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Shock-wave processing of powder mixtures
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Krueger, Barry Robert
(1991)
Shock-wave processing of powder mixtures.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/f01e-9k60.
Abstract
The effects of shock waves on the initiation of exothermic chemical reactions in mixtures of powders is explored experimentally and compared to thermal initiation at atmospheric pressure in this thesis. A full understanding of shock initiated chemical reactions and shock compaction of composites requires knowledge of the Hugoniot of the mixture. A model for calculation of the shock Hugoniot of non-reacting solid or powder mixtures up to moderate pressures using only thermodynamic properties of the components is presented. In addition, conditions for the production of dense, bulk samples of a metallic glass from the metastable powder are determined.
Previous models for the Hugoniot of a mixture assume the components in the shock front are in mutual thermal equilibrium, and use measured or calculated Hugoniot data for the components. The model proposed in this thesis does not presuppose either the relative magnitude of the thermal and elastic energies or temperature equilibrium between the components. It assumes the components are at equal pressures and have equal particle velocities. For a mixture, it is shown that the conservation equations define a Hugoniot surface, and that the ratio of the thermal energy of the components determines where on that surface the shocked state of the mixture lies. This ratio, which may strongly affect shock initiated chemical reactions and the properties of consolidated mixtures, is found to have only a minor effect on the Hugoniot. It is also found that the Hugoniots of solids and solid mixtures are sensitive to the pressure derivative of the isentropic bulk modulii of the components at constant entropy.
The initiation of the reaction forming the compound NiSi from elemental powders by shock waves of varying energy and pressure and by thermal initiation at atmospheric pressure was investigated. Using plane wave shock geometry with well-defined shock pressure and energy, it was determined that a sharp energy threshold, between 384 and 396 J/g, exists for the initiation of the reaction (with 20 µm to 45 µm Ni and -325 mesh Si). The threshold energy range heats the powder mixture to a temperature between 631 and 648° C (with no chemical reaction) after local thermal equilibration is achieved. The reaction goes to completion when the shock energy is above the threshold energy, and melting of the compound is indicated. Differential thermal analyses (DTA) of powder mixtures of Ni and Si (1:1 atomic ratio) at atmospheric pressure show the reaction starts at a temperature which depends upon the porosity of the mixture. Higher porosities give higher initiation temperatures. Reaction starts at about 900° C in a mixture with 50% porosity and at about 650° C in a sample statically pressed to 23% porosity. The sharp energy threshold for the initiation of the reaction, and the correlation with the shock temperature and the reaction initiation temperature in the DTA indicates that the homogeneous temperature determines whether or not the reaction occurs rather than local particle conditions of temperature or pressure as has been proposed in the literature.
The conditions for initiation and propagation of the reaction forming Ti5Si3 from elemental powders (5:3 atomic ratio) of varying porosity have been investigated using shock waves of different pressure in vacuum, and using hot wire ignition in an argon atmosphere. In powders with a high initial porosity, evacuated to 0.1 torr, a low energy regime (producing low shock pressures) triggers the reaction in the presence of residual oxygen while no reaction is observed with a 128% higher shock energy and a lower initial porosity (producing a higher shock pressure) in an inert residual gas. Hot wire ignition of porous powder at room temperature initiates a self-propagating high temperature reaction (SHS) in air or (less readily) in an Ar atmosphere, while the Ni/Si powder must be heated to allow the reaction to propagate in high or low porosity mixtures. These observations are compared to published work on self-sustaining reactions in multilayer films.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Shock-waves ; powder mixtures
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Vreeland, Thad
Thesis Committee:
Unknown, Unknown
Defense Date:
6 May 1991
Record Number:
CaltechETD:etd-06222007-081112
Persistent URL:
DOI:
10.7907/f01e-9k60
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No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
2689
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CaltechTHESIS
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16 Apr 2021 22:28
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SHOCK-WAVE PROCESSING OF
POW'DER MIXTURES
Thesis by
Barry Robert Krueger
In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
Advisor: Prof. Thad Vreeland, Jr.
California Institute of Technology
Pasadena California
1991
(Submitted May 6, 1991)
ii
In Memory of Barry Robert Krueger
July 19,1965 -October 29, 1990
Dedicated to his family Reinhold, Evelyn, Linda, and Rita Krueger
and to Anita Harper
iii
ACKNOWLEDGEMENTS
The assistance of Barry's friend and office-mate, Andrew H. Mutz, in
developing the facilities used in this research and in the compilation of this thesis is
gratefully acknowledged.
Zezhong Fu generously assisted in the running of the
differential thermal analyses.
Barry was a promising scientist and a valued friend who made many positive
contributions to the Caltech community.
His colleagues and the many under-
graduates who came to know him fondly remember the exuberant way he lived his
life.
Thad Vreeland, Jr.
Professor of Materials Science
Caltech, April1991
iv
TABLr~ OF CONTENTS
Dedication .......................................................................................................... ii
Acknowledgements ............................................................................................. iii
Abstract .............................................................................................................. vi
1. INTRODUCTION .......................................................................................... 1
REFERENCES .......................................................................................... 5
2. CALCULATION OF THE SHOCK HUGONIOT FOR MIXTURES ............... 6
2.1 "A Hugoniot Theory for Solid and Powder Mixtures,"
by Barry R. Krueger and Thad Vreeland, Jr., published
in the Journal of Applied Physics, January 1991. ............................ 6
3. SHOCK INITIATION OF THE REACTION FORMING NiSi ...................... 33
3.1 "Shock Initiated Chemical Reactions in 1:1 Atomic Percent
Ni/Si Powder Mixtures," by B. Krueger and T. Vreeland, Jr.,
to appear in the Proceedings of the International Conference
on High-Strain-Rate Phenomena in Materials, UCSD
(Explomet '90, in Press) ............................................................... 33
3.2 "Correlation of Shock Initiated and Thermally Initiated
Chemical Reactions in a 1:1 Atomic Ratio Nickel-Silicon
Mixture," by Barry R. Krueger, Andrew H. Mutz, and Thad
Vreeland, Jr., submitted to the Journal of Applied Physics,
March 1991 ................,.................................................................. 44
4 . SHOCK INITIATION OF THE REACTION FORMING Ti 5Sis ................... 68
4.1 "Shock Induced Reactions in 5:3 Atomic Ratio
Titanium/ Crystalline Silicon Powder Mixtures,"
by B. R. Krueger, A. H. Mutz and T. Vreeland, Jr.,
submitted to Metallurgical Transactions, A, March 1991. .............. 68
5. SHOCK CONSOLIDATION OF A METALLIC GLASS ................................. 79
5.1
"Shock Wave Consolidation of a Ni-Cr-Si B Metallic Glass," by J.
Bach, B. R. Krueger and B. F. Fultz, Materials Lett.,
(1991, in press) ............................................................................. 79
ABSTRACT
The effects of shock waves on the initiation of exothermic chemical reactions
in mixtures of powders is explored experimentally and compared to thermal
initiation at atmospheric pressure in this thesis.
A full understanding of
shock-initiated chemical reactions and shock compaction of composites requires
knowledge of the Hugoniot of the mixture.
A model for calculation of the shock
Hugoniot of non-reacting solid or powder mixtures up to moderate pressures using
only thermodynamic properties of the components is presented.
In addition,
conditions for the production of dense, bulk samples of a metallic glass from the
metastable powder are determined.
Previous models for the Hugoniot of a mixture assume the components in the
shock front are in mutual thermal equilibrium, and use measured or calculated
Hugoniot data for the components..
The model proposed in this thesis does not
presuppose either the relative magnitude of the thermal and elastic energies or
temperature equilibrium between the components. It assumes the components are
at equal pressures and have equal particle velocities.
For a mixture, it is shown
that the conservation equations define a Hugoniot surface, and that the ratio of the
thermal energy of the components determines where on that surface the shocked
state of the mixture lies.
This ratio, which may strongly affect shock-initiated
chemical reactions and the properties of consolidated mixtures, is found to have only
a minor effect on the Hugoniot. It is also found that the Hugoniots of solids and
solid mixtures are sensitive to the pressure derivative of the isentropic bulk modulii
of the components at constant entropy.
The initiation of the reaction forming the compound NiSi from elemental
powders by shock waves of varying energy and pressure and by thermal initiation at
m~
atmospheric pressure was investigated.
Using plane wave shock geometry with
well-defined shock pressure and energy, it was determined that a sharp energy
threshold, between 384 and 396 J / g, exists for the initiation of the reaction (with 20
J.fJI1 to 45 J.fJI1 Ni and -325 mesh Si). The threshold energy range heats the powder
mixture to a temperature between 631 and 648° C (with no chemical reaction) after
local thermal equilibration is achieved. The reaction goes to completion when the
shock energy is above the threshold energy, and melting of the compound is
indicated.
Differential thermal analyses (DT A) of powder mixtures of Ni and Si
(1:1 atomic ratio) at atmospheric pressure show the reaction starts at a temperature
which depends upon the porosity of the mixture.
initiation temperatures.
Higher porosities give higher
Reaction starts at about 900° C in a mixture with 50%
porosity and at about 650° C in a sample statically pressed to 23% porosity. The
sharp energy threshold for the initiation of the reaction, and the correlation with the
shock temperature and the reaction initiation temperature in the DT A indicates
that the homogeneous temperature determines whether or not the reaction occurs
rather than local particle conditions of temperature or pressure as has been proposed
in the literature.
The conditions for initiation and propagation of the reaction forming Ti 5Si 3
from elemental powders (5:3 atomic ratio) of varying porosity have been
investigated using shock waves of different pressure in vacuum, and using hot wire
ignition in an argon atmosphere. In powders with a high initial porosity, evacuated
to 0.1 torr, a low energy regime (producing low shock pressures) triggers the
reaction in the presence of residual oxygen while no reaction is observed with a
128% higher shock energy and a lower initial porosity (producing a higher shock
pressure) in an inert residual gas.
Hot wire ignition of porous powder at room
temperature initiates a self-propagating high temperature reaction (SHS) in air or
viii
(less readily) in an Ar atmosphere, while the Ni/Si powder must be heated to allow
the reaction to propagate in high or low porosity mixtures. These observations are
compared to published work on self-sustaining reactions in multilayer films.
1. INTRODUCTION
The isentropic compressibility in most materials decreases with increasing
pressure. Then the velocity of propagation of acoustical disturbances increases with
pressure. A pressure wave whose profile is not constant will therefore steepen as
higher pressure components overtake the low pressure components at the beginning
of the wave. A narrow shock transition region is reached across which there is a
jump in the pressure profile and the width of this region, the shock front, is on the
order of the atomic spacing in solids, the mean-free-path in gasses, and the particle
size in powders.
The theory of the formation and propagation of shock waves is
covered in several comprehensive texts.[1,2]
Shock-induced chemistry in solids was explored as early as 1920 in an
attempt to synthesize diamond.[3] :Explosive loading of graphite produced the first
successful synthesis of diamond in the early 60's.[4] Early experiments on chemical
reactions in solids initiated by shock wave loading were conducted in the 50's and
60's,[5] and continued in Russia in the 70's and 80's.[6,7] An assessment of work on
chemical synthesis in metallic and inorganic substances under high pressure shock
loading was given by R. A. Graham et al., in which examples of shock-enhanced
solid state reactivity
are given.[8]
R.
A.
Graham has
attributed the
shock-enhancement to what he has termed "catastrophic shock" conditions as
opposed to "benign" conditions of temperature and pressure increase associated with
the shock.[9]
The "catastrophic" shock conditions include: a) the breaking of
chemical bonds, b) the formation of activated complexes, c) mass mixing, and d)
introduction of crystal defects such as vacancies which accelerate processes such as
atomic diffusion.
This thesis presents the results of research on shock wave processing of
metallic materials under controlled plane-wave shock conditions.
Changes in
particle velocity, internal energy, and pressure across a steady-state plane shock
front are obtained from the equations of conservation of mass, momentum and
energy (the Rankine-Hugoniot equations). The set of shock states that a medium
can reach across a single shock wave, from a known initial state, is obtained from
knowledge of the material properties in the form of pressure vs. specific volume,
pressure vs. particle velocity, or shock velocity vs. particle velocity (Hugoniots of
the
medium).
experimentally.[lO]
Hugoniots
of a number of solids
have been obtained
Theoretical models have been developed for obtaining
Hugoniots of solid mixtures from Hugoniots of their components by McQueen,[ll]
and by use of a thermodynamically consistent procedure, based on the Gibbs free
energy by Duvall and Taylor.[l2]
Both of these models assume temperature
equilibration of the mixture components occurs in the shock front. This assumption
is not accurate, as recognized by Duval and Taylor, but it introduces little error in a
solid as opposed to a powder mixture because in the shocked solid the elastic energy
is larger than the thermal energy.
The opposite is true in a shocked powder in
which the pressure is sufficient to reduce the porosity significantly. Chapter 1 of
this thesis presents a model from which the Hugoniot of solid or porous
two-component mixtures can be calculated (up to moderate pressures) from
thermodynamic properties of the components.
The model treats non-reacting
mixtures and does not presuppose either the relative magnitude of the thermal and
elastic energies or temperature equilibrium between the two components.
Shock initiated chemical reactions may have strong effects on the
Rankine-Hugoniot relationships and cause changes in the Hugoniot as well. These
result from the additional source (or sink) of chemical energy, from volume changes
between reactants and products, and from changes in thermodynamic properties. In
order to account for these effects on the shock parameters, the rate of reaction as·
well as the property changes must be known. The rate of reaction is typically an
exponential
function
of temperature.
Surface
temperatures
in
shocked,
non-reacting powders have been measured, and it is found that: a) the temperature
rises during passage of the shock front in a time very nearly equal to the time for
the shock wave to travel one particle diameter (i.e., the shock rise time which is a
few tens of nanoseconds for typical powders of about 50 Ji.ID diameter), b) the
surface temperature of the particles reaches a maximum (limited by the melting
point of the powder material) at the end of the shock rise time and then decreases as
heat flows to cooler particle interiors, and c) the temperature reached after thermal
equilibration of the particles (the homogeneous temperature) correlates well with
heating by essentially all of the shock energy calculated from the Rankine-Hugoniot
relations.[ll] Surface melting plays an important role in helping to bond particles
together, and the rapid cooling (rates up to 10
10
degrees C/s) are sufficient to retain
properties which are metastable at the homogeneous temperature or to form
metastable properties from the shock-formed melt.
Quantitative data on the rate of shock induced chemical reactions in solid
materials is not available, but a large body of data has been obtained in a number of
systems for thermally induced reactions at atmospheric pressure.
"Explosive"
reactions (which propagate rapidly with the emission of light) have been observed
upon heating of alternating elemental thin films which have a large negative heat of
mixing.[12]
These reactions generally involve melting of one of the layers which
removes the diffusion barriers formed by solid state reactions at the layer interfaces.
Solid state reactions have been extensively studied using differential thermal
analyses, and the nature and extent of compounds formed have been observed using
high resolution electron microscopy in some systems.
Self-propagating high temperature synthesis of compounds from elemental
powders (SHS) has been explored for making ceramic materials at atmospheric
pressure.[13]
These reactions are thermally initiated locally, and propagate
through the powder at rates typically on the order of a centimeterfs.
Shock
initiated reactions in powders differ from SHS and more conventional thermally
initiated reactions in that they are initiated under high pressure and the initiation
takes place throughout the powder in the time taken by the shock wave to traverse
the sample.
Chapter 2 of this thesis presents studies of the formation of the intermetallic
compound NiSi from the elemental powders.
The uniform shock conditions,
produced by the impact of a stainless steel flyer plate with the powder mixture held
in a cylindrical steel cavity, permitted determination of the shock energy required to
initiate the reaction. The initiation behavior was compared to thermal initiation at
atmospheric pressure.
