum size of one cm or more.
The first thick metallic glass formation was reported by Chen and Turnbull in
1969 [31]. They added Cu, Ag, and Au to the well known Pd-Si glass forming
binary system [32]. By dropping liquid droplets onto copper substrates, they
made 1.0 mm thick glassy samples. A, typical composition was Pd77.5hIbSi16.5
(M=Ag, Au, Cu). They also found that these metallic glasses have better thermal
alloy 40 K
stability than others. For example, they heated a glassy Pd77.5C~6Si16.5
above the glass transition without crystallization at a heating rate of 20 K/min.
Most other metallic glasses crystallize before the glass transition temperature has
been reached.
Later, Chen investigated glass formation in (PdlPXMX)0.835 Si0.165,
(Pdl-xTx)l-zPZ, (Ptl-xNix)l-zPz

(T = Ni, CO,and Fe and M = Rh, Au, Ag,

Cu and T) systems [33]. He found that the replacement of Pd and Pt with
elements of smaller size (e.g., Ni, Co, Fe, and Cu) greatly facilitated the formation
of metallic glass and lowered the critical cooling rates down to 103 K/s. Ni was
especially effective; giving the largest replacement of Pd and Pt and thicker glass
formation. 1-3 mm diameter rods of glassy samples were obtained by quenching
the melt, sealed in a capillary quartz tube, into water. He attributed this
enhanced glass formation to the increased reduced glass transition temperature
TT due to additional alloying. These alloys have been found especially useful for

more reliable and comprehensive mechanical testing of metallic glasses. Two of
the well known compositions are Pd40Ni40P20 and Pd77.5Cu6Si16.5.The Pt- base
alloys were not extensively studied due to their prohibitive cost.
In 1982, Lee, Kendall and Johnson [34] reported thick glass formation in another
noble metal based alloy, Au55Pb22.5Sb22.5. 1.5 mm diameter spheres of this alloy
formed metallic glass upon quenching molten droplets into LN2. They noticed
heterogeneous nucleation on surfaces of bigger samples. This glassy alloy has
such good thermal stability that its heat capacity was measured up to 50 K above
the glass transition temperature [35].
In 1982, David Turnbull and his colleagues demonstrated the first cm thick glass
formation in a Pd40Ni40P20 alloy though with a cumbersome method. Turnbull
had predicted that when the reduced glass transition temperature Tyg reaches a
value of 0.67, bulk glass formation should occur provided heterogeneous
nucleation of crystals is prevented 161. To demonstrate the pronounced effect of
heterogeneous nucleation on glass formation, they tried to obtain unusually thick
metallic glass by eliminating the hete:rogeneoussurface nucleation. They used
Pd40Ni40P20, since it had the highest reported Trg=0.66 [36], and is thus favorable
for bulk glass formation. Initially, they tried to eliminate the surface
heterogeneities by successive melting, solidification and etching cycles. This
resulted in a 6 mm diameter spheroid-a1glassy alloy with marginal crystallization
[37]. Later, they improved the elimination of heterophase nucleants by using a
molten surface flux of dehydrated boron oxide [38]. This technique proved to be
powerful, producing more massive, vlrholly glassy specimens more consistently.
They obtained a glassy sample having a minimum dimension of 1.0 cm with no
superficial crystallinity at cooling rates of -1 "C/s. This was the largest metallic

glass specimen formed by melt cooling until 1993 1301. They also demonstrated
that glassy alloys with a proper flux, which deactivates heterogeneous crystal
nucleation sites, have better thermal s'tability. They successfully heated a fluxed
Pd40Ni40P20 glassy alloy from room temperature to the melting temperature of

the equilibrium crystal at the rates of -1 "C/s without any crystallization [39].
However, this very interesting work did not receive broad attention and in some
cases was totally ignored.
Another noteworthy alloy is Ni62Nb38 which was found to be a glass former in
1967 [lo]. Until the 1990's, it was the only reported alloy with no noble metals,
having a high reduced glass transition temperature, Tyg=0.66, and an estimated
critical cooling rate of approximately 103 K/s [36]. We have been able to cast 1.0
mm thick glassy strip of this alloy which is consistent with the estimated critical
cooling rate [40]. However, there has been very little reported information on its
"thick glass formation," and no work has been reported on efforts to improve its
glass forming ability.

1.5 Bulk metallic glass work at Tohoku University
The first extensive and systematic search for bulk glass forming alloys was
carried out by the group of Masumoto and Inoue at Tohoku University, Japan.
Recently they published several papers on metallic glasses having exceptional
glass forming ability and high thermal stability. Their starting point was that
better thermal stability of a metallic glass above the glass transition leads to a
lower critical cooling rate for glass formation. This is generally true for the
earlier thick glass forming alloys such as Pd77.5Cu6Si16.5 and Au55Pb22.5Sb22.5.
First they tried to form metallic glasses by melt spinning which gives a cooling
rate of 105-106 K/s. Then, they performed calorimetric measurements on readily

glass forming alloys to determine their glass transition temperature and
crystallization temperatures at a typical heating rate of 40 K/min. They looked
for a wide super cooled liquid region which is quantitatively given by AT=T,-Tg,
defined as the difference between cry!stallizationand glass transition
temperatures. Assuming higher AT values reflect lower critical cooling rates,
they tried to find thick metallic glasses from the alloys exhibiting high AT values.
Various methods were employed to form thick metallic glasses such as water
quenching and metallic mold casting. They found La-base, Mg-base, and Zr-base
metallic glasses, which require cooling rates less than 103K/s and exhibit good
thermal stability above the glass transition.
1.5.1 La-base alloys

The first thick glass forming alloy they reported is La55Ni20A125having AT=70 K
[41]. Glassy samples of this alloy having cylindrical shapes with a 1.2 mm
diameter were prepared by quenching the melt, sealed in a quartz capillary, into
water. The enhanced glass forming ability was attributed to a high value of the
reduced glass transition temperature Tub', which was reported to be 0.68. From
the correlation between reduced glass transition and critical cooling rate,
proposed by Davies and co-workers [36], they expected a critical cooling rate of
102 K/s which was in agreement with the water quenching experiment. Later,
they increased the maximum diameter of glassy cylindrical samples up to 2.5
mm by metallic mold casting [42]. The detailed study of La-Al-Ni ternary system
revealed that AT correlates with reduced glass transition temperature Tq, both
having maximum values around the composition of La55Ni20Al25 [43].
Replacement of Ni with Cu gave similar good results, i.e., high AT and Trg with
maximum values of 59 K and 0.68 respectively at the cornposition of

L u ~ ~ A Z [44].
~~C
Water
U ~ quenching
yielded glassy samples with cylindrical
shapes up to 1.0 mm diameter.
The mixture of ternary alloys, La55Ni20A125and La55Cu20A125, resulted in a better
glass forming alloy, LassNizoCuloAl25. The quaternary alloy can be cast in up to 7
mm diameter glassy rods by high pressure die casting, whereas ternary alloys
can be cast only up to 3 mm diameter glassy rods [45]. Even better is a pentiary
~ A l 2can
5 , be cast into 9 mm diameter glassy rods.
alloy, L ~ ~ ~ C u ~ 0 N i ~ C owhich
Similar improvement was reported for AT, which is 60 I(,90 K and 100 K for
ternary, quaternary, and pentiary alloys respectively. All the alloys, ternary,
quaternary and pentiary, have values of Trg around 0.69, although they show a
significant difference in critical cooling rates. It was proposed that the increase in

AT is the dominant factor for the drastic decrease in the critical cooling rates.
This proposal has been further supported by work on Mg-base and Zr-base glass
forming alloys.
1.5.2 Mg-base alloys

The first alloy system reported having a wide supercooled liquid region is the
ternary Mg- base system, Mg-Ni-La, having a maximum 473358 K at the
optimum composition of Mg50Ni30La20 [46]. However, no work has been
reported on the thick glass forming ability of this alloy. In a later work, the
Tohoku group studied Mg-Cu-Y and Mg-Ni-Y ternary systems 1471. Maximum
values of AT were reported to be 41 K for Mg-Ni-Y at the composition of
Mg50Ni30Y20 and 61 K for Mg-Cu-Y at the composition of Mg65Cu25Y10. Thick
glass formation was demonstrated in the Mg-Cu-Y ternary system by the metallic
mold casting method 1481. The largest glassy sample was obtained at the
Mg65C~2~Yzo
composition as a 4 mm diameter rod. Surprisingly, the reduced

glass transition temperature T,s has a relatively low value of 0.60 compared to
the very low critical cooling rate. Further, TTgvalues change slowly with respect
to the composition, whereas AT and critical cooling rates are strongly dependent
on the composition. This conflicts with the well known correlation between the

Trg and critical cooling rate proposed by Davies [36]. It was proposed that the
compositional dependence of the required cooling rates is mainly dominated by
the AT value.
1.5.3 Zr-base alloys

Although Zr-base binary glass forming alloys, Zr-Cu and Zr-Ni, have been
among the most studied glassy alloys,,very little work has been reported for
glass formation in Zr-base ternary systems. The group of Masumoto and Inoue
carried out extensive work on ternary and higher order Zr-base alloys. The
values of AT were especially well characterized as a function of composition. The
glass formation in the ternary Zr-TM-,A1(TM=Mn, Fe, Co, Ni, Cu) system was
well determined and the highest values of AT were found in Zr-Cu-A1 and Zr-Ni
-A1 ternaries, e.g., 77 K for Z r 6 0 N i 2 ~ A l1491.
i ~ The reduced glass transition was
reported to be highest, 0.64, around the vicinity of Zr60Ni20A/20 and gradually
changing to 0.60 around the composition of Zr60Ni25A115 1501. Usually high AT
values were reported to be associated with high Trg. Using the empirical relation
between Trg and critical cooling rate [36], they expected a low cooling rate for the
composition of Zr60Ni20A/20which was confirmed by water quenching yielding a
1.4 mm diameter glassy rod.
The detailed study of higher order sy:;tems, Zr65A17.5Cu2.5TM25 (TM=Co, Ni,
Cu), revealed that the quaternary system has improved glass formation
compared to the ternary systems [51]. The optimization of composition for a

high value of AT gave rise to a remarkably high AT= 127 K at the composition of
Zr65Cu17.5Ni10Al7.5. Unexpectedly, no glassy alloy was found with a Trg value
above 0.60 and no close relation was found between Trg and AT. Metallic mold
casting yielded glassy rods as large as 7.0 mm diameter at the composition of
Zr65Cu17.5Ni1oAl7.5, having the largest AT. Although the Trg is almost
independent of the TM composition, the maximum diameter of glassy rod shows
a strong dependence on composition, decreasing with the value of AT down to
1.5 mm at AT=40 K. Later, it was clairned that glassy rods having a diameter as
large as 16 mm were obtained by water quenching at the composition of
Zr65Cu17.5Nil~A17.5
[52]. However, we have failed to reproduce this result.
Further, we couldn't get a glassy rod of 7 mm diameter by water quenching at
the composition of Zr65Cu17.5NiloA17.5[53].
The effect of adding other metals to the Zr-Cu binary glass forming alloys has
also been studied. Ternary systems have always been found to have larger AT
values with a strong dependence on the specific element added, A1 being the
most effective [54,55].

References

[I] W. Kauzmann, Chem. Rev., 43,21.6 (1948).
[2] For a review of historical development of liquid quenching, see: P. Duwez,
Trans. ASM, 60,607 (1967).
131 P. Duwez, R. H. Willens, and W. J. Klement, J. Appl. Phys., 31,1136 (1960).
[4] W. J. Klement, R. H. Willens, and P. Duwez, Nature, 187,869 (1960).
[5] M. H. Cohen and D. Turnbull, Nature, 189,131 (1961).
[6] D. Turnbull, Contemp. Phys., 10,473 (1969).
[7] W. L. Johnson, Int. J. Rap. Sol., 1,331 (1985).
[8] P. Duwez and S. C. H. Lin, J. App:l. Phys., 38,4096 (1967).
[9] R. Ray, B. C Giessen, and N. J. Grant, Script. Met., 2,357 (1968).
1101 R. C. Ruhl, B. C. Giessen, M. Cohen, and N. J. Grant, Acta. Met., 15,1693
(1967).
[Ill M., Mehra, A. Williams, and W. L. Johnson, Phys. Rev., B 28,624 (1983).
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(1977).

19
[13] L. E. Tanner, R. Ray, Script. Met., 11,783 (1977).
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[15] H. S. Chen and D. Turnbull, Appl. Phys. Letts., 10,284 (1967).
[16] H. S. Chen and D. Turnbull, J. Chem. Phys., 48,2560 (1968).
[17] T. Masumoto and R. Maddin, Acta. Met., 19,725 (1971).
[18] R. Pond, and R. Maddin, Trans. Metall. Soc. A. I. M. E., 245,2475 (1969).
[19] P. Duwez, Annl. Rev. Mat. Sci, 6/83 (1976).
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1211 J. Vitek and N. J. Grant, Met. Trans., 6A, 1472 (1975).
[22] For a recent review of properties and applications of metallic glasses. see:
Rapidly SolidifiedAlloys: Processes, Structures, Properties, Applications,

H.H. Liebermann (ed.), (Marcel Dekker Inc., New York, 1993).
[23] J. R. Bedell, T7.S. Patent No. 3,862,658, assigned to Allied Chemical Corp.
(Jan. 1975).
[24] For a detailed account of rapid quenching techniques, see:
T. R. Anantharaman and C. Suryanarayana, in Rapidly Solidified Metals:
A Technological Overview, (Trans Tech Pub, Switzerland, 1987).
[25] For a recent review of consolidation of metallic glasses, see: R. B. Schwarz, in
Rapidly SolidifiedAlloys: Processes, Structures, Properties, Applications,

H. H. Liebermann (ed.), (Marcel Dekker Inc., New York, 1993).

20
[26] P. Shingu, Mater. Sci. Eng., 97,137 (1988).
[27] J. Kasiraj, D. Kostka, T. Vreeland, T. J. Ahrens, J. Non-Cryst. Solids, 61,967
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[28] J. Bach, B. Krueger, B. Fultz, Mater. Mat. Lett., 11,383 (1991).
[29] R. B. Schwarz and W. L. Johnson, Phys. Rev. Lett., 51,415 (1983).
[30] A. Peker and W. L. Johnson, Appl. Phys. Lett., 63,2342 (1993).
[31] H. S. Chen and D. Turnbull, Acta. Met., 17,1021 (1969).
[32] P. Duwez, R. H. Willins, and R. Ci. Crewdson, J. Appl. Phys., 36,2267 (1965).
1331 H. S. Chen, Acta. Met., 22,1505 (1974).
1341 M. C. Lee, J. M. Kendall, and W. L.Johnson, Appl. Phys. Lett., 40,382 (1982).
[35] H. J. Fecht, J. H. Perepezko, M. C. Lee, and W. L. Johnson, I. Appl. Phys., 68,
4494 (1990).
1361 H. A. Davies, Rapidly Quenched Metals 111, edited by B. Cantor (Metals Soc.,
London, 1978), Vol. 1, p. 1.
[37] A. J. Drehrnan, A. L. Greer, and D. Turnbull, Appl. Phys. Lett., 41,716 (1982).
[38] H. W. Kui, A. L. Greer, and D. Turnbull, Appl. Phys. Lett., 45,615 (1984).
1391H. W. Kui and D. Turnbull, Appl. Phys. Lett., 47,796 (1985).
[40] A. Peker and W. L. Johnson, unpublished research (1992).

21
[41] A. Inoue, K. Kita, T. Zhang, and T. Masumoto, Mater. Trans., JIM, 30,722
(1989).
[42] A. Inoue, T. Zhang, and T. Masumoto, Mater. Trans., JIM, 31,425 (1990).
[43] A. Inoue, T. Zhang, and T. Masumloto, Mater. Trans., JIM, 30,965 (1989).
[44] A. Inoue, H. Yamaguchi, T. Zhang;, and T. Masumoto, Mater. Trans., JIM, 31,
104 (1990).
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378 (1989).
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(1993).

Chapter 2

Thermodynamics and kinetics of glass formation

What is the stable form of solid substances? Is it crystal or glass? Unfortunately
we don't have any rigorous proofs that can answer these questions as yet.
However, experience tells us that crystalline phases are thermodynamically more
stable with respect to the glass in most or all substances we know. Unless we
meet a big surprise, we might well assume that new materials will behave
similarly. As such, glass formation in known (and unknown) substances should
be a kinetic phenomenon. This raises ;mother question. Can we put an arbitrary
substance into the glassy form? Theoretical and experimental accomplishments
of the last three decades encourage us to believe that the answer is "yes." The
single most important factor for glass formation in a given substance has been
found to be the cooling rate from the liquid state. A higher cooling rate is
associated with an easier glass formation in all classes of materials. Turnbull and
Cohen predicted that liquids will form glasses through the glass transition if
cooled sufficiently fast to bypass crystallization [l].As new techniques have
been developed to provide higher cooling rates from the liquid state, more
materials have been put into the glassy form [2]. Then a more practical question
is "which materials can be put into glass with available quenching techniques?"
Alternatively, "what is the required cooling rate to put a given material into

glassy form?" Answering this question is not an easy task, as the ease of glass
formation shows enormous variation. When we classify materials according to
the their bonding nature, there are some glass formers in every category of
materials. From this we can deduce tlhat the factors that govern the glass
formation may have universal features. Turnbull used the classical theory of
nucleation and growth of crystalline phases in an undercooled melt to account
for the kinetics of glass formation in general and successfully underlined its
overall features 131. It turned out that glass formation is not a purely kinetic
process. Rather, thermodynamic properties, such as crystal-liquid interfacial
energy, free energy difference between the undercooled liquid and the
corresponding crystalline phase, play important roles in governing kinetics of
glass formation.
In this chapter I will give a critical review of kinetic analyses of glass formation
and its relation to the thermodynamics of a system. First, the derivation of the
classical theory of nucleation in undercooled melts will be presented without
attempting any rigorous justification. After discussing the effects of
thermodynamic parameters appearing in the steady state nucleation rate, I will
present the well accepted kinetic treatment of glass formation by Davies and
Uhlmann. Finally, the To criterion of glass formation will be introduced.

2.1 Classical theory of homogeneous nucleation in undercooled

liquids
The liquid becomes thermodynamically unstable with respect to the crystal when
it is cooled below its equilibrium freezing or crystallization temperature, the
melting point of the crystal. As shown in figure 2.1, the liquid has higher Gibbs'

Tm
Temperature ---b
Figure 2.1: Gibbs' free energy curves for liquid and corresponding crystal with
respect to the temperature.

free energy than the crystal below the thermodynamic melting of the crystal.
This free energy difference gives the driving force for the nucleation of crystals
from the liquid. In general, the free energy difference per unit volume, AGv, is
given by 131

where mf,is the molar heat of fusion, ACp is the molar difference in heat
capacity between the liquid and the crystal, V, is the molar volume of the
crystal, T , is the reduced temperature, and AT, is reduced undercooling. T ,
and AT, are defined as

where T, and T are, respectively, the equilibrium melting temperature and
actual absolute temperature.
However, the creation of a liquid/crystal interface discourages the homogenous
nucleation of the crystal. This is the main cause of the resistance of the liquid to
crystal nucleation. The competition between the interface energy and bulk free
energy difference depends on the crystal nucleus size which in turn determines
the stability of a crystalline embryo. For a spherical nucleus with radius r, the
total Gibbs' free energy change upon nucleation is given by [4]:

where o (o>O) is the interfacial energy per unit area. In figure 2.2, AG is shown
as a function of r, where AG, and a are assumed to be independent of r.

