n. n. thadhani et al- shock-induced chemical reactions in titanium–silicon powder mixtures of...

8/3/2019 N. N. Thadhani et al- Shock-induced chemical reactions in titaniumsilicon powder mixtures of different morphologies: Time-resolved pressure measurements an

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Shock-induced chemical reactions in titaniumsilicon powder mixturesof different morphologies: Time-resolved pressure measurementsand materials analysis

N. N. Thadhania)

School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta,Georgia 30332-0245

R. A. GrahamThe Tome Group, Tome , New Mexico 87031

T. RoyalSchool of Materials Science and Engineering, Georgia Institute of Technology, Atlanta,Georgia 30332-0245

E. DunbarDepartment of Metallurgical and Materials Engineering, New Mexico Tech, Socorro, New Mexico 87801

M. U. Anderson and G. T. HolmanSandia National Laboratories, Department 1152, Albuquerque, New Mexico 87185-1421

Received 4 November 1996; accepted for publication 23 April 1997

The response of porous titanium Ti and silicon Si powder mixtures with small, medium, andcoarse particle morphologies is studied under high-pressure shock loading, employing postshockmaterials analysis as well as nanosecond, time-resolved pressure measurements. The objective ofthe work was to provide an experimental basis for development of models describing shock-inducedsolid-state chemistry. The time-resolved measurements of stress pulses obtained with piezoelectricpolymer poly-vinyl-di-flouride pressure gauges provided extraordinary sensitivity fordetermination of rate-dependent shock processes. Both techniques showed clear evidence forshock-induced chemical reactions in medium-morphology powders, while fine and coarse powdersshowed no evidence for reaction. It was observed that the medium-morphology mixtures experiencesimultaneous plastic deformation of both Ti and Si particles. Fine morphology powders showparticle agglomeration, while coarse Si powders undergo extensive fracture and entrapment withinthe plastically deformed Ti; such processes decrease the propensity for initiation of shock-inducedreactions. The change of deformation mode between fracture and plastic deformation in Si powdersof different morphologies is a particularly critical observation. Such a behavior reveals theoverriding influence of the shock-induced, viscoplastic deformation and fracture response, whichcontrols the mechanochemical nature of shock-induced solid-state chemistry. The present work in

conjunction with our prior studies, demonstrates that the initiation of chemical reactions in shockcompression of powders is controlled by solid-state mechanochemical processes, and cannot bequalitatively or quantitatively described by thermochemical models. 1997 American Institute ofPhysics. S0021-89799703215-5

I. INTRODUCTION

Materials synthesis and processing under conditions ofhigh-pressure shock-compression loading of powder mix-tures has become a subject of increasing attention. Of par-ticular interest and importance is the use of strongly nonequi-librium processes. As the conditions encountered in the

shock process are not achieved in any other environment, theprocess has the potential of yielding novel compounds, meta-stable phases, and uniquely modified microstructures.1 7 It isto be expected from elementary considerations6 that the un-usual combination of high pressure and rapid loading rates,which produce large plastic deformation and concomitanthigh pressure in powders can lead to shock-initiated chemi-cal reactions by mechanisms different from those encoun-tered in conventional processes. Unfortunately, there is little

scientific knowledge of the processes of shock deformationin porous solids with high levels of porosity. The presentwork attempts to address these fundamental questions with asystematic study of shock compression of titaniumsiliconTiSi powder mixtures under controlled shock loading.Both, nanosecond time-resolved pressure measurements andmaterials analysis of samples preserved for postshock, mi-crostructural characterization are used in the investigation.

Past work has established that the fundamental mecha-nisms controlling chemical reactions in powder mixtures andleading to synthesis of compounds are dominated by pro-cesses occurring during the few to more than a hundrednanosecond stresspulse rise time and the microsecond du-ration of the peak pressure state.3,4 The critical processesinclude particle configurational changes principally causedby plastic deformation less often, fracture or comminution,mixing of the reactant powders within and around the voidsby plastic flow and dispersion of fragments, enhanced solid-aElectronic mail: [email protected]

1113J. Appl. Phys. 82 (3), 1 August 1997 0021-8979/97/82(3)/1113/16/$10.00 1997 American Institute of Physics

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state reactivity of powders, as well as the usual temperatureincreases.6 Under such conditions, chemical reactions havebeen observed to occur in powder mixtures during the high-pressure shock state before unloading to the ambient pres-sure in time scales of mechanical equilibration.816 Chemicalreactions can also occur at times after the sample is in theambient, postshock state. Such reactions occurring in essen-tially the shock-modified activated material, due to bulkresidual shocktemperature increases in time scales ofthermal equilibration, involve mechanisms similar to moreconventional combustion-type processes,17 but are expectedto be dominated by shock-activated solid-state diffusion andthermal quenching. While these two types of chemical reac-tions, defined, respectively, as shock-induced andshock-assisted chemical reactions,7 have been distin-guished on the basis of the time period over which theyoccur, it is difficult to infer from samples preserved for post-shock analysis recovered samples alone, whether theobserved reactions occurred during the high-pressure loadingand unloading conditions, or if they occurred after unloadingto ambient conditions. Furthermore, the highly exothermicnature of these reactions leads to rapid temperature increases,

often melting the reaction products. Thus, recovered samplesshow reaction products with microstructures typical ofmelted and solidified materials, which mask the characteris-tic features of the shock-compressed powders at the time thereaction is initiated.

The objective of the work reported in the present paperis to experimentally investigate the mechanics of the defor-mation processes leading to shock-induced chemical reac-tions. The work involves direct determination of the rates ofdeformation and chemical reaction in a systematic study oftitanium and silicon powder mixtures in a highly porousabout 53% of solid density state, using both nanosecond

time-resolved pressure measurements and microstructuralanalysis of recovered samples. Further, in the present work,the effects of morphological characteristics of powders onshock deformation and reaction is extensively investigatedwith both procedures. The materials system under investiga-tion is of considerable interest in that the product of thehighly exothermic chemical reaction, Ti5Si3 is an alloy ofconsiderable technological importance. The starting materi-als, titanium and silicon, have been investigated in priorstudies1820 and represent, respectively, a metal that wouldbe expected to undergo plastic deformation, and a semicon-ductor that normally deforms in a brittle fashion.

The present work builds directly upon prior work on

shock compression of titanium and silicon powdermixtures,20 in which the authors showed the relatively low-pressure initiation threshold for onset of shock-induced reac-tion based upon evaluation of the microstructure of recov-ered samples. Further, the authors showed that the thresholdwas strongly dependent on particle morphology size, andinitial packing density of the samples. In the present paper,we will first provide a brief background on the mechanics ofshock compression of powders in both inert and chemicallyreacting states. Next, the experimental procedures and resultswill be described and discussed. The paper will then draw

broad conclusions regarding the fundamental aspects of thedeformation and chemical reaction processes, based on boththe present work and our prior investigations.

