N. N. Thadhani- Shock induced and shock-assisted solid-state chemical reactions in powder mixtures

8/3/2019 N. N. Thadhani- Shock induced and shock-assisted solid-state chemical reactions in powder mixtures

1/10

Shockinduced and shock-assisted solid-state chemical reactionsin powder mixtures

N. N. ThadhaniSchool of Materials Science and Engineering, Georgia Instituteof Technology, Atlanta, Georgia 30332-0245

(Received 2 February 1994; accepted for publication 28 April 1994)

Shock compression of powder mixtures can lead to chemical reactions, resulting in the formation ofequilibrium as well as nonequilibrium compounds, and rapid increases in temperature. The reactionsoccur as manifestations of enhanced solid-state chemical reactivity of powders, caused byconfigurational changes and defect states introduced during shock compression. tie types ofreactions are possible and can be distinguished on the basis of their respective process mechanismsand kinetics. Shock- induced chemical reactions occur during the shock-compression state, beforeunloading to ambient pressure, and in time scales of mechanical equilibrium. In contrast,shock-assisted reactions occur after unloading to ambient pressure, in an essentially shock-modifiedmaterial, in time scales of temperature equilibration. The mechanisms of shock-assisted reactionsinclude solid-state defect-enhanced diffusional processes. Shock-induced reactions, on the otherhand, require mechanisms different from conventional solid-state nucleation and growth processes.The complex nature of deformation of powders has precluded a detailed understanding of thereaction mechanisms of such high-rate reaction processes. Results of controlled experiments,however, suggest that shock-induced chemical reactions involve nondiffusional processes givingrise to mechanochemical effects and solid-state structural rearrangements. Mechanistic concepts thatdistinguish between shock-induced and shock-assisted chemical reactions are described. The effectsof configurational changes introduced during shock compression, and the influence of materialproperties and shock-loading -characteristics on such effects, are analyzed to identify themechanisms of complex processes leading to chemical reaction initiation and compound formation.

I. INTRODUCTION

The combination of defect states and packing character-istics produced in powders due to dynamic void compres-sion, plastic deformation, flow, and mixing, is possible sin-gularly by shock compression.-5 The enhancement inchemical reactivity resulting under such conditions can causepowder mixtures to undergo chemical reactions during themicrosecond duration shock state. Conclusive e_vidence ex-ists, based on real-time measurement studies, that indicatesthat the occurrence of chemical reaction in the microsecondduration is indeed possible during shock compression.687

Highly activated states are also- produced in shock-compressed materials which can lead to accelerated masstransport during postshock thermal treatments.8-10 Conse-quently, chemical reactions can occur in shock-modifiedpowder mixtures at temperatures substantially lower than,and at rates significantly faster than, similar self-sustainingcombustion-type reactions. J Postshock chemical reactionsoccurring as a result of shock compression simply assisting(activating or modifying) the powder mixture for subsequentthermal initiation can be classified as shock-assisted reac-tions. On the other hand, reactions initiated by shock com-pression and occurring within the pressure equilibrium ((1,u.s) ime scale can be classified as shock-induced chemicalreactions. In some cases, it may be difficult to infer if theso-called shock-induced chemical reactions in powder mix-tures occurred during the high-pressure shock state beforeunloading, or if they occurred subsequent to loading and un-loading to ambient conditions. It is possible that the bulk

(residual) temperatures generated in the shock-compressed

powders in time scales of thermal equilibrium (>lO w), cansubsequently initiate reactions in the highly reactive configu-ration produced as a result of shock-modification effects.Such reactions occurring subsequent to unloading wouldagain, in principle, be classed as shock-assisted and not

shock-induced chemical reactions.Mechanisms of shock-assisted chemical reactions, initi-ated by bulk shock temperatures in time scales of thermalequilibration, or by postshock thermal treatments, can be un-derstood on the basis of defect-enhanced solid-state diffusionprocesses in shock-modified materials. In contrast, shock-induced chemical reactions involve mechanisms that are dif-ferent from those involving usual processes of nucleationand growth from either the molten liquid or by diffusion inthe solid state. Manifestations of enhanced solid-state chemi-cal reactivity leading to shock-assisted and shock-inducedchemical reactions have brought forward a new class of en-

ergetic materials that are unique in their response to shockcompression. As a consequence, synthesis of compoundscontaining equilibrium and nonequilibrium phases or radi-cally modified microstructures is possible via these chemicalreaction processes.5

The objective of this article is to describe mechanisticconcepts that distinguish between shock-induced andshock-assisted chemical reactions occurring in shock-compressed powder mixtures. The two classes of reactionsare discussed on the basis of comparisons with other solid-state reaction processes. Analysis of configuration changesintroduced during shock compression and effects of materi-

als characteristics on such configurational changes, deduced

J. Appl. Phys. 76 (4), 15 August 1994 0021-8979/94/76(4)/2129/l O/$6.00 0 1994 American Institute of Physic s 2129

Downloaded 30 Jun 2004 to 130.207.165.29. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp


2/10

from a large number of experimental observations, are alsopresented.

II. SHOCK RESPONSE OF POWDERS

The response of powders to shock-compression effects issignificantly different from that of solid-density materials. Alarge amount of energy is dissipated in plastic deformationand crushing of the powders in the process of void annihila-tion. Various void collapse models have been developed,13

based on rate-independent and rate-dependent, as well asperfectly plastic and elastic-viscoplastic material consider-ations. Stress-wave measurements have also beenperformed,7 which reveal that crush-up of powders to soliddensity produces complex wave loading characteristics. Themeasured shock-wave rise times are observed to vary from afew tens to several hundreds of nanoseconds,7 depending onthe magnitude of the shock. While rapid-loading rates at highpressures make it necessary to incorporate rate-dependentconsiderations, long rise times at low pressures alter the oth-erwise prompt thermal effects and hydrodynamic consider-ations assumed in theoretical treatment of the shock state. A

realistic analysis of shock-compression effects, therefore, be-comes extremely complex.Experimental measurements also show that the crush

strength of powders is a function of their initial packing den-sity and powder particle morphology.7 Furthermore, in thecase of mixtures of powders, e.g., A.l+Fe203,14 it has beenshown that the crush-up behavior is dominated, alternately,by the compression characteristics of the respectivecomponents.t4 Thus, the crush-up of the mixture is influ-enced initially by the compressibility of Al (at low pressures)and later by the compressibility of FqO, (at higher pres-sures). Such characteristics of the deformation response ofpowders make it very difficult to formulate simple modelsthat can explain the process mechanisms of phenomena oc-curring during shock compression in a wide range of tempo-ral, spatial, and pressure scales.