The AG has a maximum at r" which is given as

and a maximum of AG* is given by

The r" and AG* are the result of the balancing of two competing factors, one
increasing with the area due to the interfacial tension, and one decreasing with
the volume due to the free energy difference between liquid and crystal. As seen
in figure 2.2, crystalline nuclei larger tlhan r* will grow with decreasing free
energy and be stabilized. They will be nuclei for further crystal growth.
Crystalline nuclei having a radius smaller than r" will tend to remelt, as growth
will increase overall free energy. Thus, AG* is an activation energy for
homogenous nucleation of crystals from the liquid.
Then, the classical theory of nucleation developed by Volmer, Becker, and coworkers gives the rate of homogenous nucleation as

where q is the free energy activation for atomic diffusion across the phase
boundary, k is the Boltzman constant, and K is a constant to be determined [5].

Interfacial free

Figure 2.2: Gibbs' free energy change of nucleation of a crystalline embryo as a
function of its radius.

Turnbull and Fischer derived the absolute rate of homogenous nucleation, thus
determining K, based on the previous nucleation theory and the rate of absolute
reaction rates [6]. According to their analysis, the rate of homogenous
nucleation, to an order of magnitude, is given as

in units of the number of nuclei per u.nitvolume per unit time. Here, Nvis
number of atoms per unit volume anti v, is the frequency of attempts by atoms to
cross the phase boundary. It is a characteristic vibration frequency and is given
as v, = k T / h by the classical atomic theory.
Another alternative expression has been proposed for the rate of homogenous
nucleation, which is

where Di is diffusion coefficient for atomic transport across the nucleus matrix
interface, and a, is the interatomic distance 171. This expression reduces to
previous equation [8], when atomic transport at the interface is assumed to be an
activated process:

Usually, Di is taken to be equal to the liquid diffusivity D, which is in turn
related to the viscosity by the Stokes-Einstein relation [8]:

However, equation 2.9 is valid for single component simple liquids and its
applicability to more complex systems such as good glass formers is
questionable.
It should be noted that the above description of homogenous nucleation apply
only to the limiting conditions in which a quasi-steady distrubution of embryos
has been established. When the assembly is suddenly changed from a stable to a
metastable condition, the nucleation rate is then a function of time until the
quasi-steady state is attained. This effect will be unimportant if the transient is of
short duration compared with the period of the observation [8,9]. The transient
nucleation behavior of a condensed system is approximated by

where It is the nucleation frequency at:time t and z is the transient time [8,9]. z
is given with order-of-magnitude accuracy by the relation:

where Ns is the number of atoms on the surface of a critical nucleus, v =

the frequency of atomic transport at the nucleus-matrix interface and the n* is
the number of atoms in the critical nuclei given by equation 2.3.
The transient effects have been usually neglected in kinetic analyses of glass
formation and same will be followed j.n this thesis. This can be justified
whenever the time required to establish the steady-state conditions is small
relative to the total transformation time and to the time scale of the experiment.
When transient effects are important, their negligence will usually underestimate

the glass forming ability and thermal stability of glass above the glass transition
[101.

2.2 The effect of thermodynamic parameters on the rate of

homogenous nucleation
Turnbull analyzed the rate of homogenous nucleation with respect to the
thermodynamic parameters such as reduced glass transition Tyg= TB/Tm,
interfacial tension and entropy of fusion, and presented the overall features of
their effect [3]. Further, he predicted the glass forming ability for certain values
of thermodynamic parameters. He assumed that formation of one nucleus
precludes the glass formation. Thus the total number of appearing nuclei, n,

should be less than one in the course of cooling of liquid. In this equation V is
the sample volume, t is the time in which liquid is cooled. This condition of
bypassing crystallization is valid for h.igh crystal growth velocity (-1 cm/sec.)
and small sizes of sample (-100 microns).
To calculate the homogenous nucleation rate, he assumed that the atomic jump
time scales with the viscosity and no difference between the heat capacity of
liquid and crystal, i.e., ACp = 0. Putting ACp = 0 into the equation 2.1 gives the
famous "Turnbull approximation" for free energy difference between the
undercooled liquid and the corresponding crystal:
AG, = M~,(AT,)-

= Asfm(Tm-TI-

where AS^, is the molar entropy of fusion at equilibrium melting point. AS^,
corresponds to the difference between the slopes of free energies of liquid and
crystal. Further, he introduced two new parameters a and /3 which replaces the
interfacial tension and entropy of fusion respectively. They are defined as:

where N is Avogadro's number and Ft is the gas constant. Physically, a is the
number of monolayers of crystal which would be melted at Tm by an enthalpy
equivalent in magnitude to interfacial energy, and it is the principal resistance of
the liquid to the nucleation.
Then, the steady rate of homogenous nucleation becomes

where N is the Avogadro's number, and kn is a constant to be determined. kn is
taken from Turnbull and Fischer's kinetic analysis [5], which is set approximately
to 1032 dyne. cm. (1023 N m).
To calculate the steady rate of nucleation as a function of

viscosity was set

to a constant value of 10-2 poise, a typical value for liquid metals. This will give
an upper bound for the nucleation rate as viscosity increases with undercooling.
Accordingly the computed values of log I, as a function of reduced temperature
is shown in figure 2.3. The corresponding values of

are also indicated.

Figure 2.3: Variation of the logarithm of the frequency (in cm-3s-1)of
homogenous nucleation of crystals in undercooled liquid with reduced
temperature for various assignments of ap1/3 calculated from equation 2.16.
Viscosity was set to a constant value of 10-2poise. Reproduced from ref. 3.

As seen from figure 2.3, the homogenous nucleation rate has a broad peak
around two thirds of reduced temperature independent of the values of a/31/3.
The value of the maximum nucleation rate depends strongly on the value of

,becoming larger at small values. Typically, a nucleation event cannot be
detected on the laboratory time scale when its rate is below 10-6nuclei/ cm3 s.
When a/31/3 = 0.9, the liquid, unless seeded, will freeze to glass since the rate of
homogenous nucleation is extremely small. Metals have been found to have
typical values of a = 0.5 and /3 = 1.0 [Ill, so their nucleation rates will be around
1025 cm-3s-1at the maximum. The rapid cooling techniques would not be
sufficient to quench any metallic liquid into a glass unless Tg were much greater
than 0 K.
The undercooled liquid has another means to resist nucleation far below melting
point. This is due to the drastic decrease of atomic mobility which is related to
viscosity. As undercooled liquid freezes configurationally during the glass
transition, no nucleation is expected below the glass transition temperature.
Further, the nucleation frequency should drastically decrease around the glass
transition in accordance with the atomic mobility. Thus the relative position of
melting point and glass transition temperature should be very important in
nucleation kinetics.
To express the temperature dependence of the viscosity, Turnbull used a Fulcher
type equation [12], which reasonably describes the viscosities of glass forming
liquids in the range of 10-2-107 poise. The viscosity 77 was equated to:

Figure 2.4: Variation of the logarithm of the frequency (in cm-3s-1)of
homogenous nucleation of crystals in undercooled liquid with reduced
temperature calculated from equation 2.16. ap1/3 was set equal to 1/2 and
viscosity was calculated from equation 2.17 with indicated assignments of Trg.
Reproduced from ref. 3.

Notice that the Fulcher equation fails at temperatures very close to Trg, the
reduced glass transition temperature.
The effect of different values of Trg on the rate of homogenous nucleation is
calculated from equation 2.16, with 0!p1'3= 0.5 and using equation 2.17 for the
viscosity. The computed I,-Trgrelation with indicated values of Trg is shown in
figure 2.4. The peak of the nucleation frequency is lowered, sharpened and
shifted to higher T,at high values of ITrg. Particularly, liquids with Trg = 2/3 can
crystallize only within a narrow temperature range and very slowly provided
heterogeneous nucleation is prevented. These liquids have the best potential to
form bulk glasses easily. Taking an average value of 1,= 10-3cm-3s-1, a sample
size of 1cm, and a temperature range of 100 K to cool, equation 2.12 will predict
a low critical cooling rate of 0.1 K/s for glass formation when Trg = 2/3 in the
absence of heterogeneous nucleation. Most of the early-known metallic glass
formers have Trg -0.5 [13] and can only form glasses in small volume and high
cooling rates. Taking an average value of 1,= 1012 cm-3s-1, and a temperature
range of 100 K to cool, the equation 2.12 will predict a critical cooling rate of 106
K/s for a sample size of 20 microns for metallic glass formation. This is in broad
agreement with experimental observations.

2.3 Davies - Uhlmann kinetic analysis
Uhlmann was first1 to introduce formal transformation theory into the kinetic
treatment of glass formation 1141. He was concerned with the magnitude of
cooling rate required to avoid a certain amount of crystallization in the course of
cooling of liquid. The maximum amount of crystalline fraction for glass
formation was set to the 10-6with the justification that this is the limit of the
routinely used analytical techniques such as X-ray diffraction and TEM. Later
we shall see that this value can be set somewhat arbitrarily provided it is small,
as the final results depend on this value very weakly. Using the accepted
theories of homogenous nucleation and crystal growth, he constructed the TTT
(Time-Temperature-Transformations)diagrams for a certain fraction of crystal
formation from the liquid and estimated the critical cooling rates for classical
glass forming systems. This was an improvement to Turnbull's criteria of glass
formation in which formation of one nucleus precludes glass formation [3].
Then, Davies applied this formalism to the glass formation of metallic systems
and successfully estimated the critical cooling rates [15-171. Here, I will present
this formalism as applied to metallic systems by Davies [18].
The Johnson-Mehl-Avrami isothermal transformation kinetics gives the volume
fraction of transformed material, X,as:

1D. Turnbull and M. H. Cohen noted the formal transformation theory for glass

formation in "Modern Aspects of Vitreous State, J. D. Mackenzie (ed.)
Butterwoths, London 1960." As they found the calculations complicated, they
haven't used the actual formulation. Instead, they used limiting cases for glass
formation and took an average value of 10-l2 nuclei/sec. cm3 for I, u j to
calculate the critical cooling rate for glass formation.

38
where I, is the nucleation frequency and u, is the crystal growth rate and t is time
taken to transform X [19]. In the early stages of transformations, or for small
values of X, the value of X can be approximated as:

It was assumed that only the homogenous nucleation is occurring and the same
expression as equation 2.7 has been used for the rate of homogenous nucleation.
Using the "Hoffman approximation" [20] for AG,, the volume free energy
difference between the liquid and crystal,

and following Turnbull [3,11]

the activation energy for homogenous nucleation is given by the expression:

AG*/kThas been expressed more appropriately as:

where the constant A is given by A = 16IIa 3 ~ s L / 3The
~ . constant A can be

estimated by taking AG*/kT 50 when AT, = 0.20 [7], which is equivalent to the
AG*/kT

- 60 when AT, = 0.18 1191. Then the rate of homogeneous nucleation

becomes:

Following the previous derivation, the crystal growth rate is given by [22]

where Dg is a diffusion coefficient for atomic motion required for crystal growth,

AG, is the molar free energy change, and f is the fraction of sites at the interface
where growth occurs. For rough interfaces, as in the case for closely packed
crystal structures having low entropy of fusion,

all sites are considered to be equally available for growth and f = 1.For alloys
having high entropy of fusion, f = 0.2 AT, was chosen. Using the Turnbull
approximation (equation 2.13), the crystal growth rate becomes [8]:

It is interesting to note an inconsistency. The Turnbull approximation has been
used for free energy difference in the expression of crystal growth rate, whereas
other approximations, such as the Hoffman approximation, have been used for
the free energy difference in the expression of homogenous nucleation rate.
For simplicity, it was assumed that Di = Dg= D where D is the bulk diffusion
coefficient and it was related to viscosiity by Stokes-Einstein relation:

After combining and arranging equations 2.28,2.27,2.24 and 2.19, the time t to
form a small fraction of crystal, XI at temperature T is given by

Notice that t depends on the 1/4th power of X which gives a relatively weak
dependence of t on X. In calculation of TTT diagrams, interpolated viscosities
based on the empirical Fulcher relation
77 = Aexp

i iJ
(T mBTn

have been used [13]. The constants A, B and T q were derived by fitting the
expression to respective estimated 77 values at the experimentally measured
liquidus temperature Tl, and assuming 77 = 1013poise at experimentally
measured Tg [13]. Where Tg has not been thermally manifested, the
crystallization temperature was assumed as the lower bound for the value of Tg.
The viscosity at the liquidus point is estimated from the extrapolation of the
Arrhenius relation for liquid Ni above its melting point T;, 1171.
CCT (Continuous - Cooling - Transformations) diagrams have been constructed
from the TTT diagrams by the method of Grange-Keifer [23]. Thus the critical
cooling rate T c was calculated by the cooling curve that just avoids interception
of the nose of the CCT curve, i.e., T c = (TI- T,)/t,

where T, and t, are the

temperature and the time at the nose respectively. Accordingly, the estimated
critical cooling rates of several metallic glass forming alloys are shown against
the corresponding Tygin figure 2.5, which is reproduced from ref. 13. The
predicted cooling rates agree with experimental observations within uncertainty

Figure 2.5: Calculated critical cooling rates for glass formation (based on CCT
curves for the formation of a fraction crystal of

plotted against reduced glass

transition temperature T,y for a representative range of elements and alloys.
Reproduced from ref. 13.

of calculations and errors in estimating cooling rates in rapid solidification
techniques. Obviously, TTgappears as a crucial parameter in glass formation.
The higher Trg corresponds to the lower critical cooling rates. Notice that the
critical cooling rate decreases much more rapidly as T,g approaches the value of
0.67. However, the case of Pd40Ni40P20 needs further attention. Initially, the
observed critical cooling rate of Pd40Ni40P20 was reported to be -103 K/sec. 1241.
Later, Turnbull and his colleagues successfully undercooled a cm thick
Pd40Ni40P20 alloy into glass by employing fluxing to eliminate surface

heterogeneous nucleation at cooling rates of 1-2 K/sec [25]. According to the
Davies-Uhlmann analyses, the critical cooling rate of Pd40Ni40P2~was predicted

- 100 K/sec., thus overestimating it b y two orders of magnitude. In this case, the
observed cooling rate is determined much more accurately than with other
techniques such as splat quenching artd melt spinning [25], and the discrepancy
can be explained only in the uncertainties in the kinetic analyses. These
uncertainties and possible improvements will be discussed in the next section.
Later, several refinements were added to this model by several researchers.
Saunders and Miodownik used the thermodynamic parameters obtained from
phase diagram calculations to derive the values of energy barrier for nucleation,
free energy driving forces, and melting points, and used them in calculation of
TTT diagrams [27]. This approach makes it possible to calculate the critical
cooling rates for metastable crystalline phases. Other approximations for AGv
have been proposed as an improvemeint to the Hoffman approximation [28,29].
However, none of them give satisfactory results compared to the extrapolation of
experimental data for AGv [lo].

Ramachandrarao et al. suggested a Doolittle type expression [30] to represent the
viscosity of undercooled liquid [30]:

[I r

q=Aexp B exp -.
:TI1
They argued that this expression' gives better approximation to experimental
values of viscosity over the full range of T, to Tg for Au77Ge13.6Si9.4 [32].
Tanner and Ray used Davies-Uhlmann analysis to account for the difference
between the critical cooling rates of Zr65Be35 and Ti63Be37 1331. Their calculations
did not give satisfactory results and they proposed that the energy barrier for
homogenous nucleation should be modified. They were able to account for the
difference in glass forming ability by taking AG*/kT

- 55 for Zr65Be35 and AG*/kT

- 40 for Ti63Be37 at ATr = 0.20.
2.4 Limitations of Davies - Uhlmann kinetic analysis
The main limitations of Davies-Uhlmann kinetic analyses stem from the limited
theoretical understanding of nucleation and crystal growth and inadequate
experimental data for parameters used in these equations.
First of all, the expressions used for the homogenous nucleation rate and crystal
growth velocities are valid only for single component or congruently melting
multi-components systems, which is usually not the case for metallic glass
forming systems, i.e., this model is true for partitionless crystallization [8,14]. In
principle this deficiency can be eliminated by using models for nucleation and
crystal growth of multi component systems which are not congruently melting.
For example, Thompson and Spaepen developed a model for homogenous
crystal nucleation in binary metallic melts 1341. In the light of apparent success of

their model, Davies argued that 1181the main competing crystalline phase with
glass formation is a metastable crystalline phase having the same composition as
the liquid. This is experimentally evidenced in some cases [33], but cannot be
generalized. Assuming there is a competing metastable crystalline phase which
crystallizes polymorphically, then the parameters should be adjusted
accordingly. The most important of these is the melting point, and thus the
critical Trg,as the metastable phase will have a lower melting point than the
equilibrium crystalline phases. Moreover, the free energy difference should be
modified, as it will be smaller between the liquid and metastable crystalline
phase. However, these corrections are difficult to install, because of the
experimental difficulties in obtaining the thermodynamic parameters of
metastable crystalline phases.
Further, the existing theories of nucleation and crystal growth rates are solely
based on experiments at small underc:ooling (AT, I 0.2) of liquid metals. Their
applicability to the high undercooling;regime is also questionable. Assuming
these theories are valid for the whole range of T,, to Tg, we need the properties
of the highly undercooled liquid (ATT> 0.2), such as viscosity, diffusion constants
and heat capacity. These are important parameters in determining the nucleation
rate and crystal growth rate. Unfortuinately, we lack a good knowledge of these
parameters in the highly undercooled regime, which is the most crucial
temperature region between T, and Tg for glass formation. Moreover, we have
very little data on viscosity of multi component metallic alloys at the melting
point. This further lack of knowledge causes pronounced uncertainties in the
calculations, since it may affect critical cooling rates significantly [I$].

Recently it has been shown that heterogeneous nucleation can be an important
factor for glass formation even at very high cooling rates [35]. The critical
thickness of glassy NiY5B17Si8alloy was increased by four times when further
purification of liquid alloy was employed eliminating heterogeneous nucleation.
If we assume that all of the observed :metallic glass formation is limited by
heterogeneous nucleation rather than homogenous nucleation as suggested by
many experimental observations, then the rate of homogenous nucleation should
be significantly overestimated in the Davies-Uhlmann kinetic analysis.
Alternatively, the resistance of a liquid to homogenous nucleation is highly
underestimated. This was also proposed by Perepezko, based on the
undercooling studies of fine droplets of liquid metals [36,37]. Similar
observations was also reported by others [38]. Then, the interfacial energy
constant a should have a larger value than the -0.5 suggested by Turnbull [9].
This may explain the case of Pd40Ni40P20,where the critical cooling rate was
earlier predicted to be two orders of magnitude less. As we shall see in chapter 4,
the heterogeneous nucleation rate can be expressed in the same form of equation
2.7 with an extra parameter appearing;in the energy barrier for nucleation.
Taking this extra parameter and interfacial energy constant a together as an
effective interfacial energy constant a,, the formalism of Davies-Uhlmann kinetic
analyses can be preserved to use in cases where heterogeneous nucleation is the
rate limiting factor. From the good agreement between the calculations of Davies
(and others) and experimental observations of metallic glass formation, it seems
that a,

- 0.5 is a good choice for metallic glass formation at high cooling rates.

Finally, the assumption of Di= Dr = D requires some caution. It was already
noted by Davies that [16] these diffusion constants can be quite different. For
example, Dgwas found to be substantially greater than the corresponding D in

the Fe-Ni alloys [39]. For the time being, the lack of experimental data and
theoretical understanding of diffusion phenomena in highly undercooled liquids
leaves us no choice. Recently, the group of Inoue and Masumoto reported a
novel Al-base alloy, which formed nanometer sized crystallites embedded in an
amorphous matrix upon rapid solidification [40]. Though no valid explanation
for the formation of this unusual micirostructure has been given, a possible
mechanism is that the diffusion constants involved in nucleation and crystal
growth may differ by several orders of magnitude.