Chapter 3 of this thesis presents studies of the reaction forming Ti 5Si 3 from
the elemental powders. The heat of mixing for this reaction is approximately seven
times greater than that for the reaction forming NiSi, while the melting temperature
for the compound is 2130° C (vs. 992° C for NiSi). The thermal conductivity of Ti
is about one-fourth of that of Ni.
Shock conditions for initiation of the reaction
were compared to the conditions for thermal initiation of the reaction at
atmospheric pressure. The SHS behavior of the Ti and Si mixtures is compared to
that of Ni and Si mixtures.
Chapter 4 presents a study of the consolidation of a metallic glass powder
undertaken to produce bulk samples of the material for mechanical property
measurements.
REFERENCES
[1]
Y. B. Zel'dovich and Y. P. Raizer, "Physics of Shock Waves and
High-Temperature Hydrodynamic Phenomena, Vols. I and II," Academic Press,
San Francisco {1976).
[2]
"High Velocity Impact Phenornena," R. Kinslow (ed.), Academic Press, New
York (1970).
[3] C. A. Parsons, Phil. Trans. Roy. Soc., London A220, 67 {1920).
[4] P. S. DeCarli and J. C. Jamieson, Science 133, 821 (1961).
[5]
R. A. Graham, B. Morosin, and B. Dodson, "The Chemistry of Shock
Compression:
Bibliography,"
Sandia
National
Laboratories
Report
SAND 83-1887.
[6]
G. A. Adadurov, V. I. Gol'danskii, and P. A. Yampolskii, "Mendeleev
Chemistry Journal18, 92 {1973).
[7]
G. A. Adadurov and V. I. Gol'danskii, Russian Chemical Reviews 50, 948
(1981 ).
[8] R. A. Graham, B. Morosin, Y. Rorie, E. L. Venturini, M. Boslough, M. J. Carr,
and D. L. Williamson, in "Shock Waves in Condensed Matter," Y. M. Gupta (ed.),
Plenum Publishing Corporation, New York, 693 (1963).
[9] R. A. Graham, J. Phys. Chem. 83, 3048 (1979).
[10]
"LASL Shock Hugonoit Data," S. P. Marsh (ed.), University of California
Press, Los Angeles (1980).
[11] R. B. Schwarz, P. Kasiraj, and T. Vreeland, Jr. in "Metallurgical Applications
of Shock Waves and High-Strain-Rate Phenomena," L. E. Murr, K. P.
Staudhammer, and M.A. Meyers (eds.), Marcel Dekker, New York, 313 {1986).
[12] F. Bordeaux and A. R. Yavari, .J. Mater. Res. Q., 1656 (1990).
[13] W. F. Henshaw, A. Niiler, and T. Leete, ARBRL-MR-03354.
2. CALCULATION OF THE SHOCK HUGONIOT FOR MIXTURES
2.1
A Hugoniot theory for solid and powder mixtures
Barry R. Krueger and Thad Vreeland, Jr.
Keck Laboratory of Engineering Materials
California Institute of Technology, 138-78
Pasadena, CA 91125
ABSTRACT
A model is presented from which one can calculate the Hugoniot of solid and
porous two component mixtures up to moderate pressures using only static
thermodynamic properties of the components.
The model does not presuppose
either the relative magnitude of the thermal and elastic energies or temperature
equilibrium between the two components.
It is shown that for a mixture, the
conservation equations define a Hugoniot surface and that the ratio of the thermal
energy of the components determines where the shocked state of the mixture lies on
this surface.
This ratio, which may strongly affect shock initiated chemical
reactions and the properties of consolidated powder mixtures, is found to have only
a minor effect on the Hugoniot of a mixture. It is also noted that the Hugoniot of
solids and solid mixtures is sensitive to the pressure derivative of the isentropic bulk
modulus.
INTRODUCTION
The Hugoniot of a mixture is intimately related to the current interest in
shock initiated chemical reactions.[l-5]
With the high temperature and pressure
associated with shock wave processing, it may be possible to concurrently synthesize
and form near net shape parts of intermetallic compounds and other materials.
Shock processing is potentially a viable technology for producing composite
materials in which it is necessary to control chemical reactions between the matrix
and reinforcing powders since such reactions often have deleterious effects on the
mechanical properties of the composite.
Fully understanding shock initiated chemical reactions and shock compaction
of composites is dependent upon knowing the Hugoniot of the mixture of interest.
To this end, several models have been put forth.
A popular approach has been
Their theory requires the Hugoniots of the
components and assumes the thennal energy of a shocked mixture to be small
compared to the elastic energy. This assumption is necessary since their model does
not account for a difference in the temperature rise of the components which will
occur in shocked solid and particularly powder mixtures.
Duvall and Taylor [7]
have used a mixture method that relies on knowing the component's Gibb's free
energy, and they assume the components to be in thermal equilibrium.
Both of these approaches assume conditions not necessarily valid in the shock
state. In shocked porous media the relative magnitude of the thermal and elastic
energy is just the opposite of McQueen's assumption. The difference in temperature
of the two components of a mixture may be large,[8] and in many materials will not
equilibrate quickly relative to the shock rise time.[7]
In light of this, we have
developed a formulation which allows for large thermal energies and does not require
either thermal equilibrium between components or a large ratio of elastic to thermal
energy.
This calculation is employs a simple Hugoniot theory based on the
Mie-Griineison equation of state and a linear relation for the isentropic
compressibility as a function of pressure. It is sufficient to allow discussion of the
effect of energy partitioning between components of a powder mixture.
More
sophisticated equations of state for solids have been developed [9-11] and
discussed [12], but are somewhat less amenable to the mixed media Hugoniot
formulation.
PRELIMINARY DISCUSSION
For the proposed Hugoniot theory of a two component mixture, two
preliminary assumptions are made:
(i) the components are at equal pressures.
(ii) the components have equal particle velocities.
(iii) chemical energy is not released during the shock rise time.
Assumption (i) is justified as follows.
If the pressures were initially different,
equilibration would occur within a few multiples of a time t = d/c
, where dis an
average particle diameter and c is the compressive sound velocity.[7] For example,
in copper c is on the order of 5x10 mfsec.
A powder size of 100 J1m gives a
characteristic pressure equilibration time of approximately 100 nsec. This is on the
order of the shock rise time measured in ductile powders [13] indicating that
pressure equilibration will occur in a time scale similar to the shock rise time. The
time required to establish a well--defined pressure in the shock state may be
considered a definition of the rise time.
The second assumption, that the components have equal particle velocities
behind the shock, is based on experimental evidence.
In shock compaction
experiments on 1:1 atomic percent Ni/Si, Ni/Ti and Ni/Cu powders, we see no
evidence that the components maintain different particle velocities.
If this were
true, the lower shock impedance m.aterial would segregate in the shock direction
which is not observed.
There is also no known experimental evidence in the
literature that the two components of a mixture maintain different particle
velocities, although differences in particle velocities have been used to explain some
shock initiated chemical reactions.[3]
The third assumption, excluding consideration of chemical energy, is
generally valid given the relative slowness of diffusional transport to sound velocity.
In systems subject to chemical reactions, it has been shown that the reactions may
initiate within the shock front in ultra-fine powders.[14] If extensive reactions do
occur within the shock rise time, the present model is not applicable.
Assumptions (i) and (ii), together with conservation of mass, momentum,
and energy, imply that the two components absorb different amounts of energy and
are therefore, in general, at different average temperatures immediately behind the
shock front.
An example supporting the implied energy partitioning is the
theoretical and experimental work on the shock consolidation of Al/SiC metal
matrix composites from AI and SiC rods, (i.e., two dimensional powders).[8]
Further evidence is shown in Figure 1 which is a micrograph of a shock consolidated
mixture of hard and soft maraging steel powders heat treated to VH 620 and 280,
respectively.
The softer, light etching particles have deformed significantly in
comparison with the harder particles. Intuitively, in a mixture of soft and hard,
small and large or irregular and regularly shaped particles, one would expect the
former to absorb more energy than the latter which will result in different average
particle temperatures behind the shock.
A simple argument reveals that for typical powders, a temperature difference
will not equilibrate quickly, but in fact, orders of magnitude more slowly than any
pressure difference. Significant ther:mal conduction will occur over distances d={if,
where "' is some average thermal diffusivity.
Using typical parameters of
d = 100 J1m and the thermal diffusivity of a good thermal conductor such as Cu
indicates that temperature differences will equilibrate 2 to 3 orders of magnitude
more slowly than pressure differences and in a time which may be longer than the
shock duration itself.[7] Obviously, the temperature must be continuous across the
particle boundaries of the two cotnponents, but the proposed theory is a bulk
thermodynamic model which considers average component temperatures.
If the particle size is approximately 100 nm or smaller, the difference
between pressure and temperature equilibration times becomes small, and the
10
equilibration times are on the order of the shock rise time. This effect has been
exploited by Boslough in his measurements of shock temperatures in thermite and
other systems using radiation pyrometry.[l4,15]
The theory presented here can
treat ultra-fine particle shock consolidation by assuming a thermal energy ratio
such that the components are at equal temperatures as will be explained below.
THEORY
With the assumptions discussed above, the laws of conservation of mass,
momentum and energy will be no different for a mixture provided that no chemical
reactions occur:
(1)
Conservation of Mass.
where the PooAB is the initial density of the mixture; plAB is the shocked density; C8
is the shock velocity; u is the particle velocity; P is the initial pressure; P is the
shock pressure, and E and E are the initial and final specific internal energy of the
mixture, respectively. Substituting (1) and (2) into (3) and dividing the specific
internal energy between the two components gives:
(4)
where x is the mass fraction of material A; VOOAB and V lAB are the initial and
shocked specific volumes of the mixture, respectively.
D.EA and D.EB are the
11
changes in specific internal energy of the two components, and the initial pressure is
assumed to be zero. Equation (4) is a simple expansion of the familiar equation
E= ;P[v -v
00
].
The fl.'s can be removed if the ambient energy is used as a
reference.
The energy and pressure of each constituent can be separated into thermal
and elastic (isentropic) components,
(5)
E A = ETA + EEA ' EB = ETB + EEB'
(6)
p A = pTA + pEA = p B = p TB + p EB'
where the E and T subscripts refer to the elastic and the thermal components,
respectively. The second equality in (6) is due to the equal pressure assumption.
Using the definition of the Grtineisen parameter 1 =V( OP / OE)v and assuming each
component's Grtineisen parameter to volume ratio is constant and temperature
independent, the thermal pressure in terms of the thermal energy of the two
components becomes:
dPTA -
"YA dETA ..., loA dETA
...,
VA
:}
PTA -
VOA
"YoA ETA
V OA
(7)
dPTB -
"YBdETB ..., "YoBdETB
...,
VB
V OB
:}
PTB -
"YoB ETB
V OB
This is a simpler assumption than that applied by Jeanloz.[12] Equations (5)-{7)
can be substituted into (4) yielding:
(1-x)EEB(AB)
(8)
where
vOA VOB
12
aA.
(1-x)
' aB =
1'oA.VOB
(1-x)
' 'TlA = -- ' 'TlB =
1'oBVOA
VOB
VOA
V lA. and V lB are the shocked specific volumes of the A and B components,
respectively. The volume dependence (.\) of the elastic pressures and energies is
indicated, and hydrodynamic material behavior is assumed. The distension of the
powder, m =VOOAB/VoAB where VOAB is the solid volume of the mixture at standard
conditions, enters equation (8) through the parameter cp.
Next, one must choose expressions for the elastic pressures and energies. By
assuming a linear dependence of the isothermal bulk modulus with pressure,
Murnaghan [16] derived the equation:
(9)
where PoT is the isothermal bulk modulus at standard conditions, and PoT is its first
derivative with respect to pressure at constant temperature.
Anderson [18] has
shown that ( 9) is a good approximation over a wide range of materials and to
volume ratios of around 0.8. However, the elastic pressure in the shock process is
not isothermal but rather isentropic.
Integrating at constant entropy, a linear
relationship between the isentropic bulk modulus and pressure yields a similar
equation,
(10)
Pos [.:\
-,f3os
-P~s -1 ]
13
where p
08
is the isentropic bulk modulus at standard conditions, and {308 is its first
derivative with respect to pressure at constant entropy.
integrated to get the elastic energy.
Then, (10) can be
It is typically derived from ultrasonic
measurements. Under moderate pressures and non-cryogenic temperatures, {308 at
constant entropy and {3
08
at constant temperature will be similar (within 0.1%) for
s] s = ,8~ ~ [::s] which has
most materials. [17] It has been assumed that [ ::
been determined for many substances using static pressure sound velocity
measurements. [17 ,18]
To examine the reliability of the model in a variety of
materials, it has been assumed that ,8~
[::T]T ,
and [~T]T was calculated
from equation of state data.[19] According to Anderson's data, the value of the two
approximations for {3 do not differ greatly.
Note that (8) is valid for all porosities since no assumptions were made in its
derivation concerning the relative magnitude of the thermal and elastic energy
components except that the ratio 1/V is constant and independent of temperature.
Oh [20] has shown that the constant 1/V approximation is inaccurate at very high
energies, however this discrepancy has been allowed since most shock compaction
and shock initiated reaction experiments are conducted at moderate energies.
Equation (8) gives the shock pressure in terms of the two component's
volumes. For a single material, the shocked volume is determined as a function of
pressure. Then, this equation together with the equation u 1 = jP75.V and a known
flyer pressure-particle velocity relationship can be used to determine all the shock
parameters. However since (8) gives the pressure in terms of both volumes, there is
one more unknown parameter.
In other words, (8) is a Hugoniot surface which
14
depends on the individual volumes of the components rather than simply the total
shocked volume.
Since there exists one more unknown, we initially considered measuring one
more shock parameter, specifically the shock velocity since it lends itself easily to
measurement. With a known shock velocity, (1), (2), (8) together with (9) and a
known flyer pressure-particle velocity relationship constitute a system of four
equations with four unknowns, P 1' u 1, V lA' and V lB.
Once the unknowns are
determined, (6), (7) and {10) can be used to determine the thermal energy of the
two components and hence their temperatures.
Calculations show that small variations (a few percent) of the shock speed
away from the value calculated assuming averaged properties may lead to
nonphysical results such as a negative thermal energy for one of the components.
Therefore, the theory predicts the shock velocity in a mixture is near the shock
velocity assuming averaged properties and that any difference will probably be
smaller than the resolution of a shock speed measurement. Another approach is to
assume the shock speed is the value calculated using averaged properties.
This
results in calculated energy partitioning which is non-intuitive and contradicts
experiments in certain powder mixtures such as TiAl-6V-4 and SiC where the very
hard SiC deforms relatively little while the Hugoniot assuming a shock velocity
calculated from averaged properties predicts that it absorbs significant thermal
energy.
A third approach is to obtain a fifth equation by recognizing that at given
shock conditions, there exists a thermal energy partitioning ratio which is
determined by the relative mechanical properties, sizes and shapes of the two
components.
The softer, smaller and irregularly shaped component absorbs more
thermal energy, or if one wished to assume equal temperatures, as in the case of
ultra-fine powders, it is possible to determine an approximate thermal energy ratio
15
based on the specific heats of the components over some expected temperature
range.
Except for the last case, quantitatively predicting the thermal energy
partitioning for a given mixture is difficult. Nevertheless, at given shock conditions,
there does exist a thermal energy ratio of the form:
(11)
Using equations (6), (7) and (11), we obtain the equation,
VOB 'YoA
e=--VOA 'YoB
(12)
Equations (1), (2), (8), (12) and a known flyer pressure-particle velocity
relationship constitute a system of five equations and five unknowns, C , P 1, u 1,
V lA' and V lB which can be solved numerically.
To determine the effects of therrnal energy partitioning on a mixture's
Hugoniot, we have assumed the simplest possible form for (11),
e = constant.
