D. E. Eakins and N. N. Thadhani- Shock compression of reactive powder mixtures

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Shock compression of reactive powdermixtures

D. E. Eakins and N. N. Thadhani*

The shock compression of reactive powder mixtures can yield varied chemical behaviour with

occurrence of mechanochemical reactions in the timescale of the high pressure state, or

thermochemical reactions in the timescale of temperature equilibration, or simply the creation of

dense packed highly reactive state of material. The principal challenge has been to understand

the processes that distinguish between mechanochemical (shock induced) and thermochemical

(shock assisted) reactions, which has broad implications for the synthesis of novel metastable or

non-equilibrium materials, or the design of highly configurable next generation energetic

materials. In this paper, the process of shock compression in reactive powder mixtures and the

associated role of various intrinsic and extrinsic characteristics of reactants in the triggering of

ultrafast shock induced chemical reactions are discussed. Experimental techniques employing

time resolved diagnostics and results which identify the occurrence of shock induced reactions

are reviewed. Conceptual and numerical models used to describe the heterogeneous nature of

such reactions through mesoscopic details of shock compression are presented. Finally, a

discussion of the application of recent results for the design of reactive material systems with

controlled reaction initiation and energy release characteristics is provided.

Keywords: Shock compression, Reactive powders, Intermetallics, Mechanochemical reactions, Shock synthesis, Ballotechnic, Mesoscale modelling,Imported microstructures, Review

IntroductionThe application of pressure on a solid material cancompress the lattice and bring atoms closer together inordered or disordered configurations. As noted byBridgman1 in 1956, pressure can ‘break down’ theelectronic structure of atoms, and as a result, totallyalter the properties of materials. Pressure has since beenconsidered to play a revealing role in obtaining afundamental understanding of condensed matter and forcreation of new phases.2,3 Dynamic application ofpressure, or more appropriately, shock compression ofcondensed matter, generates even more unique and non-homogeneous states, and allows studies of materials inthermodynamic regimes not accessible by any othermethod. The response of materials to shock compressionis dominated by effects of the deviatoric (shear)component of stress, manifested by the creation ofcrystalline defects (or disordered states) and significantlyaccelerated kinetics of chemical and physical changes,which can form radically modified structures, metastablephases, and even novel compounds or alloys, which mayotherwise not be possible.4–6

Shock compression of materials has been used tostudy structural phase changes since 1956, with the first

notable scientific achievement being the discovery of the13 GPa bcc to hcp martensitic transformation in iron.7

The shock induced graphite to diamond transformationis an example of a standard commercial method,employing explosively generated shock waves, for theproduction of industrial diamond powder abrasives.8,9

The most notable recent achievement of shock generatedphase transformations has been the purported synthesisof metallic hydrogen.10 These phase transformationsrepresent examples of structural changes from an initiallow density phase to a final high density state. Shockinduced phase changes from high to low densitystructures, e.g. martensitic transformations and crystalto amorphous phase transitions have also been stu-died.11–21 Solid state structural phase transformationsfrom low to high or from high to low density states havebeen considered to occur via reconstructive or displacivemechanisms.22 Such displacive phase transformationsinvolve coordinated shifts of atoms comprising ofhomogeneous strain and shuffle, and hence, arefavoured under high pressure, while reconstructivetransformations are less likely to occur at high pressuresdue to the reduced mobility of atoms. According toAl’tshuler,4 shock induced phase formation due todisplacive phase changes occur via creation of nuclea-tion centres at defects formed in the shock front, and acooperative motion of many atoms to small distances.

Chemical changes involving shock induceddecomposition of compounds, oxidation reduction

School of Materials Science and Engineering, Georgia Institute ofTechnology, Atlanta, GA, USA

*Corresponding author, email [email protected]

� 2009 Institute of Materials, Minerals and Mining and ASM InternationalPublished by Maney for the Institute and ASM InternationalDOI 10.1179/174328009X461050 International Materials Reviews 2009 VOL 54 NO 4 181

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(displacement) reactions, as well as reactions betweentwo or more highly exothermic (DHR%0) components,have also been extensively investigated for applicationsin materials synthesis, and more recently for applica-tions in high density energetic materials.23–27 Studies ofsuch shock induced chemical reactions have drawnsignificant interest in recent years for several reasons:

(i) initiating reactions at the high pressure state maylead to the synthesis of novel phases, notobtainable through conventional ambient pres-sure techniques

(ii) the formation of high pressure phases and theirpossible reversion upon unloading will result inunique reaction pathways and associated enthal-pies, effectively altering the energetics of nextgeneration materials

(iii) understanding the reaction initiation behaviourgives potential control of energy release char-acteristics over a wide range of spatial andtemporal scales.

While the mechanisms of shock induced physicalchanges involving phase transformations from low tohigh (or high to low) density states are well understood,the mechanisms responsible for shock induced chemicalchanges (or reactions) and their associated kinetics,remain to be fully established. It has been proposed that‘shock induced’ chemical reactions occur as a conse-quence of mechanochemical effects, via processes invol-ving solid state structural rearrangements of atomicconstituents forming compounds via displacive typeprocesses.6,28–30 Thermochemical mechanisms includingliquid phase reactions, founded on the observation oflocalised melts (or ‘hot spots’) at interparticle regionsin powder mixtures have also been proposed.31–34

However, the lack of availability of time resolvedspectroscopic measurements has inhibited direct obser-vation and thus, not provided conclusive evidence of themechanism(s) and kinetics of shock induced chemicalreactions. It has been difficult to characterise thephysical processes associated with high rate deformationleading to initiation of reactions, particularly at thedifferent length and timescales that affect the micro-,meso-, and macroscopic response of reactants.Additionally, the present state of the art in experimentaldiagnostics is not yet able to provide a reliable probe ofthe above mentioned processes that may encompassspatial resolution across atomic to macroscopic lengthscales and the temporal regime ranging from a fewpicoseconds to several milliseconds.

It is the intent of this article to review the current stateof the understanding of the mechanisms and kinetics ofshock induced chemical reactions in highly exothermicintermetallic forming powder mixture systems and theirassociated effects. The review will seek to describe thechemical response of reactive powder mixtures subjectedto shock compression, with particular focus on reactionsinitiated at very short timescales, i.e. tens to hundreds ofnanoseconds corresponding to the shock rise time andimmediately following it. Post-shock chemical reactionsin powder mixtures occurring after unloading from thehigh pressure state, due to temperature increases in thetimescale of thermal equilibrium (tens of microsecondsto milliseconds), will only be briefly discussed. In thesections to follow, we will first describe the fundamentalchallenges associated with description of chemical

reactions under dynamic high pressure. Next, we willreview the main features of the mechanics of shockcompression (dynamic densification) of powders. In thesection on ‘Review of diagnostic techniques’, a descrip-tion of the time resolved diagnostics used in shock-compression experimentation to deduce the occurrenceof ultrafast chemical reactions will be provided, withemphasis on supporting evidence of the occurrence (orlack) of shock induced chemical reactions. This will befollowed by descriptions of thermodynamic argumentsemployed for occurrence of reaction and its influence onthe equilibrium shocked state of reaction products. Theproposed mechanisms for reaction initiation and effortsto model these mechanisms, or the powder compressionprocess itself, will also be presented. Finally, based onthe recent experimental and mesoscale numerical work,an analysis of the design and control of shock inducedchemical reaction initiation is offered in the form of amap that combines the effects of the intrinsic (materialinherent) and extrinsic (process dependent) properties ofconstituents, influencing the configurational changesoccurring during shock compression and leading toreaction initiation and product formation. The reviewends with a summary and concluding remarks, whichalso includes challenges that lay ahead and suggestionsfor future research.

Challenges associated with shockcompression of reactive mixtures

Varied reaction responseReactions in powder systems due to shock loading canbe separated into two categories:

(i) fast reactions that occur while the material is stillcompressed at high pressure (few nanoseconds totens of microseconds)

(ii) slow reactions that occur at much later timesfollowing unloading from the high pressure state.

These fast reactions have been termed ‘shock induced’reactions, and are initiated within the shock pulse due tothe processes occurring during crush-up of the powdersto their full density. The formation of reaction productsimmediately or shortly behind the shock front influencesthe equilibrium shock state, the changes of which canonly be verified through time resolved measure-ments.35–40 The category of slow reactions are knownas ‘shock assisted’ reactions, which result as a conse-quence of the disturbed microstructure and elevatedshock generated residual temperatures. Reactions of thistype are driven by atomic diffusion in the timescale ofbulk temperature equilibration (tens of microseconds tomilliseconds), and typically occur after the material hasrelaxed and the high pressure has abated.

A schematic illustrating the differences between shockassisted and shock induced reactions is shown in Fig. 1.Consider Fig. 1a and b, which depicts a shock pulsetravelling from right to left through a close packed bedof spherical particles. The pulse, represented by thepressure profile ‘P’, rapidly eliminates the void spacebetween the particles, consolidating the powder to fulldensity. Also shown is a profile of the bulk temperature,‘Tbulk’, which rises to a peak value long after thematerial has unloaded. Regions indicating reaction forthe shock assisted and shock induced cases are shown,with initiation dependent upon temperature for the

Eakins and Thadhani Shock compression of reactive powder mixtures

182 International Materials Reviews 2009 VOL 54 NO 4

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former, and upon the mechanical state and its associatedthermal effects for the latter. If time resolved metallo-graphy could be performed, the evolution of micro-structures that one might observe is shown in Fig. 1cand d. The onset of phase formation for shock assistedreactions coincides with the build-up of temperature,yielding an equilibrium microstructure. For shockinduced reactions, the critical thermal/mechanical statesdeveloped at the high pressure state result in phaseformation at pressure. Since these phases or stoichio-metries may not be energetically favourable at ambientpressure, unloading may trigger the formation of thevery same equilibrium microstructure shown in Fig. 1c.

Mechanisms of reactionUnderstanding the mechanisms that govern shockassisted and shock induced reactions is an importantstep to gaining control over these types of chemicalbehaviour. If it is assumed that the propensity forreaction is fundamentally linked to the availability ofactivated, reactive complements, it follows that it is theprocesses bringing unbound atoms into contact thatinevitably lead to reaction. For shock assisted reactions,this is accomplished through thermal energy, and theresulting increased atomic mobility and diffusivities. Forshock induced reactions, however, the mechanism(s)responsible for bond breakage and atomic intermixing isless clear. The influence of diffusion at these ultrashorttimes is negligible, the mobility imparted on the order oftens of angstroms. On the other hand, the timescales forshock induced reaction and the crush-up to full densityare commensurate. It is therefore assumed that themechanisms responsible for the initiation of shockinduced reactions are related to the crush-up process.Determining the critical micromechanical processes forthe onset of initiation has been the focus of manyinvestigations dealing with solid state reactions. Whilethe specifics of microscale mechanochemical processesare quite vague, it has been suggested by Matteazziet al.41 for ball milling of powders, that the generation of

free radicals, deformed bonds, and ions and freeelectrons at newly formed, nascent surfaces, duringinterparticle collisions can give rise to a so-called‘triboplasma’, which can make it possible for inter-particle bonding and/or mechanical alloying to occur inthe solid state.42

Identifying reaction productsIn addition to determining the type and mechanism ofreaction, investigations of reactive powder mixtures arealso challenged with the task of identifying the productsformed and their extent. Since powders and theirmixtures are a class of heterogeneous material, the localcomponent makeup and thermal/mechanical landscapesall vary greatly throughout the shock compression andthermal equilibration events. This heterogeneous naturemay lead to the formation of multiple phases that do notnecessarily share the stoichiometry of the starting bulkmixture. Furthermore, at extended timescales, the moststable phases are dictated through equilibrium thermo-dynamics and kinetics. Thus, the phases present in themicrostructure may also vary with time (Fig. 1).Depending upon the operating timescale of diagnosticsor characterisation, very different interpretations of thephases present and their amounts in the microstructuremay be deduced.