2.5 To criterion of glass formation
The To temperature is the temperature at which the free energies of the liquid
and crystalline phases, Gx and GI, are equal. To (c) curve is the locus of To
temperatures as a function of composition c 1411. The To(c)curve can be
constructed if Gx and GI are known as a function of temperature and composition
as shown in figure 2.6. Since the To(c) curve must lie between the solidus and
liquidus curves (because of the common tangent construction, see fig. 2.6), the

To(c)curve in a system can be roughly inferred from its equilibrium phase
diagram. For the purposes of glass formation, the position of To(c)curve can be
roughly approximated as a curve lying halfway between the solidus and liquidus
curves.
We can infer from the definition of To temperature that it becomes
thermodynamically possible to solidify a liquid completely into a single
crystalline phase below the To(c) curve (figure 2.7). Alternatively, the To(c) curve
represents the thermodynamic composition limit for a composition invariant
crystallization (partitionless crystallization). In the early seventies, the concept of

To temperatures was proposed for the interpretation of extended solid solubility

Coimposition
Figure 2.6: Construction of the f i ( c ) curve from the free energy curves of the
crystalline and liquid phase.

Composition
Figure 2.7: The possibility of partitionless solidification of an undercooled liquid
at two different compositions. Partitionless solidification is possible at cl (below
the To(c)curve) and impossible at c2 (beyond the To(c) curve).

observed during rapid solidification of metallic melts [42]. Later, Massalski used
the Tote) curve to give a thermodynamic account of metallic glass formation near
deep eutectics. He proposed that glass formation occurs at compositions beyond
the intersection of the To(c)curve with the TX(c)curve (the composition
dependence of the glass transition temperature). This is known as "To criterion
of glass formation" and is presented in the following paragraph.
The possibility of a composition-invariantsingle phase crystallization, in the
form of a metastable phase, constitutes the main competition to the glass
formation in the eutectic region [42]. If crystallization of a single phase is not
possible, a eutectic must form (growtlh may start with dendrite formation, but it
should end up with eutectic solidification). Since eutectic growth requires solute
partitioning and simultaneous growth of several phases, the growth velocity of a
composition invariant single crystalline phase should be much faster than for
eutectic crystallization. Thus, factors which facilitate single-phase composition
invariant crystallization into an easy forming crystal structure should sharply
reduce the glass forming ability. According to the To criterion, the possibility of a
single-phase metastable crystallization should be excluded for glass formation;
i.e., no driving force should exist for partitionless solidification. This is
determined by the relative position of Q(c) curve and Tg(c)curve of the system in
question, i.e., by the thermodynamics.
Since the glass transition is taken as the configurational freezing of liquid, no
nucleation and growth of crystalline phases is allowed below the glass transition
temperature. The thermodynamic possibility of partionless crystallization
precludes glass formation according to the To criterion. Thus, glass formation is
possible only if both To(c) curves of terminal solid solutions (or compounds)

plunge deep enough to cross the Tg(c)curve and the borders of possible glass
forming compositions are given by the intersection points of To(c) and Tg(c)
curves as shown for the third type of binary system where its glass forming
composition range is given by the shaded area in figure 2.8~.
Figure 2.8 shows three possible To(c)curves for a simple binary eutectic phase
diagram. These are:
(i) A continuous To(c) curve above the Tg(c)curve. This is true for shallow
eutectics like Ag-Cu.
(ii) To(c) curves of a and p phases crossing above the Tg(c)curve.
(iii) To(c)curves of cl and /3 phases not crossing above the Tg(c)curve. This is
the case for deep eutectics with plunging To(c) curves such as Au-Si. Only this
type of phase diagram gives a good glass former. The possible glass forming
range is shown by the shaded area.
Since diving To(c)curves are invariably associated with deep eutectics, the To
criterion gives a good account of metallic glass formation since it has been
primarily observed around deep eutectics. In principle, To criterion can be
extended to ternary and higher systems, where the To(c) and Tg(c) curves are
replaced by the Totcl, c2) and Tg(cbc2) surfaces.
Some apparent violations of the To criterion has been observed experimentally
143,441. It was found that the To criterion significantly underestimates the glass
forming range, especially at very high cooling rates of 1010 K/s. These exposed
two difficulties encountered in applying the To criterion quantitatively. Schwarz
et al. gave a good description of these difficulties [45,46]. First of all, in the

calculation of To(c)curves, a good knowledge of the free energies of the phases as
a function of composition and temperature is needed. However, our knowledge
of these thermodynamic properties, especially the thermodynamic properties of
the highly undercooled liquid, is very poor. Though several free energy models
provide satisfactory fits to the experimentally determined solidus and liquidus
curves of a binary system, these models give severely conflicting To temperatures
in the high undercooling regime which is experimentally not accessible.
The second difficulty arises from the complete neglect of kinetic constraints in
partionless crystallization, which then underestimates the glass forming ability as
compared with the experiments. As we have seen in the earlier sections of this
chapter, a significant undercooling (AT, > 0.2) is required for the onset of copious
homogenous nucleation. In fact, the Davies -Uhlmann kinetic analysis is exactly
valid for partionless crystallization. When other kinetic constraints are taken into
account, a better description of the glass forming range can be obtained as shown
by Nash and Schwarz [46].

Composition
Figure 2.8: Three possible arraignments of To curves for simple eutectic systems.

References

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[2] W. J. Klement, R. H. Willens, and P. Duwez, Nature, 187,869 (1960).
[3] D. Turnbull, Contemp. Phys., 10,473 (1969).
[4] W. Kurz and D. J. Fisher, Fundamentals of Solidification (Trans Tech
Publications, Switzerland, 1986), Chap. 2.
[5] R. Becker, Ann. Physik, 32,128 (1938).
[6] D. Turnbull and J. C. Fischer, J. Chem. Phys., 17/71(1949).
[7] D. R. U h l ~ ~ a nJ.x I,;.Hays, and B. Turrhu!!,

Pln;rs. Chexn. Glasses, 7,159

(1966).
[8] D. R. Uhlmann, in Materials Science Research, Vol. 4 (Plenum, New York,
1969).
[9] J. W. Christian, The Theory Of Phase Transformations In Metals And Alloy, 2nd
ed. (Oxford, Pergamon Press., 1975), p. 442.
[lo] H. J. Fecht, J. H. Perepezko, M. C. Lee, and W. L. Johnson, J. Appl. Phys., 68,
4494 (1990).
[ l l ] D. Turnbull, J. Appl. Phys., 21,1022 (1950).

54
[I21 G. S. Fulcher, J. Am. Ceram. Soc., 6,339 (1925).
[13] H. A. Davies, in Rapidly Quenched Metals ZII, B. Cantor (ed.) (Metals Soc.,
London, 1978), Vol. 1, p. 1.
[I41 D. R. Uhlmann, J. Non-Cryst. Solids, 7,337 (1972).
[15] H. A. Davies, J. Aucote, and J. B. Hull, Scripta., Metall, 8,1179 (1974).
[I61 H. A. Davies, J. Non-Cryst. Solids, 17,266 (1975).
[17] H. A. Davies and B. G. Lewis, Scripta. Metall., 9,1107 (1975).
1181 H. A. Davies, Phys. Chem. Glasses, 17,159 (1976).
[19] J. W. Christian, The Theory OjPhase Transjorrnations Zn Metals And Alloy
(Oxford, Pergamon Press., 1965), p. 377.
[20] J. D. Hoffman, J. Chem. Phys., 29,1192 (1958).
[21] E. R. Buckle, Nature, 186,875 (1960).
[22] D. Turnbull, J. Chem. Phys., 66,609 (1962).
[23] R. A. Grange and J. M. Keifer, Trans. Am. Soc. Metals, 29/85 (1941).
[24] H. S. Chen, Acta. Met., 22,1505 (1974).
[25] H. W. Kui, A. L. Greer, and D. Turnbull, Appl. Phys. Lett., 45,615 (1984).
1261 C. F. Lau and H. W. Kui, J. Appl. Phys., 73,2599 (1993).
[27] N. Saunders and A. P. Miodownik, J. Mater. Res., 1/38 (1986).

55
[28] K. S. Dubey and P. Ramachandrarao, Acta. Metall., 32,91 (1984).
[29] C. V. Thompson and F. Spaepen, Acta. Metall., 27,1855 (1979).
[30] A. K. Doolittle, J. Appl. Phys., 22,471 (1951).
[31] P. Ramachandrarao, B. Cantor, and R. W. Cahn, J. Non-Cryst. Solids, 24,109
(1977).
[32] H. S. Chen and D. Turnbull, J. Chem. Phys., 48,2560 (1968).
[33] L. E. Tanner and R. Ray, Acta. Metall., 27,1727 (1979).
[34] C. V. Thompson and F. Spaepen, Acta. Metall., 31,2021 (1983).
[35] L. Q. Xing, D. Q. Zhao, X. C. Chen, and X. S. Chen, Mat. Sci. Engg., A157,211
(1992).
[36] J. H. Perepezko, Mat. Sci. Engg., 65,125 (1984).
[37] J. H. Perepezko and D. H. Rasmussen, Met. Trans, 9A, 1490 (1978).
[38] D. W. Gomersall, S. Y. Shiraishi, and R. G. Ward, J. Aust. Inst. Met., 10,220
(1965).
[39] D. Turnbull, Trans. Metall. Soc. AIME, 221,422 (1961).
[40] Y. H. Kim, A. Inoue, and T. Masumoto, Mater. Trans., JIM, 32,599 (1991).
[41] T. B. Massalski, in The Proceedings of the 4th International Conference on Rapidly

Quenched Metals, T. Masumoto and K. Suzuki (eds.) (Japan Institute of
Metals, Sendai, Japan, 1981), p. 203.

[42] J. C. Baker and J. W. Cahn, in Thevmodynamics of Solidification (ASM, Metals
Park, Ohio, 1971), p. 23.
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[44] C. J. Lin and F. Spaepen, Appl. Phys. Lett., 41, 716 (1982).
1451 R. B. Schwarz, P. Nash, and D. Turnbull, J. Mater. Res., 2,456 (1987).
[46] P. Nash and R. B. Schwarz, Acta. Metall., 36,3047 (1988).

Chapter 3

Zr41.~Til3.~Cul2.5Ni10.0Be22.5
: An example of bulk

metallic glass forming alloys

We have seen in chapter 2 that the kinetics of crystallization strongly depend on
the properties of the highly undercooled liquid. The knowledge of viscosity,
diffusion constants and heat capacity of the highly undercooled liquid is highly
desirable for understanding the kinetics of nucleation and crystal growth.
However, the high undercooling regime has not been easily accessible to
laboratory measurements in metallic systems. This poses severe limitations on
LL-

-"-:*-I

LL-

WTT

L I L ~ : ~ ! d 5 3 1 L a l LLLCOL

"f ItuL!eationas we!! as the kinetic t r e a t ~ ~ esnf tw-""
-1
-**n

formation. The properties of highly undercooled metallic liquids can play
important roles in understanding of the microstructures developed during
crystallization and in designing novel materials. Highly processable and bulk
forming metallic glasses are useful not only for technological applications but for
the advancement of scientific knowledge as well. Obviously, the highly
undercooled regime is easier to access in good glass formers since the liquid has
higher resistance to the crystallization. Until recently, there were not many good
bulk glass forming alloys on which to measure the properties in the highly
undercooled regime.

In this chapter, I will present an example of a highly processable metallic glass:
Zr41.2Til3.8C~12.5Ni10.0Be22.5
[I]. This metallic alloy is far superior to its

predecessors for its bulk glass forming ability and high thermal stability above
the glass transition. The alloy belongs to an exceptionally large family of
excellent glass forming metallic system, which was found and developed in the
course of this thesis. The bulk glass forming range of this system will be
presented in Appendix I. The general characteristics of this alloy will be
discussed and its properties which distinguish it from conventional metallic glass
formers will be emphasized. First I will introduce the various preparation
methods of the glassy alloy. Then a description of the mechanical properties
will be given. The measured thermal properties will be presented and a
preliminary attempt will be made to construct a TTT (Time - Temperature Transformations) diagram for this alloy. The TTT diagram will be used to
account the observed thermal properties of the glassy alloy. Finally the origins of
exceptional glass forming ability will be discussed.

3.1 Preparation
Initial ingots, having the nominal composition Zr41.2Til3.8Cul2.5Ni10.~Be22.5
were prepared by induction melting of the constituent elements in a closed
system on a water cooled copper or silver boat under a Ti-gettered argon
atmosphere. Raw elements of two different purities were used according to the
purpose of work. Raw elements of higher purity have been used for
characterization of glassy alloys such as thermal analyses. Their purity, form and
suppliers are shown in table 3.1.

Table 3.1: The purity, form and suppliers of raw elements used in
characterization of glassy alloy.
Element

Form

Purity

Supplier

crystal bar turnings

99.5 %

Johnson Matthey

pellets

99.99 %

Cerac

rod

99.999 %

Johnson Matthey

pellets

99.97 %

Cerac

pieces

99.9 %

ESP1

Table 3.2: The purity, form and suppliers of raw elements used in production of
bulky glassy alloy.
Element

Form

Purity

Supplier

lump

99.2 %

Johnson Matthey

pellets

99.7 %

Johnson Matthey

rod

99.9 %

Johnson Matthey

rod

99.5 O/O

Johnson Matthey

pieces

99.9 O/O

ESP1

Raw elements of lower grade were used in the preparation of larger pieces to
demonstrate the bulk glass forming ability of Zr41.2Til3.8Cu12.5Nil0.0Be22.5alloy.
Their purity, form and suppliers are shown in table 3.2.
Typically, samples of 3-9 grams were used in preparation of preliminary ingots.
The nominal compositions have been accepted for the rest of the work, as the
total mass loss during alloying was consistently less than 0.01 percent (actually
below detectable limits of our electronic balance which is 0.1 mg). The master
ingots were found to freeze without any significant crystallization upon
completion of alloying irrespective of the purity of the elements used. Only
slight traces of crystallinity were observed on the lower surface of the glassy
ingots, where casual contact with the copper boat occurs during solidification.
Contact with the boat apparently can induce heterogeneous nucleation of crystals
with limited growth. The remainder of the ingots were completely amorphous
as confirmed by TEM, X-ray and DSC analyses. It is worth noting that the upper

--,
-L &Lr\:-- I\ ,L:l-.;t~ u +,e,
Fr
ul 11lr I I L ~ GC~X l~i v i r ~

*laSS
ltrf~ro
~c
tr=rtinn
ic
UI-CLICL\rL
U haat o ~rr
+ +r "nar ul o
k n 6
1- c
ru nnlxr jII
L\-UC

one direction. The glassy surface can be easily distinguished with its very
smooth and highly reflective appearance. The largest glassy ingot made weighed

25 grams, where the size limitation stems from the size of the copper boat used
and not from the glass forming ability of the alloy. These biggest glassy ingots
have a typical thickness of 1.0 cm. Recent experiments by Schwarz have
demonstrated that ingots of 200 grams readily freeze to bulk glass when
constituent elements are alloyed by plasma melting on an electropolished copper
hearth [ 2 ] . The ingots were further processed into more useful shapes by metallic
mold casting or water quenching of molten alloy sealed in a silica glass tube.

The schematic picture of a metallic mold casting unit has been shown in figure
3.1. The unit consists of a vacuum chamber containing a cold copper block,
which is used as a quenching media, a silica glass tube containing the sample,
and rf heating coils surrounding the silica tube. The silica tube has a small
orificeat the bottom end which is firmly seated into a channel which feeds a hole
in the copper block. The top end of the silica tube is connected to a pressure
reservoir. Upon melting of the alloy, the valve connecting the pressure reservoir
is opened and the flow of inert gas, He or Argon, injects the molten sample into
the hole of copper block through the orifice of the silica tube. Typically, a
pressure of 10-20 psi has been used for injection of molten sample. The copper
block has internal cavities with different shapes and sizes resulting in glassy
samples in the form of rods and plates.
Water quenching has been performed after sealing the samples in a silica tube,
General Electric 99.9 % fused quartz, under an inert atmosphere. The sealed
sample has been melted by rf heating and plunged into water and stirred until
solidification is complete. Typically, glass tubes with one mm wall thickness
have been used. Large fully amorphous rods up to 14 mm in diameter have been
prepared by this method. We have not as yet established an upper bound on the
rod diameter which can be quenched to the glassy state.
Figure 3.2 shows several glassy samples obtained by various processes described
above. Two rods, 7 mm and 12.6 mm diameter, were prepared by water
quenching in silica tubes. Figure 3.2 also includes a rectangular bar and a plate
prepared by casting in copper molds. The figure shows both a top view and
cross-sectional views of bar, plate and rods. Also shown are top views of three
glassy ingots, readily frozen into glass on a copper boat. X-ray diffraction

rf coil

&LU

Figure 3.1: Schematic picture of metallic mold casting unit.

yulliy

V ~ C U U ~ L ,-.L
**-,.

T7nfl..*,-

Figure 3.2: Samples of glassy alloy prepared by various processes, from left to
right: 12.6 mm diameter rod and its cross-section, 7.0 mm diameter rod and its
cross-section, 5x5 rnrn bar and its cross-section, 3x8 mm plate and its crosssection, 2 oval shape of ingots of 9 g each, bar-like ingot of 8 g.

patterns were obtained from the outer surfaces as well as on various crosssectioned surfaces of the samples. No evidence of crystallization has been found
in any of the X-ray patterns.
Figure 3.3 shows a typical x-ray pattern of glassy Zr41.2Til3.8Cul2.5Ni10.oBe22.5
alloy, taken from the cross-sectional surface of the 12.6 mm rod obtained by
water quenching in a silica tube. This X-ray diffraction pattern was obtained
with an Inel position sensitive detector using Co Ka radiation ( A=0.1790 nm).
The sample is completely amorphous as evidenced by the absence of any Bragg
peak. This is further supported by TEM characterization. Several transmission
electron microscopy samples were prepared and neither electron diffraction
patterns nor dark field images gave any evidence of crystalline inclusions.
Figure 3.4 shows typical bright and dark field images of
Z~41.2Ti13.8Cu12.5Ni10.0Be22.5
alloy taken from a glassy ingot of 6 grams. Figure

3.5 shows the corresponding electron diffraction. The sample is completely
nnnnA h
n c ~ T E R A r n i..Avo
r r n arupA
r ~ h c -and
amorphous, a3 c<;dcALLcu
~y F n ~ - * ~ n lbr
,. hmad
---- halos
- .--rnn

I\-

I L ~ C U

LALO

mrDTr
uJ

-.-

in the electron diffraction pattern.
Figure 3.6 shows a high resolution TEM image of a similar sample. No lattice
fringes are observed beyond the range of 1.0 nm. The observed short range
ordering should be interpreted as ordering of liquid due to entropy loss upon
cooling rather crystallization. As we have seen in chapter 1,undercooled liquids
tend to have higher heat capacity than the corresponding crystal. We shall see in
section 3.3 that the same is true for our Zr alloy and it should therefore lose
substantial configurational entropy thus becoming more ordered during cooling.
This kind of short range ordering is generally not as pronounced in conventional
metallic glasses, since the very high rate of cooling results in entropy trapping

Two Theta [degrees]
Figure 3.3: X-ray diffraction pattern (Co Kn radiation) taken from the crosssectional surface of 12.6 mm diameter rod obtained by water quenching in a silica
tube.

Figure 3.4: TEM micrographs of Zr41.2Til3.8Cul2.5Ni10.0Be22.5alloy taken from a
glassy ingot of 6 grams: (a) bright field and (b) dark field.

Figure 3.5: The electron diffraction pattern of Zr41.2Til3.8Cul2.5Ni10.0Be22.5alloy
taken from a glassy ingot of 6 grams.