Shock compression of powders and powder mixturesalso results in various types of mechanical, physical, andchemical effects. A large number of defects are introduced inthe powders due to the kinetic energy of the shock pulse.Extensive plastic deformation, fluidlike turbulent flow, heat-ing, particle comminution, and mixing of constituents withfresh and cleansed surfaces is possible. These effects signifi-cantly alter the mechanical, physical, and chemical charac-teristics of powders, thereby influencing their solid-state re-

activity.The various processes occurring in powders duringshock compression are best characterized in a mechanisticconcept developed by Graham.r5 The overall concept is de-scribed as occurring in three stages: an initial configuration,transition zone, and final compressed configuration. The ini-tial configuration strongly influences the overall process be-cause of its control on energy localization, tluidlike flow, andmass mixing. The transition region lasting for a few to hun-dreds of nanoseconds corresponds to peak rise in pressure.Finally, the release zone accommodates the reduction inpressure, with release occurring along the solid shock-modified state. The transition zone is the most critical event,

and forms the basis of a model defmed by CONMAH (con-figuration change, mixing, activation, and heating),15 whichaddresses processes occurring during shock compression ofpowders and ultimately leading to either shock-induced orshock-assisted chemical reactions, or simply unreactedshock-modified state.

During shock compression, irreversible changes arecaused in the starting configuration. The individual powderparticles are substantiahy deformed to fill the voids, therebyproducing a significantly altered final configuration. The degree of deformation of particles, and hence the total configu-rational change, is influenced by differences in properties ofconstituent materials, volumetric distribution of constituents,powder morphology, starting porosity (or void volume), andshape of voids. The defect substructure within the solid par-ticulates is also substantially changed at the atomic and mi-croscopic levels. Mass mixing during the transition zone oc-curs due to the turbulent flow of particles in and around thevoid space during the process of pore collapse. Shock acti-vation occurs due to the extensive plastic deformation ofindividual particles and their relative flow past each otherwhich results in generation of large defect densities, cleans-ing of particle surfaces as well as opening of fresh surfaces.Finally, localized and bulk heating, provides a thermal envi-ronment, which can either facilitate reaction processes, oreven anneal out defects and produce recrystallized micro-structures. The various attributes of processes occurring dur-ing shock-compression, as described by CONMAH,r5 can besummarized schematically in Fig. 1. Thus, the overall sce-nario leading to shock-induced chemical reactions in timesscales of mechanical equilibrium, or shock-assisted reactionsin time scales of thermal equilibrium, or simply unreactedshock-modified states attained upon equilibration with theambient, can be generalized in a phenomenological concept.

The mechanisms of shock-assisted and shock-inducedchemical reactions are discussed in more detail next.

Ill. SHOCKZASSISTED REACTIONS IN POWDERMlxTURES

It is well established that the defects generated due toshock compression can significantly modify and enhance thesolid-state reactivity of powders.-578 Brittle ceramics andeven metaIs, such as silicon, undergo significant grain sizereduction due to shock compression, via grain fracturing orby generation of subgrain structures.16 Increasedmass trans-port rates are possible in shock-compressed materials due to

introduction of defects and creation of new paths for motionof point defects along grain boundaries.17 Such characteris-tics play a vital role in enhancing the solid-state chemicalreactivity of powders and their mixtures, essentially by cre-ating a shock modified material. Various attempts have beenmade to advantageously utilize the enhancement in reactivityof shock-modified materials by postshock controlled-ratethermal treatments. Successful examples of these includesintering of difficult-to-consolidate oxide and nonoxideceramics,lr7 improving catalytic activity of materials,81and enhancing the kinetics of nucleation of precipitation-strengthening phasesIpressure phases.

or other types of metastable high-

2130 J. Appl. Phys., Vol. 76, No. 4, 15 August 1994 N. N. Thadhani



3/10

Reactant A I Reactant B I

+ configurational changes

+ plastic flow and mixing

+ defect generation

Q fracture of particles

+ heating

,Y\

b

sh~-A.Ysisted

rl

OhemicalReactioru

FIG. 1. Schematic illustrating the effects of shock compression of powdermixtures and processes resulting from these effects.

Enhanced reactivity also leads to altered solid-statechemical reaction behavior of shock-modified powder mix-tures. A brief description and typical examples of enhancedchemical reactivity evidenced by differential thermal analy-sis of shock-compressed intermetallic-forming powder mix-tures are presented next, followed by calculations of solid-state diffusion, to explain the mechanisms of shock-assistedchemical reactions.

A. Thermal analysis of shock-modified powdermixtures

The postshock thermally initiated chemical reaction be-havior of shock-compressed powders was first studied byHammetter et aZe9 n M-Al mixtures. They used differentialthermal analysis (DTA) and observed that mechanical mix-tures of Ni-Al powders in unshocked condition showed areaction exotherm at 650 C, corresponding to the occur-rence of a self-sustaining reaction initiating with the melting(eutectic) of Al. The shocked mechanical mixtures revealedtwo reaction exotherms, the main exotherm at 650 C andanother preinitiation exotherm at -550 C correspondingto a solid-state reaction.