II. SHOCK COMPRESSION MECHANICS OF INERTAND REACTIVE POWDERS

Shock mechanics of the time-dependent compression ofhighly porous solids powder compacts or distended solidswith porosities of tens of percent cause wave propagation

features, which are qualitatively different from the samesolid in the fully dense state. The sample responses revealedby shock-pressure measurements are completely dominatedby the porous state and have the macroscopic appearance ofa radically different class of materials, which indeed theyare. It is to be expected that it is these deformation features,which lead to the observed chemical reactions in the shockstate.6 The overall features of deformation processes associ-ated with highly porous solids in which voids are notisolated in a solid matrix but are interacting in the deforma-tion process, can be considered from a thermodynamic equi-librium viewpoint to identify first-order features of the wavemechanics. Figure 1a shows an idealized shock pressure

versus volume curve for a porous solid of 50% theoreticaldensity, and a vertical line corresponding to the dense solid.In the case of the porous solid, the application of increasingshock pressure leads to large compression at low pressure asthe particles deform into voids. At a critical pressure definedcrush strength, the observed compression approaches thesolid density and the sample becomes fully dense. With in-creasing pressure, the compression follows the solid densitybehavior offset by a small expansion due to shock-compression heating.

The first-order consequences of such a behavior in termsof the expected shock velocities of waves propagatingthrough a sample, can be directly inferred from equilibrium

mechanics of shock propagation, as shown in Fig. 1b. Theslopes of the Rayleigh lines connecting the initial statewith a shock-pressure state for both a material with a zero-crush strength and a finite-crush strength, represent equilib-rium wave velocities; higher slopes represent higher wavevelocities. In both cases, as pressure is increased, the wavevelocity is expected to increase. As indicated in Fig. 1 c forzero strength, however, the wave velocities will be less thanthe finite strength case for the same pressure. The wave ve-locity versus pressure behavior expected from the zero-crush-strength response can be accurately estimated asshown by the dotted line in Fig. 1c. Corresponding to thecrush strength shown in Fig. 1b, the filled circles describe atypical wave velocity versus pressure behavior for a materialwith finite strength. Thus, wave velocities higher than thosepredicted for zero strength are expected at pressures belowthe crush strength, and approximately the same values atpressures higher than the crush strength. The essential, first-order differences between the behavior of highly porous sol-ids and fully dense solids are well illustrated by comparingthe wave velocities shown schematically in Fig. 1d. Theextraordinarily low wave velocities at low pressure and thelarge influence of pressure on wave velocity, dominate thebehavior of the porous solid, in contrast to a dense material.

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can account for the reaction mechanisms. Constant volumereactions have been used to interpret the few available shockvelocity data obtained by the Batsanov group.10,11 Althoughsuch an analysis is sufficient to demonstrate that a chemicalreaction is likely to have occurred, it does not provide aphysically descriptive model for the mechanical and chemi-cal features of reaction.

A model, called CONMAH configuration, mixing,activation, and heating has been proposed by Graham,6

identifying the processes in a conceptional sense and consid-ering all relevant effects occurring prior to, at the onset, andsubsequent to reaction initiation. It presumes that chemicalreactions in highly porous solids are fundamentally mecha-nochemical in character, and are controlled by the intense

mechanical deformations induced by the presence of thevoids and the heterogeneity of the stresses at the interparticlesolid contacts. In the model, the two reactant particles areseparated by a large void.6 The deformation works to closethe void in time, and after some time, the reactants can beexpected to become mixed in the sense of a more intimatespatial relationship. With further mechanical action and itsintense shear, those reactants that are in sufficiently intimatecontact, begin to react. As reaction proceeds, the system be-comes increasingly heterogeneous, and at some stage, pro-

ceeds to the degree of completion possible for the mecha-nochemical conditions. The unreacted starting materials alsoplay a critical role due to their thermal quenching effects.32

An important consequence of the mixing concept is that vari-ables such as the volumetric ratios of substituents play acrucial role. If volumetric ratios are substantially unbalanced,the reaction cannot proceed because mixing will be limited.Thus, the overall CONMAH concept defines stages corre-sponding to the configuration change of reactants prior toand at the onset of reaction, leading to the evolution of theproducts.

Microstructural characterization of samples preservedfor postshock analysis has been successful in bringing outfeatures of the deformation processes and configurationchanges in reactants; however, direct quantification of theeffects has been difficult. Semiquantitative evaluation of theeffects, such as shock activation and mixing, has been pro-vided by differential thermal analysis,3335 revealing reduc-tions in temperatures at which reactions occur upon heatingof recovered samples, and x-ray diffraction XRD line-broadening analysis,3638 showing retained microstrain andcrystallite size reductions.

III. EXPERIMENTAL PROCEDURES

The approach adopted in the present work was to inves-

tigate the chemical reaction response of a low-reaction-threshold titaniumsilicon system by performing a system-atic series of combined time-resolved pressure measurementsand shockrecovery experiments on the same powder mix-tures. The titaniumsilicon powder mixture system has theunusual characteristic of a small density differential betweenreactants, approximately the same shock impedance, and ahigh reaction exothermicity. Both Ti and Si are expected toundergo shock-induced polymorphic phase transitions atpressures greater than about 10 GPa in homogeneous defor-mation modes.39 Table I summarizes physical properties ofthe starting powders along with those of their stablecompounds.4042 Prior shock synthesis studies on TiSipowders by the Vreeland group20 revealed that shock-induced chemical reactions in this system occur at very lowpressures few GPa and corresponding shock-induced mean-bulk-temperatures below the melt temperature of Si, formingthe Ti5Si3 compound. It was also reported that the propensityfor reaction initiation in TiSi shows a very large depen-dence on the particle size, with powders approximately 45m in size reacting at lower shock-pressure thresholds andalso with lower porosities, than the coarser about 100 mpowders. Such a particle size dependence has also been ob-served during combustion synthesis as well as mechanical

FIG. 2. Schematic of a pressurevolume curve illustrating first-order ef-fects of reaction under conditions of constant pressure Ref. 21, in whichthe exothermic energy transformation causes an expansion to larger vol-umes; b equilibrium wave velocity vs pressure behavior in a chemicallyhighly exothermic reacting powder mixture calculated based on the reac-tion effects shown in a. It can be seen that at low pressures without reac-tion, higher wave velocities are anticipated until the crush strength isexceeded. At pressures greater than the crush strength, if chemical reactionoccurs, then the observed behavior will show higher wave speeds dashedline than those predicted for the zero-strength model solid points.




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alloying of TiSi powders,43,44 which suggests that the reac-tion characteristics of Ti and Si powders may be stronglyprocess dependent.