Figure 3.6: The high resolution TEM image of Zr41.2Til3.sCu12.5Nilo.oBe~2.5
alloy
taken from a glassy ingot of 6 grams.

during the glass transition from undercooled liquid to the glass. As the atomic
mobility is drastically reduced around the glass transition, the undercooled
liquid may not have enough time to sample its configurational phase space
completely during cooling, thus keeping some of its communal entropy which it
would otherwise lose. The glassy Zr41.2Ti13.8Cu12.5Ni10.0Be22.5
alloy has been
cooled slower by several orders of magnitude,

- 10 K/s, hence it has had more

time to come to configurational equilibrium during the glass transition. As such
it tends to lose more configurational entropy as reflected in a higher heat capacity
and more ordered structure.

3.2 Mechanical properties
The Zr41.2Til3.8Cul2.5Ni10.0Be22.5bulk glassy alloy preserves the traditional
ductility and high strength of metallic glasses [I]. Vickers hardness
measurements on this bulk glassy alloy shows a typical value of H, = 585
kg/mm2. Using the well known relation H, = 3 oy for metallic glasses [3], the
yield strength has been estimated to be oy = 1.95 GPa, which is in good
agreement with the recently reported value of oy = 1.89 GPa obtained from both
tensile and compression tests of the bulk samples [4]. The density of this glassy
alloy has been measured as 6.11 g/cm3 using the Archimedes principle. With the
given values of density and yield strength, the glassy
Zr41.2Ti13.~Cu12.5Ni10.0Be22.5
alloy has a very high specific strength. The bulk

glassy alloys are very ductile at ambient temperature when deformed under
confined geometries. For example, a plate of 1.5 mm thickness was cold rolled at
ambient temperature down to 15 micron thick ribbon without any crack
formation. The final ribbon can still sustain a 90' bend as shown in figure 3.7.
The hardness values of glassy samples before and after cold rolling do not show

Figure 3.7: Samples of cold-rolled Zr41.2Til3.gCul2.5Ni10.0Be22.5glassy alloy.
From left to right: 3mm thick glassy sample failed during cold rolled, 1.5 mm
thick glassy sample cut from 3mm thick glassy alloy and its final form after
rolling down to 30 micron thick ribbon, 1.5 mm thick glassy alloy, final form of
1,5 mm thick glassy alloy after rolling down to 15 micron thick ribbon.

any significant difference implying the absence of any work (strain) hardening.
Localized deformation markings --shear bands-- perpendicular to the rolling
direction have been observed on the rolled samples as reported by previous
researchers on other metallic glasses [5].
The sample aspect ratio is a critical geometric factor, defining the confined
geometry, in determining the ductility of glassy sample. It is given by lld, where

1 is the length of the sample in the direction of the applied force, and d is the
smallest dimension of the sample under stress in the plane perpendicular to the
applied force. When the aspect ratio is greater than a critical value, the sample
fails in the direction of maximum resolved shear stress ( at 45" degrees to the
applied force) without any apparent ductility. For example, a 3mm thick glassy
plate, which has twice the aspect ratio of 1.5 mm thick glassy plate for the same
rolling mill arrangement, failed during cold rolling without exhibiting any
apparent ductility. The fracture surface shows the typical veiny patterns
evidencing localized plastic dzformatisn 161. It seems that a loca!ized shear
mechanism causes the sample failure before global deformation can begin.
Figure 3.7 shows the glassy sample pieces which failed during rolling. The same
3 mm thick glassy sample was longitudinally cut to reduce the thickness to 1.5
mm. This eliminated any effect due to cooling rate and exposed the pure
geometrical effect on the deformation behavior of the glassy alloy. The cut
sample, 1.5 mm thick, can be cold rolled indefinitely and still keep its bending
ductility. The initial and final form of the cut sample after rolling has been
shown in figure 8. Similar results have been obtained in compression testing of
the glassy Zr41.2Til3.gCul2.5Ni10.0Be22.5alloy where a critical aspect ratio was
found to be 1.0 [4,7]. These results can be interpreted as follows. When the

applied stress on the glassy sample reaches the yield strength, a localized shear
band forms in the direction of the maximum resolved shear stress (at 45O degrees
to the applied force). The shear band will propagate (or expand) crossing
throughout the sample in a rather narrow band shearing the sample in two
pieces. The two pieces of the sample tend to move relative to each other by
sliding. When the aspect ratio is less than one, the confined geometry will
prevent sliding. Then two pieces of glassy sample will rotate rather than sliding
on each other as shown in figure 3.8 (a). This will result in deformation of the
glassy sample by a length comparable to the thickness of shear band. As new
shear bands form, their combined effect will give a significant overall ductility.
A good example of this is given by the rolling of glassy alloys where deformation
markings have been observed in the direction perpendicular to the rolling.
When the aspect ratio is greater than one, two pieces of glassy sample split by the
shear band will slide freely on each other resulting in failure as illustrated in
figure 3.8 (b). If there were work hardening in the glassy alloy, the propagation
of a shear baiid and free sliding of parts of the glassy sample would be
terminated in favor of new shear band formation. Thus, it is the complete
absence of work hardening that results in the localization of shear deformation
into narrow bands.
The Young's modulus of Zr41.2Til3.8Cul2.5Ni10.0Be22.5
glassy alloy has been
reported to be 93 GPa, from which we find the ratio of Elcry = 50 in close
agreement with other metallic glasses [3]. However, its constituent elements
have a weighted average value of 165 GPa for Young Modulus [8] which gives
the ratio of Eglass /Ecrystal =O.56. This number averages around 0.75 for other
metallic glasses [3,9]. This extra "softening" may be due to the abnormally high
Young's modulus of Be, which is 356 GPa, compared to 98 GPa for Zr [B].

Figure 3.8: (a) Deformation of glassy alloy when aspect ratio is less than one.
(b) Failure of glassy alloy when aspect ratio is greater than one.

Relatively low concentration of Be may substantially reduce its contribution to
Young's modulus of the glassy alloy. In particular, this may be related to the
absence of direct Be-Be bonding in the glass.
As Zv41.2Ti13.8Cu12.5Ni1o.oBe22.5glassy alloy can be easily produced in bulk
forms, it is exceptionally well suited for highly reliable mechanical tests which
were not possible with earlier metallic glass forming systems. Recently,
comprehensive quasistatic mechanical tests on the Z~41.2Ti13.8Cu12.5Ni10.0Be22.5
bulk glassy alloy were reported [4]. Further mechanical properties such as
fracture toughness are under investigation [7].

3.3 Thermal analyses
Thermal analysis of the glassy alloy was carried out using a Perkin-Elmer DSC 4
scanning calorimeter interfaced to a personal computer for data processing and
analysis. The samples were contained in aluminum pans and scanned in a
IIU
' - - .w
- : - -11

-----

a1~

L~
-~
L -~-L=L- V\J
-*
Yn
I GIG.

Tn
Iu U
rl*tn*rninn
L C ~ I A ~ L ~Lb~ tho
rr rL r
Lr ~ ~
.rrrrrl
~ e t ~a1ln
----)
l l ri mpltina.
n ~

pointi a

Seteram DSC 2000 K high temperature calorimeter was used in the DSC mode.
Figure 3.9 shows DSC (Differential Scanning Calorimetry) scans of the glassy
Zr41.2Til3.8Cul2.5Ni10.0Be22.5
alloy using a heating rate of 20 K/min. and 200

K/min. In the 20 K/min. scan, a heat capacity anomaly characteristic of the glass
transition can be seen beginning at 625 K with a heat capacity maximum at
slightly higher temperature. At higher temperatures, two crystallization events
are seen. The onset of the first occurs at 705 K while the onset of the second is at
735 K. The location of both peaks depends strongly on the rate of heating as can
be seen by comparison with the DSC scan at higher heating rate. This relatively
large supercooled liquid range has been successfullyutilized in fabrication and

+-'
(d

.z8

Fr;l

\I/

550

600

650

700

750

800

850

Temperature [K]
glassy alloy at heating
Figure 3.9: DSC scans of Zr41.2Til3,8Cul2.5Nilo.oBe22.5
rates of 20 K/min. and 200 K/min. The corresponding glass transition
temperature and crystallization temperatures are shown for the heating rate of
K/min.

shaping of the Zr41.2Ti13.8C~12.5Ni10.~Be22.5
bulk glassy alloys. Thickness
reductions of 90 percent were easily obtained with small pressures of

- 5 MPa at

50-70 K above the glass transition temperature during a time duration of 10-20
minutes [lo]. Also, fine details of the mold pattern can be reproduced at the scale
of less than one micron [lo]. The samples still keep their glassy nature after the
fabricating and shaping process as would be suggested by the DSC results.
Figure 3.10 shows a high temperature DSC scan of the crystalline Zr alloy at the
heating rate of 20 K/min. There are two endothermic peaks, the first one being
much stronger. The solidus temperature is determined to be 937k3 K taking the
onset of first endothermic peak. The liquidus temperature is determined by
taking the offset of second peak and found to be 993k5 K. The heat of fusion was
measured as AH; = 6.3 50.3 kJ/mole. We believe that the solidus temperature
should be a eutectic temperature for the five component Zr-Ti-Cu-Ni-Be system.
From the comparison of relative magnitudes of endothermic signals, we can
deduce that the alloy is very close to a e~tecticorLposition.Therefme, the
Zr41.2Til3.8C~l2.5Ni~o.oBe22.5
alloy will be assumed to represent the eutectic alloy

for the rest of the thesis. The boundaries of the bulk glass forming range include
a rather large region of the pentiary phase diagram. The
zr41.2~i13.8Cu12.5Ni1~OoBe22.5
alloy composition lies somewhere near the center of

this region. The exact eutectic composition should have similar or possibly better
glass forming ability. Further, the properties of the glassy alloys do not show
any drastic change with composition, thus our assumption should be valid for
purposes such as calculation of the TTT diagram.
The experimentally observed heat capacity difference between the undercooled
liquid and crystalline phases was approximated with a linear equation. DSC

850

900

950

1000

1050

Temperature (K)
Figure 3.10: High temperature DSC scans of Zr41.2Ti13.8Cu12.5Ni10.0Be22.5
crystalline alloy at heating rates of 20 K/min. The corresponding solidus Tsand
liquidus Titemperatures are also shown.

scans of the glassy alloy and crystalline alloy with a continuous heating rate were
used to obtain the linear fit to the heat capacity difference in the supercooled
liquid region. The linear equation is given by

Accordingly, the calculated molar free energy difference between the liquid and
corresponding crystal is plotted as a function of reduced temperature in figure
3.11. Turnbull's approximation is also shown [22]. It is clear that Turnbull's
approximation diverges significantly from the experimentally extrapolated
values at high undercooling, whereas it gives satisfactory values at small
undercooling (AT,<0.15).

3.4 The critical cooling rate
A molten sample of typical dimension R and initial temperature T , (the
melting point of the material) will require a total cooling time .r: to ambient
temperature (below glass transition) which is given by

where K is the thermal diffusivity of the material [ll]. It is given by

where K is the thermal conductivity and Cp is the heat capacity per unit
volume. Then we can find an average value of cooling rate from the melting
point to the ambient temperature by the equation

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Reduced Temperature ( T,flm

Figure 3.11: The free energy difference between undercooled liquid and
which is assumed to
corresponding crystal for Zr41.2Ti13.~Cu12.5Ni1000Be22.5
represent the eutectic alloy. Both the Turnbull approximation and
experimentally extrapolated values are shown. Here, T , is taken to be the
eutectic temperature.

where we use the average values of K and Cp throughout the temperature
range of AT. The critical cooling rate for glass formation is evaluated from
the maximum possible value of R for a glassy sample.
The thermal conductivity of undercooled liquid can be calculated from the
"Wiedemann-Franz" law which is stated as:

T is the absolute temperature, p is the resistivity and L is the Lorenz number
having a value of 2.45 x 10-8watt ohm/deg2 1121. This expression should be
valid for undercooled liquids due to their highly disordered nature. Taking p =

2.5 x 10-4 ohm cm., the value of glassy Zr~oBedoalloy [13], and T = 780 K we find
an estimated value of K = 7 x 10-2watt/cm. deg. The heat capacity of
undercooled liquid can be calculated by the sum of the Dulong-Petit value of the
corresponding crystal and using equation 3.1. We will get an average value of

Cp = 10 cal/mol. or C p = 4 J/cm3 for the liquid. We can easily get 1.0 cm thick
glassy ingots where heat is extracted from one direction. Using a value of 400 K
for AT and plugging other numbers into equation 3.4, we find a average cooling
rate of

- 7 K/sec. for typical glassy ingots. In practice cooling rate changes with

temperature, being highest around the melting point and decreasing as the glass
transition is approached. As we have not yet set any upper bound for the
maximum thickness of ingots which will form glass when cooled on metallic
crucibles, the critical cooling rate could be substantially smaller.

3.5 TTT Diagram
TTT diagram (Time - Temperature - Transformations) and its derivative CCT
(Continuous - Cooling - Transformations) have been used solely for estimating
critical cooling rates [14]. These diagrams can be applied more generally to study
the thermal stability of metallic glasses in the supercooled liquid region. This is
especially true for very recent exceptional glass forming metallic alloys as they
are more stable in the supercooled liquid region. The TTT diagram and its
derivatives can also give us very useful information for fabrication of these hard
and strong materials above glass transition using small forces. A preliminary
attempt to construct the TTT diagram will be presented and it will be used to
account for the observed thermal properties of our recently found excellent
metallic glass formers [15].
The Uhlmann [16] and Davies [17] kinetic formulation was followed to construct
a TTT diagram for the Zr41,2Ti13.sCu12.5Nilo.oBe22.5
alloy (which is assumed to
represent the eutectic composition). A Doolittle-type expression was used to
model the viscosity [18]

where the constants are determined by taking a viscosity of 1013 poise and 1
poise at the glass transition temperature and at the eutectic melting point
respectively. The experimentally determined values of the free energy
difference between the liquid and corresponding crystal were used. In order
to get agreement with a critical cooling rate of 5 K/s, AG* was set to 75 kT for
a reduced undercooling AT, = (T,-T)/T, = 0.2. AG*corresponds to the

energy barrier for nucleation in the kinetic formulation of Uhlmann and
Davies. The CHT (Continuous- Heating -Transformations) curve was
obtained approximately from the TTT curve using the method of GrangeKeifer [19].
In figure 3.12, TTT and CHT curves are shown together with DSC heating curves
as well as a 5 K/sec cooling curve appropriate for a 1.0 cm thick glassy ingot.
Also shown are experimental onset crystallization temperatures on the
corresponding DSC heating curves. The observed crystallization temperatures
are below the estimated temperatures from the calculated TTT diagrams. (When
transient nucleation effects are included, it will push the TTT and CHT curves
further to the right thus increasing the observed discrepancy.) At a heating rate
of 200 K/min, no crystallization should be observed according to calculated TTT
and CHT curves. To explain the differences between calculated and
experimental crystallization temperatures, it is proposed that heterogeneous
nucleation has intervened in the DSC experiments. This is supported by further
experiments. For example, the development of a surface oxide has been
observed above 675 K in samples scanned in flowing argon. Such oxidation can
be suppressed by fluxing the sample surface with a layer of borosilicate glass or
encapsulation in a thin glass ampoule. When this is done, surface oxidation is
suppressed, and contact with the aluminum DSC pan is also prevented. Under
these conditions, the experimental crystallization peaks have been found to shift
to significantly higher temperatures. In fact, heterogeneous nucleation has
previously been shown to be very important in the determination of critical
cooling rates for glass formation as well as crystallization temperatures of glassy
alloys. For example, Turnbull and co-workers undercooled liquid Pd40Ni40P20

Figure 3.12: Calculated TTT and CHT curves for Zr41.2Ti13.8Cul2.5Ni10.0Be2~.5
are
shown along with DSC heating curves at different heating rates and estimated
critical cooling rate for glass formation. Also shown on the DSC heating curves
are onset crystallization temperatures of the glassy alloy at corresponding
heating rates (full circles).

samples with dimensions of one cm to the glassy state after removing
heterogeneous nucleation catalysts by fluxing [20]. They estimated a critical
cooling rate of order 1K/s whereas it was earlier believed to be of order 103
K/s. They also showed that glassy Pd40Ni40P20 can be heated to its melting
point without crystallization at a heating rate of 2 K/s [21]. The effects of
heterogeneous nucleation in glass formation and thermal stability of metallic
glasses will be discussed in more detail in the next chapter.
An interesting feature of the TTT and CHT diagrams for this highly processable
metallic glass is that the crystallization nose is very close to the continuous
heating curves at the typical heating rates used in DSC experiments. For
example, the continuous heating curve at the rate of 80 K/m just misses the
crystallization nose. This will give a relatively wide supercooled liquid region
above the glass transition as well as a strong dependence of crystallization
temperatures on heating rates. The crystallization nose is far to the left in the
TTT diagrams of conventional metallic glasses. In these systems it is necessary to
use heating rates of 105-106 K/sec to encounter the crystallization nose. This is
ordinarily not achieved in DSC experiments. Hence, typical DSC experiments
give heating curves which fall to the far right of the crystallization nose of
conventional metallic glasses. Here the slope of the TTT curve approaches zero.
For very good glass forming alloys, the continuous heating curves at the typical
heating rates used in DSC experiments should fall very close to the
crystallization nose, where the TTT curve has a steeper slope and a rapidly
changing value. As a result, crystallization temperatures should be strongly
dependent on the typical heating rates used in DSC experiments. Thus any
conclusions regarding the crystallization temperature and glass forming ability
of these very good glass forming alloys should not be based on a single DSC

scan. This is illustrated in figure 3.13 where curve "a" represents a conventional
metallic glass, e.g., Zr65Be35 and FegoB20, curve "b" represents a thick glass
former, e.g., Pd77.5Cu6si16.5and Zr60Ni25A115 I and curve "c" represents a bulk
Two typical DSC heating rates
glass former such as Zr41.2Ti13.8Cu12.5Ni10.0Be22.5.
are also shown. Obviously, the crystallization temperatures change more
dramatically on curve "c" (representing the good glass former) for different
heating rates. These TTT diagrams also suggest that the metallic glasses which
require lower critical cooling rates have better stability above glass transition
temperature, i.e., broader supercooled liquid region before crystallization on
heating.