In a similar but more detailed study, Dunbar and

co-workers investigated Ni and Al powders of three differ-

FINE, SPHERICAL

COARSE, SPHERICAL

0 200 400 600 800

TEMPERATURE, OC

FIG. 2. DTA traces of shock-processed samples of JNiflAl mixtures ocoarse, flaky, and fine morphology powders showing different reaction characteristics. While coarse morphology powders show mostly a liquid-statereaction exotherm following a minor solid-state reactioti exotherm, the finand flaky morphology powder mixtures show predominantly solid-state reaction with little or no reaction in the liquid state (Ref. 10).

ent particle morphologies, all mixed in a volumetric distribution corresponding to the stoichiometric Ni,Al compounand packed at the same density. Figure 2 shows the DTAtraces of shock-compressed flaky, fine, and coarse/roundedmorphology M-AI powder mixtures, all shocked under idetical conditions. Mixtures of powders of all three morphologies exhibit the preinitiation solid-state r&action exotherm ~550 C prior to the main liquid-state reaction exotherm a650 C, similar to Hammetter et al.s9 observations. However, the relative magnitudes of the liquid- and solid-stateexotherms are strongly dependent on effects of powder mor-phology on shock modification. Considering the magnitudof the exotherms to correspond to the extent of the reaction,it can be deduced that coarse/rounded morphology mixturesexhibit mostly a liquid-state reaction and a small amount oreaction in the solid state. Fine morphology mixtures exhibia significantly larger solid-state reaction and only limitedliquid-state reaction. Flaky powder mixtures react completely in the solid state at temperatires significantly belowthe melting of Al.

Microstructural analysis of the shock-compressed con-figuration of the three types of Ni-Al powder mixtures explains the effect of powder morphology on their chemicareaction behavior. The optical micrographs shown in Fig. 3reveal different levels of deformation and mixing of Ni anAl particles in the respective powder mixtures.l Flaky powder morphology mixtures show extensive deformation and

flow of both components, resulting in more intimate mixing

J. Appl. Phys., Vol. 76, No. 4, 15 August 1994 N. N. Thadhani 2131



4/10

FIG. 3. Micrographs of shock-compressed mixtures of (a) coarse/rounded,cb) fine, and (c) flaky morphology powders mixed in N&Al stoichiometryratio, packed at same initial density, showing different deformation charac-teristics (shock directionis left to right-hand side). The bright contrast par-ticles are of nickel, while aluminum particles have a dark (grainy) contrast(Ref. 10).

and a greater surface arena ontact. Fine powders show par-ticle agglomeration and lesser overall deformation, butgreater surface area contacts. In the shock-compressed con-figurations resulting with flaky and fine powder morpholo-g2es (with particles compressed to


5/10

modified to replace the bulk diff irsivityD, by an enhanced-diffusion coefficient 0; based on Harts approximationz6Thus,

D=fd4,+fP, > (2)where fL and fc are the fractions of atoms associated withthe lattice and dislocation core, respectively (the sum ofwhich is l), andDC is the diffusion coefficient along thedislocation core. Using Shewmons24 analysis and approxi-mations for number of atoms per unit length in dislocationcore (n=5), dislocation density (~10~ lines/m2), and num-ber of atoms per unit area per unit length of dislocation(lXIO1 atoms/m2 per unit length),D' is obtained a?

D'-D,+O.O05D,. (3)For T> hT,, diffusion aIong a dislocation can be assumedsimilar to atomic mobility in grain boundaries. Consideringpre-exponentials for volume and grain-boundary diffusion tobe the same and the activation energy for grain-boundarydiffusion to be about half of that for volume diffusion,= thetotal time for compound formation by defect-enhanced dif-fusion processes is

exp[ -&)I)

(4)

Using Eq. (4), the time for compound formation in M-Alpowder mixtures of -25 ,um average particle diameter (fromFig. 3) shock-modified at 22 GPa, is calculated to be -4.5 hat temperatures of one-half the melt temperature of Al. Con-sidering the reaction onset temperature of 500 C deducedfrom DTA traces in Fig.2, the defect-enhanced solid-statediffusion time is calculated to be ~31 s for reactions ob-

served to occur in the DTA. Unshocked powder mixtureswould still require -8 h for complete diffusion, at the same500 C reaction temperature. The considerably short reactiontime in the case of shock-modified mixtures is consistentwith the heating schedule achieved in the DTA at heatingrates of 10 C/min (Fig. 2).

The analytical treatment for defect-enhanced solid-statediffusion can in fact be extended to shock-assis ted chemicalreactions occurring in powder mixtures subsequent to un-loading from the shock pressure to the ambient state. Suchreactions occur due to bulk temperature increases in timescales of thermal equilibration. Thus, if one considers N&Alpowders of 25 pm diameter (from Fig. 3) and bulk shock

temperatures approaching melting of Al (---0.95T,), the timefor compound formation is calculated to be less than 100 ms.Thermal equilibrium during shock compression of powdersis attained in time scales of a few tens of w, in which casecompound formation can occur over micrometer-thick re-gions. It can, therefore, be inferred that shock-assistedchemical reactions occur by defect-enhanced solid-state dif-fusion processes with bulk shock temperature increases intime scales of thermal equilibration. Such reactions may,however, occur only in localized areas. Progress of reactionto bulk regions may depend on~diffusion through interfacialreacted region, and dissipation of heat of reaction.

IV. SHOCK-INDUCED REACTIONS IN POWDERMIXTURES

The occurrence of bulk shock-induced chemical reac-tions by mechanisms involving defect-enhanced solid-statediffusion processes is not possible during the microsecondscale duration of the shock state. Is it then possible that thesehigh-rate chemical reactions occur via solid-state diffusion-less mechanisms involving nonconventional mechanicallyinduced nucleation and growth processes? Can shock-

compression-induced plastic flow cause restructuring ofatomic arrangements as well as alteration of nature of chemi-cal bonding to induce s~uch igh-rate chemical reactions?