A. Starting materials

Three different morphologies of both silicon and tita-nium were studied in what are termed coarse, medium, andfine powder mixtures based on a measure of the size of thepowder particles. The titanium powders were: Cerac No.T-1191, fine, 13 m; Aesar No. 10386, medium, 45 m; and Cerac No. T-1219, coarse, 105149 m. The

silicon powders were: Cerac No. S-2021, fine, 10 m;Cerac No. S1053, medium, 45 m; and Cerac No. S1051,coarse, 105 149 m. Particle size distributions and scanningelectron microscopy SEM images were obtained for eachpowder. SEM images showing the morphology of the pow-der mixtures are shown in Figure 3. The medium morphol-ogy Ti was found to contain many elongated particles, whichmay be as long as 100 m, but because of the elongatedshape, they pass through the 325 mesh sieve. While the Tipowders were polycrystalline aggregates in all cases, the Sipowders were actually single-crystal particles. The Ti and Sipowders were mixed in a stoichiometric ratio to form theTi5Si3 compound, which corresponds to a weight ratio of

74/26 and a volumetric ratio of 60/40.

B. Nanosecond time-resolved pressuremeasurements

Direct time-resolved measurements allowing observa-tions of shock-compression phenomena on the nanosecondtime scale under precisely controlled loading are essential todistinguish effects occurring during shock compression fromthose that occur after unloading to ambient conditions. Thepioneering work on time-resolved observations of chemi-cally reacting powder mixtures was accomplished by Bat-sanov and co-workers and reported in 1986.10 These authors

used manganin pressure gauges to obtain records of shockprofiles, and wave speed, and observed that in equimolar tinand sulfur powder mixtures, the measured pressure pointsdeviated towards the right increased volume of the Hugo-niot curve calculated for the unreacted mixture. Additionalwork was reported in this same system45 and in tin teluride,11

where optical pyrometric measurements were also utilized.The aluminumsulfur system was also investigated in workreported in 1992.12 Other work with high-pressure shockwaves demonstrating evidence for shock chemistry usingvarious detection methods is listed in Table II.

The first use of nanosecond time-resolved measurementsusing PVDF poly-vinyl-di-fluoride stress-wave gauges in

chemically reacting powders was reported by Graham and

TABLE I. Properties of elemental Ti and Si reactants and TiSi compounds Refs. 4042.

ConstituentDensity(g/cm3)

V

%H

kJ/g atomCrystal

structure

Soundvelocitykm/s

YieldstrengthMPa Electronegativity

Melttemp.C

Ti 4.500 hcp 5220 140 1.5 1667Si 2.330 Diamond 7990 93 1.8 1412TiSi 4.320 22.9 15.5 ortho 1570Ti5Si3 4.315 27.8 73.4 hcp 2130TiSi2 4.043 27.5 10.7 ortho 1380

FIG. 3. SEM images showing particle morphologies of different 5 Ti3 Si powder mixtures: a Fine, 13 m Ti Cerac No. T-1191 and 10 m Si CeracNo. S-2021; b Medium, 10 44 m Ti Aesar No. 10386 and Si Cerac No. S-1053; and c Coarse, 105149 m Ti Cerac No. T-1219 and 45149 mSi Cerac special No. S-1051. Si particles are generally blocky single crystals with a shiny contrast, while Ti particles are rounded polycrystalline aggregates.

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co-workers in 1993.21 Dunbar and co-workers16 reported thefirst time-resolved work in titanium silicon, also in 1993.

Table III summarizes the various studies on highly poroussolids with the PVDF gauges. The literature cited in TablesII and III, shows that there is considerable evidence for theoccurrence of a strong exothermic chemical reaction ontimes scales of significantly less than the typical wave transittime of 1 s.16,21,5054 Measurements of wave profiles inshock-compressed powders reported during the past fewyears have also revealed that the powder compression pro-cess is complex and highly rate dependent.50,51 Stress pulserise times after propagation distances of a few millimetersare large, typically varying from many tens to hundreds ofnanoseconds. With these characteristics, the wave propaga-tion in powder samples cannot be realistically described on

the basis of conventional shock conservation relations. In aparticularly interesting case, a study of AlFe2O3 mixtures

51

observed that there was evidence that the transmitted waveshad distinct features in their profiles associated with indi-vidual deformation features of each constituent.

In the present work, Bauer piezoelectric polymer PVDFstress-wave gauges55 were used to quantify the responses ofthe powder samples. Typical PVDF gauge package configu-rations consisted of insulating films of FEP Teflon or Kel-Fon both sides of 25 m thick PVDF elements, with Al sput-

tering of 2000 on powder sides of the gauge package toprevent pyroelectric effects from affecting gauge response

during the possible reaction of powders. All gauges were ofhigh quality, biaxially stretched PVDF film, poled using theBauer process52 to a 9.2 C/cm2 remnant polarization, andhaving identical gold over Pt electrodes. The PVDF gaugeexperiments were performed using the Precision Impact Fa-cility at Sandia National Laboratories, which employs a 63mm diam, 25 m long single-stage, compressed-gas gun. Thefacility provides for exceptional control of tilt or mis-alignment of impact surfaces typically 200 rad or less,impact velocity measurements to 0.1%, wave speed measure-ments to 0.1%, and Gigahertz frequency response instrumen-tation. The frequency response of the gauge and recordingsystem result in timing measurements that provide an unusu-

ally precise capability for wave speed measurements. Forhigher pressure experiments, explosive loading with 4 in.diam plane-wave generators was used.51

The overall experimental arrangement is shown sche-matically in Fig. 4. The powder-mixture samples werepressed directly into copper capsules with PVDF gaugepackages placed in intimate contact with the powder-capsuleplanar surfaces to monitor both input-shock loading andthe propagated-wave characteristics. The propagation ofthe shock wave sensed by the input gauge and propagated

TABLE II. Measurements reporting evidence of shock chemistry.

Year Authors Ref. Method used Material density Observations

1986 Batsanov et al.10 Pressure, manganin gauges SnS 98% Shift in Hugoniot at 15 GPa1989 Boslough46 Optical pyrometry NiAl Temperature changes1990 Boslough47 Optical pyrometry AlFe2O3 50% Temperature increases above

5 GPa pressure1991 Gao and Jing48 Manganin gauge 2AlFe2O3 50%70% 5 GPa wave1991 Batsanov11 Pressure, manganin gauges SnTe Shift in Hugoniot at 50 GPa1992 Gogulya12 Optical pyrometry SAl( 90%)

3 sizes, 3 mix ratiosTemperature increases at 79GPa pressure

1992 Yoshida andThadhani15 Optical measurements ofbulk sound speed NbSi 50% Increases in bulk sound speedand Hugoniot changes at 20

GPa1992 Bennett et al.14 Reflected-shock pressure,

manganin gaugesAlNi 55% Excess reflected-shock pressure

at 15 GPa1993 Iyer et al.13 Pressure, manganin gauges AlNi 55% backed

by steel or lexanExcess reflected shock pressure

1994 Batsanov et al.45 Optical pyrometry and manganin pressure gauges SnS 92% Temperature increases within0.2 s at 20 GPa

1994 Chen et al.49 Impedance match BaCO3TiO2 3045 GPa discontinuity

TABLE III. Nanosecond time-resolved measurements with PVDF gauges performed on powders.