3.6 Origins of exceptional glass forming ability
We have seen in the previous chapter that the reduced glass transition
temperature, Trg = Tg/Tm (where Tg is the calorimetrically defined glass
transition temperature and T, is the alloy melting point) has often been cited in
l : ~ ~ * ~ * . . * ~

Illr: l i L t - l a L u l r :

[14,2?] as a critical paraneter which determines the glass forming

ability of metallic alloys. High values of Trg are associated with glass forming
ability. Taking Tg = 625 K and Tm = 937 K (the eutectic temperature), we obtain
Trg = 0.67 for the eutectic alloy, which should have comparable glass forming
ability as Z~41.2Ti13.sCul2.5Ni~o.oBe22.5.
This is among the highest values of Trg
reported for metallic alloys so far [14] and is consistent with the exceptional glass
forming ability of the material.
To explain the exceptional glass forming ability of these alloys, both
thermodynamic and kinetic factors must be taken into account. The large values
of Trg imply a small relative temperature range over which nucleation and
growth of crystals can occur. From our DSC studies, we estimated the total

10-6

10-4

10-2

lo2

104

Time (seconds)

Figure 3.13: Schematic TTT diagrams for three different metallic glass formers.
Curve a, b, c respectively represent a conventional metallic glass former, a
moderately good glass former and an exceptionally good glass former. Also
shown schematically are DSC traces at the heating rates of 80 K/min and 5
K/min. It is assumed that all the glassy alloys have the same value of Tg.

entropy of fusion, AS,f of these alloys, to be approximately 6.6 J/mole-K. This is
a very low value compared to well known "Richard's rule" of AS;

2 8.4 J/mole

K for metallic alloys [23]. Using the Turnbull approximation [22] for the free
energy difference between the liquid and crystalline phases in the undercooled
regime,

AGm =

AS^ IT,,-T) + higher order terms

gives a very small driving force for crystallization. The higher order terms
involve the heat capacity difference between the liquid and crystal and
generally reduce the driving force for crystallization relative to the first term.
For example, at 780 K, corresponding to a reduced undercooling of 0.18 we
estimate AGm = 1.1 kJ/mole. When heat capacity corrections are taken into
account, figure 3.11 gives AG, = 1.0 kJ/mole. This relatively small driving
force for crystallization will tend to result in a relatively large nucleation
barrier fcr crystals in the restricted rmdercooled region. At lower
temperatures, kinetic freezing of the melt sets in rapidly due to the small
temperature interval between the melting point and glass transition (i.e.,
high value of Trg). As evidenced by the TTT diagram, the undercooled
liquid has a very small temperature range for crystallization.
A second factor which may influence crystallization is the "complexity" of
the five component alloy. We note, for example, that the atomic radii of the
elemental constituents vary over a large range. The atomic radius of Be is
0.111 nm, those of Ni and Cu are 0.124 nm, while those of Zr and Ti are 0.160
and 0.147. These differing sizes are expected to limit the solubilities of these
elements in crystalline phases having a small number of non-equivalent

positions in the unit cell, thus requiring large chemical fluctuations to form
critical nuclei of the crystalline phases. In support of this argument, we note
that Tanner has studied glass formation by rapid quenching in Zr-Be and TiBe alloys [24]. In the Ti-Be system, glass formation is preempted by
formation of a metastable CsC1-type structure near the equiatomic
composition. Nucleation of this metastable phase is suppressed when Zr is
substituted for Ti in the alloys. Apparently, the larger atomic diameter of Zr
limits its solubility in the CsC1-type phase and makes nucleation of this
phase more difficult in the ternary alloys. Masumoto and Inoue [25,26] have
suggested that atomic size differences in multicomponent alloys lead to
efficient packing of atoms in the glassy phase. Recall that the atomic radius
alloy covers a broad range which
of elements in Zr41.2Til3.8Cul2.5Ni10.0Be22.5.
will help in efficient packing. The packing should be further enhanced by
isotropic metallic bonding which is characteristic of these metallic elements.
It should be noted that Be, a crucial element for bulk glass formation, is the
I1

srnailest" atoiil which bonds meta!!iza!!y

in the entire periodic tzble. This in

turn leads to a smaller ground state energy difference between the
amorphous and crystalline phases. This small difference together with the
lowering of the free energy of the liquid due to chemical mixing entropy
effects can be related to the existence of deep eutectic structures such as
found in our alloys. The existence of deep eutectic structures will be
discussed in more detail in chapter 5.
The crystal growth velocity is also an important factor in glass formation.
Eutectic and dendritic crystallization may have substantially low growth
velocities due to extensive solute partitioning [27]. For example, Boettinger
demonstrated that there is a maximum crystal growth velocity for eutectic

crystallization of Pd77.5Czh6Si16.5.This leads to glass formation at higher
solidification velocities [27]. A low crystal growth velocity will be especially
valuable in suppressing the effects of heterogeneous nucleation. When
heterogeneous nucleation sites are dilute enough, the limited crystal growth will
keep the bulk of the undercooled liquid unaffected. A good example of this is
glassy ingots. These samples have
given by Zr41.2Ti13.8Cul2.5Nilo.oBe22.5.
crystalline traces at the bottom surface. Crystallization does not extend to the
ingot interior during cooling. This suggests a limited crystal growth velocity.
This example also shows that there are no active or at least very few
heterogeneous nucleation sites in the bulk of the Zr41,2Til3.8Cul2.5Ni1o.oBe22.5
liquid. Comparing this to bulk glass formation in Pd40Ni40P20 by fluxing, we see
that this alloy is "self fluxing." We have, in fact, found that the liquid
Zr41.2Ti13.8C~12.5Nilo.oBe22.5
alloy can dissolve up to 1%oxygen and still form

bulk glass. It seems that the high oxygen solubility in the liquid results in an
absence of oxide particles in the melt. Such particles would act as a catalyst for
'neterogeneous nucieatioii. "1lnls
' -.-:I1
I- -' '-"..""-A
will vt. U I ~ L U ~ ~ ili
C Umme detail in the next
chapter.

References

[I] A. Peker and W. L. Johnson, Appl. Phys. Lett., 63,2342 (1993).
[2] R. B. Schwarz, Los Alamos National Laboratory (private communication,
October 1993).
[3] L. A. Davis, in Metallic Glasses: Papers Presented at a Seminar of the Materials

Science Division of the A S M in 1976 (American Society for Metals, Ohio, 1978).
[4] H. A. Bruck, T. Christman, A. J. Rosakis, and W. L. Johnson, Script. Met., 30,
429 (1994).
[5] S. Takayama and R. Maddin, Acta. Met. 23,943 (1975).
[6] H. J. Leamy, H. S. Chen, and T. T. Wang, Mett. Trans. 3,699 (1972).
[7] H. A. Bruck, A. J. Rosakis, and W. L. Johnson (private communication, 1993).

[8] B. S. Berry, in Metallic Glasses: Papers Presented at a Seminar of the Materials

Science Division of the A S M in 1976 (American Society for Metals, Ohio, 1978).
[9] Smithells Metals reference Book (edited by E. A. Brandes and E. B. Brook;
Butterworth-Heinemann, Linacre House, Jordan Hill, Oxford) 15-2,15-3
(1992).
[lo] A. Peker, E. Bakke, and W. L. Johnson, (unpublished research, 1993-1994).

[ l l ] H. S. Carslaw and J. C. Jaeger, Conduction ofheat in solids, 2nd ed.
(Clarendon Press, Oxford) p. 59.
[12] C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York,
1986) p. 68,
[I31 R. Hasegawa and L. E. Tanner, J. Appl. Phys 49,1196 (1978).
[I41 H. A. Davies, in Rapidly Quenched Metals TI1 ,B. Cantor (ed.) (Metals Soc.,
London, 1978), Vol. 1, p. 1.
[I51 A. Peker and W. L. Johnson, in Prod. 8th Int. Conf. on Rapidly Quenched Metals,
to appear in Mater. Sci. Eng. (1994).
[I61 D. R. Uhlmann, J. Non-Cryst. Solids, 7,337 (1972).
[17] H. A. Davies, Phys. Chem. Glasses, 17,159 (1976).
[18] P. Ramachandrarao, B. Cantor, and R. W. Cahn, J. Non-Cryst. Solids, 24,109
(1977).
[19] R. A. Grange and J. M. Keifer, Trans. Am. Soc. Metals, 29,85 (1941).
[20] H. W. Kui, A. L. Greer, and D. Turnbull, Appl. Phys. Lett., 45,615 (1984).
[21] H. W. Kui and D. Turnbull, Appl. Phys. Lett., 47,796 (1985).
[22] D. Turnbull, Contemp. Phys., 10,473 (1969).
1231 D. A. Porter and K. E. Easterling, Phase Transformations in Metals and
Alloys (Van Nosttrand Reinhold, England) p. 11.
[24] L. E Tanner and R. Ray, Acta. Metall., 27,1727 (1979).

91
[25] T. Zhang, A. Inoue, and T. Masumoto, Mater. Trans., JIM, 32,1005 (1991).
[26] T. Zhang, A. Inoue, and T. Masumoto, Mater. Lett., JIM, 15,379 (1993).
[27] W. J. Boettinger, in Rapidly Solidifi'ed Amorphous and Crystalline Alloys, B. H.
Kear, B. C. Giessen, and M. Cohen (eds.) (North Holland, 1982),p. 15.

Chapter 4

Heterogeneous nucleation and glass formation

In chapter 2, the theory of homogenous nucleation was presented and used in
accounting for glass formation. However, homogenous nucleation is rarely
realized in practice, as another mode of nucleation, heterogeneous nucleation,
preempts homogenous nucleation. There are two sources of heterogeneous
nucleation: the container and foreign particles (such as oxides). These are hard to
avoid in routine practice of metallurgy, making heterogeneous nucleation very
common. In fact, the theory of homogenous nucleation has very limited

d-nrimer?t2! cQnditionShave
a p p''l l -'-'
c a v l l ~lux
~ ~~~1 ^l ,-sallic
~ e +caaviL. 1- a F n ~ * roacnr.
Luobo, nu
L,.pL1llrr
'A--

---n-*

LIL

lcVV

been achieved such that homogenous nucleation was realized or became
competitive with heterogeneous nucleation.
In this chapter, I will discuss the origins of heterogeneous nucleation and its
pronounced effect on glass formation. First, the theory of heterogeneous
nucleation will be developed in analogy with that of homogenous nucleation.
Then examples of heterogeneous nucleation induced by container walls will be
presented for the bulk glass forming Zr-Ti-Cu-Ni-Be system. Some examples of
metastable interfaces between the Zr-Ti-Cu-Ni-Be bulk glassy alloy and
elemental crystalline phases will also be introduced. Later, the effect of
heterogeneous nucleation induced by foreign particles, mainly oxides, will be

93
discussed in bulk glass formation of several different alloy systems. Finally, I
will present examples demonstrating how thermal stability of metallic glasses is
affected by heterogeneous nucleation.

4.1 Origins of heterogeneous nucleation
The principal resistance of an undercooled liquid to nucleation is related to the
creation of an interface between the crystalline nuclei and liquid. Nucleation can
be enhanced at small undercooling, when this effective interfacial energy is
reduced. This can be effectively achieved by forming crystalline nuclei on the
surface of the container or on foreign particles which exist incidentally (or are
introduced intentionally) in the liquid. The existence of an interface between
liquid and container (or foreign particles) before formation of a crystalline
embryo is the primary cause of heterogeneous nucleation.
Let us consider a crystalline embryo forming on a flat contaii~ersurface or
foreign particle surface as shown in figure 4.1. If we assume the crystal-liquid
interfacial energy y x is
~ isotropic as we did in the classical theory of homogenous
nucleation, it can be shown that the total interfacial energy of the system is
rninimized if the crystalline embryo has the shape of a spherical cap [I]. The
"wetting angle" 8 can be expressed as

where YXL,
YXM, YMLare the interfacial energy (or interfacial tension) between the
crystal and the liquid, the crystal and the container, and the container and the
liquid respectively [I]. This expression is derived from the balance of the
interfacial tensions in the plane of the container (or foreign particle) wall. The
wetting of container wall by the crystalline embryo can be enhanced

substantially if two crystals are lattice matched to each other (not necessarily in
the same crystallographic planes). When their interatomic spacings differ
significantly, a strain energy due to this mismatch will result in a high interfacial
energy thus discouraging good wetting between the crystalline embryo and
container wall [2]. Obviously, the same is true for the case of a foreign particle
instead of the container.
The total Gibbs' free energy change upon formation of a crystalline embryo is
given by [I]

where r is the radius of spherical cap and S(0) is a shape term given by
s(0)= (2 + cos 0)(1- C O S ~ ) ~ / ~
Note that the expression for AGhet is the same as the one obtained for

horn-ogenous nucleation, equation 2.2, except for factor S(0). The S(0) has a
numerical value less than 1 as shown in figure 4.2. The value of S(0) approaches
zero at small values of wetting angle 0; for example, S(0) equals 0.0027 when 0 is
20". The critical radius r" and activation energy for heterogeneous nucleation,
G;,~, can be obtained by differentiation of equation 4.2, and they are given as:

container wa

Figure 4.1: Heterogeneous nucleation of crystalline embryo having a shape of
spherical cap on a flat container (or foreign particle such as oxide) wall.

100

120

140

160

Wetting Angle 0 (Degrees)
Figure 4.2: The value of the expression S(0)= (2 + cos0)(1- c0s0)~/4 as a
function of wetting angle 0.

180

Notice that the critical radius of a crystalline embryo has the same value for
homogenous and heterogeneous nucleation, whereas the activation energy of
nucleation can be substantially smaller for heterogeneous nucleation depending
on the value of 0. This is illustrated in figure 4.3, where the total Gibbs free
energy change of a crystalline embryo is shown as a function of its spherical
radius for homogenous and heterogeneous nucleation. At small values of
wetting angle, 0

- 20°, the activation energy, G * ~decreases
, ~
by three orders of

magnitude.
Then the volume rate of heterogeneous nucleation is given by a similar
expression for homogenous nucleation equation 2.6:

where N,is the number of atoms in contact with heterogeneous nucleation sites
per unit volume of liquid [I].
The heterogeneous nucleation can be further enhanced by the crevices on the
surfaces of container or foreign particle walls. This type of heterogeneous
nucleation can be highly effective even at high values of 0. As an example, a
Let us consider a crack with a
special case will be presented where 7~/4<0<7~/2.
conical shape on the container wall (or foreign particle wall). For simplicity, it
will be assumed that the base angle of the cone has the same value of the
"wetting angle" 0 as shown in figure 4.4. It can be shown that the total Gibbs'
free energy change upon formation of a crystalline embryo at the crack tip is
given by

Figure 4.3: The total Gibbs' free energy change of a crystalline embryo for
heterogeneous and homogenous nucleation as a function of its radius.

Liquid

Container

Crystalline
embryo

Figure 4.4: The formation of a crystalline embryo at the crack tip on a container
wall (left). In this case r',,,,;,

is smaller than r'h,

and the crystalline embryo

can grow out of the crack into the bulk of liquid when the crack has a large
enough opening radius (right). Also shown is the critical radius for homogenous
nucleation, r*ho,.

AGcmck =

xr3 tan 0
AG, + ~ l r ~ ~ ~ ~ ( l - c o t ~ )

where r is the radius of base of cone. Then, the critical radius for stable crystalline
embryo at the crack tip,

is given by
2yxL (tang)-1
tanO ) = y * b r n [

~ * ; m c Ak~v= (

(tan 0) - 1
tan 2 0

From equation 4.7 we can deduce that
'crack

*horn

for values of 0 between 7c/4 and x/2. Thus a stable crystalline embryo with a
smaller radius than ?horn can form at a crack tip. These embryos will grow from
the crack tip to the crack opening. If the crack has a large enough opening radius
(an opening radius of r*homwill suffice), the crystalline embryo can sustain its
growth out of the crack thus starting crystallization into the bulk of liquid (figure
4.4). Otherwise the growth of the crystalline embryo will be limited to the inside
of the crack. Using the general relation

where V* is the critical volume of crystalline embryo [I], we can deduce the
heterogeneous nucleation if the crack tip has significantly smaller activation
energy than heterogeneous nucleation on a flat wall. The above analyses can be
further generalized to show that crevices on the surfaces of a container and
foreign particles may greatly facilitate the heterogeneous nucleation.

4.2 Examples of heterogeneous nucleation in preparation of Zr-Ti-

Cu-Ni-Be bulk glass forming system due to container walls
Figure 4.5 (a) shows an X-ray diffraction pattern taken from the as-cast surface of
a 3.0 mm thick plate of Zr41.2Ti13.8Cu12.5Ni10.~Be22.5
alloy produced by metallic
mold casting. Obviously, there are glassy phases as well as crystalline phases in
the cast sample. The relative amount of crystalline phases changes significantly
depending on the composition of the bulk glass forming alloy and other
parameters involved during processing of the alloy. What is not changing is the
location of the crystalline phases within the samples. In all cases, the crystalline
phases were found to be localized within the top few hundred microns of the
surface layer. Progressively less crystalline phase was observed as one moves
deeper from the sample surface. Figure 4.5 (b) shows the X-ray diffraction
pattern of the same 3.0 mm thick Zr41.2Ti13.8Cu12.5Nilo.oBe22.5
sample after it was
polished to remove the upper 100 microns from the surface. No crystalline
phases are observed within the resolution of X-ray difiraction, i.e., the sample is
completely glassy in the interior. The cooling rate is generally higher at the
surface of the sample as the liquid is in casual contact with the cooling medium
at the surface. Based on the cooling rate considerations, one would expect
crystals to form in the interior of the sample rather than at the surface if only
homogenous nucleation is operational. This example is a vivid illustration of
heterogeneous nucleation due to container walls in the Zr-Ti-Cu-Ni-Be bulk glass
forming system. It seems that the crystals nucleate heterogeneously on the
container walls but cannot grow more than a few hundred microns from the
surface due to a very low crystal growth velocity. Thus, the rest of the liquid, the
interior part, is left unaffected by surface heterogeneous nucleation provided no

Two Theta
Figure 4.5: X-ray diffraction patterns taken from the surface of 3.0 mm thick
Zr41.2Ti13.8C~12.5Ni10.~Be22.5
alloy obtained by metallic mold casting: (a) as-cast

surface and (b) polished surface by 100 microns. Co K a radiation.

other heterogeneous nucleation sites, such as oxide particles, exist in the bulk of
the liquid.
However, one could argue that the polishing may damage the surface and may
result in deformation induced amorphization as observed in some systems [3].
To clarify this point, two more examples will be presented. One way to avoid
damaging the surface of the alloy is by using two different X-ray radiations to
characterize the structure of the sample with respect to the depth from surface.

A harder X-ray radiation can penetrate further into the bulk, thus giving more
sampling of the interior compared to a soft X-ray radiation. This will give us a
non-destructive method to find out the relative amount of crystalline phases at
the surface and away from the surface. For this purpose Mo K a and Cu K a
radiation were used. The linear absorption coefficient of Zr for Mo K a radiation
is 105 cm-1whereas it is 890 cm-1 for Cu K a radiation [4]. Mo K a radiation can
penetrate 8.5 times deeper into a Zr base sample than the Cu K a radiation. For
example, we can calcukite fro= tP[e relation [5]

that the intensity of Mo K a radiation reduces to one-third of its initial value after
passing through a Zr sample of
for Cu K a radiation is

- 100 micron thick. The corresponding thickness

- 12 microns. Thus Mo K a radiation can give us more

sampling from the interior, whereas Cu K a radiation will sample mostly the
volume close to the surface. Since Zr is the best element for this purpose (for the
case of Mo K a and Cu K a radiation) [4], the composition of glass forming alloy is
optimally set to the Zr70Ni7.5Be22.5such that all the other elements (Ti, Cu, and
Ni) are minimized. Be is practically transparent to both radiations [4]. Figure

4.6(a) shows an X-ray diffraction pattern with Mo K a radiation taken from the as
cast surface of a 1.0 mm thick ZryoNi7.5Be22.5 alloy produced by metallic mold
casting. Obviously there are both amorphous and crystalline phases. Figure
4.6 (b) shows the X-ray diffraction pattern with Cu K a radiation taken from
exactly the same region of the same sample. The amount of amorphous phase is
drastically reduced. Again the crystalline phases are observed disproportionally
on the surface. The interior of the sample has more amorphous phase. Figure 4.7
shows the X-ray diffraction pattern with Cu K a radiation taken from the
polished surface of the same sample. Only a trace amount of crystalline phases
are left.
As a last example the glassy ingots produced by melting on water cooled metallic
crucibles (Cu or Ag) are discussed. Figure 4.8 shows X-ray diffraction patterns
taken from the various surfaces of a Zr41.2Til3.gCul2.5Ni10.0Be22.5
ingot. The
ingot weighs about 6 grams and it is approximately 7 mm thick. Shown in figure
4.8 (a) is a typical
X-ray diffraction pattern taken from the bottom surface of the

Zr41.2Ti13.gCu12.5Ni10.0Be22.5
ingot where casual contact with the silver (or

copper) boat occurs. As evidenced by numerous Bragg peaks, the sample is
crystalline on the bottom surface. Figure 4.8 (b) shows another X-ray diffraction
pattern taken from a cross sectional surface of the Zr41.2Ti13.8Cul2.5Ni10.0Be22.5
ingot parallel to the silver boat. The top surface of the ingot gives a similar X-ray
diffraction pattern. The corresponding electron diffraction pattern as well as
dark field and high-resolution TEM images taken from the interior of a similar
ingot were already shown in chapter 3.1. The conclusion is
Zr41.2Til3.gC~12.5Ni10.0Be22.5
ingot is amorphous everywhere except the surface

where it has contact with the container. The crystalline phases form a slight trace
on the bottom of the surface.