Shock-induced martensitic transformations in iron,27,28as well as the shock-induced graphite-to-diamondtransitions,29-31 are examples of solid-state structuralchanges occurring in materials at shock speeds. Evidence ofshock-induced phase transitions has been provided by directtime-resolved in situ measurements of changes in bulk prop-erties (Hugoniot characteristics) accompanying, thetransformation.27,B Real-t ime detection of such changes inbulk properties, or kinks. in shock adiabats, are direct evi-dence of phenomena occurr ing at the shock front or iu itsvicinity. ,iil

Shock-induced chemical reactions are generally accom-panied by relatively small changes in bulk material proper-ties. Thus, most conventional pressure and velocity measure-ment systems may fail to accurately respond to reaction ratemeasurements . Rapid temperature increases, which are com-monly associated with such exothermic reactions, are- theonly direct property change accompanying the chemical reaction. However, it is difficult to distinguish the react&ntemperature from the heterogeneous temperature increasesassociated with shock compression of powders. Thus, at-tempts to measure the reaction temperature in real time us-

ing, for example, radiationpyrometry techniques,3i33 havedemonstrated conflicting results due to temperature increasesfrom shock compression (void collapse) masking the tem-peratures produced due to chemical reaction. Time-resolvedmeasurement studies which provide evidence for reactionsoccurring in the shock-compression state are presented next;follotied by discussions of various phenbmenological con-cepts explaining mechanistic processes leading to shock-induced chemical reactions.

A. Evidence of shock-induced chemical reactions -..afrom time-resolved experiments

In spite of the many limitations of time-resolved tech-

niques, various shock-compression experiments have beenperformed that have shown that the exothermic energy-ac-companying shock-induce~d chemical reactions can be re-leased in reactive powder materials in time scales shorterthan the duration of the shock state. Sheffield and Schwartz34performed time-resolved experiments and measured waveprofiles in shocked titanium subhydride and potassium per-chlorate mixtures. They observed possible evidence of reac-tions occurring in a microsecond time scale, and proposedthat the reaction front moves through reactive-material atshock wave velocity, similar to that in-initiation of high ex-plosives. Kovalenko and Ivanov35 performed Hugoniot mea-

J. Appl. Phys., Vol . 76, No. 4, 15 August 1994 N. N. Thadhani 2133



6/10

surements as well as recovery experiments on lead nitrateand aluminum powder mixtures. They found that chemicalreactions forming the observed products were also evident inthe Hugoniot data, thus providing the evidence that chemicalreactions occur at a rate commensurate with shock wavepropagation.

Hugoniot measurements have also been performed byBatsanov.et aL6 to determine the extent of reaction as a func-tion of shock pressure in stoichiometric mixtures of tin andsulfur. They used manganin pressure gauges to obtainrecords of the shock profile, and observed that at pressures>I5 GPa the measured pressure points deviate towards theright-hand side (increased volume) of the Hugoniot curvecalculated for the unreacted mixture; however, because oflarge uncertainties in the measured Hugoniots relative to thedifference in pressure at a given specific volume, their deter-mination of the reacted fraction was only an estimate.

The most revealing and comprehensive results providingevidence of shock-induced chemical reactions include piezo-electric PVDF (poly-vinyl-di-flouride) gauge36 stress-wavemeasurements performed by Dunbar et aL7 on Ti-Si powdermixtures of various powder particle morphologies, at shockpressures up to 5 GPa. The stress recorded by the inputgauge and the wave velocity measured by timing the traveltime of the wave between the input and backer gauges (sand-wiching the Ti-Si powder mixture sample) were used to cal-culate the pressure-volume compressibility characteristics.Crush-up of the powders to solid density was observed at 1GPa pressure. With increasing pressure, the compressibilityshifted to larger volumes and an increase in volume to asmuch as 20% was observed at 5 GPa pressure. The volumeincrease is attributed to the thermal expansion due to suddentemperature increases caused by the chemical reaction.Higher magnitudes of stress were also recorded by the

backer gauge, and higher wave velocities were measured forinput stresses greater than 1 GPa. The combination of theseresults provide conclusive evidence of chemical reactions oc-curring during shock compression and resulting in the forma-tion of Ti-Si intermetallic compounds in time scales of me-chanical equilibration.7 The measurements also showed thatthe Ti-Si power mixtures of different morphology have dif-ferent crush strengths and, therefore, reveal different reactionthresholds, consistent with results of recovery experimentsperformed on the same powder mixtures.37

In samples obtained from shock-compression recoveryexperiments, it is not possible to directly ascertain the kinet-

ics or the mechanisms of processes leading to shock-inducedchemical reactions. Postshock microstructural characteriza-tion of the recovered materials reveals the final state of theproduct attained after equilibration with the environment.Furthermore, the large exothermicity of the reaction -oftenresults in melting of the products, leaving no evidence ofhow and when the reaction may have occurred. The finalstructure simply reveals characteristics typical of a reacted,melted, and resolidified material. Figure 4 shows examplesof typical microstructures of compounds formed via shock-induced chemical reactions in powder mixtures of Ni-Al, Ni-Si, and Ti-Si. A uniform contrast microstructure and presenceof spherically shaped voids (indicating possible gas escape

FIG. 4. Micrographs showing examples of typical microstructures of compounds formed via shock-induced chemical reactions in powder mixtures ofNi-Al, Ni-Si, and Ti-Si. A uniform contrast microstructure and presence ospherically shaped voids ( indicating possible gas escape or shrinkage) aretypical of a fuully reacted microstructure.

or shrinkage) are typical of a fully reacted material. Micro-structures showing shock-compressed unreacted powdermixture constituents (similar to what is seen in Fig. 3) provide significantly more information about the mechanisticharacteristics of the powders and their configuration at-tained prior to the onset of reaction.