The primary concern when characterising shockassisted reactions (occurring following unloading fromthe high pressure state) is this possibility of an evolutionof multiple phases. The study of shock induced reactionsmust contend with the additional complexity of phasesynthesis under high pressure. Such non-equilibriumphases are particularly difficult to identify, as they maybecome unstable and revert to ambient pressure phasesupon unloading.43 For example, extreme conditionshave been known to alter the equilibrium physicalstructure of single component materials, resulting inpressure induced phase transformations in metals(a–e transition in iron), ceramics (a-quartz to coesite/stishovite transition in silica) and molecular liquids

1 Schematic illustrating the spatial proximity of reactions proceeding through a shock assisted and b shock induced

mechanisms. The black line represents the applied stress profile, while the red is the bulk temperature profile. The

use of colour within the idealised microstructure is symbolic of reaction. Shock assisted reactions occur due to ther-

mal mechanisms, once bulk temperatures and diffusion controlled transport are significant. Reaction occurs on the

order of microseconds to milliseconds, long after the shock front has passed. Shock induced reactions, however,

occur shortly behind the shock front, while the material is at the high pressure state. Also shown are examples of

microstructures throughout the complete shock loading event for the c shock assisted and d shock induced cases.

Note that due to temperature increases at later times, both reaction types can yield an equilibrium microstructure,

complicating the interpretation from observations of recovered post-shock specimens


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(crystallisation of water).1,7,44,45 This task becomesmarkedly more difficult for multicomponent mixtures,the constituents of which may be susceptible toformation of high pressure allotropic phases (e.g. Si insilicide forming intermetallic systems).

Solid state detonationAs will become clear in the following sections, there isdirect evidence that ultrafast shock induced reactionsexact a change in the equilibrium high pressure state. Inmany works, this change is signalled by a measuredincrease in shock velocity for a given pressure. Such anincrease has led several investigators to question whetheror not shock induced reactions share similar character-istics with detonation reactions.46,47 Detonation is aphenomenon observed in high explosives, such astrinitrotoluene (TNT), cyclotrimethylene trinitramine(RDX) and ammonium nitrate/fuel oil (ANFO), wherethe reaction front propagates in a self-sustaining manner.Determining the propagation behaviour of reactionfronts in powder mixtures is a key step to understandingthe kinetics of phase synthesis and exothermic heatrelease in shock induced reactions, which will in turn leadto control over the incubation time, exothermicity andtransformation extent of chemical reactions. It should benoted that revealing the mechanisms of reaction, phasetransformation pathways and subsequent reaction frontpropagation behaviour does not immediately accord thiscontrol. Only after these behaviours are correlated toconfigurable parameters, such as particle size/shape,distributions and mixture density, may one begin toregard shock induced reactions as a designable phenom-enon. Extending this understanding throughout thegamut of heterogeneity can ultimately provide the abilityto synthesise new materials with predefined behaviour, orallow control of reaction and associated energy release forenergetic material applications.

Compression of powders/distendedsolidsAny discussion of the shock compression response ofmaterials begins with an introduction of the

Hugoniot.48,49 The Hugoniot is a surface in pressure,volume and energy space that prescribes the equilibriumstates reached through shock compression. When amaterial is subjected to shock loading, delivered by theimpact of a high velocity projectile or upon explosivedetonation, a discrete shock wave front is producedseparating the undisturbed state from material atpressure. As this shock wave propagates, materialentering the front is brought instantaneously to someelevated state found on the Hugoniot. An example of theHugoniot in P–V space is shown in Fig. 2a. The P–VHugoniot gives an indication of the shock compressi-bility of a material, and also reveals the velocity withwhich a shock wave of particular amplitude willpropagate. This shock velocity Us is proportional tothe slope of the segment joining the initial and finalstates (Rayleigh line) on the P–V Hugoniot.Alternatively, it can be said that in the absence ofphysical and/or chemical changes, shock waves (ofspecific amplitude) in a given material will propagateat a characteristic velocity Us. This is an importantstatement, as it is the underlying basis used to infer thephysical or chemical changes occurring in the timescaleof the high pressure shock state.

The Hugoniot of a powder differs from that of itscorresponding, fully dense solid. In the first case, theinitial state of a powder does not lie on the Hugoniot,but is instead displaced to some expanded volume V00,due to the interparticle void space. Upon shockcompression, the powder is rapidly consolidated to fulldensity, achieving a large net reduction in volume. Thedensification and collapse of voids during this consoli-dation process (absent in the compression of fully densesolids) raises the internal energy of the material, yieldinga powder Hugoniot shifted from the solid Hugoniottowards higher volumes.50 There are two generalapproaches usually employed to construct theHugoniot of a powder. The isochoric method locatesthe powder Hugoniot by performing a constant volumeshift from the Hugoniot of the solid material. In Fig. 2b,it corresponds to the shift from P1 to P2 at a constantV1. This shift is typically performed using the well

2 Hugoniots in pressure–volume space, illustrating a the relationship between shock amplitude (P1, P2) and shock velo-

city (Us1, Us2) in a given material, and b the increase in energy due to shock loading for a porous and solid material



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known Mie–Gruneisen equation of state, which relatesthe change in internal energy associated with a pressurechange at a constant volume51

P{P0~c

V(E{E0) (1)

where P, E and the Gruneisen parameter c aredependent upon the specific volume V, and P0 and E0

refer to the pressure and internal energy at ambientconditions. This was the approach used by Herrmann,52

McQueen et al.53 and Dijken and de Hossen,54 to arriveat relations of the form

P~2V{c(V0{V )½ �C2(V0{V )

2V{c(V00{V )½ � V0{S(V0{V )½ �2(2)

where V00 is the starting density of the powder, C is thebulk sound speed and S is the first order coefficient tothe Us–Up equation of state. For cases where theGruneisen parameter is unknown, the Gruneisen ratiois usually approximated by50

c

V&

c0

V0

(3)

where the Gruneisen parameter at ambient conditionsc0, can be calculated in a straightforward manner fromthermodynamic properties. Criticism of the accuracy ofthis approximation for large differences in internalenergy has led to the alternate isobaric approach, whichperforms a constant pressure adjustment from the solidreference Hugoniot. In Fig. 2b, it corresponds to theshift from V2 to V1 at a constant P2. The contributionsby Oh and Persson,55 Wu and Jing,56 Jones et al.,57

Krueger and Vreeland, Jr,58 and Boshoff-Mostert andViljoen59 follow this second scheme. In the case of highlyporous solids, both the isochoric and isobaricapproaches show poor correlation with measuredHugoniot, with the isochoric approach typically failingwith porosity .50 vol.-% and the isobaric approachlimited typically to porosity less than 60 vol.-%. Withnanometre sized particles, correlation of both models

with the measured Hugoniot is even more limited as theinternal energy contribution associated with the largesurface area of the nanopowders dominates the densi-fication response.60 Example Hugoniots for a solid andporous material are shown in Fig. 2b. The shaded areasbelow the Rayleigh lines are the respective energyincreases due to shock compression, as given by theconservation of energy50

E{E0~1

2(PzP0)(V00{V ) (powder) (4)

E{E0~1

2(PzP0)(V0{V )(solid) (5)

where the subscripted terms refer to the initial,unshocked states. It should be quite apparent from theshaded areas in Fig. 2b that the energy increase due toshock compression for the powder is greater than thatfor the solid.

From the powder Hugoniot shown in Fig. 2b, onemight conclude that full density is achieved withnegligible load, i.e. above P50, there is an instantaneousjump from the initial state V00 to V0. In practice,however, all powders exhibit a certain resistance to com-plete densification at low stresses. The stress required toreach full density is known as the ‘crush strength’, andvaries greatly depending upon powder properties such asyield strength, particle size and morphology, and initialpacking density. Below the crush strength, the appliedload is insufficient to completely eliminate the voidvolume, often resulting in an expanded, off-HugoniotP–V state. The path of off-Hugoniot states below thecrush strength is known collectively as the ‘crush-up’curve, illustrated in Fig. 3a. Several models have beenproposed to describe the densification response ofpowders within this range, such as the P–a and P–lmodels.52,61–63 The crush-up curve shown in Fig. 3a isan example of the P–a model, the lower stress linearportion representing the extent of elastic response. Itshould be recognised that the crush-up curve applies

3 a Illustration showing the crush-up curve for a powder system, which is a path joining the initial state at V00 to the

Hugoniot of a fully densified powder. The crush-up curve intersects the Hugoniot at the crush strength. The shape of

the particular crush-up curve shown derives from the P–a model, the low pressure linear portion representing the

extent of elastic response. b Comparison of Hugoniot and quasi-static compression data for a WC powder (adapted

from Vogler et al.64)



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only to dynamic compression, and does not necessarilycoincide with the densification curve obtained underquasi-static loading. To illustrate this point, the dynamicdensification response of WC powder within the crush-up regime is shown along with quasi-static compressiondata in Fig. 3b.64 Notice that WC is more readilydensified under quasi-static loading for an equivalentapplied stress. Similar observations have been made forelemental Fe nanopowders and mixtures of Ni and Alnanoparticles.60,65,66 On the other hand, Ni and Alpowder mixtures of micrometre scale particles collapseto full density more easily under shock compression.66 Ithas also been shown that the dynamic densificationbehaviour of powder mixtures can be strongly affectedby mixture configuration. The varying crush-upresponses of three distinct configurations of NizAlpowders, as shown in Fig. 4, are related to the amountof particle surface area, and have been fit using amodified form of the Fischmeister–Arzt equation66,67

Py~2:97r{r0

1{r0

� �sy

n

n0

� �0:473

(6)

where Py is the crush strength, sy is the yield strength ofthe mixture, r0 is the initial relative density, r is the finalrelative density, and n0 and n are configuration para-meters for equiaxed and non-equiaxed powder mixturesrespectively. In short, the properties of powders andtheir mixtures, i.e. interatomic bonding, flow strength,particle morphology and particle size, have a stronginfluence over the crush strength, and overall densifica-tion response.