Two Theta

50
Two Theta

Figure 4.6: X-ray diffraction patterns with different radiation taken from the ascast surface of 1.0 mm thick Zr70Be22.5Ni7.5 alloy obtained by metallic mold
casting: (a) Mo K a radiation and (b) Cu K a radiation.

Two Theta
Figure 4.7: X-ray diffraction pattern taken from the polished surface (by -100
microns) of a 1.0 mm thick Zr70Be22.5Ni7.5 alloy obtained by metallic mold
casting. Cu K a radiation.

100

Two Theta

60
Two Theta

Figure 4.8: X-ray diffraction patterns taken from various parts of a 6 gram ingot
alloy: (a) Bottom surface where contact with the
of Z~4~.2Ti~3.~Cu~~.~Nil0.0Be22.5
silver boat occurs and (b) cross section surface parallel to the plane of the silver
boat surface. Cu Ka radiation.

Given the above examples, how can one solve the problem of heterogeneous
nucleation due to container walls if one has to use a container? The first try is to
use a container which is not crystalline. When the container is amorphous, we
expect a higher interfacial energy for the amorphous container-crystal interface
than of the amorphous container-liquid interface, i.e., the liquid will wet the
amorphous container better than the crystal. To test this idea we have used a
fused silica tube as a container. The glassy nature of the fused silica also gives a
relatively smoother surface compared to the crystalline surfaces, thus making
heterogeneous nucleation less effective from crevices. The
Zr41.2Ti13.sCu12.5Ni10.0Be22.5
samples were sealed in glass tubes under an inert

atmosphere. After the samples were melted, the glass tube was plunged into the
water and stirred until solidification was complete. The outcome was superb.
No crystalline phases were observed in any part of the sample. A typical X-ray
diffraction pattern of this sample is shown in figure 3.3. The wetting angle
between the fused silica and glassy Zr41.2Til3.8Cu12.5Nilo.oBe22.5
alloy was
deterrlined to be less tf-lan290.

113 TJ C
nI
r-r

L L Langle
~ g evidences a Very ~ Q W

TAT
V v TV%TO++;

interfacial energy between the liquid Zr41,2Til3.sCul2.5Ni10.0Be22.
and
5 fused
silica as predicted. In fact, the glassy Zr41.2Tis3.sCu12.5Ni10.~Be22.5
alloy and
fused silica glass container made an extremely strong bond (as strong as the base
glassy alloy) evidencing good wetting. This is a profound observation when we
consider the extremely brittle behavior of fused silica. This strong bond could be
utilized by employing silica as a reinforcing and weight reduction material in the
metallic glass alloys.
Another approach to the solve surface nucleation problem is to use a container
made out of a crystalline phase which can form a metastable interface with a
molten glass forming alloy. For example, the growing amorphous phase and

crystalline elemental phases form metastable interfaces in the solid state
amorphization of Ni-Zr diffusion couples [6,7]. Further, it is found that the
equilibrium intermetallic phases almost invariably nucleate on the Zr side of the
growing amorphous phase, i.e., the interface of amorphous phase and crystalline
Ni seems less likely to induce nucleation [7]. Recently, our experiments reveal
that similar metastable interfaces can be formed between the liquid
Zr41.2Ti13.8Cu12.5Ni10.oBe22.5and crystalline Ti and Zr [B]. Though our work is

still in progress, we have promising results showing that Ti and Zr can be used
as containers in processing of Zr-Ti-Ni-Cu-Be metallic glasses. The preparation
and characterization of these metastable interfaces are described in the following
paragraphs.
The ingot of elemental Zr (or Ti) and previously prepared ingot of
Zr41.2Til3.gCu12.5Ni10.0Be22.5
alloy were put on a water cooled copper boat under

a Ti-gettered inert atmosphere. Initially they were separated at a distance so that
each of them can be melted separately. First, the ingot of Zr (or Ti) was melted to
dissolve any surface oxide so that a clean metallic surface can be exposed. After
the ingot of Zr was cooled, the ingot of Zr41.2Til3.8Cul2.5Nilo.oBe22.5alloy was
melted and driven onto the cold Zr ingot. This formed a strong bond between
the elemental Zr and the frozen alloy. (When the joined metal piece was torn
apart, the Zr failed before the interface.) The molten alloy was further frozen to
the glass as evidenced by a highly reflective surface and the lack of recalescence.
The glassy nature of the amorphous ingot was further confirmed by TEM and Xray analyses. The interface between elemental Zr and glassy alloy was analyzed
by a Philips EM 430 300 -keV transmission electron microscope with high
resolution and analytical capabilities. Figure 4.9 shows a high resolution TEM
image of this interface. As evidenced by the existence of lattice fringes on one

side and lack of lattice fringes on the other side, there are obviously both a glassy
phase and a crystalline phase (which belongs to the elemental Zr) separated by
an atomically sharp interface. The EDAX analyses (Energy Dispersive X-ray
Spectroscopy) showed that there is no chemical mixing on the elemental Zr-side
of the interface. The electron diffraction further confirmed the glassy nature of
the Zr41.2Til3.gCul2.5Ni10.0Be22.5alloy side of the interface and the nature of the
equilibrium crystalline phase of elemental Zr. No other crystalline intermetallic
phases were observed along the interface separating the original elemental Zr
from the amorphous alloy. Since the amorphous alloy was solidified from the
melt at a relatively low cooling rate, we can conclude that the interface with
elemental Zr is not a favorable site for hetoregeneous nucleation of crystalline
intermetallic phases from the undercooled alloy melt! The undercooled liquid is
in metastable equilibrium with crystalline Zr along the interface.
Figure 4.10 shows a dark field TEM image of the interface of the glassy
Zr41.2Ti13.gCu12.5Ni1o.oBe22.5alloy and crystalline elemental Ti prepared with

the same method described above. The electron diffraction confirmed the glassy
nature of the Zr41.2Til3.gCul2.5Ni1o.oBe22.5
alloy side of the interface. Further, the
EDAX analyses detected no chemical mixing on the crystalline elemental Ti-side
of the interface. Thus, the glassy phase and crystalline elemental Ti are separated
by a sharp boundary and no nucleated intermetallic phase has been observed
from the interface. Similarly, Zr41.2Til3.gCul2.5Ni10.0Be22.5
molten alloy can also
form a metastable interface with elemental Ti.
If we have to use a crystalline container, removing the crevices on container walls
should be very useful to prevent heterogeneous nucleation. Crevices are very
effective in inducing heterogeneous nucleation even at high values of wetting

Figure 4.9: The high resolution transmission electron image of metastable
interface of Zr$l.2Til3.8Czi12.5Ni10.oBe22.5glassy alloy with elemental Zr. Glassy
alloy is on the left side.

Figure 4.10: The darkfield TEM image of metastable interface of
Zr41.2Til3.8Cz~12.5Ni1o.oBe22.5
glassy alloy with elemental Ti. Glassy alloy is on

the left side.

angle between the crystalline embryo and container. Recently, Schwarz used an
electropolished copper hearth as a water cooled metallic crucible to prepare
glassy Zr41.2Til3.8Cul2.5Ni10.0Be22.5
ingots by plasma arc melting [9]. The
electropolishing removes all the asperities and crevices on the copper hearth
making an almost atomically smooth surface. According to the experiments of
Schwarz, no crystalline phases were observed on the surface of these plasma
melted amorphous ingots, which weigh as much as 200 grams [9].

4.3 Heterogeneous nucleation from foreign particles and its effect

on bulk glass formation
We have seen in chapter 2 that the metallic alloys having a reduced glass

transition temperature, TTg 2/3 (where Tm, the melting point, can be taken as
the solidus temperature in the case of a general alloy), should exhibit very low
rates of homogenous nucleation and should be bulk glass formers as suggested
by Turnbull [lo]. However, prior to 1982, no metallic glass could be made with a
thickness of more than a few mm, although there were known metallic alloys
having TTg=0.66, such as Pd40Ni40P20 and Nb40Ni60 several years earlier [Ill.
The main obstacle was believed to be heterogeneous nucleation due to container
walls and foreign particles such as oxides. In the early eighties, Turnbull and his
co-workers used fluxing to prevent heterogeneous nucleation in Pd40Ni40P20
melts and obtained the largest bulk metallic glass samples at that time using
cooling rates of -1-2 K/s [12]. By contrast, no glassy alloy of Nb40Ni60 thicker
than one mm has yet been obtained.
alloy, which we have discovered recently, also
The Zr41.2Ti13.gCu12.5Ni10.~Be22.5
has TTg=0.67 and bulk pieces of this alloy readily undercool to glass unlike any

other glass forming alloy. Although the alloys, Zr41.2Ti13.gCul2.5Ni1o.oBe22.5
Pd40Ni40P20 and Nb40Ni60, have almost the same TTg,their bulk glass forming
ability shows drastic differences. For example, the Zr41.2Til3.gCul2.5Ni10.oBe22.5
alloy is prone to surface heterogeneous nucleation due to container walls,
whereas no sign of any significant crystallization has been observed in its
interior. The Pd40Ni40P20alloy needs a careful and delicate fluxing treatment for
bulk glass formation. Otherwise, its glass forming ability is very limited. For the
time being we do not know whether or not we can find a similar fluxing
treatment for Nb40Ni60. These differences can be accounted for by heterogeneous
crystal nucleation induced by crystalline debris incidentally existing in the bulk
of the liquid. These crystalline debris can be various types of refractory particles;
oxides are possibly the most common form of them. It seems that the flux used
in the Pd40Ni40P20 experiment, B 2 0 3 which is also a glass, can dissolve the oxide
particles thus eliminating heterogeneous nucleation and giving rise to bulk glass
formation.
Since no flux has been used in production of Zr41.2Ti13.gCu12.5Ni1o.oBe22.5bulk
glasses, there should be another mechanism to eliminate the heterogeneous
nucleation sites in the bulk of the liquid. This can be achieved if liquid reacts
with incidentally existing crystalline debris, such as oxides, and dissolves them
without detrimentally effecting its bulk glass forming ability. We can examine
this by intentionally introducing crystalline debris into the liquid such as by
bulk
slight oxidization. To test this proposition, Zr41,2Ti13.8Cu12.5Nilo.oBe22.5
glassy ingots were oxidized in a controlled atmosphere of oxygen by heating to
the melting point of the crystalline alloy on a water cooled copper boat with a
levitation melting system. Upon subsequent cooling, recalescence was observed
evidencing crystallization. The alloy was visibly oxidized and exhibited a rough

surface with a dark color rather than a smooth and reflecting surface unique to
the glassy phase. The oxidizing atmosphere was then replaced with a clean inert
atmosphere as in the routine preparation of glassy ingots. In the next few
heating and cooling cycles (from ambient temperature to the melting point), the
alloy crystallized on cooling. This could be easily detected by the final surface
luster and recalescence during cooling. Solid particles, most probably oxides,
were also observed floating on the surface of the liquid. After keeping the alloy
above the melting point for a few minutes, it was observed that these oxide
particles gradually dissolved. Following the dissolution of the oxide debris, the
alloy again froze to glass upon subsequent cooling. We have found that liquid
samples as large as 9 grams can dissolve up to 1atom percent oxygen (as
detected by weight measurements) and still form glass on a water cooled metallic
crucible as easily as non-oxidized samples, provided that all solid oxide debris is
dissolved in the melt before cooling.
It can be said that Zr and Ti have the distinguishing property of forming
crystalline solid solutions with oxygen content up to 30 atom percent. This large
oxygen solubility [13] may eliminate the oxide formation which creates the sites
for heterogeneous nucleation. We believe that what is significant is not the
oxygen solubility in solid solutions, but rather oxygen solubility in undercooled
liquid! The maximum oxygen solubility in undercooled liquid Zr can be
estimated from the metastable liquidus line of ZrO in the Zr-0 phase diagram

[13]. The metastable liquidus line can be constructed by extending the
thermodynamic liquidus line of ZvO in the direction of less oxygen in the Zr-0
phase diagram. This also approximately gives the equilibrium and metastable
liquidus line of ZvO in a Zr- base alloy which has a very depressed melting point

. This is illustrated in figure 4.11. The
such as Zr41.2Ti13.gCu12.5Ni10.~Be22.5

Zrl-~4(

Atom percent Oxygen

ZrO,

Figure 4.11: Construction of metastable liquidus line of ZrO2 in a Zr alloy. "A"
corresponds to an alloying element(s) which depresses the liquidus line of Zr
base crystalline solid solutions.

metastable liquidus line suggests a maximum oxygen content of -10 atom
percent at 350 "C and -20 atom percent at 1100 "C in the undercooled liquid Zr or
Zr base alloy. (The additional alloying elements may have detrimental effects on
the oxygen solubility in the liquid Zr-base alloy, thus overestimating the
maximum oxygen content.) The oxide, ZrO, starts to precipitate from the melt at
higher oxygen content. These oxide precipitates will serve as heterogeneous
nucleation sites for further crystallization.
Let us consider the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5
alloy which has a glass
transition temperature, Tg = 350 "C. When this alloy was kept above its melting
point for a certain time in a reasonably clean atmosphere, all the incidentally
existing oxygen should be dissolved in the liquid. As we cool down the liquid,
no oxides should precipitate down to the glass transition temperature provided
the oxygen content is low enough. Upon further cooling, the undercooled liquid
configurationally freezes to glass below the glass transition temperature, 350 "C.
As the metastable iiquidus line of ZrG suggests, t t ~ eammint of oxygen that can
be dissolved in the undercooled liquid Zr41.2Ti13.sCu12.5Ni1~.~Be22.5
down to 350

"C is significantly larger than the amount of oxygen incidentally existing in an
alloy which is prepared in a reasonably clean atmosphere. This is also
demonstrated by the experiment presented above. When all the incidentally
existing oxides are dissolved in the liquid and the precipitation of oxides is
hindered thermodynamicaly at lower temperatures, there will not be any
heterogeneous nucleation sites, thus making bulk glass formation much easier.
We have found that the Zr-Ti-Cu-Ni-Be system has an exceptionally large bulk
glass forming range [14]. Further, the bulk glass forming alloys are extremely
forgiving to impurities in the constituent raw elements [15]. In fact, a substantial

amounts of elements other than Zr, Ti, Cu, Ni and Be can be added to this system
without damaging the bulk glass formation 1141. All of these observations
suggest that the Zr-Ti-Cu-Ni-Be bulk glass forming alloy will tend to react with
any crystalline debris incidentally existing in the liquid state provided necessary
time and temperature are provided. The dissolving of the crystalline debris will
not affect the bulk glass formation as the alloy system has a large bulk glass
formation range including elements other than its constituents.
In the case of Nb40Ni60 and Pd40Ni40P20, the maximum solubility of oxygen in
the undercooled liquid should be extremely low. This can be shown from the
phase diagrams of Ni-0 and Nb-0 [12]. The liquidus lines of NbO and NiO
exhibit a shallow depression with lowering oxygen content, i.e., the oxygen
content of the liquidus lines of oxides of Nb and Ni decreases very rapidly with
respect to temperature. We can roughly construct the metastable liquidus lines
for these systems as described above. The case of Nb-A-0 has been illustrated in
figure 4.12, where A stands for an element depressing the liquidus line of a Nb
alloy (such as Ni). As seen in figure 4.12, the metastable liquidus line of NbO
reaches -0.0 percent oxygen content at temperatures

- 1000 "C. At higher

temperatures the Nb-base liquid has some increasing solubility of oxygen with
increasing temperature (e.g., a few percent at 1300 " C). The case of Ni also shows
very similar behavior. For liquid alloys having an oxygen content > 0, oxides
will precipitate at lower temperatures (below 1000 "C), whereas all the oxygen
can be dissolved in the liquid at high temperatures. This is possibly the cause of
heterogeneous nucleation in Nb40Ni60 and Pd40Ni40P20 alloys. The liquid alloys
can pick up and dissolve some small amount of oxygen at high temperatures
employed in the alloy preparation (or its constituent elements). However,
crystalline oxides will precipitate in the undercooled liquid thus inducing

Nbl-x Ax

Atom percent oxygen

NbO

Figure 4.12: Construction of metastable liquidus line of NbO in a Nb alloy. "A"
corresponds to an alloying elementts) which depresses the liquidus line of P\Tb
base crystalline solid solutions.

heterogeneous nucleation sites even at the very small oxygen concentrations
suggested by the phase diagrams.
We can further elaborate our discussion to account for the success of fluxing in
Pd40Ni40P20bulk glass formation and for predicting whether or not we can have

similar success for Nb40Ni60.It was found that the equilibrium crystalline
compounds of Nb40Ni60 can dissolve a significant amounts of oxygen such as r\
phase, NbsoNisoO, (W3Fe3C type) [16]. Thus the oxygen (or oxide particles) will
be dissolved in crystalline compounds upon crystallization of Nb40Ni60.As the
liquid state can also dissolve a significant amount of oxygen above the melting
point, the fluxing medium will not have any chance to dissolve any oxide
particles and will not be effective. Alternatively, the oxygen (oxide particles)
should not be dissolved by crystalline compounds for fluxing techniques to be
effective. It seems that the oxides of Pd40Ni40P20precipitate and stay separate
from the equilibrium compounds. This will allow the oxide particles to be
dissoived by the fluxirig medium (Bz03) allowing bulk glass famation.
Finally, I would like to point out that the Zr41.2Til3,gCul2.5Ni10.0Be22.5
alloy is
ideally suited for containerless undercooling experiments in view of the
experimental observations presented in the last two sections of this chapter. That
is, there are no effective heterogeneous nucleation sites in the interior of the
molten alloy. Further, surface nucleation is caused by container walls. The
earlier undercooling experiments in undercooled metallic melts were severely
limited by heterogeneous nucleation and high critical cooling rates for glass
formation. In our experiments the critical cooling rate of
Zr41.2Ti13.gCu12.5Ni10.0Be22.5was estimated to be less than 5 K/s. This number

has been estimated for the conditions where effective heterogeneous nucleation

sites, such as container walls, exist. We believe that the critical cooling rate of
this system may be several orders of magnitude less when the condition of
homogenous nucleation is achieved. This extremely low cooling rate for glass
formation is good enough for any conceived undercooling experiment to cover
the whole temperature range from the glass transition to the melting point. This
allows us to perform a true test of the homogenous nucleation theory in the high
undercooling regime of this alloy in a containerless experiment, such as in the
TEMPUS facility in the Space Shuttle. For example, undercooling of 3 mm
diameter liquid balls of Zr41.2Til3.8Cul2.5Ni1o.oBe22.5alloy down to the glass
transition has recently been realized in containerless undercooling experiments
made possible by the high vacuum electrostatic levitation unit at the Jet
Propulsion Laboratory [16]. In the experiments, the sample cools only by
radiation. The estimated cooling rates are about 5 K/s.