B. Conceptual mechanisms of shock-inducedchemical reactions

Theoretical confirmation of shock-induced chemical reactions has been provided by the modeling scheme devel-oped by Hwang38 and Horie and Sawaoka,39 based on a fam-




7/10

ily of constitutive models termed VIR. In principle, the VIRmodels characterize the macroscopic behavior of porous re-active mixtures f rom those of three ingredients: voids, inertspecies, and reactive species: however, these modelingschemes are based on an assumed kinetics, without consid-eration of initiation mechanisms and are therefore more use-ful in predicting the state of shock-compressed powder mix-tures subsequent to reaction initiation. Mechanistic processesoccurring at the onset of reaction initiation and leading toreaction completion are not explained by these models. Sev-eral other mechanisms based on thermochemical, nondiffu-sional, mechanicaVdeformationa1, and mechanochemicalconcepts have also been documented in the literature, and arediscussed next.

1. Thermochemical concepts

Mechanistic modeling of shock-induced chemical reac-tions was first attempted by Maiden and Nutt4 using ther-mochemical analysis. They developed a heterogeneousmodel to calculate shock-induced reaction initiation thresh-olds by assuming that the reaction is ignited when the sur-face temperature of a pore meets a hot-spot ignition criterion.Jn essence, the reaction initiation process was assumed to besimilar to that for high explosives. Russian researchers Eni-kolopyan et aZ.41have contradicted the hot-spot ignition cri-terion, based on the argument that the extremely rapid reac-tions for both strongly and weakly exothermic powdermixture systems are independent of the starting temperature.Thus, they proposed that the observed explosive like reac-tions in powder mixtures, occur due to unique chemical pro-cesses not requiring thermal activation, but instead throughmechanical disintegration and mixing of the constituents bythe shock wave.

In recent studies on silicide forming powder mixtures,Yu and Meyers42 proposed that if the energy generation dueto the chemical reaction is greater than the energy dissipatedby thermal conduction, a steady-state reaction can start fromlocal hot-spot areas and propagate into the interior of theparticles. Accordingly, critical molten hot-spot regions werecalculated, based on a shock energy threshold correspondingto the mean bulk temperature which must be above that re-quired to initiate reactions at ambient pressure; however, theshock energy threshold criterion is based on time scales ofthermal equilibrium corresponding to time duration of tensof ,us. Thus, the energy threshold criterion and the hot-spotinitiation mechanism may be applicable to shock-assisted

chemical reactions occurring after unloading to ambientpressure, but not to shock-induced chemical reactions occur-ring during the shock-compression state in time scales ofmechanical equilibrium.

2. Pressure-assisted diffusional and nondiffusionalconcepts

Generation of high pressure and its effect on accelerateddiffusional transport cannot account for the high rates ofshock-induced chemical reactions. Analytical calculationsdescribed in Sec. III B reveal accelerated diffusion due toshock-compression effects causing localized shock-assisted

reactions to occur in not less than tens-of-ms-scale time du-

rations. High pressure can thermodynamically assist innucleation by providing additional driving force,,but it cannot alter the kinetics of processes involving diffusion-dependent phenomenon. Dremin and Breusov3 have dis-cussed the role of shear stresses and argued that whencombined with high pressures, the rates of chemical reactionand phase transformations become higher, and the processesgo to completion during the application of shear stress. Ingeneral, shear deformation has also been shown to formphases which may otherwise not be observed in absence ofshear.

, Attempts to investigate nondiffusional processes forshock-induced chemical reactions, have evolved aroundatomic rearrangements similar to structural phase transitions.Formation of diamonds during meteoritic impact isbelieved43944 o occur by direct solid-state transformationsunder the action of shock waves. Altshule? has proposedthat the diamonds form by a process similar to martensitictransformations, with the large number of point, line, andplanar defects, generated in the shock front at supercriticalpressures, forming the crystal nucleation sites. The rapidtransition of the parent lattice into the diamond phase is fa-cilitated by nondiffusional martensitic rearrangements, basedon the cooperative motion of many atoms to small distances.More recent Russian studies4 have shown that graphite-to-diamond conversion occurs via a martensitic transformationto the lansdellite phase which then transforms to diamond viaa diffusion-controlled process. On the other hand, transfor-mations from amorphous carbon to diamond and similarlyfrom amorphous analogues of boron nitride to cubic boronnitride have been proposed to occur via reconstructive phasetransformation process.6

Reaction mechanisms involving processes similar tomartensitic transformations require structural rearrangements

of reactant lattices and mixing of the constituents in a con-tinuum, to yield the product compound and microstructure.The reaction may go through an intermediate noncrystallinecompound before forming the final product lattice, ormaydirectly transform to the product lattice state, with accompa-nying volume change and energy release. Probes to monitorthese paths in real time need to be developed, similar to insitu x-ray-diffraction techniques available to monitor phaschanges in materials. 47A necessary condition for transforma-tions involving nondiffusional structural rearrangementssuch as in martensitic transformations, may also include ori-entation dependence between the initial constituents and the

final product states. Determination of such a criterion wouldbe necessary if shock-induced chemical reactions are consid-ered to occur via similar nondiffusional structural rearrange-ments.

3. Mechanochemical concepts

Mechanisms of shock-induced chemical reactions inpowder mixtures have also been explained on the basis ofmechanochemical concepts. The ROLLER model proposedby Dremin and Breusov,3 and the CONMAH model pro-posed by GrahamI are both based on mechanochemical con-cepts, and describe the possible mechanistic processes lead-

ing to shock-induced chemical reactions.




8/10

FIG. 5. Pbotomicrographs showing shock-compressed configuration of mix-tures of (a) Nb with silicon, equivolumetric, (b) Ni with Al, equivolumetric,and (c) Ni with volumetric abundance of Al. The premature melting of Si(dark cellular structure) in (a) and of Al (dark grainy structure) in (b), andthe virtually negligible deformation of the harder Ni in an abundant matrixof the more deformable Al in (c), inhibits intimate mixing and thus reducesthe propensity for subsequent shock-induced chemical reactions, except atlocalized regions where the molten metal wets the solid particles.