The processes of void collapse, viscous flow in andaround the voids, and crushing of the powder particles

in the process of void annihilation, give rise to wavepropagation features, such as shock wave speeds, whichare different from those observed in the same solid in thefully dense state. Stress wave measurements haverevealed that crush-up of powders to solid densityproduces complex wave loading characteristics.38 Asillustrated in the schematic in Fig. 5, shock propagationthrough highly porous solids (powders) shows largechanges in wave speed, while only modest increases areobserved in solid density materials at pressures of theorder of y10 GPa. The measured shock wave rise timesare also observed to vary from a few tens to severalhundreds of nanoseconds, depending on the magnitudeof the shock.38 Various void collapse models have beendeveloped, based on rate independent and rate depen-dent, as well as perfectly plastic and elastic–viscoplasticmaterial considerations.68 While rapid loading rates athigh pressures make it necessary to incorporate ratedependent considerations, long rise times at lowpressures alter the otherwise prompt thermal effectsand hydrodynamic considerations assumed in theoreti-cal treatment of the shock state. A realistic analysis ofshock compression effects, therefore, becomes extremelycomplex.

Experimental measurements also show that the crushstrength of powders is not only a function of the initialpacking density, but also the powder particle size andshape.38 In the case of mixtures of powders, e.g.AlzFe2O3, a two-step crush-up behaviour is observed,with each step indicating a response dominated by thecompression characteristics of the respective compo-nents.69 Thus, the crush-up of the mixture is influencedinitially by the compressibility of Al (at low pressure)and later by the compressibility of Fe2O3 (at higherpressure). Such characteristics of the deformationresponse of powders make it very difficult to formulatesimple models that can explain the mechanisms orphenomena occurring during shock compression in awide range of temporal, spatial and pressure scales.

A number of interesting particle level processes alsooccur during the crush-up of powders to full density. Asthe void volume is eliminated, powder particles mayexperience several stages/regions of deformation, asillustrated in Fig. 6. Rearrangement refers to initialdensification accomplished by particle reorientation andinterparticle sliding, likely at the expense of minorprotuberances. Localised flow describes heterogeneous

4 Crush-up behaviour of three distinct configurations of

NizAl powder mixtures, revealing the dramatic influ-

ence of both particle size and particle morphology on

the stress required to reach full density. The crush

strength for these three mixtures has been fit using

the Fischmeister–Arzt equation, modified to account for

differences in surface area (from Eakins and

Thadhani66)

5 Schematic of wave speed versus pressure plots illus-

trating differences in the response of solid density

materials and powders (highly porous solids) to shock

compression (from Thadhani et al.38)



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deformation through shear and normal stress into thevoid regions. Lastly, bulk deformation takes placefollowing the collapse of the voids, in response to astate of pressure.25,64 The particular micromechanicalmodes active within these regions will vary according tothe strain rate and powder configuration, once againdefined by the particle size, morphology, orientation,distribution and initial density. The recent review bySethi et al.70 provides an in-depth discussion of thedynamic consolidation of single component powders.For multicomponent powder mixtures, the addedheterogeneity of dissimilar yield strengths, mass densi-ties and sound speeds will also play an important role inhow shock energy dissipation is partitioned andlocalised. These factors result in spatially inhomoge-neous states of stress, defect densities and microkineticresponse, ultimately controlling the extent of mixing (ordispersion) between reactive components during crush-up. The extensive deformation and flow at particleinterfaces will generate adiabatic, plastic work inducedtemperature, and steep thermal gradients extending intothe particle interior. Once the material reaches theHugoniot (complete densification) or a state along thecrush-up curve (incomplete densification), it is assumedto be in mechanical equilibrium, bringing athermal massmixing to an end. Thermal equilibrium, however, is notachieved until much later in time (micro- to millise-conds), only after the irregular thermal landscape hasbeen homogenised. Mixing at these extended timescalesmust be accomplished through atomic diffusion, accel-erated by the enhanced temperatures and presence ofdefects or disorder. Thus, mass mixing may occur over awide range of timescales, as facilitated by eithermechanical or thermal processes. Under certain condi-tions, mixing may be sufficient to trigger a chemicalreaction over a wide timescale.

Review of diagnostic techniquesShock compression can be used to probe the response ofmaterials to extreme conditions, and establish their

compressibility, the thermodynamic equation of stateand the high pressure stability. For example, meltingand evaporation at high temperatures provide anunderstanding of atomic bonding. Likewise, plasticdeformation and fracture during straining describe thegeneration and interaction of defects, and chemical and/or electrical changes at high pressure are signatures ofbond stability. Investigation of each of these phenomenaand their like requires the use of specific experimentalapproaches and diagnostics; the study of chemicalreactions initiated by shock waves is no exception. Thediagnostic techniques employed fall into the categoriesof either time resolved measurements or post-shockmicrostructural analysis of recovered shock compressedmaterials. In terms of probing chemical reactions inshock loaded powder mixtures, time resolved and post-shock recovery analyses can provide very differentinformation.

Time resolved diagnostics are used to obtain measure-ments of material properties during the shock loadingevent. In most impact or explosively driven shocks(several to hundreds of GPa), the entire shock loadingevent (rise to peak pressure, equilibration and release)occurs over a time span of no more than a fewmicroseconds. The rise and equilibration of the highpressure state occurs over an even shorter time, any-where from a few nanoseconds to a couple hundrednanoseconds. Correspondingly, the study of the res-ponse of materials within this very narrow interval islimited to only a handful of diagnostics. Examples oftime resolved diagnostics include polyvinylidene fluoride(PVDF) and manganin stress gauges, resistivity mea-surements, optical pyrometry, velocity interferometry(VISAR) and optical spectroscopy, all of which operateand collect data during the shock compressionevent.35,72–81 What temporal resolution is gainedthrough time resolved measurements is often lost inspatial resolution. In many of the techniques mentioned,measurements are obtained from an averaged area, suchas the PVDF gauge area, or a limited region, such as thespot size for optical methods. This presents a problem ifthe characteristic scale of the feature or process ofinterest is not well matched to the resolution limit orsampling field of the chosen diagnostic. In addition,most of the mentioned diagnostics act upon a fixedsurface. Line VISAR, for example, gathers informationfrom a rear surface, with an averaged response of shockwave propagation through the thickness of the speci-men.82 One notable exception is ultrafast dynamicellipsometry, which can deduce the time resolved motionof the shock front in thin films.83 The utility of thismethod, however, is limited to samples transparent tothe diagnostic wavelength. It remains a challenge tomonitor the evolution of mechanical/thermal/chemicalstate ahead and behind the shock front within an opaquematerial at the mesoscopic level.

Efforts to understand the mesoscopic response ofreactive materials to shock loading have led to post-shock analyses of the recovered specimen microstruc-ture. Compared to time resolved diagnostics, recoveryanalyses are far more numerous, and comprise the vastcollection of materials characterisation techniques,which can be used to probe over a wide range of spatialscales. For example, precise measures of phase composi-tion, configuration and distribution can be obtained

6 Illustration showing distinct regions of deformation dur-

ing the shock consolidation of equiaxed powders.

These regions mark the transitions between consolida-

tion accomplished by rigid body translations/rotations

(Region I), shear/normal stress driven deformation into

the voids (Region II) and bulk volume reduction under

pressure (Region III) (from Linse71)



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through combined metallography, X-ray diffraction(XRD), and scanning and transmission electron micro-scopy (SEM, TEM) analyses.30,84–87 Measures of thedegree of shock activation (change in reactivity) can bedetermined through differential thermal analysis (DTA)and/or differential scanning calorimetry (DSC).30,88 Theonly limitation to recovery is that measurements onlyapply to the final, as shocked state, with very littleinformation concerning the critical particle configura-tions leading to reaction, or the product phase trans-formation pathways. As shown in Fig. 7, whichillustrates an optical micrograph (Fig. 7a) and XRD(Fig. 7b) trace of Ti5Si3 reaction product formed from aTi and Si powder mixture of the same stoichiometry, thecomplete formation of the equilibrium reaction productat extended timescales can mask evidence of ultrafastchemical reactions that may have occurred at earlytimes.38 Thus, while recovery techniques permit verydetailed, spatially resolved analysis of reaction products(e.g. Ti5Si3 grains of y10 mm average size, as shown inFig. 7), they are hard pressed to locate the onset time ofreaction, and distinguish between products formed dueto shock induced and shock assisted reactions.

It should be quite clear by now, that the occurrence ofultrafast shock induced reactions can only be verifiedthrough time resolved measurements, as positive prooflocates the onset of reaction within the several hundrednanoseconds of shock equilibration. Subsequent recov-ery analysis can supply potentially important informa-tion, in the cases where reaction does not go tocompletion, and the relative configurational changes inreactants and products are not obscured. Shock assistedreactions however, require more rigorous validation. Inaddition to showing evidence of reaction products in thefinal, recovered specimen, complementary time resolvedmeasurements are required to show that the specimenremained inert during the initial shock compressionevent, but reacted subsequently following unloading toambient pressure, and in the timescale of thermalequilibration.

The next section will summarise prior investigationsof reactive powder mixtures and the results of timeresolved and recovery techniques used to infer theoccurrence of chemical reactions initiated by shockwaves.

Experimental evidence of chemicalreactions under shock loading

Shock recovery experiments and analysesThe reactive system that has perhaps been mostthoroughly studied throughout the history of shocksynthesis has been that of NizAl. In 1985, Horie andco-workers89 were the first to report the synthesis ofnickel–aluminium intermetallics following shock com-pression, using the well calibrated Sandia Laboratories’Bear series shock recovery fixtures.90 Micrometre scalepowders were combined at a 7 : 3 Ni/Al volumetric ratio(corresponding to Ni3Al product formation), andstatically pressed to 60% theoretical maximum density(TMD) within Sandia’s Momma Bear (A) recoveryfixture. The powders were subjected to explosivelydriven plane wave shocks in the range of calculatedshock pressures of 14–22 GPa, and peak bulk (residual)temperatures nearing 600uC. Recovery microstructurecharacterisation and electron beam microanalysisrevealed the formation of reaction products in selectregions. A combination of the Ni3Al phase and residualNi was found at the compact periphery, where the shockgenerated temperatures reached their peak due to two-dimensional radial wave focusing effects caused by theimpedance difference between the low density powderscontained in high density (copper) fixtures. Additionally,amounts of NiAl and Ni2Al3 were discovered borderinga largely unreacted central zone (Fig. 8a). Earliersimulations of the compaction event in Momma Beartype recovery capsules showed this central zone tocoincide with the region of the highest pressure(Fig. 8b).91 The lack of reaction within this zone,coupled with a clear link between temperature andproduct formation, strongly suggests a thermallyinitiated reaction due to shock assisted mechanisms.This work also clearly illustrates the possibility offorming multiple phases, and the resulting complexityintroduced in the study of reactions occurring at varioustimescales in heterogeneous mixtures.