Year Authors Material Density Observations

1993 Graham et al.21 3NiAl, 5Ti3Si, TiO2 Powder compression, wave rise times1994 Anderson et al.50 TiO2 60% dense

0.216.1 GPawave dispersion in porous rutile, rise timesin HMX, 5Ti3Si, 3NiAl,

1994 Holman et al.51 2AlFe2O3 mixture53% dense, 0.6710 GPa

Structured waves, P V stiffening

1994 Dunbar et al.16 5Ti3Si 45%53% Wave-profile measurements1994 Sheffield et al.52 HMX explosive (1.24 g/cm3) Wave-profile and reaction behavior of

HMX1996 Anderson et al.53 HMX explosive Simultaneous PVDF and VISAR experiments1996 Holt et al.54 Teflon, two morphologies Wave rise time, crush strengths




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shock-recovery fixtures have been extensively used for gen-erating a range of controlled and reproducible shock condi-tions in numerous single-component and multiple-component powders.2 The plane-wave explosive-loadingsystem utilizes standard P-22 plane-wave generators and ex-plosive pads, designed and manufactured at U.S. DOE Labo-ratories.

The copper capsule encasing the powders permits theirpressing to preselected densities with accuracies of less than1%. To assure well-defined loading conditions, all surfaces

incident to the shock direction are mechanically lapped tooptical flatness. In these fixtures, the loading history is domi-nated by an initial low-pressure planar wave, followed by aradial wave, caused by wave trapping occurring as a result ofthe low impedance powder mixture relative to that of solid-copper containment. The resulting pressures calculated fromnumerical simulations on 55% dense rutile powders, showthat the PBB fixtures subject the powders to an average peakpressure of 5 1 GPa with a shock-induced temperature riseof 150 C in the bulk region and 75 C in the outer volume.The MBB fixtures subject the powders to an average peakpressure of 7.5 2.5 GPa in the bulk region and a pressure of27 GPa along the axial region with temperatures of 225 C inthe bulk and 250 C in the outer volume. Because of the lowstarting density of typical powder compacts and resultingradial wave-focusing effects, the shock pressures and tem-peratures are relatively insensitive to materials properties.Details describing the recovery fixtures and numerical simu-lations are provided in prior works.5861

The shock-compressed samples preserved for postshockanalysis are typically removed intact from the fixture afterexperiment, then sectioned, and polished to view the crosssection of the hockey-puck shaped compacts. Optical andscanning electron microscopy were performed to identifyspacial variations in sample characteristics, including

whether partial or complete reaction was present, and tocharacterize the shock-deformed configuration of unreactedconstituents. A typical reacted sample shows a smooth oruniform contrast of individual grains of the product micro-structure along with spherical or rounded voids in the case ofhighly exothermically reacting systems. Unreacted samplesshow the dissimilar contrast of the constituent particles, aswell as distinct interparticle boundaries. X-ray diffractionline-broadening analysis, using the WilliamsonHallmethod,62 was also performed on the unreacted powder mix-tures of different morphology, to determine the amount ofmicrostrain retained and crystallite size reductions in theshock-compressed reactants. These XRD measurements

build upon the extensive work of Morosin36,37 who employedthe WarrenAverbach technique, which is important forlower symmetry materials such as ceramics.

IV. EXPERIMENTAL RESULTS

A. Time-resolved pressure measurements

The time-resolved PVDF-gauge pressure measurementswere performed in two sets. In the first set, experiments wereconducted on medium-morphology TiSi powders at differ-ent stresses and a constant packing density of about 53%

TMD.16

In the second set, the experiments were extended tocoarse at 53% TMD and fine at 45% TMD powders,through the same range of pressures.

Representative traces of the gauge output in current-versus-time and the corresponding integrated traces of stress-versus-time for gauge packages located at both input-shockand propagated-wave locations, for experiment No. 2476, areshown in Figs. 5a5d. The input PVDF gauge generates apiezoelectric current as the shock wave transits the gauge,with a rise time less than the shock transit time through the25 m film thickness. In interpretation of the records, it isimportant to consider the detail of wave propagation in thePVDF gauge packages. The input shock propagates through

the 50 m FEP Teflon insulation film to the Teflonpowderinterface, where a reflection is caused due to the impedancemismatch between the Kel-F and the powder. The reflectedrelease wave then arrives back at the input PVDF gaugeabout 40 ns after the initial input shock, as shown in Figs.5a and 5b. The magnitude of the input stress entering thepowder is taken as the stress at the time 40 ns, where thearrival of the reflected release is indicated on the currenttime trace. Thus, as shown in Fig. 5c, the input stress of1.49 GPa propagates through the 4 mm thick powder sample,and arrives as a dispersed wave at the propagated PVDFgauge location, and generates a piezoelectric current Fig.5b with wave rise time typically increased by an order ofmagnitude from that recorded by the input gauge. As shownin the resulting stress-versus-time profile in Fig. 5d, theoutput stress recorded by the propagated gauge is 1.17 GPa.

The experimentally measured and calculated parametersfrom all time-resolved PVDF gauge experiments on the pow-der mixtures and the corresponding sample configurationsare listed in Table IV. Data in the input stress column corre-spond to the stress in the powder measured by the input-shock gauge as indicated above. The wave velocity is thewave speed through the powder, obtained by measuring tran-sit time between the two gauges placed in direct contact with

FIG. 5. Representative traces of gauge output in current vs time and corre-sponding integrated traces of stress vs time for gauge packages located atinput-shock a and c and propagated-shock b and d locations, separat-ing the 4 mm thick TiSi powder mixture layer for sample No. 2476.




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opposite surfaces of powder compact less propagation timesfor the insulation. The output stress, measured by thepropagated-wave gauge placed between the powder andpolymer backing material, corresponds to the stress resultingfrom the interaction between the powder mixture and thepolymer backing. The magnitudes of these stresses will de-pend strongly on the backing material due to the impedancemismatch.

The relative volume shown is calculated from the knowninitial density, measured input stress and wave velocity, andfrom shock jump conditions for conservation of mass andmomentum. In reality, the stress pulses propagating throughthe 4 mm thick powder mixtures have a structure character-istic of wave-dispersion effects, with shock rise times greaterthan several hundreds of nanoseconds.50,51 With such wave-dispersion effects, the calculation of the relative volumebased on jump conditions applied to a steady-state shockwave, may not be appropriate. One can, however, use thecalculated relative volume along with the measured inputstress to obtain first-order powder-compressibility effects.This calculation is more meaningful for fully dense solidsthan for highly porous solids due to the large compressionsinvolved in the latter case.