Doing so simplifies the calculations, but more importantly, assuming
eis constant
includes the extreme possibility that one component absorbs no thermal energy
(i.e.,
e= Q Or
CD ).
VALIDATION OF THE MODEL FOR HOMOGENEOUS MATERIALS
To test the model, the Hugoniots of solid single component materials were
calculated.
As discussed earlier, this is the degenerate case of a two component
mixture, and defining a thermal energy ratio is not necessary. The materials were
chosen based on the the availability of thermodynamic data to approximate {3 and
the availability of statistically significant Hugoniot data over a range of compression
where a first order thermal expansion of a material's isentropic bulk modulus is
16
expected to be valid. The materials and the thermodynamic data used are shown in
Table I.
A result of the calculations is that the C - u 1 relationship is nearly linear as
is found experimentally.
For all the calculated single component Hugoniots, the
correlation coefficient between C and u 1 is greater than 0.995.
Therefore, the
proposed model qualitatively fits the experimental Hugoniot data. The results are
shown in Table II in the form C = A + B*u 1 along with the values of A and B
determine from a linear regression fit of the experimental data [21] over the velocity
ranges indicated. As can be seen in Table II, the calculated shock intercepts match
the experimental values well.
The average absolute difference between the
calculated and experimental values is only 59 mfsec.
However, the calculated
particle velocity coefficients are consistently higher than the experimental values
with an average difference of 14.4%.
By varying the thermodynamic parameters within a reasonable range of
uncertainty, it was determined that the calculated particle velocity coefficients are
sensitive to {3~.
This is consistent with the result of Ruoff,[24] who derived
B = ({38 + 1)/4
from
the
Murnaghan
expression,
formula
(10).
The Hugoniots of the solids in Table I were recalculated with the same
parameters except for {3
, which were adjusted so the calculated particle velocity
coefficients fit the experimental values. Table III shows the values of {3 necessary
to fit the experimental particle velocity coefficients and the ratio of the fitted value
to the original estimate.
This ratio lies between .69 and .91 and roughly varies
inversely with the material's bulk modulus. Also shown are the new values of the
calculated shock intercept which differ little from the values calculated originally
and the experimental values.
17
These comparisons of calculated and experimental data show that the model
qualitatively fits experimental solid Hugoniots using estimates of {3 and that the
values of {3
can be varied so that the calculated solid Hugoniots fit the
experimental data better.
This is not strictly correct, but can be used as an
approximation strategy when the Hugoniot and thermodynamic data are both
available.
The data necessary for a comparison between experimental and calculated
results for porous materials is available for Cu. The Hugoniot of this powder was
calculated with the value of {J~ used to fit the experimental solid Hugoniot particle
velocity coefficients, however it should be noted that the results change by no more
than five percent and usually less than 2 percent by using the original estimate of {3
since the elastic energy in a shocked powder is only a small fraction of the total
For this reason, the formulation derived here is expected to be most
energy.
applicable to porous media. As can be seen in Table IV, the calculated values of
both the shock intercept and particle velocity coefficient match the experimental
data well.
The comparison between calculated and experimental Hugoniots in Table IV
shows that the theory can quantitatively determine the Hugoniots of a distended
single component material. It is important to emphasize that small variations in {3
do not greatly affect the calculated Hugoniot for a distended media. This, together
with the results discussed for solid materials, shows that the model accurately
describes a porous material's shock response. This implies that the extension of the
model to a porous mixture should be sufficiently accurate to make certain
conclusions about a mixture's Hugoniot since the physical description of a material's
shock response is the same in the full two component theory.
In the following
section, the Hugoniots of mixtures of the materials in Table I are discussed.
18
APPLICATION TO MIXTURES AND DISCUSSION
For the following calculations, properties were averaged volumetrically using
the Reuss averages for the elastic properties:
(13)
OAB
= ~x.V.,
• 1 1
(14)
-1
[ f-li~s/
~x.V 0 .]
(15)
/JOSAB = VOAB
(16)
Unfortunately, few Hugoniots of well characterized mixtures have been
determined experimentally over a range of composition. There is sufficient data for
a comparison with slightly distended mixtures of sintered W infiltrated with 24 and
45 wt.% Cu.[22] The calculated and experimental results for W - 24 wt.% Cu are
shown as C vs. u plots in Figure 2. The three curves correspond to the Hugoniot
calculated assuming averaged properties and the extreme cases in which the W or
Cu absorb no thermal energy. A good fit to data is the calculated Hugoniot where
the W absorbs no thermal energy which is closer to what one might expect,
however, this conclusion is poorly supported since the Hugoniot assuming the
opposite extreme also fits the data well and better than the calculated Hugoniot
assuming averaged properties.
19
Interestingly, the calculated Hugoniots are non-linear at low particle
velocities.
The linearity of the Cs-u 1 relationship is solid materials is
well-known.[23,24]
Some evidence of curvature in the relationship in distended
solids exists for sintered aluminun1. and copper.[25]
Although the number of
experimental points is small, the data is well fit by the non-linearity. All three of
the calculated Hugoniots fit the non-linearity well, however little difference is
expected in this range because the thermal energy is smaller at lower particle
velocities.
McQueen et al.[6] supposed, by comparison with experimental single
component porous Hugoniots, that the curvature is due to the initial porosity of the
samples. Calculations assuming no initial porosity do show the C8 -
relationship
to be linear, thereby confirming this conclusion, however since our model assumes
hydrodynamic material behavior and matches the curvature in the experimental
data, it can be concluded that the curvature is not the result of material rigidity
effects.
The calculated Hugoniot for W - 45 wt.% Cu is linear over the range of
particle velocities investigated which was higher than in the previous case due to the
lack of experimental data at lower particle velocities. The calculated values of A
and B are 3.108 km/sec and 2.014 respectively, assuming averaged properties, 3.125
km/sec and 1.917 respectively, assuming the Cu absorbs no thermal energy and
3.137 and 1.954 respectively, assun1ing the W absorbs no thermal energy.
The
values of A and B determined from the experimental data over the particle
velocities 189 mfsec to 878 mfsec are 3.003 and 2.021, respectively. It should be
noted that one experimental data point was excluded because the density of that
particular sample was significantly lower.
The calculated values of A and B
assuming mass averaged properties are very close to the experimental values. As
with the other W-Cu mixture, the two extreme Hugoniots lie on the same side of
the Hugoniot calculated assuming average properties in the C - u plane.
20
The Hugoniots of several other mixtures, listed in Table V, have been
calculated to investigate the effects of the thermal energy partitioning ratio on the
Hugoniots although no experimental data is available for these systems. The weight
fraction of the components was taken to be 50% and the distension to be 1.5. It was
assumed that a 304 stainless steel flyer was impacting the sample at velocities from
800 to 2000 mfsec. These systems were chosen because they represent a wide range
of possible mixtures, and the shock conditions were chosen because they are typical
of shock compaction and shock initiated reaction experiments.
The results are
shown in Table V in the form C = A + B(u 1). The results for the Mg/ Au system
when the Mg absorbs no thermal energy have been excluded because the calculated
volume of Au was found to be unrealistically high.
One observation drawn from Table V is that unlike the W - Cu system, the
Hugoniots in the C - u plane assuming that one component absorbs no thermal
energy straddle the Hugoniot assuming averaged properties.
Also unlike the
W-24 wt% Cu mixture, the C - u relationships are highly linear. The Hugoniots
of these mixtures may be non-linear at lower particle velocities with finite
distensions, however these possibilities were not explored.
Another observation is that in a system where one would expect the thermal
energy of one component to be nearly zero, it appears possible to experimentally
determine e in equation (11), however there would be many difficulties in such
experiments. First, the calculations have assumed
that
eto be constant. It is unlikely
e will remain constant over a wide range of shock conditions.
More
significantly, the resultant effect on the macroscopic shock parameters is relatively
small. For example, the largest difference found between an extreme Hugoniot and
a Hugoniot assuming averaged properties occurs in the Cd/Nb system.
This
translates into a difference of 4.7%, 6.3%, 8.8%, 2.4% and 8.8% in total energy,
pressure, shock velocity, particle velocity and total thermal energy, respectively at
21
the highest impact velocity. The difference in the total elastic energy is 52% in this
case which may be important in systems with, for example, pressure induced phase
transitions, however in general, this is not as significant as it may seem since the
total elastic energy, assuming average properties, is only 7. 7% of the total energy
deposited. In the other systems and with lower projectile velocities, the percentage
difference in the macroscopic shock parameters is smaller and typically less than
3%. Therefore to determine
e, a large number of carefully conducted experiments
would be required to get statistically significant results, and even then, a small error
in the measured shock parameters would result in a large uncertainty in
e.
Since the above calculations are for extremes in thermal energy partitioning
and a wide range of possible mixtures have been investigated, it appears that a
Hugoniot assuming averaged properties is a valid approximation to the Hugoniot of
a mixture under the typical conditions of a shock compaction or shock initiated
reaction experiment even though the thermal energies, and hence temperatures, of
the components may differ significantly. Therefore, equations {13) - (16) can be
used to determine the averaged properties and equations (1), (2), the flyer
pressure-particle velocity relationship and a reduced form of equation (8) can be
used to calculate the shock parameters for a given flyer velocity. Unfortunately, if a
mixture's distension is close or equal to 1, the solid Hugoniots of the components
need to be known to determine /3 until further theoretical or experimental work is
done, but in porous mixtures an estimate of /3 is sufficient since the elastic energy
is relatively small.
CONCLUSIONS
A theory has been presented to determine the Hugoniot of solid and powder
two component mixtures using only static pressure data. In developing the model,
it was assumed that the pressures and particle velocities of the components were
22
equal while no assumptions were rnade regarding the relative magnitude of the
thermal and elastic energies or temperature equilibrium between the components.
The validity of the equal pressure assumption and the fact that temperature
equilibrium will not be reached imn1ediately behind the shock front was argued in
terms of characteristic equilibration times. The equal particle velocity assumption
is based on experimental evidence.
In addition, it was assumed that significant
amounts of chemical energy are not released during the shock wave rise time.
The model was shown to qualitatively fit the solid Hugoniots of single
component materials using approximations to P~ =
[::s] s [::s] T [::T]T .
Furthermore, the experimental data could be better fitted by adjusting {3 . Using
the values of {3 fitted to the experimental data, it was shown that the calculated
Hugoniots of distended single component materials fit experimental data well,
Approximations to {3
are adequate for porous materials since thermal energy
greatly exceed elastic energy.
The relatively simple Reuss averages were used for the bulk moduli of the
composite mixtures. More complex methods for bounding the elastic properties of
mixtures could be applied,[27] but we do not believe that they would change the
conclusions which follow.
The mixture Hugoniot model was compared to experimental Hugoniot data
in the W-Cu system. The calculated Hugoniots for this system were interesting in
that the Hugoniots assuming either the W or Cu absorb no thermal energy lie on
the same side of the Hugoniot calculated using averaged properties in the C - u 1
plane. An interesting feature of the data for slightly distended W -Cu with 24 wt.%
Cu is the non-linear C - u relationship.
Hugoniot model.
porosity.
This non-linearity is well-fit by the
The model fits the non-linearity as a result of a small initial
23
A series of calculations were then performed on mixtures of materials under
typical shock compaction and shock initiated reaction conditions. It was shown that
extreme changes in the thermal energy ratio did affect the Hugoniot, however it was
argued that the resultant effect on the macroscopic shock parameters is relatively
small and would be difficult to determine experimentally. Given this result, it can
be concluded that a Hugoniot calculated with equations (1), (2), a reduced form of
(8) and the known flyer pressure-particle velocity relationship and assuming
averaged properties using equations (13) - (16), is a reasonable approximation for
determining the total energy, pressure, thermal energy etc. of a shocked mixture
regardless of the component thermal energy ratio, and an accurate approximation
for a porous mixture.
This indicates that the thermal energy partitioning ratio,
which will have an important effect on the shock compaction and shock initiated
reaction processes, will need to be determined by experimental and theoretical
means other than by measuring macroscopic shock parameters.
ACKNOWLEDGEMENTS
We would like to thank Andrew Mutz for Figure 1 and his work on the maraging
steel experiment.
We would also like to thank Ricardo Schwarz of Los Alamos
National Laboratories for helpful conversations and his thoughtful insight.
This
work was supported under the National Science Foundation's Materials Processing
Initiative Program, Grant No. DMR 8713258.
24
REFERENCES
[1] M. B. Boslough, in "Proceedings of the Ninth Symposium (International) on
Detonation, 11 (In press, 1990).
[2] M. B. Boslough, J. Chern. Phys. 92, 3, 1839 (1990).
[3] S. S. Batsanov, G. S. Doronin, S. V. Klochdov, and A. I. Teut, in "Combustion,
Explosions and Shock Waves," 22, 765 (1986).
[4] R. A. Graham, B. Morison, Y. Horie, E. L. Venturini, M. B. Boslough, M. Carr,
and D. L. Williamson, in "Shock Waves in Condensed Matter," Y. M. Gupta (ed.),
Plenum Press, New York, 693 (1986).
[5]
N. N. Thadhani, M. J. Costello, I. Song, S. Work, and R. A.Graham, in
"Proceedings of the TMS
Symposia on
Solid State Powder Processing,"
Indianapolis, (October 1--4, 1989), to be published.
[6] R. G. McQueen, S. P. Marsh, J. N. Taylor, J. N. Fritz, and W. J. Carter, in
"High Velocity Impact Phenomena," R. Kinslow (ed.), Academic Press, New York,
293 (1970).
[7] G. E. Duvall, and S. M. Taylor, .Jr., J. Composite Materials.§., 130
(April, 1971).
[8] R. L. Williamson, R. N. Wright:~ G. E. Korth, and B. H. Rabin, J. Appl. Phys.
66, 1826 (1989).
[9] R. Grover, I. C. Getting, and G. C. Kennedy, Phys. Rev. B. 7_, 567 (1973).
[10] S. Eliezer, A. Garak, and H. Hora, "An Introduction to Equations of State:
Theory and Practice," Cambridge, New York, (1986).
[11] P. Vinet, J. Ferrante, J. R. Smith, and J. H. Rose, J. Phys. C 19, 467 (1986).
[12] R. Jeanloz, J. Geogh. Res. 94, 5873 (1989).
[13] R. B. Schwarz, P. Kasiraj, and T. Vreeland, Jr., in "Metallurgical Applications
of Shock Waves and High-Strain-Rate Phenomena," L. E. Murr, M.A. Meyers and
K. Staudhammer (eds.), Marcel Dekker, New York, 313 (1986).
25
[14] M. B. Boslough, and R. A. Graham, Chern. Phys. Lett. 121, 446 (1985).
[15] M. B. Boslough, J. Chern. Phys. 92, 1839 {1990).
[16] F. D. Murnaghan, Proc. Nat'l. Acad. Sci. 30, 244 {1944).
[17] G. Simmons and H. Wang, in "Single Crystal Elastic Constants and Calculated
Aggregate Properties: A Handbook," MIT, London, 295 (1971).
[18] 0. L. Anderson, J. Phys. Chern. Solids 27, 547 (1966).
[19]
V. N. Zharkov and V. A. Kalinin, "Equations of State for Solids at High
Pressures and Temperatures," Consultants Bureau, New York (1971).
[20] K. Oh and P. Persson, J. Appl. Phys., submitted.
[21]
P. E. Marsh ( ed. ), "LASL Shock Hugonoit Data," University of California
Press, Berkeley {1980).
[22] See Reference #18, 523 and 525.
[23] B. J. Adler, in "Solids Under Pressure," W. Paul and D. W. Warschauer (eds.),
McGraw-Hill, New York (1963).
[24] A. L. Ruoff, J. Appl. Phys. 38, 4976 (1967).
[25] See Reference #18, 177 and 64.
[26] D. Lazarus, Phys. Rev. 76, 4 {1949).
[27] J. P. Watt, Rev. Geophys. and Space Phys. 14, 541 (1986).