According to the ROLLER rnodeL3 when two layers of asubstance are displaced relative to one another, the nucleat-ing phase located between them can be regarded as a kind of

a roller in which mixing and alloying of the constituentsoccurs. Since the time required for rearrangement of electronshells (10-3-10-14 s) is much shorter than the time requiredfor contact between atoms (lo-l2 s), it implies that all atomspassing in the immediate vicinity of the nucleus have suffi-cient time to combine with it and form the new phase.Thus,in contrast to usual growth of the nucleating crystals, inwhich the atoms diffuse to the nucleation site via randomwalk, with the available thermal energy, formation of thenew phase during shock compression occurs via transport ofthe entire mass of initial phase by plastic flow, to the nucle-ation center. The required atoms then combine selectivelywith particles of the new alloy phase, thereby undergoingcontinuous growth. According to Dremin and Breusovscalculations,3 the new phase thus formed can have dimen-sions of -2.9X104 atoms (or -3 pm).

The ROLLER model demonstrates a possible scenario ofthe reaction process, assuming that an ideal globally mixedconfiguration has been attained; however, unlike the CON-MAH model,15 it does not describe the processes leading toconfiguration changes prior to the inception of reaction. Themechanochemical nature of shock-induced chemical reac-tions has been clearly illustrated in the different studies per-formed on intermetallic- and ceramic-forming elementalpowder mixtures (reviewed in Refs. 4 and 5). From these

studies it is evident that plastic deformation, flow, and mix-ing of both (or all) constituents, is essential for the occur-rence of shock-induced chemical reactions. If only parts ofconstituent particles, or only one constituent undergoes plas-tic deformation and flow, then shock-induced chemical reac-tions may not occur except only at localized interfacial re-gions due to shock-assisted rather than shock-inducedprocesses. Examples of such a behavior are clearly observed5in mixtures of Nb with Si and Ni with Al, as shown in Fig. 5.Ln the case of premature melting of either Si or Al [revealedby its cellular structure in Figs. 5(a) and 5(b)], no deforma-tion of the other metallic constituent (e.g., Nb or Ni, respec-tively) is observed leaving them with the same undeformed

morphology in the recovered product. Meltingmay, how-ever, result in localized shock-assisted reaction [as shown inFigs. 5(a) and 5(b)], due to wetting of melted Si (or Al) atinterfaces of Nb (or Ni) particles. Likewise, the virtuallynegligible deformation of Ni particles in an abundant matrixof the softer, more deformable Al [as shown in Fig. 5(c)],again limits mixing between the two metals resulting in areduced propensity for subsequent shock-induced reactioninitiation. Mechanochemical effects involving plastic defor-

mation and flow of powders into and around voids (from thestarting porosity), causing fluidlike flow, mass mixing, anddispersion of constituents can, therefore, be defined as anessential part of process leading to shock-induced chemicalreactions.

V. CORRELATION OF CONCEPTS WITHEXPERIMENTAL OBSERVATIONS

Quantifying the relationships that include mechanisms ofsolid-state shock-induced chemical reactions, based on themechanochemical concepts discussed above, still remains tobe performed. On the other hand, what is available is con-

clusive evidence that chemical reactions in powder mixtures,leading to formation of compounds, occur during shockcom-pression in time scales of mechanical equilibrium. In addi-tion, analysis of properties influencing the reaction behavior(initiation thresholds bdetermined from controlled recoveryexperiments) and product formation characteristics (micro-structure of reacted and unreacted statesj is also available.Such characteristics of the reaction behavior and the micro-structure can be used to formulate and develop quantifiablemodels of reaction mechanisms. A careful review of experi-ments on shock-induced chemical reactions also alludes tothe very important but complex role of the intrinsic proper-ties of reactant materials, in influencing the reaction behaviorof powder mixtures during shock compression, in addition toshock loading conditions and powder morphology character-istics. In particular, as discussed in the previous section, thedeformation response of powders during shock compression,controlling the flow and mixing of reactants and introducingconfigurational changes, is the most important property in-fluencing the initiation of shock-induced chemical reactions.Subsequently, the reaction behavior and product formationcharacteristics may be influenced by thermodynamic proper-ties of the reacting system.

In the case of metal-metal powder mixtures, the extent ofplastic flow and mixing, the type and level of defects formed,

and the packing configuration generated during the shockstate is controlled by the deformation characteristics of themixture const ituents, and extrinsic properties including par-ticle morphology, void volume, and shock-compression con-ditions. In turn, the deformation characteristics are affectedby the intrinsic high-strain-rate flow stress of the constitu-ents. For example, metallic Si is typically brittle, however,depending on particle size and shock conditions, it can eitherfracture, plastically deform, or even undergo melting [atpressures >ll GPa (Ref. 48)]. Figure 6(a) shows a scanningelectron microscopy (SEM) micrograph of Ti-Si powdermixtures reveal ing plastic deformation, flow, and intercon-stituent mixing with small- and medium-sized Si powders




9/10

TABLE I. Property differences between Si-based binary systems.

FIG. 6. SEM micrographs of unreacted configuration of Ti-Si powder mix-tures (I3 bright, Si dark contrast), showing the effects of particle morphol-ogy and loading conditions on the shock-compression response of Si: (a)extensive fracture of medium morphology, -45 pm particles, at 5 GPa: (b)fracture and fragmentation of coarse morphology, -150 ,um particles, at 5GPa: and (c) extensive plastit deformation and flow of medium morphology,e4.5 pm particles, at 7.5 GPa (Ref. 37).

(~40 pm). On the other hand, extensive fracture and frag-mentation is observed with coarse (>lOO pm) Si powderswith limited deformation of Ti particles [as shown in Fig.6(b)] under the same shock conditions. With increase in

shock pressure, the same coarse Si powders undergo exten-sive plastic deformation and flow, as shown in Fig. 6(c).It has also been observed that the shock-compression

response of Si is different in mixtures with different metallicconstituents. When mixed with Ni or Ti, Si powders showextensive fracture and fragmentat ion or even plastic defor-mation, while metallic constituents also undergo significantplastic deformation and flow. However, when Si powders aremixed with Nb, then at the same stress levels Si alone un-dergoes fracture or plastic deformation, while the Nb par-ticles remain undeformed and maintain the starting morphol-ogy. The different metal-silicon mixtures, therefore, requiredifferent threshold conditions for initiation of shock-inducedchemical reaction: 40 GPa for theMo-Si system, at the same 55% initial density.20037he dis-similar shock-compression response of Si with different me-tallic constituents further illustrates the mechanochemicalnature of shock-induced chemical reactions, unlike processesin which thermochemical mechanisms dominate the thresh-old conditions.