Nearly identical experiments were performed onmixtures of TizAl (micrometre scale powders, 7 : 3volumetric ratio, 60%TMD), with shock pressuresand bulk temperatures ranging within 5–27 GPa and

7 a Microstructure of a shock compressed and recovered TizSi mixture, revealing a homogeneous structure of reaction

product grains and voids, typical of melting and solidification. b An accompanying XRD spectrum shows the product

to be Ti5Si3. Any evidence of ultrafast, mechanochemical reactions is obfuscated by thermal equilibrium processes at

later times (from Thadhani et al.38)



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Ltd 150–800uC respectively.92 Once again, reaction products

were localised at the periphery of the recovered compact,identified by microanalysis to be a mixture of Ti3Al,Ti2Al and TiAl (Fig. 9). Extensive reaction was observedin only those compacts for which the shock generatedtemperature within the reacted zone exceeded 450uC.The authors also observed unique deformation andmixing features in otherwise unreacted regions whichwere absent in the NizAl compacts, and attributedthese to the relative differences in the hardness and melttemperature of the transition metal constituents (Ni, Ti).

Similar recovery experiments on the TizAl systemwere conducted by Royal et al.93 on micrometre scale(2325 mesh) powders, mixed at a 3 : 2 volumetric ratio,

and pressed to y53%TMD. By varying the explosiveused with Sandia’s Momma Bear recovery assembly,maximum shock pressures of 5, 7?5 and 22 GPa weredelivered. Only the specimen shocked to 22 GPa under-went reaction, though products were localised at theedge and axial regions due to the two-dimensional wavefocusing effect similar to that observed in Horie’s earlierexperiments. The presence of shrinkage pores withinthese regions suggests that the products solidified from aliquid state (Fig. 10a). As shown in Fig. 10b, theunreacted material contained mostly undeformed Tiparticles embedded within an Al matrix. This apparentpreferential deformation of the Al phase showcases theinfluence of relative component yield strength indictating the micromechanical response of heteroge-neous powder mixtures during shock compression.

Under more extreme conditions with the use of the 12-capsule Sawaoka type shock recovery fixture (Fig. 11),shock induced reaction synthesis in Ni and Al powders(y20 mm particle size) mixed at a 3 : 1 atomic ratio, hasbeen observed with the formation of the L12 phase(Ni3Al) at the initial shock pressure (calculated) ofy12 GPa.94,95 The same powder mixture, upon shockloading at a higher initial pressure of y17 GPa, showedformation of the bcc B2 phase (NiAl) but with Ni rich(3NizAl) stoichiometry (deduced from XRD latticeparameter measurements). It was argued that under theextreme conditions, the solubility of B2-NiAl wassignificantly increased, to even encompass the Ni3Alstoichiometry. Increased solubility due to extreme shockloading conditions has also been observed in the immi-scible CuzNb system, with the formation of isomor-phous CuzNb alloys and compounds.96 Solubility of asmuch as 10 wt-% solute in each phase and submicro-metre scale mechanical mixing of Cu and Nb into eachphase has been observed (Fig. 12).

Shorokhov and co-workers43 reported on the synth-esis of intermetallics in the TizAl system under theaction of spherical, converging shock waves. Micro-metre scale (,63 mm) powders were mixed at Ti/Alatomic ratios of 3 : 1 (48%TMD) and 1 : 1 (59%TMD),and loaded into a thin walled spherical steel capsule,18 mm in diameter, itself encased within a thick(y3 mm) brass shell. An explosive charge delivered

8 a Illustration showing the configuration of phases through the cross-section of a recovered NizAl compact; the shock

wave entered the powder from the top. Regions of predominant phase formation coincide with the greatest shock-

generated temperatures, as shown by the calculated contours (from Horie et al.89). b For comparison, the region of

highest pressure produced in Momma Bear type recovery capsules lies along the sample axis, as shown from two-

dimensional numerical simulation (adapted from Davison et al.91)

9 Micrograph showing the periphery of a recovered

TizAl powder compact containing multiple reaction

products: (A) Ti3Al, (B) Ti2Al, (C) TiAl, (D) Ti (from

Horie et al.92)



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peak shock pressures in the capsule wall of y50 GPa(calculated). Recovery analysis of the 3 : 1 stoichiometricmixture revealed a mixture of b-Ti and a disorderedTi3Al intermetallic. An equiaxed grain structure sup-ports the conclusion that these phases solidified from amelt. The 1 : 1 stoichiometry contained a mixture ofweakly ordered Ti3Al and TiAl. Light microscopyrevealed a dendritic microstructure, evidence of meltingand solidification.

A great deal of work has also been conducted on thesilicides, specifically TizSi, NbzSi, NizSi and MozSi

mixtures. These mixtures differ from the work onaluminides, in that silicon is a metalloid, and will notnecessarily deform through the same mechanisms as a

10 Backscattered electron micrographs from a recovered TizAl mixture taken from the a edge, showing a reacted micro-

structure and shrinkage pores, and from the b unreacted bulk (adapted from Royal et al.93)

11 Schematic detailing the 12-capsule Sawaoka fixture

used in shock recovery experiments. Powder samples

are loaded into each of the 12 steel capsules, and

held within a steel capsule holder plate. The uniform

detonation of a main charge launches a thin metal

flyer plate, which subsequently impacts the holder

plate, driving a shock through capsules and compres-

sing the powders. The rugged design permits recov-

ery of the powder compacts for post-shock

characterisation (from Song and Thadhani97)

12 Bright field image (TEM) showing submicrometre

scale mixing in a CuzNb powder mixture produced

by shock loading. Energy dispersive spectroscopy

obtained from the as labelled Cu and Nb regions

revealed increased solubilities in each phase of up to

10 wt-% (adapted from Advani and Thadhani96)



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metal. Furthermore, silicon exhibits reverse Clausius–Clapeyron behaviour, its melting temperature decreas-ing with increasing pressure.

An explanation for reaction initiation based uponthermal energy was developed by Krueger et al.,33,98

following their work on NizSi powder. Micrometrescale powders (Ni: 20–45 mm, Si: 2325 mesh) weremixed at a 1 : 1 atomic ratio and pressed to 60%TMDwithin a steel containment fixture. The powder wasimpacted directly by a stainless steel flyer launched froma 35 mm diameter gas gun. By avoiding initial contactwith the fixture, their carefully designed experimentsallowed a highly unidirectional shock wave to be appliedto the NizSi mixture, significantly reducing the two-dimensional wave focusing effects inherent of theMomma Bear or Sawaoka recovery fixtures.90,97,99 Byperforming experiments at several impact velocities andstarting densities, the shock energy E deposited in thepowder from P–V work was varied (Table 1). Also listedare the thermal energy thresholds for reaction ET,determined through DTA. The presence of reactionproducts in the recovered specimens as related tocalculated shock energy indicated a clear energy thresh-old (384–396 J g21), below which reaction did notoccur. Recovery analyses of unreacted systems showeddeformation of nickel, cracking and fracture of silicon,and the presence of resolidified regions from possible‘melt pools’ concentrated at the interfaces between thetwo parent phases (Fig. 13). Quantitative energy dis-persive spectroscopy (EDS) suggested the reacted phaseto be that of NiSi4. From these results, Krueger et al.concluded that a critical ‘threshold’ shock energy forreaction initiation is more appropriate than the previousnotion of a critical shock pressure, since reaction couldbe confirmed at lower stress amplitudes in mixtures

containing higher porosity. This is consistent withresults shown in Fig. 8, which revealed a closercorrelation with shock temperature than shock pressure.Vecchio et al.100 and Meyers et al.31 obtained similarresults using the Sawaoka capsules.

It should be pointed out that the only directmeasurement in the experiments by Krueger et al. wasof the impact velocity; the shock pressure and energyvalues listed in Table 1 were calculated values obtainedfrom this measured velocity and a calculated shockHugoniot of the powder mixture. The analysis andconclusions relied solely upon observations of post-mortem microstructural analysis to identify reactionproduct phases, and their correlation with the calculatedvalues of shock pressure and energy. Consequently, theconditions observed contain the effects of both the highpressure shock state and the post-shock bulk (equili-brated) temperature, which makes it difficult to deduce ifany or what part of the reaction was shock induced orshock assisted.

One of the first explanations for the effect of ultrafastchemical reaction on the high pressure state was offeredby Yu and Meyers,87 following their recovery work onmicrometre scale (2325 mesh) Nbz2Si powder mix-tures. The Nb and Si powders, mixed at an atomic ratioof 1 : 2, were pressed to 60%TMD within a Sawaokarecovery fixture, and impacted by a flyer plate at2 km s21. The recovered NbzSi specimen containedthe NbSi2 product phase throughout most of thecompact, with unreacted regions at the impact sidecorners. Numerous pores were observed in the reactedzone, along with needle and dendritic shaped structures,which are characteristic of a microstructure evolvingfollowing melting and resolidification processes. Theinfluence of shock induced chemical reaction on theequilibrium shocked state of the mixture was estimatedfollowing a thermodynamic analysis in which the heat ofreaction was assumed to affect the energy of the shockprocess through an increase in pressure, similar to theanalysis applied to detonation reactions in explosivesand used previously by Boslough101 for heat detonationtype reactions in thermite mixtures50

E2{E00~1

2P2(V00{V )~

1

2P1(V00{V )zER (7)

where P1 is the pressure of the inert powder, E2 and P2

are the energy and pressure of the reacted product, ER isthe heat of reaction, and E00 and V00 refer to the energyand volume of the porous mixture. The result, as shownin Fig. 14, reveals a difference in the slope of Rayleighlines joining the starting porous state to points on theinert and reacted Hugoniots. Evaluating equation (7)for the 2 km s21 flyer impact, Yu and Meyers87

estimated an increase in pressure and shock velocityon the order of 33%. Though recovery techniques wereemployed, the analysis from this work was the first to

Table 1 Details of recovery experiments performed by Krueger et al.98 on NizSi powder mixtures: results suggestcritical shock energy of y400 J g21, above which reaction is observed in recovered specimen

Porosity, % Velocity, m s21 P, GPa E, J g21 ET, J g21 React (Y/N)

37.5 1020 5.6 380 367 N41.2 1060 5.38 421 410 Y37.5 1050 5.86 398 384 N39.9 1050 5.46 407 396 Y

13 Electron micrograph of a recovered NizSi specimen

showing the presence of a product phase concen-

trated at the interface between Ni and Si (from

Krueger et al.33)



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reveal the metrics required to infer the occurrence ofshock induced chemical reactions on the basis of shockvelocity increases.