26
Table I.
Materials and thermodynamic data used to calculated single material
Hugoniots. Most data is derived from equation of state data from [19]. Data for
copper is from [26]. Data in [17] is similar.
Material
Density
( gfcm3)
(GPa)
Cu
8.94
Zn
f3s
f3s
'Yo
139.76
4.994
2.04
7.14
65.40
5.421
2.38
Nb
8.60
175.40
3.551
1.69
Au
19.24
179.50
5.270
3.05
Pd
11.95
189.00
5.655
2.18
Co
8.82
194.60
4.700
1.99
19.20
308.10
3.996
1.54
Cd
8.64
48.57
7.015
2.20
NaCl
2.16
24.70
5.270
1.57
Mg
1.74
35.58
4.050
1.50
Ag
10.50
108.70
5.660
2.46
Ni
8.90
192.50
4.620
1.91
Ph
11.34
46.36
4.350
2.78
27
Table II. Results of Hugoniot calculations for single components materials.
Experimental values of A and B are taken from linear fits to data in [21].
Material
A Exp.
A Calc. B Exp.
u(m)min~
u(m )max~
sec
sec
(km/ sec) ( km/ sec)
B Calc.
Cu
350
1324
3.898
3.918
1.526
1.632
Zn
588
1237
3.040
2.989
1.539
1.765
Nb
490
1038
4.514
4.478
1.127
1.256
Au
342
680
3.058
3.016
1.568
1.759
Pd
431
1416
3.963
3.944
1.611
1.792
Co
471
946
4.709
4.664
1.381
1.544
340
1156
4.008
3.975
1.278
1.361
Cd
572
1181
2.389
2.394
1.733
2.040
NaCl
326
1746
3.488
3.361
1.309
1.658
Mg
876
1935
4.620
4.459
1.180
1.398
Ag
471
987
3.262
3.183
1.570
1.818
Ni
475
987
4.656
4.698
1.355
1.520
Pb
263
890
2.042
1.976
1.446
1.574
28
Table III. Values of {38 ={JSFit required to fit experimental particle velocity
coefficients. The very simple constitutive relationship results in the relatively large
differences between measured and best-fit values of {3 . Experimental values of A
are taken from linear fits to data in [~21].
Material
{JSFit
{JSFit/ {JS
A Exp.
(km/ sec)
A Calc.
(km/ sec)
Cu
4.525
0 . 906
3.898
3.912
Zn
4.340
0 . 801
3.040
2.963
Nb
3.025
0 . 852
4.514
4.476
Au
4.450
0 . 844
3.058
3.010
Pd
4.830
0 . 854
3.963
3.930
Co
4.025
0 . 856
4.709
4.660
3.650
0 . 913
4.008
3.973
Cd
5.380
0 . 767
2.389
2.345
NaCl
3.630
0 . 689
3.488
3.329
Mg
3.100
0 . 765
4.620
4.435
Ag
4.550
0 . 804
3.262
3.166
Ni
3.940
0 . 853
4.656
4.614
Pb
3.750
0 . 862
2.042
1.968
29
Table IV. Results of Hugoniot calculations for distended copper. Experimental
values of A and B are taken from linear fits to data in [21].
Material
A Exp.
A Calc. B Exp.
u(m}minl
u(m }maxJ
sec
sec
( km/ sec) (km/ sec)
B Calc.
Cu
m=l.13
610
1789
2.092
2.155
-2.084
2.059
m=l.41
730
2018
0.718
0.805
2.208
2.166
m=l.57
769
2112
0.548
0.469
2.105
2.130
30
Table V. Results of mixture Hugoniot calculations
System
( 112)
Mass Averaged
Therm. En. 1=0
Therm. En. 2=0
(km I sec)
(kmlsec)
(km I sec)
CuiNb
0.345
2.378
0.337
2.372
0.281
2.472
MgiAu
0.595
2.006
0.593
2.012
CdiW
0.393
2.331
0.399
1.991
0.299
2.385
CoiZn
0.362
2.331
0.177
2.692
0.383
2.221
CdiNb
0.394
2.219
0.391
2.151
0.210
2.631
Na.CIIW
0.612
1.861
0.631
1.702
0.598
1.987
31
Figure 1. Shock consolidated -100 +200 mesh maraging steel powders. The dark
and light particles had a pre-shocked vickers microhardness of 280 and 640,
respectively. The initial porosity was 32.0%. The 50/50 hard to soft mixture was
impacted by a 304 stainless steel flyer at 986 m/sec. The soft particles deformed
significantly compared to the hard particles as can be seen by the concavity of the
interfaces. The very light material at the interfaces is rapidly quenched materiaL
32
-.0.
,..-...,.
4500
A·t{-·
-Averaged Hugoniot
---Therm. En. W==O
··· ··· Therm. En. Cu=O
1:::. Exp. Data
./
./
. -:- :.·.
.-··
/>:e.
:.··
(f)
:.··
·E
. 4000
Q.)
.:::c.
..c
(f)
3500
200
400
600
800
1000
Particle Vel. (m/sec)
FIG. 2. Calculated and experimental Hugoniots of sintered W infiltrated with 24
wt.% Cu. The distension calculated from the experimental data is 1.014.
33
3. SHOCK INITIATION OF THE REACTION FORMING NiSi
3.1
Shock Initiated Chemical Reactions in 1:1 Atomic
Percent Nickel-Silicon Powder Mixtures
B.R. Krueger, T. Vreeland, Jr.
W. M. Keck Laboratory of Engineering Materials
California Institute of Technology, 138-78
Pasadena, CA 91125
ABSTRACT
A series of shock initiated chemical reaction experiments have been
performed on 1:1 atomic percent mixtures of nickel and silicon powders. It has been
observed that only minor surface reactions occur between the constituents until a
thermal energy threshold is reached above which the reaction goes to completion as
evidenced by large voids, bulk melting, and scanning electron microscopy and x-ray
diffraction results. The experiments show the energy difference between virtually no
and full reaction is on the order of 5 percent. A sharp energy threshold indicates
that with the particular morphology used, the bulk temperature determines whether
or not the reaction occurs rather than local, particle level, conditions.
INTRODUCTION
The first systematic investigation of the shock-induced formation of
intermetallic compounds was reported by Horie et a1.[1,2,3] Aluminides of Ni and
Ti were formed from mechanically mixed elemental powders. More recently, Song
and Thadhani presented further studies on the shock synthesis of Ni aluminides.[4]
These investigators concluded that shock-enhanced reactivity strongly influenced
34
the synthesis process.
A series of experiments have been performed on two mixtures of 1:1 atomic
percent elemental nickel and silicon powders in a well characterized propellant
driven plate system.
The experiments reveal the existence of a thermal energy
threshold below which little or no .reactions occur and above which full reaction
occurs as evidence by bulk melting and x-ray diffraction and scanning election
microscopy (SEM) results. The experiments also show the width of the threshold to
be on the order of 5 percent.
From the existence of a sharp thermal energy
threshold, certain conclusions can be made about the parameters which determine
whether or not bulk reactions occur.
EXPERIMENT
Two mixtures of 1:1 atomic percent (67.6 wt % Ni) powders of Ni and Si
were used. The first, Mix A, consisted of 15 p,m spherical Ni from Inco Metals and
-325 mesh irregular Si of unknown purity. The second, Mix B, was 20 p,m- 45 J.liD
spherical nickel ( Aesar Stock # 10581) and -325 mesh irregular silicon ( Cerac
Stock# S-1052). The elemental powders were mechanically mixed in petroleum
ether to avoid particle agglomeration and then dried. No special care was taken to
remove or prevent formation of oxides on the particle surfaces. Optical images of
the two mixtures are shown in Figures la and lb.
The shock facility used is the Keck Dynamic Compactor, a 35 mm smooth
bore cannon. Experiments with a metallic glass have shown that the gun and target
assemblies used result in highly one dimensional shock conditions.(5) A 5 mm 303
stainless steel plate was used as the flyer.
The geometry of the target assembly
limits the shock duration by the reflection from the back of the flyer plate, and
therefore the duration is governed by the flyer thickness. The effects of duration
have not been explored. The shock facilities are discussed in further detail in Ref. 1.
35
Preliminary experiments were conducted with porous bronze inserts, pressed
into a target fixture, which contain 4 smaller cavities. These experiments have the
advantage of identical impact conditions for each sample and four samples per shot.
A disadvantage is that the impedance mismatch between the inserts and samples
may give rise to two dimensional effects. To insure that two dimensional effects
were not the determining factor, critical results were confirmed using a full cavity.
RESULTS AND ANALYSIS
The shock conditions were determined using an averaging method which
assumes that the mixture's bulk modulus is linear with pressure and the mixture's
Griineisen parameter to specific volume ratio is constant. With these assumptions,
the Rankine-Hugoniot relationships and the known Hugoniot of the flyer, the mass
averaged shock conditions can be determined.[6]
The homogeneous shock
temperature was determined by matching the thermal energy to the integration of
the mixture's heat capacity of the form C = a + l0-3bT + 105c/T2, where Cis the
heat capacity and T is temperature.
capacity for pressure effects.
No attempt was made to correct the heat
The thermodynamic parameters used are listed in
Table I, and the calculated shock results of the experiments discussed below are
listed in Table II.
The first set of experiments were conducted with Mix A.
The green's
porosity was typically 40%, and flyer velocities were varied from 700 to 1600 m/sec.
Optical microscopy of the compacts recovered from low energy shots showed no
evidence of chemical reactions, and the compacts were poorly bonded.
In higher
energy shots, the reaction apparently went to completion as evidenced by large
voids, bulk melting and a homogeneous appearance under the optical microscope.
Further experiments showed the energy difference between no and full
reaction to be small. In a four cavity experiment at a flyer velocity of 1.02 km/sec,
36
no reactions occurred in a sample pressed to a porosity of 35.9 ± 0.8 percent while
the reaction went to completion in the sample pressed to a porosity of 41.1 ± 0.8
percent.
These porosities and impact conditions correspond to calculated
homogeneous temperatures of 594° C and 622° C, respectively, or a total energy
difference of less than 4 percent. Two full cavity experiments confirmed the energy
difference to be less than 12 percent. No attempt was made using full cavities to
narrow down the threshold width further.
An analogous procedure was conducted with Mix B. Since the morphologies
of the two mixtures are similar, it is not surprising that the results for Mix B are
nearly identical.
A four cavity experiment showed the energy threshold to lie
between thermal energies corresponding to homogeneous temperatures of 631 o C and
648° C, or a total energy difference of less than 3 percent. Full cavity experiments
confirmed that the separation in total energy between no and full reaction was less
than 10 percent.
No attempt was made using full cavities to narrow down the
threshold width further.
It is interesting to note that, except for the very small
amount of surface reactions discussed below, no compacts of either mixture were
recovered in an intermediate condition between no and full reaction.
Scanning electron microscopy of compacts shocked to just below the reaction
threshold revealed that minor surface reactions had occurred which are not
detectable optically or with x-ray diffraction. As can be seen in the back scattered
electron image shown in Figure 3, the extent of the reaction was very limited. The
nature of the reacted region differed slightly between Mix A and Mix B.
The
reactions in Mix A were very uniforn1 along the interfaces where they occurred with
a typical thickness of 0.5 p,m. The M:ix B compact also had a uniform reaction zone
on a small portion of the interfaces, but there also existed pools of reacted material.
A back scattered electron image of a typical reacted interface for mix B is shown in
Figure 4, which also contains the far more typical interface showing no reaction.
37
DISCUSSION
From the existence of a sharp threshold, it can be reasoned that the shock
parameter governing whether or not bulk reactions occur in a 1:1 mixture of this
particular morphology is the homogeneous temperature. The experiments rule out
the possibility that the threshold is a pressure or elastic energy effect since the more
porous compacts react but are shocked to a lower pressure and elastic energy.
One may argue that local particle level conditions change significantly across
the threshold, however any such explanation is unlikely since it must exclude the
possibility that the same local conditions exist anywhere at lower shock energies.
For example, the existence/kinetics of shock initiated chemical reactions has been
explained by local mass mixing and other similar terms describing local differences
in the particle velocities of the coustituents.[7-9]
However, as can be seen in
Figure 2, there is no evidence of mass mixing, and it is unlikely that increasing the
energy by as little as 3 percent will greatly enhance mass mixing, especially with a
lower shock pressure since one would expect greater constituent mixing at greater
pressures.
Another local condition which may arguably change as the threshold is
crossed is that a critical melt pool size is attained, however this is also not likely.
Since the energy difference between practically no and full reaction is small, there is
a high probability that there exists some local pre-shock particle configuration in
the less porous green which will result in a "critical" melt pool size upon
compaction. Furthermore, if the reaction is determined by some local pre-shock
particle configuration, reactions would occur sporadically, depending on local
particle placement during the pressing of the greens.
Another argument may be
that a critical density of melt pools is attained above the threshold, however this
can not be true since, in the time it takes to "communicate" between melt pools ·
through heat conduction, the melt pools no longer exist.[10] It is possible to argue
38
other particle level explanations, however, as mentioned above, a necessary feature
of such an approach would be that the same local conditions can not exist in lower
energy samples.
We therefore conclude that the homogeneous temperature determines
whether or not reactions occur in 1:1 atomic percent Ni/Si mixtures of the
particular morphologies used here. This is the only parameter which undoubtedly
varies across threshold and is a reasonable explanation as to why lower energy
compacts do not reacted while slightly higher energy compacts react fully. Since the
homogeneous temperature determines whether or not bulk reactions occur, one can
also conclude that the reaction kinetics are slower than the time required for
temperature equilibration. Assuming a linear heat conduction time constant of, r =
r2/ ;;., where r is the Ni particle radius and ;;, is nickel's thermal diffusivity, gives that
the reaction occurs on a time scale greater than several microseconds.[10]
CONCLUSION
Experiments on two mixtures of similar morphology of 1:1 atomic percent Ni
and Si powders reveal the existence of a sharp energy threshold below which no
significant reactions occur and above which the reaction goes to completion as
evidenced by bulk melting and SEM and x-ray diffraction results.
From the
existence of a sharp energy threshold, it can be reasoned that the homogeneous
temperature determines whether or not the bulk reaction occurs rather than particle
level conditions. One can also conclude that the reaction occurs on a time scale
greater than several microseconds.
ACKNOWLEDGEMENTS
This work was supported under the National Science Foundation's Materials
Processing Initiative Program, Grant No. DMR 8713258. We would like to thank
39
Phil Dixon, formally at the New ]Mexico Institute of Technology for preparing
Mix B.
REFERENCES
[1] Y. Rorie, R. A. Graham and I. K. Simonsen, Mat. Lett. a, 354 (1985).
[2] Y. Rorie, R. A. Graham and I. K. Simonsen, in "Metallurgical Applications of
Shock-Wave and High-Strain-Rate Phenomena," L. E. Murr, K. P. Staudhammer,
and M.A. Meyers (eds.), Marcel Dekker, New York, 1023 (1986).
[3] N. N. Thadhani, M. J. Costello, I. Song, S. Work, and R. A. Graham, in
"Solid-State Powder Processing," A. H. Clauer and J. J. deBarbadillo (eds. ), The
Minerals, Metals, and Materials Society, Warrendale, PA, 97 (1990).
[4] I. Song and N. N. Thadhani, presented at the TMS Symposium on Reaction
Synthesis of Materials, New Orleans, (Feb. 1991), to be published in Met. Trans.
[5]
A. H. Mutz and T. Vreeland, Jr., in "Shock Waves and High-Strain-Rate
Phenomena in Materials," M. A. Meyers, L. E. Murr, and K. P. Staudhammer
(eds), Marcel Dekker, Inc., New York, (1991, in Press).
[6] The averaging method used was similar to M. B. Boslough, J. Chern. Phys. 92,
1839 (1990).