Some of the physical, chemical, and mechanical prop-erty differences between Si and metallic constituents Ti, Nb,Ni, and MO are listed in Table I, along with product forma-tion properties (including maximum heat of reaction AH,,volume change, cohesive energy AHc, and the ratioHRIAHc) of Ti-Si, Nb-Si, Ni-Si, and Mo-Si compounds.Consistent with the results of reaction thresholds and theproperties listed in the table, the propensity for initiation ofshock-induced chemical reactions made possible by appro-priate changes in configuration, correlates best with differ-ences in the yield strength of constituents. Once initiated,reaction completion and product formation characteristicscorrelate best with the heat of reaction normalized with thecohesive energy. The normalization with cohesive energy isused to include the effects of binding energies between likeand unlike atoms. Other properties of reactants have only

minor indirect effects on- the reaction behavior. Thus, al-

Property Systems and corresponding valuesb

Electronegativity Ti-Si Nb-Si Ni-Si Mo-Si1.5-1.8 1.6-1.8 1.8-1.8 2.1-1.8

Density @/cmJ) Mo-Si Ni-Si Nb-Si Ti-Si10.2-2.33 8.9-2.33 8.6-2.33 4.5-2.33

Sound velocity (km/s) Nb-Si Ni-Si Mo-Si Ti-Si4.44-7.99 4.58-7.99 5.12-7.99 5.22-7.99

Thermal conductivity Mo-Si Ni-Si Nb-Si Ti-Si(W/cm K) 1.38-1.49 0.909-1.49 0.537-1.49 0.219-1.49

Yield strength (MPa) Mo-Si Nb-Si Ti-Si Ni-Si400-93 207-93 140-93 59-93

Heat of reaction, AHR Ti-Si Mo-Si Ni-Si Nb-Si(kJ/mol) -32.9 - 17.5 -13.4 -8.8

Volume change (%) Mo-Si Ti-Si Ni-Si Nb-Si-40.6% -27.8% - 12.6% -7.8 -

Cohesive energy AH, Ti-Si Mo-Si Nb-Si Ni-Si(kJ/mol) -58.9 -51.3 -42.5 -38.4

AH,yIAHc Ni-Si Ti-Si Mo-Si Nb-Si0.66 0.56 0.35 0.21

aProperties of products refer to those of compounds with maximum AHa.

hDifference decreasing left- to right-hand side.AH,= 1/2(fiA -!-AHB) + AH,, where AH, and AH, are cohesive enegies of solids A and B [from C. Kittel, Introduction to SolidState Phys(WiIey, New York, 1976)].

though models with quantifiable relationships describing treaction mechanisms, are not available, domains correlatingmaterial properties with the reaction behavior may be obtained to better understand the mechanochemical processesleading to shock-induced chemical reactions.

VI. SUMMARY

Manifestations of enhanced solid-state chemical reactivity caused by configuration changes introduced during shoccompression of powder mixtures can lead to shock-assistedor shock-induced chemical reactions. Shock-assisted reactions occur via solid-state defect-enhanced diffusion after unloading to ambient pressure, in time scales of temperatureequilibration. Shock-induced reactions, on the other handoccur during shock compression upon mechanical equilibration and before unloading to ambient pressure. Analysis othe effects of configuration changes introduced during shoccompression and the influence of material properties anshock-loading characteristics on such effects reveal thashock-induced chemical reactions occur via mechanisms involving nondiffusional processes giving rise to structural rarrangements and mechanochemical effects. Thus, processesthat account for mechanisms dominated by simultaneous mechanical deformation effects determine the onset criterionand the extent of bulk reactions occurring during shock compression of powders. Compound formation characteristicare, however, influenced by thermochemical properties. It also evident that thermally activated processes cannot account for shock-induced chemical reactions, except in thcase where shock compression simply assists by creatingconditions favorable for reaction to occur in time scales

thermal equilibration or by postshock thermal initiation




10/10

Such shock-assisted reactions can be explained on the basisof thermally activated defect-enhanced solid-state diffusionmechanisms. It can, therefore, be concluded that shock-induced chemical reactions occur by mechanisms dominatedby solid-state diffusionless mechanochemical processes, un-like the defect-enhanced solid-state diffusional mechanismsof shock-assisted chemical reactions.

ACKNOWLEDGMENTS

Funding for the authors research has been provided inpart by the National Science Foundation Grant No. DMR-9396132 and the Army Research Office Grant No. DAAHO4-93-G-0062 at Georgia Institute of Technology, and by theSandia National Laboratories Contract No. 42-5737 for worksupported at New Mexico Tech. The author wishes to ac-knowledge the valuable discussions and the continued moti-vation and encouragement provided by Dr. Robert A. Gra-ham, Sandia National Laboratories, for this work. Thecontributions of past and present graduate students are alsogratefully acknowledged.

G. Duvall, Chairman, Shock-Compression Chemistry in Materials Synthe-sis and Processing, NMAB Report No. 414 (National Academy Press,Washington, DC, 1984).

aR. A. Graham, Solids Under High Pressure Shock Compression: Mechan-ics, Physics, and Chemistry (Springer, Berlin, 1993).

3A. N. Dremin and 0. N. Breusov, Russ. Chem. Rev. 37, 392 (1968).4R. A. Graham, B. Morosin, E. L. Venturini, and M. J. Carr, Ann. Rev.