The measured input stress plotted as a function of thecalculated relative volume is shown in Fig. 6. A calculatedcurve for an inert TiSi powder mixture at 53% density, isalso shown in the plot, with crush-up to full density assumedto be occurring at zero stress, followed by marginal expan-sion from that of the soliddensity curve. This zero-strengthinert curve can be calculated with confidence due to themuch smaller compression compared to the porous state.Points corresponding to experimentally measured input

stress and calculated relative volume for the three differentmorphologies of the powder mixtures show significantly dif-ferent trends. It can be seen that points for medium-morphology powders indicate crush-up to full density occur-ring at pressures less than about 1 GPa, followed by asubsequent shift to the right of the calculated inert powder-mixture curve. The observed volume expansion indicatesstrong evidence for rapid chemical reaction, consistent withthe constant pressure model21,22 and the shock-compressionmechanics description provided earlier. The constant pres-

sure model was proposed on the basis of consideration ofmechanical relaxation times for heterogeneous states of thereactants and products, and contrasts sharply with the con-stant volume model in which large pressures will result fromthe exothermic energy products.10,63,64

The plot of measured input stress versus calculated rela-tive volume Fig. 6 also shows that in contrast to themedium-morphology powders, the points corresponding tothe coarse and fine powder mixtures, do not deviate from thecalculated inert curve, demonstrating that these powder mor-phologies do not undergo reaction under the conditions used.It is significant to note that the data for both the coarse- andfine-morphology mixtures, indicate crush-up to full densityat stress levels higher than that for the medium-morphologypowders. The observed different crush strengths are overtindications of the strong influence of morphology on the de-formation process.

While the results of measured input stress plotted as afunction of calculated relative volume may be consideredsufficient only to reveal first-order effects, the measuredwave speed as a function of the measured input stress per-haps provides a more direct indication of chemical reactionsin the shock state. Figure 7 shows the wave speed-versus-input stress data for the powder mixtures, obtained from the

FIG. 6. Measured input stress plotted as a function of calculated relativevolume for medium, coarse, and fine TiSi powder mixtures, along with acalculated vertical curve for a solid inert TiSi powder mixture. Pointscorresponding to experimentally measured input stress and calculated rela-tive volume for the three different morphologies of powder mixtures showsignificantly different trends. Points for medium-morphology powders indi-cate crush-up to full density at 1 GPa pressure, followed by volume ex-pansion shift to right of calculated solid inert mixture curve , indicatingevidence for rapid shock-induced chemical reaction, while points corre-

sponding to coarse and fine powders show crush-up at higher pressures andno significant deviation from the solid curve, indicating no reaction at pres-sures up to 3 GPa.

FIG. 7. Plot of experimentally measured wave speed as a function of mea-sured input stress for the three morphologies of TiSi powder mixturesshowing trends similar to those revealed by pressurevolume compressibil-ity characteristics shown in Fig. 6. The points for medium-morphology pow-ders approach the calculated curve for the inert powder at the crush-upstrength, and at input stresses greater than the crush strength, the experimen-tal points deviate from curve showing increased wave speed correspondingto the occurrence of chemical reaction and formation of an intermetalliccompound in the shock state. Points for the fine and coarse mixtures remainclose to the calculated curve indicating no reaction.




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PVDF gauge measurements. Trends similar to those revealedby the pressurevolume compressibility characteristics areobserved. At shock pressures above the crush-up strength,the points for medium-morphology powders appear to devi-ate from the calculated curve for the inert powder, showingincreased wave speed corresponding to the occurrence ofchemical reaction and formation of an intermetallic com-pound in the shock state. On the other hand, points for thefine and coarse powder mixtures remain close to the calcu-lated curve, indicating no reaction with these morphologiesunder the conditions of the experiments. Thus, the compres-sion characteristics, and measured wave speed-versus-measured input stress reveal consistent evidence for shock-induced chemical reactions in medium-morphology powdermixtures and no reaction in coarse and fine mixtures. Theresults provide the data needed to determine the extent of

reaction. The data also provide the critical observationsneeded for development of realistic deformation descriptionsin mixture theory models.

B. Sample preservation experiments

Six shock-recovery experiments were performed on thepowder mixtures of medium morphology packed at an initialdensity ranging between 53% and 64% with the MBB fix-tures, and 45% and 53% with the PBB fixtures. Two experi-ments were performed on fine- and coarse-morphology pow-ders, each with packing density of 64% with the MBB, and53% with the PBB fixture. Controlled gun-impact experi-ments at 52% initial density were also performed, one eachon fine-, medium-, and coarse-morphology powders at im-pact velocities of about 370 m/s. It should be noted thatunlike the more dispersed wave produced in the Momma andPoppa Bear explosive loading configurations due to thewave-shaping effect of the explosively generated pulse as itis transmitted through a steel driver undergoing the 13 GPaphase change, a flat pulse is generated during experimentswith controlled plateimpact loading. Thus, with gun recov-ery experiments, the incident conditions in the powders aresimilar to those produced in time-resolved experiments. Thepeak conditions, however, are dominated by radial wave-

focusing effects, and at impact velocities of about 370 m/s,approach conditions similar to the PBB fixture. Details ofpowder characteristics and experimental configurations usedfor the recovery experiments are listed in Table V.

The overall results of shock-recovery experiments, basedon optical and SEM analysis, are illustrated in the reactionmap shown in Fig. 8. For medium-morphology powders,MBB experiments showed complete reaction in samples with 46% porosity, and no reaction in samples with 36% poros-ity. The PBB experiments showed no reaction in sampleswith 41% and 47% porosity, but complete reaction with 55%

TABLE V. Parameters and results of recovery experiments in 5Ti3Si powders of different morphology Refs.5760.

Experimentnumber

Packing densityg/cm3 %

Porosity% Configurationa

Powdermorphology

Reactionbehavior

NMG-9122 1.92 52.8% 47.2 PB-B Medium NoneNMG-9121 1.93 53.1% 46.9 MB-B Medium CompleteNMG-9120 1.95 53.6% 46.4 MB-B Medium CompleteNMG-9212 1.625 44.7% 55.3 PB-B Medium CompleteNMG-9123 2.147 59.0% 41.0 PB-B Medium NoneNMG-9211 2.33 64.1% 35.9 MB-B Medium None

NMG-9252 1.633 44.9% 55.1 PB-B Coarse NoneNMG-9251 1.916 52.7% 47.3 MB-B Coarse NoneNMG-9254 1.626 44.7% 55.3 PB-B Fine NoneNMG-9253 1.989 54.7% 45.3 MB-B Fine LocalizedSNL-2506 1.912 52% 48.0 gun Medium NoneSNL-2572 1.901 52% 48.0 gun Coarse NoneSNL-2573 1.904 52.6% 47.4 gun Fine Not recovered

aMB-BMomma Bear Baratol, Peak P 7.5 GPa; PB-BPoppa Bear Baratol, Peak P 5 GPa.

FIG. 8. Reaction map showing overall results of shock recovery experi-ments, based on the effect of initial density and shock pressure on thereaction threshold in TiSi powder mixtures of medium Ti,Si1044 m, coarse Ti105149 m and Si45149 m, and fineTi13 m, Si10 m. Cross-hatched bars correspond to reacted mate-rial, and horizontally hatched bars with dark lettering correspond to unre-acted material, as evidenced from microstructural optical and XRD analy-sis of recovered shock compressed samples.




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porosity. The reaction trends for medium-morphology pow-ders were used to guide experiments on fine and coarse pow-ders. In general, the microstructure of fully reacted samplesshowed a uniformcontrast grain structure, interdispersed

with spherical voids, typical of a melted and resolidified ma-terial. Figure 9 shows the general characteristics of the re-acted sample with the optical micrograph in a revealing thegrain structure (size10 m), and the XRD trace in bshowing peaks corresponding to the Ti5Si3 product.