Mechanisms of shock induced reaction have beenproposed by Vecchio et al.100 and Meyers et al.31

through observations of the morphology and configura-tion of reaction products in NbzSi and MozSi powdermixtures. Following shock compression delivered byexplosive detonation using the 12-capsule Sawaokafixtures, the recovered compacts were examined forevidence of chemical reaction. In both mixtures, regionsof partial reaction contained nodules of silicon richintermetallics (NbSi2, MoSi2). As shown in Fig. 15 for aNbzSi mixture, nodules of NbSi2 are observed border-ing the Nb particles, and dispersed throughout thesilicon matrix. From the morphology and sheer numberof the nodules, the authors concluded that the formationof the nodules was associated with the melting of silicon.Dissolution of Nb into molten Si at the particle interfaceresulted in the formation of molten NbSi2. Duringsolidification, the disilicide was ejected into the Si melt,exposing fresh Nb to continue the reaction.

While this mechanism of reaction based on melting,dissolution and precipitation is highly plausible, Vecchioet al.100 and Meyers et al.31 supply no evidence for thetime over which reaction is initiated and completed. Infact, had the nodules formed within the shock front atshort timescales, it stands to reason that there would beevidence of heterogeneous transport of nodules withinthe silicon melt, which is absent in Fig. 15. Reactions

14 Proposed P–V Hugoniots of the solid, powder and

reacted powder for a Nbz2Si powder mixture. The

slope of the Rayleigh line for reacted behaviour (2) is

greater than for inert behaviour (1), indicating an

increase in shock velocity (adapted from Yu and

Meyers87)

15 Micrographs (SEM) of recovered NbzSi compacts revealing a an unreacted portion, b the transition zone between

unreacted and partially reacted material, c a partially reacted region and d the transition zone between partially

reacted and fully reacted material. The reaction product consists of NbSi2 nodules, which are concentrated near the

Nb particle interfaces (from Vecchio et al.100)



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based on melting, dissolution and reprecipitation aregoverned by thermally activated processes similar tothose observed during self-propagating or combustiontype chemical reactions, which are more consistent withshock assisted reactions occurring in the timescales oftemperature equilibration.102

As mentioned previously, both time resolved andrecovery analyses are needed to establish the timescaleof initiation for shock assisted reactions. Of the largeamount of recovery work conducted on powdermixtures, only a few have included both of thesetechniques.

One of the first sets of dual time resolved/recoveryexperiments was performed by Vandersall andThadhani85,103 on Moz2Si powder mixtures. Powdermixtures of micrometre scale molybdenum and siliconwere combined at 1 : 2 stoichiometry, and shock loadedin cylindrical implosion and planar pressure geometryexperiments. The maximum peak pressure and meanbulk temperature at various locations in each config-uration were estimated through two-dimensional simu-lations, while correlations to intermetallic phaseformation were provided through post-experimentalmicrostructural analysis. Results suggest the extent ofreaction to be closely linked to pressure induced meltingand bulk temperature equilibration. In specimenssubjected to pressures and temperatures exceeding themelt conditions of silicon, partial reaction resulted frommolybdenum dissolution in the silicon melt and pre-cipitation of MoSi2. Complete reaction was observed inregions experiencing melting of both silicon andmolybdenum, yielding a solidification microstructure.The timescale of temperature initiated reactions of thistype is on the order of milliseconds, and occurs longafter the initial shock front has passed. Supporting theseconclusions, time resolved Hugoniot state measurementsconducted on identical mixtures indicated inert com-pressibility behaviour within the duration of the shockpulse.103

Similar evidence of shock assisted reactions wasobserved in the NizAl system. Eakins and Thadhani86

combined micrometre scale, spherical Ni and Alpowders at 1 : 1 volumetric ratio, prepressed to60%TMD, and subjected them to input shock stressesof up to 6 GPa. Rather than performing Hugoniot andrecovery analyses on separate experiments, a soft catchrecovery technique permitted time resolved measure-ments and post-shock microstructure characterisationfrom the same specimen. Above 5 GPa, the microstruc-ture of the recovered sample contained the NiAl3intermetallic phase at the boundaries between the Niparticles and a molten and resolidified Al matrix.Reaction was believed to proceed following dissolutionof Ni into the molten aluminium. As in the case of theMoz2Si work, time resolved measurements revealed noevidence of reaction behaviour at the high pressure statein this NizAl powder of spherical morphology.

Time resolved instrumented experimentsThe investigations just described utilised post-shockrecovery analyses to determine the reaction productcharacteristics and the calculated conditions (pressure,temperature, shock energy) under which chemicalreactions are initiated. Most, however, did not coupletime resolved measurements, and therefore cannot

unequivocally establish the timescale of the formationof the observed reaction product(s).

Evidence of shock induced reactions was first demon-strated by Batsanov et al.35 in their work on SnzSmixtures. Starting tin and sulphur powders ranging insize from 5–10 mm were mixed at an equiatomic ratio,and statically pressed to y92%TMD. The powdercompacts were then subjected to explosively generatedshock pulses up to 40 GPa, which travelled first througha polytetrafluoroethylene (PTFE) driver before reachingthe specimen. The incident and reflected shock pressureswere recorded using a piezoresistive manganin stressgauge located within the driver, several millimetres fromthe specimen. Evidence of reaction was providedthrough differences observed between the experimen-tally measured and calculated reflected stress amplitudes(Fig. 16). By assuming that reaction at high pressuremanifests as a constant volume increase in pressure(consistent with detonation theory), the change inspecific internal energy of the inert powder and reactedmixture were written from the Rankine–Hugoniotrelationship

E1{E00~1

2(P1zP0)(V00{V ) (8)

E2{E00~1

2(P2zP0)(V00{V ) (9)

where E00 and V00 refer to the initial energy and specificvolume of the starting powder, and the subscripts 1 and2 are for the inert powder and reacted mixturerespectively. Solving for the heat of complete reactionQv

16 Shock compressibility of SnzS mixtures measured by

reflected shock measurements. Curve 1 is for the tin

sulphide dense product. Curve 2 is the results of

experiment conducted on stoichiometric mixtures of

tin and sulphur. Curve 3 is the expected compressibil-

ity behaviour of an inert SnzS mixture. At pressures

below 15 GPa, the mixture exhibits inert behaviour.

Above 15 GPa, the mixture deviates to the right

(adapted from Batsanov et al.35)



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Qv~E2{E1~1

2(P2{P1)(V00{V ) (10)

and then relating Qv calculated in this manner to theenthalpy of formation of SnS, the extent of reaction wasestimated. This early model has been criticised forignoring the effect of specific volume and equation ofstate changes between reactants and products.Additionally, the standard enthalpy of formation wasused when in fact, the enthalpy at high pressure wouldhave been more appropriate. Finally, it fails to considerthe influence of multiple (or intermediate) phase forma-tion on wave propagation.

During the mid-1990s, a reaction scheme based uponthe detection of an ‘excess pressure’ was promotedfollowing a series of thoughtful experiments performedon NizAl powder mixtures. In the first work, Bennettet al.104 considered micrometre scale powders of Ni (3–7 mm) and Al (20 mm), combined at a Ni/Al atomic ratioof 2?604, and pressed to y55%TMD. The pressedpowder was contained within a 304 stainless steel targetassembly, and impacted by a steel flyer. The response ofthe powder mixture was measured indirectly by amanganin gauge embedded within the steel backeropposite to the impact face. The recorded pressureprofile of the transmitted shock pulse was comparedwith pressures estimated from the P–Up diagramconstructed for inert behaviour. Experiments conductedat impact velocities ranging from 900–1450 m s21

indicated a critical velocity of 1075 m s21, above whichan ‘excess pressure’ was detected (Fig. 17). The increasein pressure was attributed to the dual effects ofexothermic heat release and volume change fromreactants to products. Post-shocked specimens exhibitedcomplete reaction of the aluminium to form NiAl3 andresidual Ni. A similar experiment utilising a lowerimpedance backer material to inhibit compressive wavereflection was performed at an impact velocity wellabove the supposed threshold for reaction initiation.However, lack of reaction signatures in the gauge recordor post-experimental microstructure supported the

conclusion that the observed reactions were initiatedby the reflected shock propagating through the alreadyshock compressed mixture.

Continuing Bennett’s work on NizAl powder mix-tures, Iyer et al.37 investigated the effect of particle sizeon the reaction threshold. The nickel particle size wasreduced to less than 3 mm (yet not nanoscale), while thealuminium particles were kept at 20 mm. Once again,NizAl mixtures were prepared to an atomic ratio of2?604 and initial density of 55%TMD, and tested in thesame experimental and diagnostic configuration asbefore. It was found that the threshold impact velocityfor reaction was increased to nearly 1400 m s21. Thisincrease could not be explained through thermochemicalconsiderations, as the shock energy was not altered.Rather, the dependence of critical velocity on particlesize was attributed to mechanochemical effects, specifi-cally the cleansing, exposing and intimate mixing offresh reactants through interparticle shear, of whichparticle size plays a significant role.

In an effort to provide conclusive evidence for eitherthe mechanochemical or thermochemical models, twoseries of nearly identical impact experiments wereperformed by Yang et al.105 on the NizAl powderconfigurations considered previously by Bennett et al.104

The experiments were designed to vary the reflectedwave profile to exact changes in the rate of mechanicaldeformation, while at the same time depositing the sametotal energy into the mixture. This was accomplished byintroducing a 0?254 mm aluminium layer on the rearsurface of the powder compact. The multiple wavereflections at the powder/layer and layer/backer inter-faces had the effect of producing steps in the reflectedstress profile. Alternatively, experimental configurationswithout the layer were performed to reproduce a steeprise to peak pressure. Once again, the mixture theorywas employed to calculate the shock compressibility ofthe powder mixture for an inert reference. In agreementwith the work by Bennett et al.104 and Iyer et al.,37 theinitiation of reaction within 100 ns of the shock frontresulted in a measurable ‘excess pressure’. On the basisof this measure, Yang et al.105 were able to confirmreaction in only those specimens without the aluminiumlayer. Powders subjected to a multistep reflected shockremained unreacted, even though the total input energyexceeded the supposed threshold energy (483 kJ kg21)determined by the reacted series (Fig. 18). This resultserves to refute the earlier theory of an energy thresholdfor reaction proposed by Krueger and Vreeland, Jr.33

Furthermore, the apparent link between the rise time ofthe reflected shock and chemical reactivity appears tostrengthen the hypothesis that, at least for the experi-mental configuration considered, reaction was initiatedin the precompressed, shock modified reactants uponreflection at the sample/backer interface.

In each of the works mentioned thus far, sampleconfigurations were chosen such that the reflected shockprofiles were recorded by a single manganin gauge(y50 ns resolution typical). Used in the mannerdescribed, the manganin gauges were insensitive to thedetails of shock loading within the rise time of the shockpulse. Therefore, the reflected shock set-up does notprovide for the determination of reaction immediatelybehind the incident shock front. These studies alsoinclude unknown shock quantities that are indirectly

17 Time resolved stress traces recorded in a NizAl mix-

ture at two impact velocities v. Pressures in excess of

those expected for an inert material were observed in

both experiments shown. The expected inert pressure

was y21 GPa for the closed and open data set, as

shown by the dashed line (adapted from Bennett

et al.104)



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determined. Only through the explicit knowledge of theHugoniot of all interacting materials could the powdershock state be calculated.