[7] S. Batsanov et al., Combustion, Explosions and Shock Waves 22, 65 (1986). 65.
[8] R. A. Graham et al. in "Shock Waves in Condensed Matter," Y. M. Gupta
(ed.), Plenum Press, New York, 693 (1986).
[9] M. B. Boslough and R. A. Graham, Chern. Phys. Lett. 121, 446, (1985).
[10] R. B. Schwarz, P. Kasiraj and T. Vreeland, Jr., in "Metallurgical Applications
of Shock Waves and High-Strain-Rate Phenomena," L. E. Murr, M. A. Meyers and
K. P. Staudhammer (eds.), Marcel Dekker, New York, 313 (1986).
40
Table I. Thermodynamic parameters used to determine the Hugoniots of the Ni/Si
mixtures. The isentropic bulk modulus of Ni and the Griineisen parameters for Ni
and Si were taken or calculated from. V.N. Zharkov and V.A. Kalinin, Equations of
State for Solids at High Pressures and Temperatures, Consultants Bureau,
New York, 1971. The pressure derivative of the isentropic bulk modulus of Ni was
determined by fitting solid Ni Hugoniot data. Silicon's isentropic bulk modulus and
its pressure derivative were taken from 0.1. Anderson, J. Phys. Chern. Solids ~
547 (1966).
The heat capacity coefficients were taken from, E.A. Brandes (ed.),
Smithells Metal Reference Book, Sixth Edition, Butterworth & Co., 8-42 (1983).
The units of a, band care Jf(mole-K), Jf(mole-K2) and J-K/mole, respectively.
(GPa)
ap·l
w·
Ni(a)8.90
192.5
3.94
1.91 17.00
29.48
Ni({J) 8.90
192.5
3.94
1.91
25.12
7.54
Si
97.9
4.19
0.74 23.95
2.47
-4.14
Density
(g/ em 3 )
2.33
f3s
'Yo
41
Table II. The calculated shock conditions of the experiments discussed in the
text. The column headings correspond to the mixture, porosity, flyer velocity,
pressure, total energy, thermal energy, homogeneous temperature (assuming
no reaction), and whether or not the reaction occurred, respectively. An
asterisk indicates a four cavity experiment. The enthalpy of formation of NiSi
at 298° K is -43.1 kJfmole or -593 kJ/kg from W. Oelsen, H. 0. von
Samson-Himmelstjerna, Mitt. K.-W.-I. Eidenforsch., Dusseldorf, 18, 131
(1936). The ratio of energy input from the shock plus the energy generated by
the reaction to the energy needed to heat and melt NiSi is 1.23 for the lowest
shock energy which triggered the reaction.
Mix
A*
A*
B*
B*
Por.
Vel.
( %)
(mfsec)
ET
(GPa) (kJ /kg) (kJ /kg)
37.5
42.8
35.9
39.7
37.5
41.2
37.5
39.9
1000
1040
1020
1020
1020
1060
1050
1050
5.37
4.95
5.87
5.21
5.60
5.38
5.86
5.46
364
413
374
389
380
421
398
407
352
404
359
378
367
410
384
396
THnr
( oC)
React.
581
660
594
622
605
670
631
648
(Y/N)
42
50 pm
(a) Mix A
50 pm
(b) Mix B
FIG. 1 Optical images of the Ni + Si mixes. The lighter particles are Ni.
43
FIG. 2 SEM back scattered image of Mix B shocked in a full cavity experiment to
an energy just below where bulk reaction occurs.
At this magnification, there is
little evidence of any interaction between the Ni and Si. The shock propagated from
right to left .
··~
FIG. 3 SEM back scattered image of Mix B shocked in a full cavity experiment to
an energy just below where bulk reaction occurs.
At this magnification, small
interfacial reactions can be seen as well as pools of reacted material. Also shown are
interfaces where no reactions are detectable, by far the large majority.
44
3.2
Correlation of Shock Initiated and Thermally Initiated Chemical
Reactions in a 1:1 Atomic Ratio Nickel-Silicon Mixture
Barry R. Krueger, Andrew H. Mutz, and Thad Vreeland, Jr.
W. M. Keck Laboratory of Engineering Materials
California Institute of Technology, 138-78
Pasadena, CA 91125
ABSTRACT
Shock initiated chemical reaction experiments have been performed on a. 1:1
atomic ratio mixture of 20 J.Lm to 45 J.Lm nickel and -325 mesh crystalline silicon
powders. It has been observed that no detectable or only minor surface reactions
occur between the constituents until a thermal energy threshold is reached, above
which the reaction goes to completion. The experiments show the energy difference
between virtually no and full reaction is on the order of 5 percent. The level of the
thermal energy threshold is found to correspond to the temperature at which
statically pressed powders begin to react in a differential thermal analyzer (DTA).
A sharp energy threshold and a direct correlation with DT A results indicates that,
with the the particular powder morphologies used, the homogeneous shock
temperature determines whether or not the reaction occurs rather than local,
particle level conditions. From this it may be concluded that the reaction occurs on
a time scale greater than the time constant for thermal diffusion into the particle
interiors.
45
INTRODUCTION
Shock initiated chemical reactions are currently of considerable interest.[1-6]
With the high pressure and temperature associated with shock wave processing, it
may be possible to concurrently synthesize and form near net shape parts of
intermetallic compounds and other materials.
Shock processing is also a viable
technology for producing composite materials where it is necessary to control
chemical reactions between the matrix and reinforcing particle since such reactions
often have deleterious effects on the n1echanical properties of the composite.
The chemistry and kinetics of intermetallic reactions have been explored by
observing the behavior of multilayer thin films upon heating. It has been shown
that in many multilayer composite structures, self-sustaining chemical reactions
can be initiated upon heating.[7-11]
Bordeaux, Yavari, and Desre[8] place two
basic criteria on whether or not such reactions are possible. Briefly, the first is that
the heat of the reaction must be in excess of that required to melt the mixture, and
the second is that the rate of heat generation due to the reaction must be greater
than the rate of heat dissipation to the environment. Thermally initiated reactions
which are not self-sustaining have been observed in Ni/Si multilayers as well as in a
number of other metallic multilayers. The temperature at the onset of the reaction
is observed to increase somewhat with the heating rate.[11] Ma et al.[12] observed
an "explosive" reaction propagating at about 4 m/s in thin multilayers of Ni/ Aland
observed a layer thickness effect.
Reactions did not propagate when the layer
thickness exceeded a critical value, and they suggested that the critical layer
thickness is proportional to the ratio of the heat released by the reaction to the heat
dissipated to the environment, which increases with ambient temperature.
Olowolafe et al.[13] observed the growth of nickel silicide layers upon heating
Ni films vacuum deposited on a single crystal, polycrystalline, and amorphous Si
(a-Si) annealed from 200° C to 325° C. Only Ni 2Si formed on (111) and (100) Si
46
and on polycrystalline Si while Ni S:i and NiSi formed in two distinct sublayers on
a-Si. Ma et al.[14] observed solid state interdiffusion reactions in Ni film and a-Si
bilayers, and observed only crystalline Ni 2Si formation with high purity a-Si. For
the case where the a-Si contained about 5% carbon an amorphous Ni 2Si layer was
also observed. Clevenger and Thompson,[15] using isothermal and constant heating
rate differential thermal analysis (DTA) of evaporated multilayer films of Ni and
a-Si (2 Ni to 1 Si), found distinct exothermic peaks associated with the formation of
amorphous nickel silicide and crystalline Ni 2Si.
Combustion synthesis (CS or SHS, self-propagating high temperature
synthesis) of intermetallic and other systems employs a thermally initiated
self-sustaining chemical reaction. In CS, the reaction is externally initiated in one
section of a usually porous sample, with a specific contact area between particles
much less than in multilayer films. The sample may be in either a vacuum or at
atmospheric pressure. The reaction then propagates through the sample at a rate
lower than that observed in the explosive reaction of multilayers, driven by the heat
of reaction conducting and radiating into the unreacted material.[13]
The initiation of reactions by shock waves in chemically active powder
mixtures is similar to thermal initiation in that the shock wave deposits a
significant amount of thermal energy in the sample.
The thermal energy is
deposited through the plastic deformation associated with void collapse and relative
inter-particle motion, however the shock wave also produces conditions which have
no counterpart in thermally initiated reactions. From a macroscopic point of view,
the shock process is different in that the material in the shock front is very rapidly
K/s) and raised to a pressure of
heated (with heating rates in excess of 10
typically several G Pa for a duration on the order of microseconds, and the material
behind the shock attains particle velocities on the order of hundreds of meters per
second.
SHS reactions typically propagate at velocities of less than 1 mfs.
47
A shock wave which triggers a reaction typically travels at a velocity on the order of
1 km/ s. Therefore substantial reaction may not occur in the shock front unless the
powder particles are of sub-micron size, but the reaction will be initiated
throughout the powder on a time scale much shorter than in the usual SHS reaction.
On the particle level, the shoek process is also quite different from thermally
initiated reaction.
As a shock wave passes through a porous media, energy is
deposited preferentially near the particle exteriors.[17]
In ductile powders the
particle exterior are deformed significantly more than the interiors in the closing of
voids. The preferential deposition of shock energy results in a positive temperature
gradient from interior to the exterior of the particle.
The time required for
temperature equilibration is dependent upon the thermal properties of the materials,
particle size, and melt pool size (when the shock energy is sufficient to cause melt to
form).
The homogeneous shock ten1perature is defined as the temperature of the
shocked compact after local particle thermal equilibrium has been achieved, and
before the compact conducts significant heat to the surrounding ambient. Assuming
spherical particles, spherically homogeneous energy deposition and no melt pools,
Schwarz et al.[18] gave the time constant for temperature equilibration to be
r /16D, where r is the particle radius, and D is the thermal diffusivity of the
powder.
Temperature measurements in shocked powders of Cu and constantan
confirmed this relationship and excellent agreement between the measured
homogeneous temperature and the homogeneous temperature calculated from the
shock energy was demonstrated.[19]
Graham et al.,[20] Thadhani et al.,[21] Batsanov et al.,[22] and others have
reported studies on shock initiated chemical reactions in a number of systems. They
have put forth several qualitative reasons for why the shock initiated chemical
reaction process might be very different from the other synthesis processes described·
above.
These reasons are summarized in what Graham has coined "catastrophic
48
shock" as opposed to "benign shock." Benign shock, as discussed by Horie et al.,[23]
is a description of the shock process from the traditional viewpoint of the
macroscopic
conservation equations,
with void collapse and the resulting
inhomogeneous energy deposition and the normal processes of thermal equilibration
and atomic diffusion. The catastrophic shock concept views the interaction of shock
waves with chemically reactive media through the formation of activated complexes,
non-diffusive transport of matter described as relative mass motion and fluid-like
flow, and the critical involvement of crystal defects in chemical reactions.
We have recently reported the results of a series of shock initiated reaction
experiments on two similar mixtures of 1:1 atomic ratio elemental nickel and silicon
powders.[24] These experiments were conducted using a propellant gun and target
design which results in highly one-dimensional shock conditions, and therefore, in
uniform shock conditions over the majority of the sample. It was found that there
exists a thermal energy threshold below which only minor surface reactions occur
and above which the reaction goes to completion as evidenced by spherical voids in
the recovered compacts indicative of bulk melting.
These experiments show the
threshold is crossed with an energy increase on the order of 5 percent. It was argued
that the narrowness of the threshold indicates that the homogeneous temperature
rather than the pressure effects and local inhomogeneities determine the initiation of
the reaction forming NiSi.
The current work provides further evidence that the
homogeneous temperature is the critical parameter determining whether or not bulk
reactions occur and that phenomena described as "catastrophic" shock may be of
secondary importance in this chemical system.
EXPERIMENT
The mixture of 1:1 atomic ratio (67.6 wt% Ni) elemental Ni and Si consisted
of 20 p,m. - 45 p,m. nickel ( Aesar Stock # 10581) and -325 mesh crystalline silicon
49
(Cerac Stock# S-1052). The powders were mechanically mixed in petroleum ether
to avoid particle agglomeration and then dried.
No special care was taken to
remove or prevent the formation of oxides on the particle surfaces.
A back-
scattered SEM micrograph of the starting mixture is shown in Figure 1.
The shock facility used is the Keck Dynamic Compactor which employs a
35 mm smooth bore launch tube. In our target, the flyer plate strikes the sample
directly and does not strike the sample containment fixture, a schematic of which is
shown in Figure 2.
There exists strong evidence that the target assembly and
impact conditions result in highly one-dimensional, and therefore well defined,
shock conditions as discussed below.
Figure 3 shows metallic glass (Ni 76 .4cr 19 .7B2.3c 0.08 ) which has been shock
consolidated with a 5 mm thick 304 stainless steel flyer at a velocity of 1
km/sec.[25] The sample has been cut with a low speed diamond saw, polished and
etched with Marbles reagent. The shock propagated from left to right in the figure.
A macro-photograph of the recovered compact is inset to the right of the figure,
and an optical micrograph of the region of changing contrast is on the left. X-ray
diffraction has confirmed that the darkened region crystallized while the light region
remained amorphous,
Although the properties of this metallic glass are not well
characterized, the transition region occurs at a distance from the flyer/sample
interface at which a release wave from the rear of the flyer is expected to overtake
the initial shock. This strongly implies that the shock energy heated the compact to
a temperature in excess of the crystallization temperature.
The sample's salient
feature is the highly planar interface between the two uniform regions indicating
nearly one-dimensional shock conditions.
Although a numerical simulation has not been conducted for our target
fixture, a recently presented simulation of a similar target indicates that the target
assembly and impact conditions used should result in highly one-dimensional shock
50
conditions.[23] For the simulation, a thick cover plate was assumed, and to achieve
one-dimensional conditions, it was determined that the ratio of the flyer to sample
diameters should be slightly greater than one.
With our target and impact
conditions, no cover plate is used and the flyer to sample diameter ratio is equal to
one. Although the precise effect of these differences has not been investigated, the
similarity in the two target designs indicates that deviations from one-dimensional
shock conditions should be small.
Finally, a simple argument shows that shock parameters calculated assuming
one-dimensional conditions give the maximum pressure and shock energy in the
sample, given that the release wave from the rear of the flyer overtakes the initial
shock within the powder sample (the thickness of the powder sample was adjusted
to assure this in the present investigation). Since the sample containment fixture is
not impacted, the pressure at the sample edges releases radially in the target and
containment fixture, and there is no increase of pressure due to the "wrap-around"
waves which occur when the sample as well as the target fixture is impacted by the
flyer.[27-29]
In all the experiments, a 5 mn1 thick 303 stainless steel plate was used as the
flyer. Flyer velocities were measured. by timing the interruption of two light beams
just prior to impact.
A doppler radar system was used to verify that the flyer
achieves a nearly constant terminal velocity before it reaches the light beams. As
discussed above, the geometry of the target assembly limits the maximum shock
duration in the powder by the reflection from the back of the flyer plate, and
therefore the maximum shock duration is governed by the material and thickness of
the flyer and the shock wave velocity in the powder. The effects of shock duration
were not explored in this investigation. The launch tube and target were evacuated
to about 0.1 torr prior to impact.
Preliminary shock experiments were conducted with porous bronze inserts,
51
with four separate powder cavities, pressed into a target fixture (Figure 4).[30]
These experiments have the advantage of identical impact conditions for each of
four samples per shot. A disadvantage is some impedance mismatch between the
insert and samples due to a difference in porous and solid density and wave speed
between the samples and porous bronze. This impedance mismatch will give rise to
some two-dimensional effects. To check that the two-dimensional effects were not
governing the reaction initiation in the four cavity experiments, critical experiments
were repeated using targets filled with only the powder mixture. The results of full
and four cavity experiments presented below were in good agreement.
The differential thermal analysis experiments were performed on a DSC 2000
manufactured by Setaram Corporation, France.