The results of materials analysis of reaction propensityin mixtures of Ti and Si powders of different morphology,shock compressed at the same pressures, shows that themedium-morphology powders, have a greater propensity forreaction, than fine- and coarse-morphology powders packedat the same density, similar to the trends revealed by time-resolved instrumented experiments. Furthermore, with higherpacking densities or lower initial porosities higher pres-

sures are required for shock-induced reaction initiation. With53% TMD packing density, the medium-morphology pow-ders react in the higher pressure MBB fixture and not in thelower pressure PBB fixture, in which case, reaction is ob-served only with the lower packing density of 47% TMD.

C. Characteristics of unreacted shocked samplecompacts

Microscopy and x-ray diffraction line-broadening analy-ses were performed on recovered compacts, which wereshock compressed at conditions below the threshold. Such

samples are useful to qualitatively and quantitatively deter-mine shock-induced configurational changes to the particlesand characteristics of reactants prior to reaction initiation.All microscopic analysis was performed on cross-sectionalsurfaces, along identical regions of every compact, namely,the bulk area away from axis and peripheral edges. Opticalmicrographs of samples of the three different morphologiesof powder mixtures, shock compressed using the PBB shockrecovery fixture are shown in Figs. 10a10c. The grainy-

contrast fine-, medium-, and coarse-morphology Ti particles,in all three micrographs show extensive plastic deformationand flow. The fine Ti particles are seen to also form largeagglomerates ( 200 m diam). On the other hand, theblocky and shiny-contrast fine and medium Si powders showextensive plastic deformation and flow around the Ti par-ticles, while the coarse Si particles show only fracture andcracking. SEM micrographs of unreacted coarse- andmedium-morphology powder mixtures, packed at higher ini-tial density and shocked with the MBB fixture, provide abetter description of the configuration, as shown in Fig. 11. Itcan be clearly seen that, while Ti powders of both coarseand medium morphology undergo extensive plastic defor-mation and flow, the qualitative nature of the response of Siparticles depends on the particle size. Medium-morphologySi powders plastically deform and flow along with Ti par-ticles Fig. 11a, in contrast to coarse Si powders, whichexhibit extensive fracture and fragmentation, and remaincontained within the Ti particles Fig. 11b, thereby limit-ing the intimate mixing of reactants. In all cases, independentof morphology and peak pressure, titanium is observed toform the matrix of the compact, indicating that titanium plas-tically flows around silicon and encapsulates the silicon frag-ments.

To quantify the deformation effects in shock-compressed

unreacted compacts, x-ray diffraction peak broadeninganalysis was performed on the initial powder mixtures ofmedium and coarse morphology, and the shocked compactsof medium morphology No. 2506 and coarse morphologyNo. 2572. The back surfaces of the compacts were lightlypolished to remove an approximately 0.5 mm layer, prior tox-ray scans with a 0.015 step size, and a 5 s hold was usedto analyze the data. Prior to performing peak-broadeninganalysis, instrumental broadening was computed using Sistandard and, subsequently, subtracted from the experimen-tally measured integral breadths for the powder-mixturesample. A 95% confidence interval of the y intercept of the

linear regression was also determined for the Si standard, tocalculate the amount of error in each subsequentWilliamsonHall value. WilliamsonHall plots int cos versus sin were generated for each sample to quantify theeffects of microstrain and crystallite size. The WilliamsonHall analysis performed on unshocked-, coarse-, andmedium-morphology Ti powders showed no microstrain,while Si powders of both morphologies showed some strain.Titanium powders are generally made by chemical tech-niques and no retained strain would be expected. On theother hand, the strain in Si powders may have been induced

FIG. 9. General characteristics of fully reacted Ti Si sample with a scan-ning electron micrograph revealing the grain structure average size 10 m, and b XRD trace showing peaks corresponding to the Ti5Si3reaction product.




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due to attrition processes used for reducing and grading pow-ders to different sizes.

A WilliamsonHall plot comparing the medium- andcoarse-morphology compacts, at the same peak shock pres-sure impact experiments Nos. 2506 and 2572 is shown inFig. 12. The slope of the shock-compressed coarse Ti pow-der is slightly greater than the corresponding slope ofmedium-morphology Ti, indicating greater microstrain in thecoarse Ti compact. However, the data on Si reveal an inter-esting trend, with considerable microstrain in the medium-morphology powder as indicated by the larger slope andminimal strain indicated by nearly zero slope in the coarse-morphology Si powder compact. The intercept of the coarseSi is, however, increased, indicating that the crystallite sizeis reduced to almost the same as medium-morphology Sipowders indicating particle fracture.

The calculated residual microstrain of Ti in shock-compressed, unreacted samples of both the medium- andcoarse-morphology system are 3.22103 and 3.98 103, respectively. In contrast, the microstrain in Si of themedium-morphology sample is 3.14103, while thecoarse-morphology Si exhibits extensive fracture and nostrain. The values of microstrain in Ti and Si correspond todislocation densities of the order of 1011 cm2 estimated us-ing the Williamson and Smallman approach.64 Such levels of

dislocation densities are typical of heavily cold-worked ma-terials.

FIG. 10. Optical micrographs comparing the configuration of deformed reactants in a fine, b medium, and c coarse morphology powders shockcompressed with Poppa Bear Baratol PBB recovery fixture at similar packing density. While the grainy-contrast Ti particles in all mixtures reveal consistentdeformation effects, the blocky- and shiny-contrast single-crystal Si particles show deformation behavior dominated by particle size effects, with fine and

medium Si particles showing extensive deformation and coarse Si particles showing extensive fracture and cracking.

FIG. 11. SEM micrographs showing unreacted configuration ofa mediummorphology and b coarse morphology TiSi powder mixtures shock com-pressed with the MBB fixture, revealing clear differences in their deforma-tion and fracture response.

FIG. 12. WilliamsonHall plot comparing the medium and coarse powdermixture compacts at the same peak pressure impact experiment Nos. 2506and 2572. The Ti peaks in both cases show substantial microstrain, with thetrace for coarse Ti indicating slightly larger strain than the medium Tishocked samples. Data for Si peaks show extensive strain in the mediummorphology shocked sample, and no strain but significantly decreased crys-tallite size increased intercept in the coarse morphology shocked sample.




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V. DISCUSSION OF RESULTS

The combination of traditional shock compression worktime-resolved measurements and traditional materials sci-ence studies microstructural characterization performed inthe present investigation, provides an unusually strong mate-rials behavior database from which the fundamental natureof the deformation characteristics of reactants and kinetics ofchemical reactions can be described.

A. Shock-induced chemical reaction behavior

It is clear from the results of time-resolved measure-ments, that sufficient evidence exists to demonstrate thatchemical reactions in TiSi powder mixtures occur duringthe rise times and the microsecond duration wave propaga-tion of shock loading. Nevertheless, the mechanochemicalprocesses leading to the initiation of reaction are extremelycomplex. The fact that coarse and fine powder morphologiesare less sensitive to the shock initiation of reactions thanmedium-morphology powders, evidenced both from time-resolved measurements and shock-recovery experiments, isan overt indication of the complex local conditions that leadto reaction initiation.