A study conducted by Graham et al.36 using Bauerpiezoelectric polymer gauges demonstrated a newexperimental set-up allowing the direct measurementof shock pressure and shock velocity. The PVDF gaugesoffered a resolution of 1 ns up to a maximum pressure of100 GPa. Used in conjunction with a gigahertz fre-quency oscilloscope, information about pressure equili-bration and shock wave reverberation could becaptured. PVDF gauges placed at the impact andpropagated specimen/fixture interfaces allowed thedirect measurement of input stress and shock transittime through the specimen. Several series of experimentshave been conducted to illustrate the capability ofperforming accurate shock compressibility measure-ments on powder systems exhibiting inert and reactivebehavior.36 Stoichiometric mixtures of 3NizAl and5TizSi, as well as rutile (TiO2) powder, were pressed toinitial densities of 35, 53 and 60%TMD respectively.Specimens were contained within a Cu fixture, andimpacted by a Cu flyer launched by a compressed gasgun, sending a shock wave through the powder anddiagnostic gauges. For the 3NizAl mixture, the P–Vstates above 3?7 and 4?7 GPa seemed to follow thecalculated mixture Hugoniot, indicating inert behaviour.On the other hand, the 5Tiz3Si powder mixture testedat 2?5 GPa revealed a measured shock state consider-ably displaced from the calculated mixture Hugoniottoward higher volumes (Fig. 19). Coupled with reportsthat the crush strength of such a mixture was in thevicinity of 800 MPa, this shift is not indicative ofincomplete densification, as was the case for the TiO2

powder, but suggestive of shock induced reaction.

Time resolved experiments on the 5Tiz3Si systemwere continued by Thadhani et al.,38 to investigate theinfluence of particle size on shock induced reactionsensitivity. Mixtures of coarse (Ti, Si: 105–149 mm),medium (Ti, Si: 45 mm) and fine particles (Ti: 1–3 mm,

Si: ,10 mm), were combined to the stoichiometry ofTi5Si3 and pressed to within 45–53%TMD. Using asimilar experimental configuration as Graham et al.,36

PVDF measurements of input stress and shock velocitywere obtained from impact experiments conducted inthe range of 0?2–2?9 GPa. Results for the coarse and finepowder mixtures revealed a regime of densificationunder y1?25 GPa, above which both mixtures followedthe calculated Hugoniot of the solid mixture (Fig. 20).On the other hand, the medium powder mixtureexhibited a lower crush strength (y1 GPa) and signa-tures of shock induced reaction above 1?5 GPa, namely,deviations from the inert solid mixture Hugoniot tohigher volumes. Since the shock energy deposited intoeach of the three mixtures at a particular pressure wasvery similar (especially so for the medium and coarsemixtures pressed to the same initial packing density), itfollows that the cause of reaction cannot be solely

18 Peak transmitted pressures as a function of shock

energy for experiments with a sharp (open circles)

and multistep (closed circles) reflected shock front.

The solid line corresponds to the calculated inert

behaviour. Excess pressures are only observed above

483 kJ kg21 when the reflected shock front is narrow

(from Yang et al.105)

19 Pressure–volume data obtained through PVDF mea-

surements for 3NizAl, 5Tiz3Si and TiO2 powders.

Reaction is only suspected in the 5Tiz3Si mixture,

which exhibits an expansion to higher volumes above

its supposed crush strength of y800 MPa (adapted

from Graham et al.36)

20 Time resolved results obtained from mixtures of

coarse, medium and fine 5Tiz3Si powders. All three

mixtures show similar densification behaviour, reach-

ing the solid Hugoniot at 1?0–1?25 GPa. Above

1?5 GPa, the medium mixture deviates from the solid

Hugoniot to higher volumes, presumably from the

effects of shock induced chemical reactions (from

Thadhani et al.38)



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attributed to thermochemical processes. Rather, thisstudy shows that particle deformation behaviour, suchas the transition from plastic deformation to cracking insilicon with changing particle size, can strongly affect theintimacy of mixing and the propensity for shock inducedchemical reaction.38

The importance of extrinsic mixture properties onshock induced reactions was further investigated by Xuand Thadhani,39 in their study of the effect of powderpretreatment on the chemical response of shockcompressed NizTi powder mixtures. Spherical shaped(rounded) Ni and Ti powders of 2325 mesh (,44 mm)were combined at a 1 : 1 atomic ratio, and staticallypressed to 50%TMD. The powders were then ball milledfor 0, 4, 8 and 18 h to introduce varying degrees ofdamage and defects. From preliminary XRD and DTAstudies, the pretreated powders exhibited increasedalloying and reduced heat of reaction with longer ballmilling duration. For the shock compression experi-ments, PVDF gauges were once again used to monitorthe input and propagated stress profiles, from which theshock transit time through the powder mixture was alsodetermined. Results from the as-pressed mixture (0 hball milling) showed a substantial deviation from theHugoniot of the inert mixture at 3?22 GPa (Fig. 21a).With increasing duration of ball milling, this deviationwas reduced until negligible for the specimen ball milledfor 18 h (Fig. 21b). This result may be in large part due

to the reduced amount of parent Ni and Ti phasesavailable for reaction with longer ball milling duration.Interesting to note are the clear distinctions between thevarious data, which altogether suggests that suchdeviations in time resolved data might be sensitiveenough to infer the extent of shock induced chemicalreactions in powder mixtures.

Building upon the recovery work of Song andThadhani97 and Dunbar et al.,88 Eakins andThadhani40 investigated the influence of particle mor-phology on shock induced chemical reactivity in theNizAl system. In the first mixture, micrometre scale(2325 mesh, ,44 mm) Ni and Al particles of roundedmorphology were combined at an equivolumetric ratio,and statically pressed to 60%TMD. For the secondmixture, the rounded Ni particles were substituted withNi flakes (2325 mesh diameter, 350 nm thick), and themixture prepared to the same equivolumetric ratio, andpressed to 45%TMD. Parallel plate impact experiments,similar to those performed by Graham et al.36 and Xuand Thadhani,39 were conducted utilising time resolvedPVDF diagnostics up to 6 GPa. As shown in Fig. 22a,the shock response of the spherical NizAl powdermixture matched well with the response of an inertmixture estimated from McQueen’s mixture theory.53

On the other hand, the flake mixture exhibited increasedshock velocities above an input stress of 3?5 GPa(Fig. 22b).

In the parallel plate impact experiments performed byGraham et al.,36,106 Thadhani et al.,38 Vandersall andThadhani,103 Xu and Thadhani39 and Eakins andThadhani,40,66 there was a strong desire to avoid two-dimensional radial focusing effects in order to promote aone-dimensional shock event. To accomplish this, verylarge aspect ratios (e.g. diameter to thickness ratio of20 : 1 for a y2?5 mm thick powder layer) wereemployed.40 While more than sufficient to recordincreases in shock velocity associated with ultrafastchemical reactions, this experimental set-up (with only asingle pair of PVDF gauges) did not allow for trackingthe propagation behaviour of the reaction front. Suchbehaviour is required to distinguish between deflagra-tion and detonation type reactions, and may be morenoticeable in thicker powder layers.

To address the possibility that shock induced reac-tions might propagate with detonation-like character,Gur’ev et al.107 performed a series of shock velocitymeasurements through ZnzS powder compacts ofvarying thickness. The mixtures were comprised of Znand S powders 3–5 mm in size, mixed at a 1 : 1 atomicratio, and statically pressed within a low sound speedcylinder (i.d.516?5 mm) to 60–70%TMD. Shock load-ing was delivered by an explosive charge, and the shockvelocity through the specimen determined from arrivalgauges located at both ends of the cylinder. The heightof the cylinder (and thus the thickness of the powder)was varied from 40 to 200 mm between experiments, thelower limit chosen such that the shock wave in an inertZnzS mixture would fully attenuate before reaching thetransmitted gauge. Data from these experiments arepresented in Table 2, where L is the sample thickness(propagation distance), Us is the reaction front velocitywith associated error d and r00 is the initial mixturedensity. In each experiment, the transmitted gauge wastriggered, which suggests that the energy released due to

21 Pressure–volume data obtained for NizTi powder

mixtures a without pretreatment and b following 0–

18 h of ball milling (BM). The reaction product states

were calculated using the Ballotechnic model, consid-

ering varying reaction enthalpies as measured for the

different BM conditions. Notice that the extent of

deviation from the inert curve appears to decrease

with increasing duration of ball milling (adapted from

Xu and Thadhani39)



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ultrafast chemical reaction serves to support and extendthe range of wave propagation, and thereby delayattenuation.

To more clearly describe the shock propagationbehaviour in this set of experiments, the data inTable 2 are plotted in Fig. 23. From the combineddensity/shock velocity plot, it is reasonable to suggestthat the large swings in shock velocity for L540–75 mmare due to the varying sample densities. However, in theL575–100 mm range, an apparent jump in Us isobserved (1?39–2?55 mm ms21), with only minor differ-ence in density (60?7–62?4%TMD). Beyond L5150 mm,any increase in shock velocity is less obvious, and mayeven indicate a steady state. These results seem toindicate a transition between an unsteady to steady solidstate detonation-like behaviour developed in the rangeof L575–150 in ZnzS powder mixtures subjected toexplosive shock loading.

Thermodynamic models for shockinduced reactionsAlthough there are uncertainties concerning the mannerin which shock induced reactions affect the high pressurestate, several analytical models have been proposed topredict the equilibrium shocked state of a reactedpowder mixture, to further support the measured statesas indicators of reaction. One of the first modelsaccompanied the observation by Batsanov et al.35 ofshock induced reaction in the SnzS system. As

discussed previously, the heat of reaction released dueto the formation of a given product phase was assumedto manifest as a constant volume increase in pressure(equation (10)). By assuming the product to be SnS andfrom the measured shift in Hugoniot data, Batsanovet al.35 estimated the degree of product formation to bey27%. A similar analysis was performed later by Yuand Meyers,87 as described in Fig. 14, although, basedon results of shock recovery experiments performed onNbzSi powder mixtures.