DT A samples were pressed in a
simple cylinder and die assembly rnade of C350 maraging steel to allow static
pressures as high as approximately 1.5 GPa.
RESULTS
The shock conditions were determined using an averaging method which
assumes the shock pressure and particle velocity of the two constituents are equal;
the mixture's bulk modulus is linear with pressure, and the mixture's Griineisen
parameter to specific volume ratio is constant.
With these assumptions, the
Rankine-Hugonoit relationships and the known Hugonoit of the flyer, the mass
averaged shock conditions can be determined.
The properties were averaged
according to the following formulas:
v OAB = Ex.v.,
. 1 1
(1)
(2)
52
-1
{30SAB = ''oAB
V ·]
£.-i:!!
[ ~X·
(3)
0 1
{3~SAB = [,B oSA!!.}: xi V oi [l+~osi]] - 1.
VOAB i
(4)
{3 OSi
The ~ubscript AB refers to the mixture. The subscript i refers to the individual
components. The subscript 0 refers to standard conditions, and V, 7, {30 s, {30 s are
the specific volume, Griineisen parameter, isentropic bulk modulus, and the pressure
derivative of the isentropic bulk modulus at constant entropy, respectively.
The homogeneous shock temperatures were determined by matching the
calculated thermal energies to an integration of the mixture's heat capacity of the
form C = a + 10-3bT + 105c/T 2 , where C is the heat capacity and T is
temperature.[33]
No attempt was n1ade to correct the heat capacity for pressure
effects. The thermodynamic parameters used are listed in Table I, and the impact
conditions and calculated shock parameters of the experiments discussed below are
listed in Table II.
A four cavity shock experirnent was then performed where the initial
porosity of the samples and flyer velocity (Table II) were chosen to give
homogeneous temperatures either just below or just above the reaction onset
temperature found in preliminary experiments. It should be noted that with a given
flyer velocity, the shock energy increases with powder porosity while the shock
pressure and the shock and particle velocities decrease with porosity. The two lower
energy compacts recovered showed no evidence of chemical reactions with either
optical or x-ray diffraction analysis, and the compacts were poorly bonded. In the
two higher energy samples, the reaction apparently went to completion as evidenced
53
by large spherical voids indicative of bulk melting and a homogeneous appearance
under the optical microscope.
The threshold was found to lie between thermal
energies of 384 and 396 J f g, corresponding to homogeneous temperatures of 631° C
and 648° C, or a total energy difference of less than 3 percent.
Full cavity
experiments confirmed the energy threshold to be at the same level and that the
separation in total energy between no and full reaction was less than 10 percent. No
attempt was made using full cavities to further narrow the threshold width.
X-ray diffractions scans of the Ni/Si powder mixture shocked to just below
and just above the energy threshold were made. Only Ni and Si diffraction peaks
were observed in the samples shocked to just below the threshold, and optical as
well as SEM examination of polished sections revealed a porosity less than 1%. All
diffraction peaks observed in the sample shocked to just above the threshold were
indexed as orthorhombic NiSi indicating that the reaction goes to completion once
the energy threshold is crossed. It is important to note that in these experiments no
compacts were recovered in an intermediate condition between no and full reaction.
DTA experiments were performed on statically pressed powders.
It was
found that the onset temperature of the first significant exothermic reaction was
dependent upon the porosity of the DT A samples. Four DT A scans on statically
pressed powder are shown in Figure 5 corresponding to 50% porosity (tap density),
a porosity of 32%, a porosity of 27~), and a porosity of 23%. As can be seen, the
onset temperature increases with increasing porosity. The magnetic transformation
at 360° C is seen on all of the scans.
A DT A run of the mixture shocked to an energy just below the threshold
where the reaction occurs is also plotted in Figure 5. It can be seen that the onset
of the reaction occurs at a temperature 30° C below that found in powder statically
compressed to 23% porosity.
Apparently, the unreacted powders were not
significantly modified by the shock process except that the porosity was reduced.
54
Scanning electron microscopy of a full cavity compact shocked to just below
the reaction threshold revealed that isolated mixing had occurred which was not
detected optically or with x-ray diffraction. The mixing occurred in regions which
appear to have been shock-induced melt pools.
As can be seen in the back-
scattered electron image shown in Figure 6, the extent of the mixing was very
limited. A higher magnification back-scattered electron image of a mixed region is
shown in Figure 7, which was found to be 21% Ni and 79% Si by dispersive x-ray
analysis.
DISCUSSION
Clemens et al.[34) observed an energy threshold for the formation of an
amorphous alloy from layered nickel-zirconium films which were heated by
microsecond current pulses. The sudden onset of reaction at the threshold energy
was attributed to chemical energy of the reaction, and the change in diffusion
kinetics as the sample temperature exceeded the glass transition temperature of the
amorphous alloy.
We postulate that in the shocked Ni-Si powder the chemical
energy and the shock energy cause the sample temperature to exceed the NiSi
melting temperature at the threshold shock energy.
Bordeaux et al.[S] observed a small increase in reaction temperature with an
increase in DTA heating rate in Pd-Sn and Zr-Al reactions triggered by melting of
one component of the mixture.
The small increase in reaction temperature with
heating rate observed for Ni-Si mixtures (going from 621 o C at 10° C /min for shock
compacted but unreacted powder to about 640° C at about 1010 ° C/s for shock
reacted powder) is comparable to that observed by Bordeaux et al.[S] in Pd-Sn and
Zr-Al for a 60-fold rate increase.
The rapid temperature rise in the shock prevents build-up of diffusion
barriers by solid state reactions which can occur at typical DTA scan rates. The
55
mixing reaction time is thereby decreased without significantly changing the time
for dissipation of the heat of reaction to the environment.
This leads to a
self-sustaining reaction in the shocked mixture when the heat of mixing is
sufficiently large as Bordeaux et al.[8] have postulated. Static pressing brings more
particle surface area into contact and also tends to break-up oxide layers which
leads to lowered onset temperatures for the reaction.
From the existence of a sharp threshold and the correlation of the
homogeneous shock temperature corresponding to the thermal energy threshold level
at the onset temperature of the reaction in the DTA, it can be reasoned that the
shock parameter governing whether or not bulk reactions occur in a 1:1 mixture of
this particular morphology is the homogeneous shock temperature.
The
experiments rule out the possibility that the threshold is a pressure or elastic energy
effect since the more porous compacts react but are shocked to a lower pressure and
elastic energy.
One may argue that local particle level conditions change significantly across
the threshold, however any such explanation is suspect since it must exclude the
possibility that the same local conditions exist anywhere at lower shock energies.
For example, the occurrence of shock initiated chemical reactions has been
explained by local mass mixing due to local differences in the particle velocities of
the constituents.[22]
However, as can be seen in Figures 6 and 7, there is no
evidence of mass mixing outside of melt pools and thin isolated surface layers, and it
is unlikely that increasing the energy by as little as 3 percent will greatly enhance
mass mixing, especially combined with a lower shock pressure and particle velocity,
as one would expect less constituent mixing as these shock parameters decrease.
Another local condition which may arguably change as the threshold is
crossed is that a critical melt pool size is attained, however this is also not likely.
Since the energy difference between practically no and full reaction is small, there is
56
a high probability that there exists some local pre-shock particle configuration in
the less porous green which will result in a "critical" melt pool size upon
compaction.
Another argument may be that a critical density of melt pools is
attained above the threshold, however this cannot be true since, in the time it takes
to "communicate" between melt pools through heat conduction, the melt pools no
longer exist. It is possible to argue other particle level explanations, but a necessary
feature of such an approach would be that the same local conditions cannot exist in
samples shocked to slightly lower energy.
The experimental findings and the above arguments are fully consistent with
recent work on self-sustained reactions in metal-metal multilayer composites by
Bordeaux, Yavari, and Desre,[8] and their description of these reactions is analogous
to what we believe is occurring in the Ni/Si mixtures used here.
We therefore conclude that the homogeneous temperature determines
whether or not reactions occur in 1:1 atomic ratio Ni/Si mixtures of the particular
morphologies used here. Since the homogeneous temperature determines whether or
not bulk reactions occur, one can also conclude that the reaction kinetics are slower
than kinetics of temperature equilibration in the particles. Therefore, the reaction
proceeds on a time scale greater than several microseconds when the particle size
exceeds about 10 microns.
CONCLUSION
Experiments on mixtures of 1:1 atomic ratio Ni and Si powders reveal the
existence of a sharp energy threshold below which no significant reactions occur and
above which the reaction goes to completion as evidenced by SEM and x-ray
diffraction results and voids indicative of bulk melting. The level of the thermal
energy threshold corresponds to the onset temperature of the reaction in statically
compressed powders in a DT A scan. From the existence of a sharp energy threshold
57
and the correlation to DTA results, it can be reasoned that the homogeneous shock
temperature determines whether or not the bulk reaction occurs rather than particle
level conditions.
These results are consistent with experiments in multilayer
metal-metal composites, and we believe the phenomological criteria put forth by
Bordeaux et al.[8] for these reactions adequately explains the basic nature of the
shock reaction process in the Ni/Si mixtures and morphologies used here. One can
also conclude that the reaction occurs on a time scale greater than several
microseconds.
ACKNOWLEDGEMENTS
This work was supported under the National Science Foundation's Materials
Processing Initiative Program, Grant No. DMR 8713258. We would like to thank
Phil Dixon, formally at the New Mexico Institute of Technology, for preparing the
powder mixture, and Zezhong Fu of Caltech for her help with the DTA e.xperiments.
REFERENCES
[1] S. S. Batsanov, S. Doronin, S. V. Klochdov, and A. I. Teut in "Combustion,
Explosions and Shock Waves," 22, 765 (1986).
[2] R. A. Graham, B. Morison, Y. Rorie, E. L. Venturini, M. B. Boslough, M. Carr,
and D. L. Williamson, in "Shock Waves is Condensed Matter," Y. M. Gupta (ed.),
Plenum Press, New York, 693 (1986).
[3]
N. N. Thadhani, M. J. Costello, I. Song, S. Work, and R. A. Graham, in
"Proceedings of the TMS
Symposia on
Solid State Powder Processing,"
Indianapolis, to be published (October 1-4, 1989).
[4] N. N. Thadhani, A. Advani, I. Song, E. Dunbar, A. Grebe, and R. A. Graham,
in "Proceedings of the International Conference on High Strain-rate Phenomena in·
Materials," UCSD (August 1990) Explomet '90 (in press, 1991).
58
[5] M. B. Boslough, J. Chern. Phys. 92, 1839 {1990).
[6] L. H. Yu and M. A. Myers, IBID.
[7] L. A. Clevenger, C. V. Thompson, and R. C. Cammarata, Appl. Phys. Lett. 52,
795 {1988).
[8] F. Bordeaux, A. R. Yavari, and P. Desre, Rev. Phys. Appl. 22, 707 (1987).
[9] J. A. Floro, J. Vac. Sci. Techno!. A4, 631 (1986).
[10]
F. Bordeaux, Doctoral Thesis, Institut National Polytechnique de Grenoble,
(October 1989).
[11] F. Bordeaux and A. R. Yavari, J. Mater. Res. Q, 1656 (1990).
[12] E. Ma, C. V. Thompson, L. A. Clevenger, and K. N. Tu, Appl. Phys. Lett. 57,
1262 (1990).
[13] J. 0. Olowolafe, M-A. Nicolet, and J. W. Meyer, Thin Solid Films 38, 143
(1976).
[14] E. Ma, W. J. Meng, W. L. Johnson, and M-A. Nicolet, Appl. Phys. Lett. 53,
2033 (1988).
[15] L. A. Clevenger and C. V. Thompson, J. Appl. Phys. 67, 1325 (1990).
[16] J. B. Holt, Mater. Res. Bull. 12, 60 (1987).
[17] W. H. Gourdin, Prog. Mater. Sci. 30, 39 (1986).
[18] R. B. Schwarz, P. Kasiraj, T. Vreeland, Jr. and T. J. Ahrens, Acta Metall. 32,
1243 (1984).
[19] R. B. Schwarz, P. Kasiraj, and T. Vreeland, Jr. in "Metallurgical Applications
of
Shock-Wave
and
High-Strain-Rate
Phenomena,"
L.
E.
Murr,
K. P. Staudhammer, and M. A. Myers (eds.), Marcel Dekker, New York, 331
(1986).
[20]
R. A. Graham, B. Morosin, Y. Horie, E. L. Venturini, M. B. Boslough, M.
Carr, and D. L. Williamson, in "Shock Waves in Condensed Matter," Y. M. Gupta
(ed.), Plenum Press, New York, 693 (1986).
59
21] N. N. Thadhani, M. J. Costello, I. Song, S. Work, and R. A. Graham, in "Solid
State Powder Processing," A. H. Clauer and J. J. DeBarbadillo (eds. ), Minerals,
Metals and Materials Society, Warrendale, P A (1990).
[22] S. S. Batsanov, G. S. Doronin, S. V. Klochdov, and A. I. Tent, "Combustion,
Explosions and Shock Waves" 22, 765 (1987).
[23) Y. Horie and M. E. Kipp, J. Appl. Phys. 63, 5718 (1988).
[24] B. R. Krueger and T. Vreeland, Jr., in "Shock Waves and High-Strain-Rate
Effects in Materials", M. A. Myers, L. E. Murr, and K. P. Staudhammer (eds.),
Marcel Dekker, New York (1990, in press).
[25] J. Bach, B. Fultz, and B. R. Krueger, research in progress.
[26] T. Thomas, P. Bensussan, P. Chartagnac, and Y. Bienvenu, see Reference #4.
[27]
R. A. Graham and D. M. Webb, in "Shock Waves in Condensed Matter,"
J. R. Asay, R. A. Graham, and G. K. Straub (eds.), Elsevier, 211 (1984).
[28] G. E. Korth, J. E. Flinn, and R. C. Green, see Reference #19, 129.
[29] T. Akashi and A. B. Sawaoka, U. S. Patent No.4 658 830 (April 7, 1987).
[30] A. H. Mutz and T. Vreeland, Jr., see Reference #26.
[31] V. N. Zharkov and V. A. Kalinin, in "Equations of State for Solids at High
Pressures and Temperatures," Consultants Bureau, New York (1971).
[32] 0. L. Anderson, J. Phys. Chern. Solids 27, 547 (1966).
[33] "Smithells Metal Reference Book, 6th edition," E. A. Brandes (ed. ),
Butterworth and Co., 8-42 (1983).
[34] B. M. Clemens, R. M. Gilenbach, and S. Bitwell, Appl. Phys. Lett. 50, 495
(1987).
60
Table I. Thermodynamic parameters used to determine the Hugonoits of the Ni/Si
mixtures. The isentropic bulk modulus of Ni and the Griineisen parameters for Ni
and Si were taken or calculated from Reference 31. The pressure derivative of the
isentropic bulk modulus of Ni was determined by fitting solid Ni Hugoniot data.
Silicon's isentropic bulk modulus and its pressure derivative were taken from
Reference 32. The heat capacity coefficients were taken from Reference 33. The
units of a, b, and c are J /(mole-o K), J /(mole-o K 2), and J-o Kfmole, respectively.
Density
(g/ em 3 )
f3s
8/Jsl
'Yo
(GPa)
or s
Ni(a)8.90
192.5
3.94
1.91 17.00
29.48
Ni ((3) 8. 90
192.5
3.94
1.91 25.12
7.54
Si
97.9
4.19
0.74 23.95
2.47
-4.14
2.33
61
Table II. The calculated shock conditions of the experiments discussed in the
text. The column headings correspond to the mixture, porosity, flyer velocity,
pressure, total energy, thermal energy, homogeneous temperature (assuming
no reaction), and whether or not the reaction occurred, respectively. An
asterisk indicates a four cavity experiment. The enthalpy of formation of NiSi
at 298° K is -43.1 kJfmole or -593 Jfg from W. Oelsen, H. 0. von SamsonHimmelstjerna, Mitt. K.-W.-1. Eidenforsch., Dusseldorf 18, 131, (1936). The
ratio of energy input from the shock plus the energy generated by the reaction
to the energy needed to heat and melt NiSi is 1.23 for the lowest shock energy
which triggered the reaction.