Mater. Sci. 16, 315 (1986).N. N. Thadhani, Prog. Mater. Sci. 37, 117 (1993).S. S. Batsanov, G. S. Doronin, S. V. Klochkov, and A. I. Teut, Combust.Explos. Shock Waves 22, 134 (1986).

7E. Dunbar, R. A. Ciraham, G. T. Holman, M. U. Anderson, and N. N.Thadhani, in Proceedings of AIRAPT/A PS High Pressure Science andTechnology Conference, 28 June to 2 July, 1993, Colorado Springs, editedby S. C. Schmidt.

R. A. Grah am and N. N. Thadhani, in Shock Wzves n Materials Science,

edited by A. B. Sawaoka (Springer, Berlin, 1993), p. 35.W. F. Hammetter, R. A. Graham, B. Morosin, and Y Horie, in ShockWaves n Condensed Matter, edited by S. C. Schmidt and N. C. Holmes(Elsevier, Amsterdam, 1988), p. 431.

E. Dunbar, N. N. Thadhani, and R. A. Graham, J. Mater. Sci. 28, 2903(1993).

Z. A. Munir and U. Anselmi-Tamburini, Mater. Sci. Rep. 3, 277 (1989).V. Hlavacek, Am. Ceram. Sot. Bull. 70, 240 (1991).s W. Tong and G. Ravichandran, J. Appl. Phys. (to be published).r4G. T. Holman, R. A. Graham, and M. U. Anderson, i n Proceedings of

AIRAPT/A PS High Pressure Science and Technology Conference, 28June to 2 July, 1993, Colorado Springs, edited by S. C. Schmidt.

R. A. Graham, in Proceedings of the 3rd International Symposium onDynamic Pressures, La Grande Motte, France, June 5-9, 1989.

e0. R. Bergmann and J. Barrington, J. Am. Ceram. Sot. 49, 502 (1966).E K Beauchamp, in High-Pressure Explosives Processing of Ceramics,.

edited by R. A. Grah am and A. B. Sawaoka (Trans Tech, Ziirich, 1987), p.139.

r8J. Golden, F. Williams, B. Morosin, E. L. Venturini, and R. A. Graham, inShock Waves n Condensed Matter, edited by W. J. Nellis, L. Seaman, andR. A. Graham (American Institute of Physics, New York, 1981), pp. 72-76.

t9N. N. Thadhani, A. H. Mum, and T. Vreeland, Jr., Acta Metall. 37, 897(1989).

WE. Dunbar, M. S. thesis, New Mexico Tech, 1992.E Bordeaux and A. R. Yavari, J. Mater. Res. 5, 1656 (1990).

G. T. Hida and I. J. Lin, in Combustion and Plasma Synthesis of HighTemperature Materials, edited by J. B. Holt and 2. A Munir (VCH,1990), p. 246.

S. C. Deevi, J. Mater. Sci. 26, 3343 (1991).P. G. Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963).=J. D. Whittenberger, in Solid State Powder Processing, edited by A. H.

Clauer and J. J. deBarbadillo (TMS, 1990), pp. 137-155.26E. Hart, Acta Metall. 5, 597 (1957).G. E. Duvall and R. A. Graham, Rev. Mod. Phys. 49,523 (1977).%L. V, Altshuler, J. Appl. Mech. Tech. Phys. 4, 93 (1978).P. S. DeCarli, U. S. Patent No. 3, 238, 019 (1 March, 1966).3oP. S. DeCarli and J. C. Jamieson, Science 133, 1821 (1961).P. S. DeCarli and D. J. Milton, Science 147, 144 (1965).32M. B. Boslough and R. A. Graham, Chem. Phys. Lett. 121, 446 (1985).73M. B. Boslough, Int. J. Imp. Eng., 5, 173 (1987).

a4S. A. Sheffield and A. C. Schwarz, in Proceedingsof he Eighth Interna-tional Pyrotechniques Symposium, edited by A. J. Tubs (IIT ResearchInstitute, Chicago, 1982), p. 972.

3SA N. Kovalenko and G. V. Ivanov, Combust. Explos. Shock Waves 19,481 (1981).

s6R. A. Graham, M. U. Anderson, Y. Horie, S.-K. You, and G. T. Holman,Shock Waves Int. J. 3, 79 (1993).

37Np N. Thadhani, E. Dunbar, and R. A. Graham, in Proceedings ofAiRAPT/A PS High Pressure Science and Technology Conference, 28June to 2 July, 1993, Colorado Springs, edited by S. C. Schmidt.

s8M D Hwang, Ph.D. thesis, North Carolina State University, Raleigh, NC,1992:

19Y Horie and A. B. Sawaoka, Shock Compression Chemistry of Materials(I&K, Tokyo, 1993), p. 235.

4oD. E. Maiden and G. L. Nutt, in Proceedings of the Eleventh InternationalPyrotechnics Seminar Vail, Colorado, 1986, p. 813.

41N. S. Enikolopyan, A. A. Khzardzhyan, E. E. Gasparyan, and V. B.Voleva, Acad. Nauk USSR Proc. Phys. Chem. 294, 567 (1987).

L. H. Yu and M. A. Meyers (unpublished).43E. Anders, Astrophys. J. 134, 1606 (1961).M. E. Lipschutz and E. Anders, Science 134, 2095 (1961).45H. H. Borimchuk and G. Kurdjumov, presented at Fifth All-Union Meet

ing on Detonation, August 5-10, 1991, Krasnoyarsk, Russia, CIS.46A N Dremin and 0. N. Breusov, in Shock Waves in Materials Science,.

edited by A. B. Sawaoka (Springer, Berlin, 1993), pp. 17-34.47R R. Whitlock, J. S. Wark, and G. Kiehn, in Shock Compression of Con-

densed Matter4989, edited by S. C. Schmidt, J. N. Johnson, and L. W.Davison (Elsevier, Amsterdam, 1990), pp. 897 and 901.

48F. P. Bundy, J. Chem. Phys. 41, 3809 (1964).


N. N. Thadhani- Shock induced and shock-assisted solid-state chemical reactions in powder mixtures

Documents