Based on their results in the 5Tiz3Si system, Grahamet al.36 suggested that phase transformations occurringwithin 100 ns of the shock front can be responsible for aconstant pressure deviation from the referenceHugoniot, in direct contrast to the constant volume

Table 2 Reaction front propagation results in a mixtureof ZnzS107

L, mm Us, mm ms21 d, % r00, %TMD

40 2.27 0.6 68.160 1.3 0.2 63.075 1.64 0.2 71.690 1.39 0.2 60.7100 2.55 0.2 62.4150 2.195 0.1 63.5150 1.915 0.1 62.4200 2.169 0.1 59.4

22 Shock velocity v. input stress for the a 60%TMD spherical NizAl and b 45%TMD flake Nizspherical Al powder mix-

tures. While the spherical mixture remained inert up to 6 GPa, the flake mixture exhibited a deviation from inert beha-

viour above 3?5 GPa, suggesting the occurrence of shock induced chemical reaction (from Eakins and Thadhani40)

23 Experimentally measured shock velocities in ZnzS

powder compacts of varying thickness. The initial

decrease and subsequent increase in shock velocity

suggests a transition to solid state detonation in the

realm of 75–100 mm. Also shown are the sample to

sample variations in packing density, which appear to

correlate with the scatter in data



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assumptions claimed previously.35,87,97 He proposed thechange in volume from reactants to products to take theform

DV~(V00{V )zbQ

Cp(11)

where V00 is the specific volume of the starting powdermixture, b is the coefficient of thermal expansion atpressure and temperature, Q is the heat influencing thewave propagation and Cp is the specific heat at pressureand temperature. With increasing shock pressure, thedeviation from inert behaviour is amplified. Grahamet al.36 described the locus of possible reaction productstates as the ‘Ballotechnic’ curve, as shown in theschematic in Fig. 24. A physical explanation for theshape of the Ballotechnic curve lies in the dispersivenature of shocked powders and their mixtures.

When a shock wave propagates through a powdermixture, a portion of the shock energy is deposited intothe densification process. Thus, as the wave propagatesthe front becomes dispersed, resulting in a decrease inloading rate.108 Therefore, while the proper conditionsfor reaction may be realised early on, broadening of theshock front profile prevents the critical environmentfrom being produced further in the specimen. Con-sequently, the heat of reaction influencing wave pro-pagation Q will be related to the fraction of materialundergoing reaction and is reflected in the measuredshock velocity. Hence, there is a range of pressureswithin which reaction is incomplete; the lower and upperbound of this range are defined when the input andoutput profiles respectively possess the critical rise timefor reaction (Fig. 24). Furthermore, at pressuresbetween these hypothetical initiation and completionpressures, the reaction front propagates at a velocitythat is an intermediate value, evidenced by the range ofinfluenced shock velocity. Increased shock velocities in

powders undergoing reaction can be explained bycomparing Rayleigh lines joining the starting state topositions on the inert and Ballotechnic curves.

Continuing the work by Graham et al.,36 Bennett andHorie109 compared the methods of calculating thereaction product Hugoniot based upon the constantvolume and constant pressure adjustment schemes. Inboth methods, the dense product Hugoniot, referring tothe compressibility curve of the compound, was used asthe reference from which adjustments corresponding tothe effects of deformation energy and heat of reactionwere made. For the constant volume approach, it wasassumed that the reaction resulted in an increase inpressure, likened to the detonation response of explo-sives. Equations for energy conservation were writtenfor the reference and hypothetical reaction productcurves

ERP{E00~1

2(PRPzP00)(V00{VRP) (12)

EH{E�0~1

2PH(V �0 {VH) (13)

where the subscripts H and RP correspond to the denseproduct Hugoniot and reaction product respectively.Using the Mie–Gruneisen equation under the assump-tions V�0 ~VRP, E005E0 and P050, the following

equation for the reaction product Hugoniot was derived

PRP~(E�0{E0)zP�H (1=2)(V�0 {VRP){(V=c)�

� �(1=2)(V00{VRP){(V=c)�

(14)

For the constant pressure adjustment, Bennett andHorie derived an expression to replace the Mie–Gruneisen constant volume relation

ERP{E�s ~(VRP{V�s ) (V=c)�(bs=Vs)�{P�s

� �(15)

where bs is the isentropic bulk modulus. Following the

24 An illustration of the Ballotechnic curve defining the locus of reacted states leading to the reaction product Hugoniot.

By comparing Rayleigh lines joining the starting and shocked states, it becomes clear that the formation of the reac-

tion product during the timescale of pressure equilibration results in an increased shock velocity. Also shown are

shock front rise times that might be observed at an input and propagated stress gauge as a function of pressure.

Reaction will be limited when the front rise time drops below the critical value for reaction t*, due to dispersive

effects through the powder mixture



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same procedure as before where instead of constantvolume, the condition P�s ~PRP is assumed

VRP~

V �s (V=c)�(bs=Vs)�{P�s

� �z(1=2)P�s V00z

ÐV�sV�0

P�s dV�s {(E�0{E0)

(V=c)�(bs=Vs)�{(1=2)P�s

(16)

This relationship allows calculation of the reactionproduct Hugoniot through a constant pressure schemereferenced from the dense product isentropic compres-sion curve. It has been argued that the constant pressureadjustment is more appropriate for intermetallic form-ing systems, since the degree of gas evolution is generallynegligible.

The constant pressure model for Ballotechnic reac-tions has been employed in the recent study of shockinduced reactions in NizTi powder mixtures by Xu andThadhani.39 Reaction product Hugoniot curves for theNiTi compound were calculated using the Ballotechnicmodel and the ambient pressure heats of reactiondetermined for each powder by DTA. The measuredshock states were in good agreement with the calculatedcurves as illustrated in Fig. 21.

It should be reminded, however, that the interpreta-tion of deviant Hugoniot data on the basis of a singleproduct phase (most often aligned with the startingmixture composition) ignores heterogeneous mixing andnucleation mechanisms. The consideration of multiplepossible phases and reaction extent greatly complicatessuch a thermodynamic analysis. This possibility wasexplored by Eakins and Thadhani40 for the flakeNizspherical Al system. Rather than assuming a fixedproduct stoichiometry, the possible formation of anymixture of the NiAl, NiAl3 and Ni3Al product phaseswas considered. Using the positions of the deviant data,inert reference and limits for complete reaction calcu-lated using the Ballotechnic model, a ternary reactioncomposition diagram was constructed (Fig. 25), whereeach surface describes the possible phase makeup of agiven deviant Hugoniot measurement. By assuming that

the series of deviant data represented varying degrees ofthe same process, it was concluded that the productmixture be predominantly composed of the equiatomicNiAl phase. Additionally, the lack of intersectionbetween the starting mixture composition (dotted) andthe reaction composition surface at 5?5 GPa suggeststhat not all material behind the shock front wasconverted to product, and that reaction proceededthrough heterogeneous mechanisms.

Proposed shock induced reactionmechanismsThrough the investigation of shock induced reactions,several models and concepts concerning the criticalprocesses responsible for reaction initiation have beenproposed.

A general conceptual scheme for the shock inducedreaction event has been described by Graham.106 Shownin Fig. 26 are several stages in the overall shockcompression event. Material in the undisturbed, initialconfiguration is brought to the high pressure, com-pressed configuration through a transition zone. Theevents in the transition zone are comprised of config-uration change, mixing, shock activation and heating(CONMAH), and are collectively responsible for theinitiation of chemical reactions. Configuration changerefers to modifications in the size, morphology anddistribution of phases; mixing characterises the evolu-tion of boundaries between reactant species; shockactivation describes the enhanced interatomic mobilitydue to increased defect concentration and cleansing ofsurfaces; and heating corresponds to the thermalenvironment caused by bulk heating, energy localisationnear collapsed voids or defects, and transport across thethermal landscape.

CONMAH outlines the important processes thatmust occur during the transition zone, but does notspecify the mechanisms of mixing responsible for theultrafast reactions similar to those observed in, e.g.

25 a Ternary composition diagram derived from the displaced Hugoniot data shown in Fig. 22, assuming complete reac-

tion. Also shown is the composition of the starting mixture (dotted). Solving across the complete range of reaction

extent yields a reaction composition diagram (b), which reveals the relative stoichiometry of the phases that may be

formed due to shock induced chemical reaction

(16)



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SnzS, TizSi and NizTi systems. It ascribes impor-tance to the intermixing and activation of reactants, butis not intended to qualitatively or quantitatively describehow these events occur. Several other investigators haveproposed mechanisms for mixing and reaction initiation.Dremin and Breusov28 conceptualised a model toexplain the synthesis of new phases during shock com-pression. Figure 27 is an illustration of the ROLLERmodel, which describes the formation of a compoundAxBy at a sliding interface between A and B crystals. It issuggested that the relative movement of the componentsurfaces produces a nucleus, which ‘rolls’ between thesurfaces, and about which adjacent atoms may attach toform a new phase. Thus, formation and growth of thenew phase is not governed by diffusion, but rather by

mechanical transport of material to the numerous nucleiat particle interfaces.

Another mechanical explanation for mass mixing andreaction initiation was offered by Batsanov et al.35

following their work on SnzS, in which they observethat the intrinsic properties of tin and sulphur (density,moduli) result in differing particle velocities at pressure.Within the range of 10–40 GPa, the difference DUp is inthe range of 0?7–2?0 km s21. The differing relative highvelocity motions between particles results in the forcedtravel of one component into another. Iyer et al.37

expanded this mixing mechanism by attributing relativeparticle velocities to the development of interparticleshear. Yano and Horie110 performed a discrete elementnumerical simulation (DM2) to calculate particlevelocity differences of 20–100 m s21 in the NizAlsystem.

Nesterenko et al.84 have also provided clues to thetype of mixing that may be promoted during the shockcompression of reactive powder mixtures. A cylindricalconverging shock was used to produce shear localisationin reactive powder mixtures. Recovered specimensexhibited distinct shear bands (Fig. 28), within whichevidence of particle comminution, vortex formation andchemical reaction was observed. The vortexes weredeemed responsible for increased temperatures and masstransfer, and were believed to form as a consequence ofthe variations in flow stress due to inherent mixture

26 Fundamental framework for shock induced reactions

proposed by Graham.106 The schematic illustrates the

transport of material from an initial configuration to a

final, compressed configuration. The transition zone is

the time interval over which the effects of configura-

tion change, mixing, shock activation and heating are

experienced. Little is known about the specific pro-

cesses occurring within the transition zone

27 Illustration of the ROLLER model proposed by Dremin

and Bruesov,28 extended to a binary system, to

explain the mechanism of ultrafast reaction initiation

under shock loading. The sliding interface between A

and B crystals produces a small AB nucleus, which

accumulates material in the formation of a new phase

28 Evidence of vortex flow in shear bands produced

through thick walled cylindrical implosion experiments

performed on NbzSi powder mixtures. The vortexes

are regions of increased temperature and mass trans-

fer, originating from instabilities in flow stress (from

Nesterenko et al.84)



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heterogeneity. Tamura and Horie111 investigated themechanism of mixing within shear bands through DM2simulations, and demonstrated the influence of voidcontent and component mechanical response on theeffectiveness of mixing.