4.4 Heterogeneous nucleation and thermal stability of metallic

glasses
We have seen in the previous chapter that the TTT diagrams suggest a higher
thermal stability above glass transition for metallic glasses requiring lower
cooling rates provided there exists a single mode of crystallization at all
temperatures. In practice, this may not be achieved as different crystallization
modes may become effective at high temperatures (around melting point) and
low temperature (around glass transition). For example, there is a significant
difference between observed thermal stability of glassy
Zr41.2Ti13,gCu12.5Ni10.~Be22.5
alloy above the glass transition and the predicted

thermal stability from the TTT diagram (which is constructed according to the
observed critical cooling rate). This was attributed to a more effective nucleation

of crystals induced by oxidation of glassy alloy around the glass transition
temperature. However, it was just demonstrated that there is a significant
oxygen solubility in undercooled liquid Zr41.2Ti13.8Cu12.5Nilo.oBe22.5
,and this
plays an important role in its bulk glass formation by melt quenching through
elimination of heterogeneous nucleation from oxide particles. These two
apparently conflicting observations can be explained easily when we consider the
temperature dependence of the diffusion of oxygen into the bulk of the
undercooled liquid. Recall that it takes some time to dissolve the oxide particles
at the melting point in the oxidation experiment presented above. When we
alloy from the melt, it is always sealed in
quench the Zr41.2Til3.8Cu12.5Ni10.0Be22.5
a closed container under a reasonably clean inert atmosphere. Since the liquid
can dissolve all the incidentally existing oxygen (not more than a few ppm) in a
reasonably short time, the diffusion of oxygen at the melting temperature is
expected to be relatively fast. Meanwhile, the DSC (Differential Scanning
Calorimetry) and other annealing experiments suggest that the
~ ~ 4 1 ~ 2 ~ ~ 1 3 ~ 8 ~ i i 1 2 ~ 5 ~ J ig!a3sy
iOOOa
~!!o~y2 ' Elas
Z . 5Exited diff*;sion of Gxygefi at lQw

temperatures (around the glass transition). For example, we have observed that
an oxide layer grows on Zr41.2Til3.8Cu12.5Ni10.0Be22.5
glassy samples above
400 "C during our thermal analyses which is carried under a nominally pure
flowing argon atmosphere. As the glassy alloy has no means to dissolve this
oxide layer (unless heated to the elevated temperatures), this growing oxide layer
may induce nucleation of crystals. Such oxidation can be suppressed by fluxing
the sample surface with a layer of borosilicate-glass or encapsulation in a thin
alloy (-40 mg)
glass ampoule. A small sample of Zr41.2Til3.8Cul2.5Ni10.0Be22.5
was sealed in borosilicate-glass tube and heated. Since borosilicate glass softens
alloy, the
around the melting temperature of Zr41.2Til3.8Cul2.5Ni10.0Be22.5

680

700

720

740

760

780

Temperature (K)

Figure 4.13: DSC scans of two Zr41.2Ti13.8Cu12.5Nilo.oBe22.5glassy alloys at a
heating rate of 20 K/min. The dashed curve corresponds to a plain glassy
sample whereas the solid curve is for a glassy sample sealed in a borosilicateglass ball.

sample can be completely covered with a thin shell of glass. The molten sample
was then water quenched resulting in a glassy sample sealed in a borosilicateglass ball. When this is done, surface oxidation is suppressed and contact with
the aluminum DSC pan is prevented. The crystallization peaks of the amorphous
alloy as observed by DSC shift to significantly higher temperatures under these
conditions. Figure 4.13 shows DSC scans of two Zr41.2Ti13.8Cu12.5Ni10.0Be22.5
glassy alloy samples at a heating rate of 20 K/min. One of the samples is sealed
in a borosilicate-glass ball as described above, and the other is a plain glassy
sample used in routine thermal analyses experiments. Obviously, the sealed
glassy sample crystallizes at temperatures 20-30 "C higher than the plain glassy
sample. However, this sealing technique has limitations at higher temperatures
as the borosilicate-glass layer cracks due to thermal expansion and
accompanying thermal stresses.

The mechanism of nucleation of crystals induced by oxidation requires further

expianation. 1 here is increasing e~periniei~ta:
evideilce which mggcsts that the
nucleation of crystals may occur as a result of a composition shift at the surface
driven by selective oxidation. This is not the same as the heterogeneous
nucleation described in the beginning of this chapter in which the nucleation of
crystals is eased by the reduced effective interfacial energy rather than by a
composition shift in undercooled liquid. For example, the study of the surface of
alloy by XPS (X-ray photoemission
the glassy Z~41.~Ti~3.8Cul~.5Ni10.0Be~2.5
spectroscopy) technique has shown that the surface oxide contains only elements
of Zr, Ti, Be. As the oxide layer grows, other elements, Ni and Cu, are expelled
into the interior from surface oxide layer [18]. Zr, Ti and Be have high negative
free energy for the formation of oxides [19]. It seems that the growing oxide

layer cannot accommodate any elements with low negative free energy of oxide
formation. Quite possibly, there exists a quaternary oxide of Zr-Ti-Be-0 with a
still higher negative free energy for formation as suggested by the Ti-Be-0
system [20]. This will further encourage the rejection of Ni and Cu from the
oxide layer. The depletion of Ni and Cu in the surface layer (and Ni and Cu
enrichment in the layer beneath the oxide surface) will drive this region out of
the good glass forming range. Then the nucleation of crystals may occur much
more easily in these compositionally altered regions. Crystallization may occur
either homogeneously or heterogeneously (provided the growing oxide layer is
crystalline).
Schneider et al. also observed that the growing native oxide layer on
Zr55Ni25Al20 glassy alloys does not contain Ni [21].The oxide of the glassy alloy

contains only Zr and A1 which have comparable heat of formation of oxides
(both much higher than Ni). Their observations further suggest that the oxide
growth is in fact limited by the uphill diffusion of Ni into the amorphous matrix.
As the growing oxide was found to be amorphous in the early stages, they
proposed that the crystallization of the glassy alloy is started by an unfavorable
glass forming composition shift beneath the oxide layer.
This type of crystallization was previously observed in other systems such as in
glassy FegoZvlo alloys [22]. Selective oxidation of Zr occurs as it has a high
affinity for oxygen. Then a Zr depleted region forms locally at the surface of
glassy ribbons which results in crystallization of a-Fe at temperatures much
lower than otherwise required for primary crystallization.
The effect of oxidation on thermal stability of glassy alloys depends on the
temperature at which the oxidation starts. If oxidation starts below the glass

transition temperature, its detrimental effect on the thermal stability of the glassy
alloy can be quite significant. As different elements in the glassy alloy will have
different affinities for oxygen, we expect a strong temperature dependence of
oxidation on composition. For example, Altonian eta1 observed that severe
oxidation of Zr50Cu50 starts around 500 "C in DSC experiments 1231. In fact, they
observed that this oxidation starts after crystallization of the glassy alloy. In this
case the thermal stability of Zr5oCu5o glassy alloy is least affected by oxidation as
the glass transition of this alloy is around 400 "C. When we introduce another
element which has a higher oxygen affinity to these glassy alloys, the thermal
stability of the new glassy alloy may change unfavorably even though it may
become a better glass former. To illustrate this, I will give three good glass
forming alloys as examples. Their compositions, estimated critical cooling rates
Tc, reduced glass transition temperatures Trp and thermal stabilities above glass
transition as quantified by AT = T,-Tg are given table 4.1. The corresponding
DSC scans of the glassy alloys are also shown in figure 4.14. The replacement of
Zr by Ti effectively reduces the critical cooiing rate for glass formation. Biir
previous analyses of the TTT diagrams suggest that the thermal stability of
glassy alloy should favorably increase in parallel with the lower critical cooling
rate provided the same mode of crystallization remains effective from the glass
transition temperature to the melting point. The initial increase in thermal
stability of glassy alloys with Ti addition is in good agreement with this
prediction. However, the further replacement of Zr by Ti deteriorates the
thermal stability of glass alloys while it still lowers the critical cooling rate. The
(Zro.65Tio.3s)55Cu7.5Nilo.oBe27.5
glassy alloy has a critical cooling rate at least two
orders of magnitude less than the Zr55Cu7.5Nilo.oBe27.5 glassy alloy, though it
has a relatively poor thermal stability above glass transition. These observations

can be explained by oxidation above the glass transition as seen in the thermal
stability of Zr41.2Til3.8Cul2.sNi10.0Be22.5metallic glass. It seems that Ti has a
higher affinity for oxygen than that of Zr at lower temperatures, i.e., around the
glass transition temperature. This will result in oxidation of
(Zrl-,TiX)55Cu7.5Nil0.oBe27.5
glassy alloy at lower temperatures, when the Ti

concentration is high enough to govern the oxidation of the glassy alloy. This
oxidation may induce crystallization by heterogenous nucleation on forming
oxide or by the selective oxidation mechanism described above. All these
observations suggest that the thermal stability and glass forming ability of glassy
alloys cannot generally be correlated from our routine DSC experiments.

Table 4.1: Various properties of three highly processable metallic glasses.

Alloy composition

- 0.60

- 110 K - 500 K/s

(Zr0.85Ti~.15)55Ni10Cu7.5Be27.5

- 125K - 50K/s

(Zr0.65Ti0.35)55Ni10Cu7.5Be27.5

- 0.67

Zr55Nil~Cu7.5Be27.5

-70K

-5K/s

300

350

400

450

500

550

Temperature ("C)

Figure 4.14: DSC scans of three bulk glassy alloys at a heating rate of 20 K/min.

References

[I] D. A Porter and K. E. Easterling, Phase Transformations in Metals and Alloys
(Van Nostrand Reinhold International, England, 1981), Chap. 4.
[2] W. Kurz and D. J. Fisher, Fundamentals ofSolidification (Trans Tech
Publications, Switzerland, 1986),Chap. 2.
[3] Phil Ashkenazy, Ph.D. Thesis, California Institute of Technology (1992).
[4] B. D. Cullity, Elements of X-Ray Difiaction, 2nd ed. (Addison- Wesley
Publishing Company, Inc., 1978),p. 512-513.
[5] B. D. Cullity, Elements of X-Ray Difiaction, 2nd ed. (Addison- Wesley

Publishing Company, Inc., i978), p. 13.

[6] W. L. Johnson, Mat. Sci. Engg, 97,l (1988).
[7] W. L. Johnson, Prog. Mater. Sci., 30,81 (1986).
[8] A. Peker, C. Garland, and W. L. Johnson, unpublished research (1993-1994).
[9] R. B. Schwarz, Los Alamos National Laboratory (private communication,
October 1993).
[lo] D. Turnbull, Contemp. Phys., 10,473 (1969).

[ l l ] H. A. Davies, in Rapidly Quenched Metals III, B. Cantor (ed.) (Metals Soc.,
London, 1978), Vol. 1, p. 1.
[I21 H. W. Kui, A. L. Greer, and D. Turnbull, Appl. Phys. Lett., 45,615 (1984).
[13] T. B. Massalski, Binary Alloy Phase Diagrams (American Society of Metals,
Metals Park, OH, 1986).
[14] A. Peker and W. L. Johnson, U.S. Patent No. 5,288,344, assigned to California
Institute of Technology (Feb. 1994).
[15] A. Peker and W. L. Johnson, unpublished research (1993).
[16] D. E. Polk, C. E. Dube, and B. C. Giessen, in Rapidly Quenched Metals III, B.
Cantor (ed.) (Metals Soc., London, 1978),Vol. 1, p. 220.
[17] Y. Kim, W. Q. Rim, and W. L. Johnson, Jet Propulsion Laboratory and
California Institute of Technology (private communication, February 1994).
1181 M. LaMadrid, A. Peker, R. Houseley, and W. L. Johnson, unpublished
research (1993-1994).
[19] F. S. Galasso, Structure and Properties of Inorganic Solids (Pergamon Press Inc.,
New York, 1970).
1201 B. C. Giessen, J. C. Barrick, and L. E. Tanner, Mat. Sci. Engg, 38,211 (1979).
[21] S. Schneider, X. Sun, M.-A. Nicolet, and W. L. Johnson, California Institute of
Technology (private communication, January 1994).

[22] U. Koster and U. Schunemann, in Rapidly Solidified Alloys: Processes,
Structures, Properties, Applications, H. H. Liebermann (ed.) (Marcel Dekker
Inc., New York, 1993).
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Chapter 5

Conclusion: How to find bulk metallic glasses

Crystallization from the liquid state involves two processes: nucleation and
growth of crystalline nuclei. Obviously, glass will form easily when there is no
detectable nucleation of crystals as the liquid cools from its thermodynamic
freezing point to the glass transition. Slow crystal growth kinetics will also result
in glass formation in the case that crystals nucleate, provided that nucleation is
not copious. (Slow crystal growth velocities are especially favored when
heterogeneous nucleation is effective.) As such, bulk glass forming systems
should have slow kinetics for either nucleation or crystal growth, compared to
conventional metallic glass forming alloys. To design bulk glass forming
systems, we must then determine the thermodynamic parameters governing the
kinetics of nucleation and crystal growth and their critical values required for
slow kinetics. This was the subject of chapter 2, and here it will be revisited
briefly. Accordingly, we can use this knowledge in engineering (or explaining)
bulk glass forming systems.
First consider the kinetics of homogenous nucleation. The rate of homogenous
nucleation is given by [I]

Here, the atomic mobility is assumed to be inversely proportional to viscosity.
Metallic liquids have viscosity values typically 0.01 -10 poise around the melting
point. This corresponds to adequately high atomic mobility for nucleation of
crystals provided the thermal activation barrier is small. However, the
homogenous nucleation rate is generally too small to detect at low undercooling
(AT, < 0.2) for metallic systems. This is due to the fact that AG,2 JYXL
is very

small and positive definitejust below T, the thermodynamic melting point. On
the other hand, the liquid is assumed to be frozen (i.e., no atomic mobility) just
below glass transition where the viscosity is assumed to be 1013 poise. Thus, no
homogenous nucleation is expected below the glass transition temperature. The
viscosity therefore becomes the governing factor for the homogenous nucleation
rate at large values of undercooling. As the rate of homogenous nucleation is
inversely proportional to the viscosity, a steeply rising viscosity from the melting
point down to the glass transition will give rise to a suppressed homogenous
nucleation rate. A narrower region between the melting point and glass
transition will yield a relative* more steeply rising viscesity fron?. the meltinc.
point downward for a given form of viscosity-temperature relation. Turnbull
quantified this by introducing the reduced glass transition temperature [Z].
Assuming a Fulcher type viscosity-temperature relation, he showed that the
homogenous nucleation rate becomes too small to detect, thus allowing bulk
glass formation, when reduced glass transition TT approaches 0.67. It should be
kept in mind that these numbers strongly depend on the assumed functional
form of viscosity with respect to the temperature (or undercooling). However, a
higher reduced glass transition temperature is always favorable for lower
homogenous nucleation rates, whatever the functional form of viscosity.

The crystal growth velocity is also inversely related to viscosity. The
corresponding equation for partitionless growth is given by [1,3]

Other types of crystal growth velocities (eutectic and dendritic) should have a
similar dependence on viscosity. Again, a high reduced glass transition
temperature (a steeply rising viscosity from the melting point) is favorable for
better glass formation.
The glass transition temperature has generally been found to be slowly varying
with composition. Thus, deep eutectic systems are invariably associated with a
high reduced glass transition temperature and in turn with good glass formation.
Deep eutectic systems possess other benefits for glass formation besides high
reduced glass transition. For example, relatively large values of viscosity and
relatively low values of the entropy of fusion have been found in deep eutectic

sy-stenis around the melting paint (possibly due t~ ordering of licpld). These will
favor better glass formation through low nucleation rates and low crystal growth
velocities as suggested by equations 5.1 and 5.2. In addition to these, the eutectic
type of growth itself may favor glass formation substantially since its kinetics are
much slower compared to other growth types (e.g., partionless growth).
Boettinger, for instance, has demonstrated that there is a maximum crystal
growth velocity for eutectic crystallization of Pd77.5Cu6Si16.5 [4]. This results in
glass formation at higher solidification velocities. Again, his analysis for glass
formation requires a high reduced glass transition temperature. Near deep
eutectics, the proximity of glass transition results in a drastic decrease of the
diffusion coefficient which in turn gives an upper bound for the eutectic growth

rate into the viscous liquid. This analysis predicts an extended range of glass
formation at a given cooling rate around the eutectic composition, unlike the
Davies-Uhlmann kinetic analysis.
Thus, the first condition for bulk glass formation can be summarized as deep
eutectic systems where "deep eutectic" is quantified by reduced glass transition

temperature TW I will take Trg 0.67 as a necessary condition for bulk glass
formation (requiring a critical cooling rate of 1-10 K/s) as it is in good agreement
with the earlier and recently found bulk glass formers. For thick glass formation
(requiring a critical cooling rate of 100-1000 K/s), a corresponding value of T,.8
0.60 seems to be supported by experimental data. Table 5.1 lists some glass
forming alloys with their reduced glass transition temperatures and critical
cooling rates.

Table 5.1: Some bulk and thick glass forming alloy compositions, their reduced
glass transition temperature Trg,and critical cooling rates Tc.

The second criteria for bulk glass formation will be taken as avoidance of
heterogeneous nucleation sites introduced through "impurity phases." As we
have seen in chapter 4, heterogeneous nucleation can be a devastating factor for
glass formation even at high values of reduced glass transition temperature. A
relatively small crystal growth velocity may lessen this effect. Unfortunately, the
kinetics of homogenous nucleation rates usually correlate with those of crystal
growth rate, thus still making the heterogeneous nucleation effective at high
reduced glass transition temperatures and near eutectic systems (i.e., at relatively
small crystal growth velocities). Thus more effective measures of suppressing
heterogenous nuclation are required. Two previously described methods are
fluxing and utilizing melt chemistry to dissolve the impurity phases. The latter
can be incorporated into alloy design along with the first criteria (high reduced
glass transition temperature). As the liquid states of Zr-base and Ti-base alloys
have relatively high reactivity for dissolving impurity phases, they offer a better
opportunity to avoid heterogeneous nucleation sites in the bulk of liquid
compared to the other alloy systems. The former technique, fluxing, can be
practiced after an alloy which satisfies the first criteria of bulk glass formation is
found. Obviously, our tools to suppress the heterogeneous nucleation are
relatively new and more work is needed in this area.
We need to know the glass transition temperature and melting point of an alloy
to decide its potential to form bulk glass. The glass transition temperature of
metallic alloys tends to increase with alloying though its dependence on
composition and alloying elements is relatively weak compared to the liquidus
temperature of the alloy. We can obtain a rough estimate for the glass transition
temperature of a new alloy based on our knowledge of currently known metallic

glasses. For example, we expect a glass transition temperature of 350 "C-400 "C
for Zr-base metallic glasses, 700 "C - 750 "C for Ta-base metallic glasses, etc. [9].
From these numbers, we can estimate the required melting point of these alloys
to have a T,g -0.67. As the melting point of metallic systems can change
drastically with alloying, knowledge of liquidus temperature becomes a highly
desirable thermodynamic parameter for estimating the glass forming ability.
If we knew all the thermodynamic phase diagrams of binary, ternary,
quaternary, pentiary and higher order systems, we could locate abnormally deep
eutectics which would be potentially good bulk glass formers. We already have
satisfactory knowledge of thermodynamic phase diagrams for binary systems for
the purpose of glass formation, and almost all promising binary glass formers
have been worked out throughout the first 30 years of metallic glass research.
However, most of the known good metallic glass formers have turned out to be
ternary or higher order systems. Obviously, we have to look for good glass
formation in ternary and higher order systems. Unfortunately, our knowledge is
rather limited concerning phase diagrams of ternary systems, and almost non
existent on higher order systems. For the time being, the wide availability of
experimental ternary and higher order phase diagrams is far from complete. It
will take thousands of years to experimentally determine all ternary phase
diagrams at our current tempo. Quite possibly, a very selective approach for
ternary and quaternary phase diagram determination will pay off in the long
run, though this will not be available in the near future. As phase diagram
calculations and computer modeling are in early stages, this will not be a good
option in the near future. A rigorous ternary phase diagram calculation is still
considered to be a formidable task. Further, extensive experimental data will be
needed as input for a good phase diagram calculation.