Porosity
Velocity
(%)
(m/s)
37.5
41.2
37.5*
39.9*
1020
1060
1050
1050
React.
THnr
(GPa)
ET
(J/g) (J/g)
(OC)
(Y/N)
5.60
5.38
5.86
5.46
380
421
398
407
605
670
631
648
367
410
384
396
62
Figure 1. Back-scattered SEM micrograph of the Ni/Si powder mixture showing
the morphology of the lumpy spherical Ni and the irregular Si.
63
~--A lSI
4340 steel
10.2 em¢ X6.35 em
heat treated to Rc 50
Powder
Cavity
Steel sleeve
(press fit)
_j
\__ Alunim.m plug
(press fit)
Figure 2. Schematic drawing of the target design.
The top surface is "0" ring
sealed to the barrel and the bottom surface is pressed against a momentum trap.
64
Figure 3. Optical micrograph of a shock consolidated metallic glass powder (left),
with a macro-photograph of the sectioned compact (right).
The shock wave
propagated from left to right, and the region on the left of the compact is
crystalline. Note the planar shape of the transition region between the crystalline
phase (darker phase) and the glass phase (non-etching) which is located at the
position where the release wave from the back of the flyer caught the shock wave.
10 nvn ¢ cov it ies
for powder
L_ 32 .2 nrn ~ X 9.4 nrn
porous bronze
Figure 4. Porous bronze insert machined with four cavities for powder samples.
65
50
Porosit = 507. (Tap)
40
Pressed to 327. porosity
30
..........
Pressed to 277. porosity
20
en
........
0 10
........
..5
· Shocked, no reaction
'-
Q)
0...10
Q.
-20
-30
-40~--~~~----~~~~~--~._--~~~
200
300
400
500
600
700
800
900
1000
Temperature (C)
Figure 5. DTA scans of Ni/Si powder statically pressed to four different porosities
and a shock compressed but unreacted powder (porosity near zero). Note that the
onset temperature of the exothermic reaction increases with porosity. Heating rate
was 10· K/min, and scans are successively displaced by 10 mcal/s from the scan
below.
66
Figure 6. SEM back scattered image of the Ni/Si powder mixture shocked in a full
cavity experiment to an energy just below where bulk reaction occurs.
At this
magnification, there is little evidence of any interaction between the Ni and Si.
67
Figure 7. SEM back-scattered image of the Ni/Si powder mixture shocked in a full
cavity experiment to an energy just below where bulk reaction occurs.
At this
magnification, some small interfacial mixed regions are observed as well as isolated
pools of a mixture of Ni and Si. The more typical interfaces show no mixing.
68
4. SHOCK INITIATION OF THE REACTION FORMING Ti 5Sis
4.1
Shock Induced Reactions in 5:3 Atomic Ratio
Titanium/ Crystalline Silicon Powder Mixtures
B. R. Krueger, A. H. Mutz and T. Vreeland, Jr.
W. M. Keck Laboratory of Engineering Materials
California Institute of Technology, Pasadena, CA 91125
ABSTRACT
The conditions for initiation and propagation of the reaction forming Ti 5Si 3
from elemental powders of varying porosity have been investigated using shock
waves of different pressure in vacuum, and using hot wire ignition in an argon
atmosphere. In each case the reaction either went to completion, or the powder
remained essentially unreacted. The conditions for the propagation of the reaction
depend upon the presence of residual air as well as the initial porosity and the shock
pressure.
Two regimes of porosity and pressure are found for the Ti/Si mixture
which cause complete reaction. A low energy regime with a high initial porosity
(producing a low shock pressure) with residual air triggers the reaction while no
reaction is observed with a 128% higher shock energy and a lower initial porosity
(producing a higher shock pressure) when the residual air is replaced with argon.
Hot wire ignition of porous powder at room temperature initiates a self-propagating
high temperature synthesis reaction (SHS) more easily in air than in an argon
atmosphere, while the Ni/Si powder must be heated to allow the SHS reaction to
propagate in high or low porosity mixtures in air. These observations are compared
to published work on self-sustaining reactions in multilayer films.
69
INTRODUCTION
A recently completed study of shock-initiated reactions in equiatomic Ni/Si
powder found a threshold shock energy for the reaction forming NiSi.[l]
The
threshold was determined to be between 384 and 396 J / g, corresponding to
homogeneous temperatures of 631 and 648" C in the consolidated mixture.
The
current study explores the shock conditions for the reaction forming Ti 5Si 3 from an
elemental mixture of the powders.
The chemistry and kinetics of intermetallic reactions have been explored by
observing the behavior of multilayer elemental thin film composites upon heating.
It has been shown that in many composite structures, self-sustaining chemical
reactions can be initiated upon heating.
Bordeaux and Yavari place two basic
criteria on whether or not such r~actions are possible.[2] Briefly, the first is that the
heat of the reaction must be sufficiently in excess of that required to melt the
mixture, and the second is that the mixing reaction time must be much shorter than
the time for dissipation of the heat of reaction to the environment.
Thermally
initiated reactions which are not self sustaining have been observed in Ti/Si
multilayers as well as in a number of other metallic multilayers.
Differential
thermal analysis (DSC) of Ni/Si powders pressed or shocked to low porosity show
exothermic reactions starting in the temperature range of the homogeneous shock
temperature for initiation of the reaction.[3] Solid state interdiffusion studies of Ni
as well as Ti layers on high purity amorphous and crystalline Si show the metal
silicide phase forms upon deposition and extends upon annealing, with the
compound phases forming as equilibrium is approached.[4] The DSC scans show at
least two exothermic peaks, the first due to the amorphous silicide formation and
the second due to crystallization of the silicide.
SHS reactions in elemental powder mixtures have been extensively explored
at atmospheric pressure. They may be initiated at one end of a porous sample and
70
may propagate in a homogeneous or heterogeneous mode.
Analytic expressions
describing the propagation of SHS reactions have been developed.[5,6]
Relevant
parameters are the rate of heat release in the reaction front, and the rate of heat loss
by thermal conduction and radiation.
Reaction fronts typically propagate at
velocities less than 1 m/s. A shock wave which triggers a reaction typically travels
at a velocity on the order of 1 km/s in a powder mixture and reduces the porosity
and deposits shock energy in powder particles in times on the order of 10 ns (for
particles of about 20 J.Lm diameter). Therefore substantial reaction may not occur in
the shock front unless the powder particles are of sub-micron size, but the reaction
will be initiated throughout the powder on a time scale much shorter than in the
usual SHS reactions.
The initiation of SHS reactions at atmospheric pressure in Ni/Si and Ti/Si
powder mixtures was compared in the present study. These observations suggest
possible explanations for the different initiation conditions found for reactions in
shocked Ni/Si and Ti/Si powder mixtures.
EXPERIMENT
Aesar -325 mesh Ti powder {99.5% nominal purity) was wet mixed in
1,1,2-trichloro-1,2,2 -trifluoroethane with Cerac -325 mesh crystalline Si powder
(99.5% nominal purity) in a 5:3 atomic ratio and dried in vacuum. Figure 1a is a
SEM image of the powder mixture, and Figure 1b is a SEM image of the Ni/Si
powder mixture, which has Ni particles more spherical than the Ti but with the
same Cerac Si.
Shock experiments were conducted on powders using propellant driven
stainless steel flyer plates and a target which produces well controlled plane-wave
shock geometry.[3] The barrel and powder mixture were evacuated to 0.1 Torr just
prior to each experiment. In one set of experiments the powder was evacuated from
71
atmosphere.
The remainder were backfilled with argon and then evacuated.
Table I lists the results of these experiments on powders pressed to different initial
porosity. Shock pressures and energies for the powder mixture were calculated using
averaged properties for an inert elemental mixture.[1]
The calculation of
homogeneous temperatures from the shock energy used heat capacities which were
not corrected for pressure and did not include reaction energies.
The shocked samples were examined by x-ray diffraction, and only Ti 5Si 3
diffraction peaks were observed in the reacted samples. Only Ti and Si peaks were
observed in the unreacted samples. An optical micrograph of a polished surface of
the recovered sample shocked to 0.8 GPa and mounted in plastic is shown in
Figure 2. The highly porous sponge-like structure is typical of SHS material which
melted at atmospheric pressure or in vacuum with the evolution of gases.[7]
Figure 3 is a back-scattered SEM image of the unreacted shock consolidated Ti/Si
mixture shocked to 2.29 GPa.
The Si particles show extensive fracture and no
evidence of local mixing or melting.
Ni/Si powder shocked to just below the
reaction threshold is shown in the back-scattered SEM image of Figure 4. The Si
particles have fractured, and isolated regions of a mixture of Ni and Si are observed
in what appear to have been melt pools. The mixed region in Figure 4 was found to
be 21 atomic % Ni and 79 atomic % Si by EDX.
The SHS ignition behavior of both equiatomic ratio Ni/Si powders and 5:3
atomic ratio Ti/Si powders of high porosity (about 55%) and low porosity (near
zero, shock consolidated but unreacted) was observed.
A 0.13 mm Ta wire was
placed in contact with the sample and a voltage which brought the wire to a white
heat was applied to the ends of the wire. The powders were tested in air as well as
in Ar to minimize oxidation. The low porosity powders did not ignite. The high
porosity Ti/Si ignited more readily in air than in Ar, and the high porosity Ni/Si
did not react. A SHS reaction in high porosity Ti/Si in contact with low porosity
72
Ti/Si resulted in complete reaction.
The low porosity Ni/Si was not ignited by
contact with a SHS reaction in high porosity Ti/Si.
DISCUSSION
The shock initiated reaction in the Ti/Si mixture shows a more complex
energy dependence than the Ni/Si mixture.
The Ti/Si mixture exhibits reaction
behavior which depends upon shock energy, initial porosity (or shock pressure), and
residual gas.
A shock energy of 104 J / g initiated the reaction to TisSi3 with
residual air, while no reaction was observed at a shock energy of 237 J/g with
residual Ar. The reaction occurs with a combination of low porosity and low shock
pressure with residual air which gives low shock energy, or with high shock energy
with residual air or Ar.
The heat of reaction for the formation of NiSi is 85.8
kJ /mole ( 42.9 kJ /g-atom to solid at 25° C) while that for the formation of Ti 5Si 3 is
580 kJ /mole (72.5 kJ /g-at om).
The critical conditions for the self-sustaining
reaction according to Bordeaux et al. [2] are: a) the heat of mixing must be
sufficiently in excess of the energy to melt the mixture, and b) the mixing reaction
time must be much shorter than the time required for dissipation of the heat of
reaction to the surrounding material to prevent quenching of the reaction.
The
critical condition a) is met in both systems when the minimum shock energy
observed for reaction initiation is added to the reaction energy.
Thermal
conductivities of Ni, Ti, and Si at ambient conditions are 0.91, 0.22, and 1.49
W /( cm-o K) respectively.
The rate of heat dissipation is greater in the Ni/Si
system and the reaction energy is smaller. Both conditions a) and b) favor SHS
reactions in the Ti/Si mixture as observed in this investigation. The strong effect of
residual air on both shock and SHS initiation may be explained by the exothermic
reaction caused by the oxidation of Ti.
The sponge-like structure of the shock
reacted material indicates the presence of a liquid phase after the shock pressure was
73
removed (after approximately 1 f.J.S).
Powder treatment to remove surface
contaminants such as titanium hydrides should significantly reduce the porosity of
the recovered titanium silicide.
CONCLUSIONS
1.
The shock-induced reaction forming Ti 5Si 3 from the stoichiometric elemental
powder mixture of Ti and Si exhibits a dependence on shock energy, initial porosity,
and residual oxygen.
2. SHS reactions are more readily initiated in the Ti/Si mixture than in equiatomic
Ni/Si powder mixtures with comparable particle sizes.
3. High shock and chemical reaction energies and low thermal conductivity appear
to favor self-propagating reactions in shocked powders as proposed by Bordeaux et
al. for thin film elemental composites.[2]
4.
The reaction produces a sponge-like structure, indicating that the reaction
initiated by the shock formed solid Ti 5Si 3 at atmospheric pressure.
ACKNOWLEDGEMENTS
This work was supported under the National Science Foundation's Materials
Processing Initiative Program, Grant No. DMR 8713258. Barry Krueger died on
October 29, 1990 as a result of injuries received in a motorcycle accident.
His
family, friends, and scientific colleagues mourn the loss of a truly gifted individual.
74
REFERENCES
[1] B. R. Krueger and T. Vreeland, Jr., in "Shock Waves and High-Strain-Rate
Effects in Materials," M. A. Meyers, L. E. Murr, and K. P. Staudhammer (eds.),
Marcel Dekker, New York, (1991, in press).
[2] F. Bordeaux and A. R. Yavari, J. Mater. Res . .Q., 1656 (1990).
[3] B. R. Krueger, A. H. Mutz, and T. Vreeland, Jr., source cited in Reference #1.
[4] K. Holloway and R. Sinclair, J. Appl. Phys. 61, 1359 (1987).
[5] A. A. Zenin, A. G. Merzhanov, and G. A. Nersisyan, Combust. Explos. Shock
Waves (Engl. Trans.) 17, 63 (1981).
[6] T. Boddington, P. G. Laye, J. Tipping, and D. Whalley, Combust. Flame 63,
359 (1986).
[7]
W. F. Henshaw, A. Niiler, and T. Leete, ARBRL-MR-03354. Ballistics
Research Laboratory, Aberdeen Proving Ground, MD, 1984.
75
Table I. Shock Reaction Experiments
Flyer
Velocity
(m/s)
Porosity
Shock
Homogeneous
(%)
Ener~y
(J/g
480
48.7
487
Tem(cerature
OC)
Shock
Pressure
(GPa)
Reaction
104
192
0.80
Yes
49.2
108
198
0.8
Not
514
47.4
118
214
0.95
Yes
570
48.7
145
256
1.11
Yes
575
44.4
144
254
1.31
No
693
46.0
206
349
1.76
Not
757
42.9
237
396
2.29
Not
837
44.4
293
470
2.61
Yes t
915
48.7
350
560
2.67
Yes t
965
48.7
386
610
2.95
Yes t
t Powder backfilled with argon and evacuated before shock treatment
76
(a)
(b)
Figure 1. Back-scattered SEM micrograph of (a) the Ti/Si powder mixture, and {b)
the Ni/Si powder mixture.
77
Figure 2. Optical micrograph of the recovered Ti/Si powder mixture which was
shocked to 0.8 GPa showing a sponge-like structure identified as Ti 5Si 3 by x-ray
diffraction.
78
Figure 3. Back-scattered SEM micrograph of unreacted Ti/Si shocked to 2.29 GPa.
No titanium silicides were found in x-ray diffraction or EDX analyses.
Figure 4. Back-scattered SEM micrograph of a Ni/Si powder mixture {1:1 atomic
ratio) shocked to an energy just below that for bulk reaction. Some thin interfacial
mixed regions are observed as well as isolated pools of a mixture of Ni and Si. The
more typical interfaces show no mixing.
79
5. SHOCKWAVE CONSOLIDATION OF A :rvlETALLIC GLASS
5.1 Shock Wave Consolidation of a Ni-Cr-Si-B Metallic Glass Powder
J. Bach, B. Krueger, and B. Fultz
W. M. Keck Laboratory of Engineering Materials
California Institute of Technology, Pasadena, California 91125
ABSTRACT
Bulk samples of metallic glass (Allied MBF 50) were obtained by shock
consolidation of powder produced by ball-milling the as received ribbon. The amorphous
samples exhibit low porosity and slightly higher hardness than the spun ribbon. Smaller
distensions and longer shock durations favored good consolidation which was obtained
with a powder distention of about 1.70 (particle size 44 to 88 J.lm) and shock energies
between 140 and 200 J/g. Higher shock energies caused crystallization of the glass, and
the shock front was shown to be planar and parallel to the flyer plate/sample interface.