Thermochemical models,18,19,65 as well as voidcollapsemodels,2931 are not capable of evaluating the powder mor-phology influence on reaction behavior. This is not just be-cause of the geometrical constraints that need to be built inthe models, but primarily because constitutive relationsavailable do not permit realistic calculation of shape-dependent deformation or fracture response. Voidcollapsemodels also cannot describe situations in which voids are notisolated but are strongly interacting during the deformationprocess.

B. Shock-induced configurational changes in

unreacted powder constituentsThe shock-induced configurational changes of reactants

in unreacted samples are observed to differ significantlyamong the different morphologies. The deformation or frac-ture response of constituents determines the extent of mixingand the nature of configurational changes occurring duringshock compression, which greatly influences the intimacy ofcontact between reactants, and therefore, the reaction pres-sure thresholds. In the powder mixtures, the Ti particles gen-erally undergo extensive plastic deformation irrespective ofparticle size, as evident from microstrain analysis and micro-structural observation. On the other hand, Si particles exhibiteither plastic deformation or cracking and fracture of par-ticles, depending on the particle size. The coarse-morphology powder mixtures show extensive fragmentationand containment of Si within deformed Ti particles. TheSEM micrograph shown in Fig. 11b illustrates this effectmost clearly. With such a behavior, mixing between the tworeactants is inhibited, restricting chemical reaction. Coarseparticles of covalently bonded materials such as diamond66

have also been shown to exhibit extensive fracture, whilepowders of small sizes undergo plastic deformation.

The fine-morphology powders, on the other hand, showagglomeration of particles forming separate aggregates of Ti

and Si, thereby limiting simultaneous deformation and mix-ing. In the present powder mixtures, shock compression ofonly the medium-morphology powders results in simulta-neous deformation of both Ti and Si, which yields an inti-mately mixed configuration more favorable to chemical re-action. Consequently, it can be argued, after the study of theconfiguration of shocked and unreacted samples, that themedium-morphology powder mixtures could be expected tohave the lowest reaction pressure threshold.

The observed strong influence of particle morphology onchemical reactions is overt evidence that equilibrium thermo-dynamic models are inadequate to describe the observed be-haviors. Indeed, the fine-morphology higher surface arealow initial density higher shock temperature compactswould be expected to initiate reaction at the lowest shock-loading conditions in many descriptions. Such is not thecase; these strong morphological effects are also characteris-tic of AlNi powder mixtures as observed from our previousstudies.23,24,34,35,67 Clearly, a scientific description of thechemical process must be based on the local micromechani-cal conditions.

In the thermochemical sense, the coarse morphology in

which interparticle contacts are fewer in number than in fineor medium morphologies, higher local stresses will result inhigher temperatures in localized hot spots. 68 For ex-ample, in recent studies on silicide-forming powder mix-tures, Meyers et al.19 proposed a thermodynamic and kineticanalysis of shock-induced reactions in Nb or Mo and Sibased systems. Their analysis is derived on a reaction initia-tion mechanism requiring a melt phase at siliconmetal in-terparticle regions. They rationaled that if the energy gener-ated due to chemical reaction is greater than that dissipatedby thermal conduction, then a steady-state reaction can startfrom local hot-spot melt areas and propagate into the in-terior of the particles. Accordingly, they calculated critical

molten hot-spot regions and melt fraction of Si, based on ashock energy threshold corresponding to the mean-bulk tem-perature, which must be above that required to initiate reac-tions at ambient pressure. However, if such local tempera-tures alone were responsible for initiation of reaction, coarseparticles would be observed to initiate reaction at a lowermean pressure than the medium-morphology powders. Suchis not the case. Indeed, existing thermochemical models,which address computation of local interfacial temperaturesthe calculated local temperature is strongly model depen-dent are sufficient to describe chemistry in only a very thinregion of material at the interface. The observed chemicalreaction behaviors indicate rapid reaction over large volumesof materials.

In the mechanochemical sense, the interparticle contactpoints control the local stresses, thereby producing stressmagnitudes and stress states, which result in enhanced plasticdeformation and more efficient filling of the voids with thereactants, leading to a more intimately mixed reactantconfiguration. The role of morphology, then, is to control themagnitude of the local stresses, thereby influencing the de-formation. The present observations are consistent with sub-stantial local stresses. The presence of a significant, morpho-logically dependent mean pressure is also required to explain




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the change from ductile to brittle deformation in silicon. Themechanochemical concept of solid-state reactivity is greatlyenhanced by defects resulting from plastic deformation.69

Hence, the mechanochemical process will lead to shock-activated conditions.

The present work provides both qualitative conceptualfeatures and quantitative data, which can be used to developrealistic models of chemical reactions induced by shock-compression processes. It also demonstrates and outlinesfundamental issues involved in shock compression of highly

porous solids. These results can now be used to developmodels explaining the mechanisms of the shock-compressionresponse of powders and, subsequently, shock-inducedchemical reactions. In the following section, we provide con-cluding remarks, which discuss these issues in light of theresults of the present work and our other prior work.

VI. CONCLUDING REMARKS: SUMMARY OFFUNDAMENTAL ISSUES

The present work adds qualitatively new aspects to ourknowledge with the use of both nanosecond time-resolvedpressure measurements and shock-recovery techniques, but

perhaps its principal significance is to bring a focus to theprior broad and deep studies of shock-induced solid-statechemistry. The various research studies have moved from theearly phrenological investigations of 30 years ago1,5,70 to acontemporary ability and realization of the need to clarify avision of the fundamental issues involved. Fundamental is-sues to be considered include i differentiation between ther-mochemical and mechanochemical processes, ii identifica-tion of materials and morphological factors controllinginitiation of reaction, modeling of deformation of porous sol-ids, and modeling of the chemical reaction process, and fi-nally iii the role of nanosecond, time-resolved measure-ments in developing scientific models.

The choice between thermochemistry and mecha-nochemistry as the fundamental paradigm used to provide ascientific description of the deformation and chemical reac-tion point i above, provides a stark contrast. The literatureis abundant in both areas, and both paradigms are supportedby theory and experiment. Thermochemical approaches arerooted in the foundations of early shock-compression sci-ence, which are based on concepts of thermodynamic equi-librium. It is generally agreed that shock-induced chemicalchanges in materials are observed principally in the porousstate. Even though it is clear that the porous solids mustexperience heterogeneous deformation, conventional Hugo-niot approaches have yielded a reasonable first-order descrip-tion in many cases.18,19,65 In this case, the additionalpressurevolume energy in the system corresponding tocompression of the extended state is assumed to appear astemperature, which adds to the pressurevolume state as anexpansion. The temperature experienced can then drivechemical reaction, particularly when the contribution ofshear deformation in shocked solids is considered. Elevatedtemperature can also result in melting with resulting in-creases in diffusion constants. The validity of the thermo-chemical paradigm for the description of shock-inducedsolid-state chemistry must rest upon detailed studies and ex-

periments, which probe the fundamental assumptions. Infact, first-principle, elementary considerations and many de-tailed experiments clearly show that shock-induced solid-state chemistry cannot be scientifically described on the basisof thermochemistry.