As we are deprived of all rigorous techniques to determine higher order deep
eutectic systems in the near future, we have to devise more simple approaches
which will be useful in locating deep eutectics in ternary and higher order
systems. Massalski et al. proposed an experimental method coupled with
analytical techniques to determine the eutectic composition (if it exists) in a
limited range of a given system [lo]. However, this method has its limitations
and will not be practical without some guidelines which suggest possible eutectic
compositions.
One proven method is to start with a binary alloy which already has a deep
eutectic and make these eutectics deeper by alloying. Hard work, intuition and
some luck are necessary, as this technique requires trial and error. A first
approach to alloying is to prepare combinations of these deep eutectic binary
alloys. The currently known good metallic glass formers are combinations of two
or more deep eutectic binary alloys such as Pd-Ni-P, Mg-Cu-Y, and Zr-Ti-Ni-CuBe good glass forming systems.
A more systematic approach would be to search for suitable eutectic systems
such that the elements of one eutectic system will suppress the stability of the
crystalline phases of the other eutectic system. Usually, elements with different
atomic radius have proven useful as in the cases of recently found exceptionally
good glass forming Zr-Cu-Ni-A1 and Zr-Ti-Ni-Cu-Be-X systems (X stands for all
other elements in periodic table and can be a significant part of the alloy content).
Here, this approach will be exercised in the example of Zr-Ti-Ni-Cu-Be bulk glass
forming system.

Figures 5.1,5.2,5.3, and 5.5 show the binary phase diagrams of Ti-Ni, Zr-Cu, ZrNi, and Ti-Cu [ll]. These systems show generally similar features with low lying
eutectics over the central portions of the phase diagrams. The existence of
intermetallic compounds, which are usually size compounds (Laves phases),
prevent the binary systems from exhibiting much deeper eutectic features.
Figures 5.4 and 5.6 show the hypothetical phase diagrams of Zr-Ni and Ti-Cu, in
which the intermetallic compounds are assumed to be non-existent. Obviously,
the hypothetical eutectics are much deeper than existing in the real binary
systems and would be easy bulk glass formers. Our objective is to attain these
hypothetical phase diagrams by the help of additional alloying elements
Figures 5.7 and 5.8 show the binary phase diagrams of Zr-Be and Ti-Be systems
[ll]. The Zr-Be and Ti-Be systems differ from the above binary systems in that
crystalline intermetallic phases are confined to the Be-rich portion of the phase
diagram. For example, in Zr-Be shown in figure 5.7, the most Zr-rich crystalline
intermetaliic is ZrBe2, a Laves phase which forms peritectica!l.y. at 1508 K. This is
separated from the Zr-base terminal solutions by a broad and deep eutectic
feature with a eutectic temperature of 1238 K at 35 at. % Be.
The essential motivation in developing bulk glass forming alloys is to find the
deepest eutectic features obtainable in the pseudo-ternary phase diagrams. The
absence of Zr-rich (Ti-rich)phases in the Zr-Be and Ti-Be systems provides a key.
It suggests, for instance, that Be will have limited solubility in crystalline binary
phases such as Zr2Cu, ZrCu, Zr2Ni, and ZrNi, since analogous phases are absent
in the Zr-Be system. As further support for this conjecture, the metallic radius of
Be is substantially smaller than that of Cu and Ni (RB,= 0.112 nm, while
Rc,=0.128 nm, and R~izO.124nm), and much smaller than that of Zr, Rz,=0.160

Atomic Percent Ti

Figure 5.1: Phase Diagram of the Ti-Ni system. Reproduced from ref. 11.

Atomic Percent Zr

Figure 5.2: Phase Diagram of the Zr-Cu system. Reproduced from ref. 11.

Atomic Percent Z r

Figure 5.3: Phase Diagram of the Zr-Ni system. Reproduced from ref. 11.

Liquid

Atomic Percent Z r

Figure 5.4: Hypothetical phase diagram of the Zr-Ni system.

Liquid

Atomic Percent Cu

Figure 5.5: Phase Diagram of the Ti-Cu system. Reproduced from ref. 11.

Liquid

Atomic Percent Cu

Figure 5.6: Hypothetical phase diagram of the Ti-Cu system.

Lquid

Atomic Percent Z r

Figure 5.7: Phase Diagram of the Zr-Be system. Reproduced from ref. 11.

Lquid

Atomic Percent Be

Figure 5.8: Phase Diagram of the Ti-Be system. Reproduced from ref. 11.

nm) [12]. In compounds such as Zr2Ni (A12Cu-type),substitution of Be on the Nisite in the crystal should be accompanied by substantial lattice strain. This in
turn should reduce the stability of the compound as Be is substituted in the form
Zr2(Nil-xBex). A similar argument applies to crystalline compound
Zr(Nil-xBex). Such compounds should have limited solubility for Be. In the
absence of a new ternary Zr-rich Zr-Ni-Be phase, one would expect to find a
ternary eutectic feature in the Zr-rich portion of the ternary diagram. This
eutectic should lie at Be concentrations exceeding the solubility limits of the
above crystalline phases. Further, this ternary eutectic should lie lower at
temperature than the binary eutectics or the corresponding liquidus features in
the binary Zr-Cu and Zr-Ni systems. Such a deep eutectic region in fact exists in
the ternary and pseudo-ternary phase diagrams. For example, high temperature
DSC scans of the melting curves of several ternary Zr-Cu-Be alloys are shown in
figure 5.9. The alloys have compositions varying over a substantial region of the
Zr-rich part of the ternary diagram. All four alloys have a solidus temperature of
about Ts .= 1070 K while the liquidus curves vary from 1080 to 1125 K. These
temperatures lie well below the corresponding binary eutectic temperatures in
the Zr-Be Diagram (eutectic at 35 at. O/O Be with T,= 1238 K), or the Zr-Cu system
(eutectics at 28 and 46 at. % Cu with T,= 1273 K, and 1201 K respectively). In
higher order alloys, this broad region of low lying solidus and liquidus features
becomes even more pronounced. Figure 3.10 shows the high temperature DSC
scan of the melting transition for the pentiary alloy Zr41.2Ti13.gCu12.5Ni10Be22.5.
Here, Ts= 937 K while TI .= 985 K. This pseudo-ternary alloy exhibits an
exceedingly low melting region. In this region, one finds Trg .= 0.67.

Figure 5.9: High temperature DSC scans of the melting endotherms for a series of
ternary Zr-Cu-Be alloys.

The Zr-Ti-Ni-Cu-Be alloys of interest here can best be viewed as pseudo-ternary
alloys of the type (Zr-Ti)l-x-y(Ni,Cu)xBey,or more generally as:

where ETM is an early transition metal (e.g. Ti, Zr, Nb, V, etc.) and LTM is a late
transition metal (e.g., Cu, Ni, Co, Fe) [13-151. Figure 5.10 shows the region where
bulk glass forming alloys were found. An extremely large region of this pseudoternary system was found to exhibit glass formation at cooling rates as low as

1K/s. Obviously Be is a very effective alloying element to improve bulk glass
formation. We have not yet found such an effective alloying element to improve
glass formation. Thus, there should be something unique with Be!
Figure 5.11 shows a plot of metallic radii of selected elements (most common
elements in metallic glass research). Obviously, Be stands out with its metallic
radius. This may explain the unique effectiveness of Be for bulk glass formation
in (ET~)~-~-y(LTivijxBey
systern. Be is i-isitELersmall enmgh to fit into interstitial
sites nor big enough for substitutional solutions without causing substantial
strain energy in crystalline phases. The unique size of Be makes crystalline
solution phases highly unstable due to strain energy, whereas liquid can sustain
larger atomic size differences. This small atom will also increase the packing
efficiency and the entropy of mixing of the liquid state. By contrast, Be cannot be
replaced by other metalloid atoms (e.g., B, C, Si) which form strong covalent
bonds. Such covalent bonding results in highly refractory and easy nucleating
crystalline compounds. Figures 5.12,5.13,5.14, and 5.15 show the binary phase
diagrams of Zr-Si, Ti-C, Ti-B, and Zr-B [Ill.

LTM (Cu, Ni, Co, Fe)

ETM
Hf, Ti,Nb)

Figure 5.10: Schematic ternary phase diagram showing the region in which bulk
glass forming alloys were found in ETM-LTM-Be alloys.

Figure 5.11: Metallic radii of selected elements. The data is taken from ref. 12.

2250

220020001800h

ru 1600-

- 1414

1370

I-

1460

4 0 0 - e

1200-

., r r 3

-J-

Grn
.L

6Zr---.

1000--si

863
800uZr600

iS ~1
v ~ ~1
t t It I~ I ~1
n ~
t ~1
l 1
~ t I~ l am
s ~~
* ~~s t ~ ~ s
~ nI 1
~ ~ S~
1 1 1 1 I t ~ I I I I 1 1 1 1 1 1 1 I I I I I I I I I II I~ II I~ II I ZI ~1I 1

Atomic Percent Z r

100

Figure 5.12: Phase Diagram of the Zr-Si system. Reproduced from ref. 11.

Atomic Percent C

Figure 5.13: Phase Diagram of the Ti-C system. Reproduced from ref. 11.

C-

Liquid

Atomic Percent B

Figure 5.14: Phase Diagram of the Ti-B system. Reproduced from ref. 11.

Atomic Percent Z r

Figure 5.15: Phase Diagram of the Zr-B system. Reproduced from ref. 11.

We can increase the reduced glass transition temperature T,X to the limit of 0.67
by increasing the glass transition temperature and/or reducing the melting point
of the alloy. Pure metals have Trgmuch smaller than 0.5 and most of the deep
eutectic binary alloys have T,h, from 0.5 to 0.6. In earlier research aimed at
developing metallic glasses, attention was devoted to the reduction in melting
point through alloying, as the glass transition temperature was found to be
slowly changing with composition. However, increasing of Trgrby increasing Tg,
should not be overlooked as an efficient method. To increase Trg from 0.6 to 0.65,
the reduction of melting point should be 1.6 times the increase in glass transition
temperature. An increase of glass transition temperature by 40-50 "C can be very
critical as it becomes harder to increase T, after it reaches a value of 0.60.
As a final comment, I include the following quotations from two currently
known experts in the field of materials science 1161.

D. DeFontaine: I would like to raise a point regarding the size of the task ahead of us if

we are to meet the needs of the industrial world. Tfwe take 80 elements as being
important, there are 3,000 possible binary systems. In the last 50 years, it appears on the
average that we have completed work on one binary per week. There are approximately
50,000 ternaries. Assuming conservatively that at the same tempo of work it takesfive

times as long to complete a study on a ternary system as it does on a binary, it would be
possible to complete ten a year. This takes us forward 5,000 years. If we go to quaternary
systems and assume that by that time our techniques have advanced suficiently so that
we can do a complete quaternary system in about the same time it now takes us to do a
ternary system, it would appear that an additional 100,000 years would be required.
This overly simplified statement brings out the enormity of the task before us. It seems

to me that we must ask ourselves what are the realistic goals and where do we stop. We
must be honest with the industrialists and say that we never really are going to be able to
develop all the information that is needed in the next hundred thousand years.

J. F. Elliot: I feel that the question is highly pertinent. One of the answers is that we
must be highly selective as to the systems on which we work because of limitations of
funding and of the available manpower. It seems to me that the latter is the more
important constraint. We must also be aware that there are limits to the patience of those
who ultimately must pay the bills --the public. We must provide the industrial researcher
with background information to assist him to get started in his work even though he may
have to develop detailed information on the system that is of immediate interest to him.

References

[I] D. R. Uhlmann, in Materials Science Research, Vol. 4 (Plenum, New York,
1969).
[2] D. Turnbull, Contemp. Phys., 10,473 (1969).
[3] D. Turnbull, J. Chem. Phys., 66,609 (1962).

[4] W. J. Boettinger, in Rapidly Solidified Amorphous and Crystalline Alloys, B. H.
Kear, B. C. Giessen, and M. Cohen (eds.) (North Holland, 1982), p. 15.
[5] A. Peker and W. L. Johnson, Appl. Phys. Lett., 63,2342 (1993).
[6] H. TAJ. Ktli, A. L. Greerl and D. Turnbull, Am1.
,.
Phys. Lett., 45,615 (1984).

[7] T. Zhang, A. Inoue, and T. Masumoto, Mater. Trans., JIM, 32,1005 (1991).
[8] This thesis.
[9] A. Peker and W. L. Johnson, unpublished research (1991).
[lo] T. B. Massalski, Y. W. Kim, L. F. Vassamillet and R. W. Hopper, Mat. Sci.
Engg, 47, K1 (1981).
[Ill T. B. Massalski, Binary Alloy Phase Diagrams (ASM International, Metals Park,
OH, 1990).

1121L. Pauling, Theory ofAlloy Phases (American Society for Metals, Metals Park,
OH, 1956).
[13] A. Peker and W. L. Johnson, U.S. Patent No. 5,288,344, assigned to California
Institute of Technology (Feb. 1994).
[14] A. Peker and W. L. Johnson, U.S. Patent application (April 1994).
[15] W. L. Johnson and A. Peker, to appear in Science and Technology of Rapid
Solidification Processing Technologies, NATO AS1 Series, M. A. Otooni (ed.),
(West Point, June 1994).
[16] In Applications of Phase Diagrams in Metallurgy and Ceramics, G. C. Carter (ed.),

NBS Special Publication 496, p. 1373.

APPENDIX I

The bulk glass forming Zr-Ti-Cu-Ni-Be alloys can be viewed as pseudo-ternary
alloys of the type

where x and Y are atomic fractions and a, b and c are atomic percentages [I-31.
Generally, a is in the range of from 30 to 75%, b is in the range of from 2 to 6O%, c
is in the range of 2 to 52%, and x and Y are in the range of from 0 to 1for good
glass formation by rapid quenching technique (T-104-106 K/s). Table A. 1 lists
glassy alloys of this type obtained by rapid quenching (T-104-106 K/s). Thick
glass formation (T-102-103 K/s) is generally observed when a is in the range of
from 38 to 72%, b is in the range of from 5 to 52%, c is in the rar;ge of 5 to 42%
and x and Y are in the range of from 0 to 1. Table A. 2 lists glassy alloys prepared
in the form of 1.0 mm thick strips. Bulk glass formation (T-1-10 K/s) is
generally observed when a is in the range of from 42 to 68%,b is in the range of
from 10 to 45%, c is in the range of 12 to 35%, and x is in the range of from 0.15 to
0.65. Table A. 3 lists glassy alloys prepared in the form of at least 5.0 mm thick
ingots. The molten alloys listed in table A. 3 usually freeze to glassy ingots on a
water cooled copper (or silver) boat under a clean inert atmosphere. When the
value of (by) --which gives the Ni content in atom percent-- is in the range of
from 5 to 15%,the largest ranges of a, b, c and x are obtained for bulk glass
formation. Figure A.l shows glass formation at two different cooling rates

(T -10 K/s and T -500 K/s) for (Zro.7sTio.25)100-b-c(Cul-yNiy)bBec
alloy system,
where Ni content (the value of by) is from 5 to 15 atom percent. Table A.4 lists
glassy alloys. Listed are
thermal properties of 1.0 mm thick ZrlOO-b-cCubNi~~Bec
the onset glass transition temperature Tg, the onset crystallization temperature
Tx, and supercooled liquid region AT, which is defined as AT = Tx.-Tg.
The (Zrl-xTix)lOO-b-c(Cul-yNiy)b(Be)c
glass forming alloy system can also
accommodate substantial amount of other elements without damaging its glass
forming ability. Generally, this alloy system can comprise any transition metal
from 0 to 30 atom percent, metalloids from 0 to 10 atom percent, any metal from
lanthanides and actinides from 0 to 15 atom percent, and a few atom percent of
any other element (including Oxygen) for thick and bulk glass formation. For
example, the Zr-Ti moiety can contain additional metals selected from the group
of from 0 to 20 atom percent Nb, from 0 to 20 atom percent V, from 0 to 15 atom
percent Y , from 0 to 10 atom percent Cr, and up to 10 atom percent of any other
early transition metal for thick glass formtion (T-102-103 K/s). When Zr-Ti
moiety contains additional metals selected from the group of from 0 to 10 atom
percent Nb, from 0 to 10 atom percent V, from 0 to 5 atom percent Y , from 0 to 5
atom percent Cr, and up to 5 atom percent of any other early transition metal,
bulk glass formation at cooling rates as low as 10 K/s can still be obtained. Zr
can be completely replaced by Hf in any of these alloys without damaging the
glass forming ability. Further, the Cu-Ni moiety can contain additional metals
selected from the group of from 0 to 25 atom percent Co, from 0 to 15 atom
percent Fe, from 0 to 10 atom percent Mn and up to 10 atom percent of any other
late transition metal for thick glass formation (T-102-103 K/s). When Cu-Ni
moiety contains additional metals selected from the group of from 0 to 15 atom

percent Co, from 0 to 10 atom percent Fe, and up to 5 atom percent of any other
transition metal, bulk glass formation at cooling rates as low as 10 K/s can still be
obtained.
When other transition metals are included, the (Zrl-xTix)100-b-~(Cu1-yNiy)b(Be)~
system can be generalized to

where ETM is a combination of early transition metals (e.g. Zr, Hf, Ti, Nb, V, Cr,
etc.) and LTM is a combination of late transition metals (e.g. Cu, Ni, Co, Fe etc.).
Generally, the values of a, b, and c are still valid as described above for glass
formation at different cooling rates. Table A. 5, A.6, and A.7 list alloys of
E T M ~ ~ O - ~ - ~ Ltype
T Mprepared
~ B ~ ~ at different cooling rates. Listed in table A. 8
are glassy alloys of Zr-Ti-Ni-Cu-Be-M prepared in the form of 1.0 mm strips,
where M stands for a metalloid atom (Si, B, Al).
It should be noted that the above boundaries are only approximate$ givert. A
variation of glass forming ability is observed slightly inside and/or outside of the
these given boundaries. Also, the given cooling rates, T,are approximately
estimated cooling rates effective in the preparation of glassy alloys and they are
not necessarily the critical cooling rates, T,, for glass formation.

TABLE A.l: Readily glass forming (?< 104-106 K/s) Zr-Ti-Ni-Cu-Be alloys.

TABLE A.2: Thick glass forming (?< 102-103 K/s) Zr-Ti-Ni-Cu-Be alloys.

TABLE A.3: Bulk glass forming (T<10 K/s) Zr-Ti-Ni-Cu-Be alloys.

Figure A.l: Glass forming range for (Zro.75Tio.25)100-b-c(Cul-~Niy)bBec
alloys for
two different cooling rates. Ni content (the value of by)is from 5 to 15 atom
percent.

TABLE A.4: Thermal properties of ZrlOO-b-cCubNil~Becglassy alloys prepared in
the form of 1.0 mm strips.
Composition

Tg("c)

&("c)

AT("C)

TABLE A.5: Bulk glass forming ( T < 10 K/s) ETM-LTM-Be type alloys.

TABLE A.6: Thick glass forming (?< 102-103K/s) ETM-LTM-Be type alloys.

1 ABLE A.7: Readily glass forniring ( T < 104-106 K/s) ETM-LTM-Be type alloys,

7 . -

TABLE A.8: Thick glass forming ( ~102-103
K/s) Zr-Ti-Ni-Cu-Be-M type alloys.

References

[I] A. Peker and W. L. Johnson, U.S. Patent No. 5,288,344, assigned to California
Institute of Technology (Feb. 1994).
[ 2 ] A. Peker and W. L. Johnson, U.S. Patent application (April 1994).
[3]W. L. Johnson and A. Peker, to appear in Science and Technology of Rapid

Solidification Processing Technologies, NATO AS1 Seuies, M. A. Otooni (ed,),
(West Point, June 1994).