INTRODUCTION
Since the pioneering work ofDuwez,[1] many alloys have been discovered which
solidify to an amorphous structure if cooled at a sufficiently high rate. To achieve the
required cooling rate, typically greater than 106 K/s, at least one final dimension of the
material must be small. Thus metallic glasses are usually available only in powder or
ribbon form. In the present work we used shock waves to consolidate metallic glass
powders into bulk compacts.
The deformation consolidation of metallic glass has been the subject of several
previous studies. At moderate temperatures below the glass transition temperature,
metallic glasses undergo a structural relaxation which, among other effects, causes an
80
increase in the viscosity of the material.[2] Since this relaxation is a time-dependent
process, the instantaneous viscosity at a given temperature will be lower with higher
heating rates.[3] On the other hand, the crystallization temperature of a metallic glass
follows the opposite trend and increases with increased heating rate. In some metallic
glasses, this decrease in viscosity and increase in crystallization temperature opens a
time-temperature "window" in which it is possible to plastically deform and even
consolidate the amorphous material without crystallization.[ 4]
The fast thermo-
mechanical cycle of the shock process would seem to offer a wide window for
consolidation of many metallic glasses, and previous workers [5-9] have shown that the
shock waves can successfully consolidate metallic glass powders.
It is doubtful, however, that the mechanism of consolidation is the same for shock
consolidation, and for deformation consolidation at lower strain rates. The deformation
of glassy metals changes from homogeneous to heterogeneous at the high stress levels of
shock wave consolidation,[lO,ll] so shock wave consolidation probably does not depend on the time-temperature window provided by decreased viscosity and higher
crystallization temperatures at high heating rates. An alternative possibility for the
mechanism of shock consolidation is provided in the next section. In the present work we
varied the shock parameters for the consolidation with the intent to find the range of
shock pressures where consolidation was possible. We characterized these compacts to
find the success of the consolidation and to learn how the deformation and bonding of the
metallic glass particles occurred.
81
SHOCK WAVES AND SHOCK CONSOLIDATION
The energy and pressure associated with the shock process are governed by the
Rankine-Hugoniot relationship.[12] The details of shock wave physics will not be
discussed, however one equation of interest is:
(1)
where E is the deposited specific inten1al energy; P is the shock pressure; Vo is the
specific volume of the initially porous material, and V 1 is the shocked specific volume.
For our work the shocked volume differs little from the solid specific volume of the
material, so V 1 can be replaced by the solid volume after consolidation. This results in
the equation:
(2)
which approximates the energy as being deposited in the form of thermal energy (where
Vo is the solid volume at STP, and m is the distension, m=V(powder)N(solid). The
pressure in Equation 2 was determined according to the model proposed by Simons and
Legner [ 13] for the compaction of porous materials. Although the model makes some
simplifying assumptions, we believe it to be sufficiently accurate for the current work.
Since the isentropic bulk modulus and Grtineisen parameter, the thermodynamic
parameters required by their model, have not been determined for this alloy, we assumed
these parameters were the same as for elemental nickel.
In a picture of shock consolidation provided previously by Kasiraj et al.,[l4]
densification and bonding of individual powder particles occurs within the shock front by
pore collapse and the preferential deposition of energy near the particle surface causing
. local melting. They showed that in ductile materials the surface regions of the particles
82
are heated on a time scale of 1Q-7 s. With such an energy deposition profile, the particle
interiors remain at a relatively low temperature during the shock process, so if melt pools
are formed at particle surfaces, they are solidified to an amorphous structure by heat flow
into the particle interiors. The size of the melt pools must be below a critical value,
depending on the properties of the material, in order for the consolidated material to be
rapidly solidified into an amorphous structure. It is also important that the homogeneous
temperature, the temperature to which the bulk material equilibrates, does not rise above
the crystallization temperature, since heat conduction to the surroundings is relatively
slow. This picture of shock consolidation is not based on the existence of the timetemperature window which permits the consolidation of metallic glasses at lower strain
rates.
EXPERIMENT
The material investigated was an amorphous alloy produced in ribbon form by
Allied Corporation under the product name MBF50 with a composition of
76.4%Ni- 19%Cr- 2.3%Si- 1.5%B- 0.08%C (concentrations in wt.%). According to the
manufacturer, its solid density and crystallization temperature are 7.49 g/cm3 and 740° K
respectively. The ribbon was ball milled into powder in an Argon atmosphere for about
8 h. The powder was sieved to obtain the desired particle size (the size for each shot is
presented in Table I), loaded into a target, and compressed in a hydraulic press to the
desired distention. A 35 mm smooth bore propellant gun [15] was used to propel either
an AISI 303 stainless steel or a teflon flyer plate to impact the powder. The velocity of
the flyer was measured using a radar doppler velocitometer and a time-of-flight optical
interrupt system. The velocity was used to obtain the Hugoniot of the flyer [13] which
was numerically compared to the Hugoniot of the powder in order to obtain the shock
pressure. The pressure was then used in Equation 2 to calculate the energy.
83
The consolidated samples were polished and etched with Marble's reagent
(4g CuSo4, 20cc HCl, 20cc H20), and were examined with a Nikon Epiphot
metallograph. For measurements of porosity, some micrographs were digitized and
mapped into a binary form with a television system interfaced to a Macintosh IT computer
that ran a public domain image analysis software program, Image. Density measurements
were also performed by the Archimedes method, but these measurements were accurate
to only 1-2%. To measure crystallization temperatures, differential scanning calorimetry
(DSC) was performed with a Perkin Elmer DSC-4 operated at various heating rates.
X-ray diffractometry was performed with a Norelco 9-29 diffractometer with Cu Ka
radiation and digital data acquisition.
RESULTS AND DISCUSSION
A total of eight shots were executed, with shock energies ranging from 133.8 J/g
to 364.6 J/g as listed in Table I. Three of the shots resulted in amorphous compacts, three
resulted in partial or total crystallization of the samples, and two shots, with the lowest
shock energy, resulted in only partial bonding of the particles.
Figure 1 shows the consolidated compacts, one of which was prepared for
compression tests. Macroscopic cracking occurred in some of the consolidated samples,
but the piece of material at the center of Figure 1 was apparently free of cracks. Optical
microscopy revealed that the compaction process caused heavy plastic deformation in the
initially spherical particles (Figure 2). This implies large localized strains, which suggest
large local heterogeneities in the deposition of the shock energy.
Our metallographic porosity measurements showed porosity between 0.64% to
1.77%, with the lower densities corresponding to the lower shock energies (an example is
presented in Figure 3). Density measurements by the Archimedes method confmned this
trend.
84
The amorphous states of the ribbon, ball milled powder, and the compacts were
verified using x-ray diffractometry (Figure 4). The crystallographic states, of the
compacts obtained with various shock parameters are presented in Table I. For shock
energies below 140 J/g, the consolidation of the powder was incomplete, although it
remained amorphous. For shock energies above 200 J/g the compact was at least partially
crystalline. Comparison of the broad diffraction peaks of the amorphous and partially
crystalline compacts showed that for shock energies above 2001/g crystallization occurs
gradually rather than abruptly, indicating a locally heterogeneous thermomechanical
history. For compacts that were fully amorphous, we scrutinized the widths and positions
of the broad diffraction peaks at 29 =45°, and it appeared that the average first neighbor
distance in the compact was slightly (< 1%) larger than that of the melt-spun ribbon. The
DSC heating curves of the ribbon, ball milled powder, and compacts had nearly the same
integrated areas, although the crystallization exotherms for the powder and compacts
were somewhat broader than for the ribbon.
The DSC runs were performed at different heating rates, and showed that the
onset of crystallization increases by about 30 K per decade of heating rate. Extrapolation
of the crystallization temperature vs. heating rate curve results in an increase in the onset
of crystallization from 471° C (at dT/dt = 20° per minute) to 582° C (at dT/dt = 106
degrees per minute).
One of the samples, obtained with a 303 stainless steel flyer impacting at a
velocity of 1060 m/s, was found to be crystalline at the impact side to a depth of about
3 mm, and amorphous at the opposite side. The interface between the layers, seen in
Figure 2, was sharp and its parallel orientation shows that the shock wave is planar. The
high energy of the shock wave caused crystallization of the frrst half of the sample.
However, the pressure of the primary wave was reduced upon the arrival of the release
wave (the unloading reflection from the junction between the flyer plate and the
85
supporting sabot), and the rest of the sample was consolidated while preserving its
amorphous state.
The Vickers miniload hardness data were slightly higher for the amorphous
compacts (HV=800+Kp/mm2) than for the ribbon (HV=650Kp/mm2). Two very
different hardness values were obtained for the crystalline samples. X-ray diffractometry
showed that these different hardness values corresponded to different crystal structures,
and we believe that differences in the crystalline phases are at least partially responsible
for the different hardness of the crystalline compacts. DSC showed a strong exotherm at
a hundred degrees above the crystallization temperature, which was shown by x-ray
diffractometry to correspond to the same change in the crystalline phases.
Taking the total shock energy to be deposited as heat, the low shock energies of
140 J/g correspond to a homogeneous temperature of 335° C, and the highest shock
energies of 200 J/g for which the compact remained amorphous corresponded to a
homogeneous temperature of 470° C (which is the crystallization temperature). The
Markomet 1064 consolidated previously by Kasiraj, et al.[6] remained amorphous to
higher shock energies (-400 J/g), but the crystallization temperature of the Markomet
1064 was 700° C. Kasiraj et a1.[6] noted that 400 J/g corresponded to a homogeneous
temperature that was higher than the crystallization temperature of their Markomet 1064,
but no such effect was observed in the present study.
Finally, we believe it is
coincidental that this temperature range for consolidation by heterogeneous deformation
seems consistent with the temperature window for consolidation by homogeneous
deformation extrapolated to very high heating rates. From measurements of the shock
rise time of 1o-7 s [ 14, 16], the shock front is on the order of one particle diameter
(60 J.lm). Energy deposition occurs within the shock front, and using typical thermal
conductivities of Ni alloys, during the shock risetime the characteristic distance for
thermal conduction is about 1-J.lm. High temperatures and melting could readily occur at
the surfaces of the particles, assuming that the surface regions are preferential sites for
86
heterogeneous deformation. It is probably necessary that some of the deformation occurs
in the particle interior, however, since a 1 Jlm surface layer is too small to absorb all of
the shock energy without vaporizing.
CONCLUSIONS
We obtained bulk samples of metallic glass by shock wave consolidation of ballmilled powder. The amorphous samples exhibit low porosity and slightly higher hardness
than the commercially spun ribbon. Smaller distentions and longer shock durations
produced better compacts. The energy range for a successful consolidation is 140-200 J/g
for powder of particle size 44
deposition near the surfaces of the particles, and probable melting of the particle surfaces.
The shock front was shown to be planar and parallel to the flyer plate/sample interface.
ACKNOWLEDGEMENTS
Helpful conversations with Andy Mutz, and differential scanning calorimetry
work by Zezhong Fu and Lawrence Anthony are gratefully acknowledged.
Barry
Krueger died on October 29, 1990 from injuries received in a motorcycle accident. We
thank Allied Chemical for the donation of the material. One of the Authors, J. Bach,
acknowledges the support of the Summer Undergraduate Research Fellowship program at
the California Institute of Technology. This work was supported in part by the National
Science Foundation grant DMR- 8811795.
87
REFERENCES
[1]
P. Duwez, Fiz.-2 Su;gpl. 2, 1 (1970) .
[2]
A. I. Taub and F. Spaepen, Scripta Metall. .U, 195 (1979).
[3]
A. I. Taub, Acta Metall. 3Q, 2117 (1982).
[4]
P. H. Shingu, Mater. Sci. Eng. 27., 137 (1988).
[5]
C. F. Cline and R. W. Hopper, Scripta Metall.ll, 1137 (1977).
[6]
P. Kasiraj, D. Kostka, T. Vreeland, Jr., and T. J. Ahrens, J. Non-Cryst. Solids Ql,
967 (1984).
[7]
D. Raybould, D. G. Morris, and G. l\. Cooper, J. Mater. Sci. ,H, 2523 (1979).
[8]
D. G. Morris, Metal Sci. 14, 215 (1980).
[9]
L. E. Murr, S. Shankar, A. W. Hare, and K. P. Staudhammer, Scripta Metall. .ll,
1353.(1983).
[10] F. Spaepen and A. I. Taub, "Amorphous Alloys: Flow and Fracture," General
Electric Report No. 83CRD068 (April 1983).
[11] F. Spaepen, Acta Metall. 2j,, 407 (1977).
[12] Y. B. Zel'dovich and Y. P. Raizer in "Physics of Shock Waves and High
Temperature Hydrodynamic Phenomena, Vol. 2," W. D. Hayes and R. F. Probstein (eds.),
Academic Press, New York, 685-715 (1966).
[13] G. A. Simons and H. H. Legner, J. Appl. Phys. ,51, 943 (1982).
[14] R. B. Schwarz, P. Kasiraj, and T. Vreeland, Jr. in "Metallurgical Applications of
Shock-Wave and High-Strain-Rate Phenomena," L. E. Murr, K. P. Staudhammer, and
M.A. Meyers (eds), Marcel Dekker, New York, 331 (1986).
[15] J. Bach, "Shock Wave Consolidation of Metallic Glasses," Proceedings Fourth
National Conference on Undergraduate Research, Vol. 1, Univ. N. Carolina, Asheville,
194 (1990).
[16] R. B. Schwarz, P. Kasiraj, T. Vreeland, Jr, and T. J. Ahrens, Bull. Am. Phys. Soc.
2.8., 460 (1983).
88
SHOCK
ENERGY
(J/g)
FLYER
POWDER SIZE DISTENSION
VICKERS COMMENTS
Material/
Jlm
364.6
d<88
1.84
303SS/5
853
171
AMORPHOUS REGION
CRYSTALLINE REGION
285.2
44 1.84 303SS/9.28 906 MOSTLY CRYSTALLIZED 209.7 44 1.72 303SS/9.02 731 AMORPHOUS 197.1 44 1.73 Teflon/9. 98 990 PARTIALL V CRYSTALLIZED 163.1 44 1.73 30355/9.23 800 AMORPHOUS 141.4 44 1.74 Teflon/9. 96 815 AMORPHOUS 134.9 d<44 1.70 303SS/8.97 715 PARTIALLY CONSOLI DATED 133.8 44 1.70 30355/9.02 625 PARTIALLY CONSOLIDATED Table L Shock conditions for the various shots. The first row shows the conditions for • . I !I ' . I I.I •t•I " Figure 1. Photograph of recovered compacts. ••• ' • ' • ' ••• ' • ' .. \. • \ . \ . \ On the left is the sample which crystallized to a depth of about 3mm, on the right is amorphous sample, and in the 89 Figure 2a. Figure 2b. A macro-photograph of the polished and etched compact. 90 .. _.. I· ,-_,.·· ,.~. \ 'w Figure 3. A typical micrograph and binary map used to calculate porosity. 16x10 14 12 CJ) 10 40 60 80 100 2e Angle
the shot in which the compact obtained was crystalline on the impact side and amorphous
on the target side. Vickers hardness for the amorphous :MBF/50 ribbon is 653.
center is amorphous sample prepared for compression testing.
showing the transition region. The shock wave propagated from left to right.
The shock wave propagated from left to right.
't•
- .·{
'\..._
Figure 4. Cu Ka diffractometer scans of Allied MBF/50 ribbon, ball milled powder,
and compact obtained with shock energy of 163.1 J/g.