Mechanochemical approaches are rooted in foundationsof the substantial mechanochemical literature and elemen-tary, first-principle considerations. It is obvious that in thehighly porous state, an assembly of particles can only bestressed through interparticle contacts. Mean pressure on thepowders is, thereby, supported locally with stresses substan-tially greater than the mean pressure. Many investigationsshow that the principal feature of shock-compressed powdersis their residual strain, typical of cold-worked metals even incovalently bonded, otherwise brittle materials.36,37 The localstresses are strongly dependent on the particle morphology,porosity, and mechanical properties of the materials. The in-terparticle localized contacts create stress states, which in-clude both mean-pressure, normal-, and shear-stress compo-nents. Further, the total mean compression from the initialextended state to the fully dense state typically, 100% mustbe accomplished through viscoplastic shear deformation. The

local thermal environment caused from localized deforma-tion results from a balance between the mechanical energyand the thermal conductivity. The viscous input mechanicalenergy rates are balanced by the heat flow away from thelocal site. As a sample compresses from the initial to thefinal state, the stress configuration and stress state will bealtered qualitatively.

From a mechanochemical viewpoint, plastic deformationof the particles will result in substantial concentrations ofdefects, which will serve to greatly enhance the solid-statereactivity.35 Observations are consistent with the maximumeffects possible in solids.36,37 Melting itself is controlled bydefect concentrations and defect configurations. Hence, the

melt phenomena will also be controlled by the shock-formeddefect state in the solid. It is interesting that from the mecha-nochemical paradigm, any tendency to soften or melt one ofthe components will reduce the interparticle shear stressesresulting in less overall plastic deformation and reduced ten-dency for reactions to occur in the duration of the shock-compression state. Observations from time-resolvedmeasurements15 and recovery experiments34 support thisview. It is, of course, no doubt that interparticle flow of themelt phase due to shock-compression and capillarity, mayfavor postshock or shock-assisted reactions occurringvia dissolution and reprecipitation or defect-enhanced solid-state diffusion processes.

Materials and morphological features ii above furthercomplicate the problem. These morphological features con-trol the interparticle stresses, which in turn, depend explicitlyon the mechanical properties of each material system. Thus,a multicomponent mixture of particles will result in differentlocal stresses than that of the same configuration of singlecomponents. Equilibrium mixture theory based on data fromsingle-component materials samples would, therefore, not beexpected to be descriptive of the mixed system. This situa-tion is well demonstrated in shock-compressed samples ofaluminum-hematite71 and aluminumtungsten oxide.72 In the




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aluminum-hematite sample, shock compressed in a MBBfixture, the hematite is observed to deform around the alumi-num particles and form the matrix phase. In the tungstenoxide mixture, the aluminum is observed to deform aroundthe oxide. Whether the effect is due to morphological factorsin the tungsten oxide case is not known, but the observationindicates that the total plastic deformation cannot be as-sumed to be a fixed value for a given porous material.

The shock-deformation process is substantially differentfrom other intense deformation process as shown in compari-sons between intensely ball-milled powders and shock-modified powders.73 The condition of 50% dense solids pro-ducing plastic deformations of about 100% at rates of106 107 s1, yields a strain versus strain-rate space not ac-cessed in any other deformation experiment. Mechanochemi-cal effects observed in mechanical alloying and shock syn-thesis also reveal striking differences. Data on paramagneticdefects in shock-modified rutile,73 and chemical changes ob-served in shock-modified MnO2,

74 provide explicit evidenceconfirming the uniqueness of the defects produced by theshock-compression process.

The results of the present work reveal an extraordinarily

low-threshold stress to initiate reaction in the titaniumsilicon system compared to other systems such as aluminumnickel,24,34 zincoxide hematite,23 and aluminum hematite,51

and raise the question of whether the materials factors con-trolling stress threshold can be identified. In general, the casecan be made that the ease of plastic deformation will lead toimproved mixing of potential reactants. Thus, low elasticlimits and high viscosity flow should act to promote reaction.In the case of titanium or silicon, neither has exceptionallylow strength, indeed silicon has a very high Hugoniot elasticlimit. The main distinguishing feature of these two materialsis that they both experience polymorphic transformations atpressures in the vicinity of 10 GPa. Even though the mean

pressure for initiation is less than this value, local stresses arelikely to be in the transformation pressure range. Certainly,volumetric changes accompanying transformations will actto promote materials deformations and could lead to bettermixing. Nevertheless, it is not clear what materials behaviorshave led to the low-threshold stress for chemical reaction inthis system.

Under rapid viscous flow, density differences betweensubstituents although not very significant in the present caseTi 4.5 and Si 2.3 g/cm

3 is expected to play a criticalrole in promoting instabilities, which can lead to materialsmixing. In that regard, any materials or morphological fea-ture that tends to promote heterogeneous motions will act toaccelerate chemical reaction. Indeed, once reaction occurs,the local reaction products themselves with their differentdensities and temperature will lead to greater heterogeneityand act to accelerate the reaction process. These mecha-nochemical characteristics are consistent with the processesdefined by the CONMAH conceptual model, which providesa framework from which various scientific models can bedeveloped. Certain critical aspects of the CONMAH pro-cesses are contained in the Horie VIR model.32 The localstresses and mechanical deformations can apparently be re-alistically treated in the Baer mixture theory models.31

The present paper uniquely combines traditional shockcompression and materials science techniques to develop amore detailed picture of the chemical processes. It is, never-theless, important to recognize that the present work followsa continuous path from the early experiments onZnOhematite,23 aluminumhematite,51 and nickelalumi-num24,34 investigations, all performed with the use of stan-dardized sample preservation fixtures, which strengthens thecomparative nature of the work and gives confidence in thesubtle conditions encountered. Taken together, the various

studies represent a broad and thorough investigation of thefundamental aspects of shock-induced solid-state chemistry.These studies demonstrate that in description of shock-induced solid-state chemistry, the question is no longerwhether, but, the extent to which. The question is notwhether shock compression can initiate complete chemicalreaction in the time of a typical shock-compression process,but under what conditions will these reactions occur. Cer-tainly, the reaction space is very limited, not unlike all as-pects of solid-state chemistry.

ACKNOWLEDGMENTS

The authors acknowledge the support provided by San-dia National Laboratories DOE Contract No. DEAC04-94AL86000 and the Army Research Office Grant No.DAAHO4-93-0062 at Georgia Institute of Technology. Theshock recovery experiments were performed using the EM-RTC explosives firing facilities at New Mexico Tech withthe assistance of Marvin Banks.

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n. n. thadhani et al- shock-induced chemical reactions in titanium–silicon powder mixtures of...

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