Each of these models seeks to explain the micro-mechanical conditions necessary for shock inducedreaction initiation. Batsanov et al.’s35 particle velocitydispersion (PVD) model is based entirely upon thedifferences in intrinsic properties of reactants. Noconsideration is made of the configuration of reactants,such as the morphology and arrangement of particles,voids or contacts. The experiments by Nesterenko et al.84

were designed to probe the micromechanical details ofparticle fracture, vortex formation and thermallyinduced reaction in deliberately created zones of intenseshear. They do not, however, explain reaction undermechanochemical mechanisms and under the initialconsolidation event, during which intense shear atinterparticle regions is a direct consequence as particlesof dissimilar characteristics come together in the processof void collapse. Dremin and Breusov’s28 ROLLERmodel, in fact, also explores reaction through amechanism grounded firmly in a particular, althoughsimplified, configuration of reactants (sliding interface).The influence of intrinsic properties of the reactants isnot incorporated.

In reality, the initiation and propagation of shockinduced reactions is intimately linked to both theintrinsic and extrinsic properties of the powder mixture.Indiscriminate shear at a phase boundary, or arbitraryselection of components based upon relative impe-dances, is hardly enough to guarantee reaction. Further-more, reactions proceeding through dissolution andgrowth rely on melting at extended timescales. A studyhas yet to be completed that seeks to explain shockinduced reaction initiation mechanisms on the basis ofboth intrinsic properties and extrinsic powder config-uration in a real, non-idealised system.

Computational and mesoscale modellingof dynamic compression/shock inducedchemical reactionsOwing to the immense restrictions on real timediagnostics imposed by the ultrashort lifetime of theshock event, there is a limit to the type and amount ofinformation that can be gathered experimentally. Asillustrated in the preceding section, the informationavailable has provided only indirect inference of shockinitiation of chemical reactions, with no spectroscopicinformation of the type of reaction product and itsextent. Many of the questions that have been posed orconceptually described concerning shock induced reac-tions have, therefore, been tackled through computa-tional approaches.

One of the first computational studies of shockinduced reactions was accomplished by Horie andKipp.112 An illustration of their model is shown inFig. 29, which conceptually describes the conversion ofpowder reactants (A, B) to products in a generalisedsystem. It is assumed that the reaction pathway includesa transition phase before arriving at the equilibrium endstate product, i.e. for a 1 : 1 stoichiometry mixture

AzB?

mAxByz(r{mx{p)Az(r{my{p)BzpAB (17)

where r, m and p are the molar amounts per unit volumeof the reactants, transition phase and products respec-tively. Rate equations of an Arrhenius form are pre-scribed to govern the conversion, and the heat generatedfrom reaction is included in the conservation of energy

rdE

dt~{(Pzq)

Lu

Lxz

:Q (18)

where E is the internal energy, r is the mass density, u isthe Lagrangian particle velocity, P is the pressure, q is

the artificial viscosity and:

Q is the rate of heat generatedfrom reaction, given by

:Q~DH

dp

dt(19)

where DH is the reaction enthalpy. Using the one-dimensional finite difference wave propagation codeWONDY-V, the influence of chemical reactions onpressure and temperature profiles in a 3NizAl systemwere investigated.113 Based upon prior work on SHSreactions in the NizAl system, and considerations oftypical liquid activation energies, energy barriers of 62?8and 16?7 kJ mol21 were considered respectively. Resultsfor a 3 cm thick specimen impacting a rigid boundary at1?5 km s21 revealed a strong correlation between theactivation energy, transformation timescale andincreases in pressure and temperature. Lowering thethreshold for reaction resulted in increased reactionrates, and more pronounced changes in the shock profile(Fig. 30). For high activation energy, the shock pulsehas constant amplitude. On the other hand, an increasein pressure of y5 GPa is observed for the lower(16?7 kJ mol21) case at 9 ms. Similarly, the shocktemperature (bottom) reflects these differences.

The authors conclude that for sufficiently quickreactions (those with low activation energy), changesin the structure or character of the shock wave can be

29 Illustration of the transition from reactants (A, B) to

products generalised from Horie and Kipp’s model for

shock induced chemical reactions. As a shock wave

propagates from left to right, the void separating reac-

tants is eliminated and mixing is accomplished. After

a threshold energy barrier is exceeded, reaction takes

place, forming initially a transition phase, which after

time forms the final end state product (adapted from

Horie and Kipp112)



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used as signatures of reaction. It should be pointed out,however, that the increases in shock amplitude resultfrom an assumed form of the P–a equation of state,which ensures that all contributions to internal energyfrom chemical reaction will directly influence thepressure

P~f(Vs,E)!CrsE (20)

No experimental evidence has yet to be supplied thatwould imply that such inorganic, gasless reactions doindeed produce an increase in pressure of 4–5 GPa. Onthe other hand, substantial changes to the shock profileare predicted for very long timescales (5–9 ms), which ismany times the shock event and diagnostic lifetimes ofmost time resolved experiments. For example, thepowder thickness for many experiments is kept to

several millimetres (and diameter being an order ofmagnitude larger) to avoid two-dimensional effects,resulting in shock event lifetimes (before reflection) ofapproximately 1–3 ms for PVDF and optical pyrometrymeasurements.40,76 In any event, this early model doesnot appear to reproduce appreciable changes in theshock state at very short timescales (or through thinpowder layers), as shown in the experimental work onNizTi, TizSi and NizAl.38–40

The likelihood of PVD being the driving mechanismof component mixing and reaction was investigatednumerically by Yano and Horie.110 Using the discreteelement method, binary mixtures of NizAl and TizPTFE were randomly assembled according to massfractions, Xm50?3, 0?6 and 0?9 of the heavier compo-nent (Ni, Ti), and an element size of 1 mm. Shock

30 Spatial profiles of stress, transition phase concentration (m/r) and temperature at 2, 5 and 9 ms following shock com-

pression at 1?5 km s21, with an activation energy of a 15 and b 4 kcal mol21. For the lower (16?7 kJ mol21) activation

energy, the stress and temperature profiles show a significant increase in amplitude due to chemical reaction after

9 ms (from Horie and Kipp112)



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compression was simulated at particle velocities of Up5

150, 300, 450 and 600 m s21, and the resulting particlevelocity for each component determined through aver-aging within a 4 mm window. The PVD was thencalculated by considering the difference between thesetwo measures. For both mixtures, the maximum PVDwas observed within the shock front, shown in Fig. 31.The following expression was used to define the spatialscale of mixing s

s~36c

r(Dup)2ls (21)

where c 51 J m22 is a representative surface energy formetals, r is the mixture density, Dup is the measure ofPVD and ls is the fraction transformed. They were ableto calculate the scale of mixing s of y60 nm for theNizAl system. Based upon this result, they concludethat PVD is a plausible mechanism for shock inducedreaction initiation.

Unfortunately, these simulations and their elegantanalysis do not directly relate to the experiments theyare based from. The model treats each binary system asa fully dense mixture, and does not consider theinfluence of porosity. Furthermore, the random arrange-ment of each component constructs element assemblageswhose size depends upon the mass fraction. As a result,the spatial character and magnitude of PVD in granularmixtures, and the resulting mixing dimension, may bequite different from those reported.

In another study, Tamura and Horie111 also appliedthe discrete element method (DM2) to investigateinterparticle mixing through shear band formation inthe NbzSi and NizAl systems, as observed in theexperimental work by Nesterenko et al.84 on Nb/MozSimixtures. The creation of a shear band was simulated byconsidering an interface between two materials (e.g. Nband Si) and prescribing a velocity boundary condition atthe upper and lower domain edges, as shown in Fig. 32a.Through the thickness (between the boundaries), theparticle velocity was varied linearly. The authorsinvestigated the influence of internal void content, strainrate, relative yield strength and melting on the degree ofmixing and chemical reaction within a shear band. Theresult was an excellent parametric study providing great

insight concerning the processes that govern massmixing. For example, by systematically adjusting theflow stress of Si in the NbzSi system, Tamura andHorie were able to show that there was an optimumstrength ratio between components that resulted in themost effective mixing. Additionally, both the width ofthe shear band and the overall extent of mixingincreased with shear strain rate, as shown by comparingFig. 32b and c. However, melting also occurred morerapidly at high strain rates, resulting in a loss ofstrength, increased strength ratio, and therefore, a nega-tive effect on mass mixing, which consequently hinderedchemical reaction.

In considering chemical reactions, the threshold forinitiation was set to the melt temperature of the lower

31 Spatial profiles of particle velocity taken 15?4 ns after impact (Up50?6 m s21) for mixtures (Xm50?3) of a NizAl and b

TizPTFE. The maximum difference in particle velocity occurs within the shock front (from Yano and Horie110)

32 DM2 model configuration a for the initial case, show-

ing a simple interface between two particles of differ-

ing materials, and shear loading prescribed by upper

and lower velocity boundaries, b following straining to

shear strain of 16 at a strain rate of 1?66108 s21 and

c following straining to a shear strain of 16 at a

strain-rate of 8?06107 s21. The unfilled regions in the

starting and final configuration represent voids. Notice

that the configuration in b shows a larger shear band

width and degree of mixing than in c (adapted from

Tamura and Horie111)



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melting point component (Si in NbzSi mixtures, Al inNizAl mixtures), and heat released due to reaction wasdeposited in the mixture through Arrhenius kinetics.The onset of Si melting at the higher strain rates in theNbzSi mixture was shown to deleteriously affect thedegree of reaction through poor mixing, as observed inthe time resolved experiments on NbzSi and MozSi.103,114 On the other hand, the much larger thermalconductivity in the NizAl mixture served to preventmelting at high strain rates, allowing the solid constitu-ents to participate in further mixing and chemicalreaction (Fig. 33).

Throughout the experimental literature, there is nosingle accepted indicator or signature of shock inducedchemical reactions. As discussed above, measures ofexpanded states, excess pressure, energy thresholds andincreased shock velocities have all been used to argue theoccurrence of ultrafast chemical reactions.33,35–37,40,98,107

The influence of these reactions on high pressure statevariables such as pressure, temperature and particle/shock velocities were investigated numerically by Doand Benson115,116 using the multimaterial Eulerianhydrocode Raven. The shock compression of a NbzSipowder mixture was simulated in two dimensions.Simulated circular particles ranging in diameter from30 to 50 mm were randomly distributed within a 50061000 mm space (180690 elements, y5?6 mm/elementedge), and packed to 60%TMD using a ‘pseudogravity’method.117 Both components were modelled with a Mie–Gruneisen equation of state; the Steinberg–Guinan andJohnson–Cook strength models were used for Nb and Sirespectively. The shock was delivered through a Nbplate moving at a constant velocity from the leftboundary, while symmetric boundaries were prescribedat the top and bottom edges. For the given NbzSisystem, reaction was assumed to form the disilicide,NbSi2. The reaction rate of the kth reaction for the ithspecies was given by

rk~ kfkPI

i~1xi½ �v’ik

� �{ kbk

PI

i~1xi½ �v’’ik

� �(22)

where I is the number of components in the system, [xi]

is the molar concentration of the ith species, v’ik and v’’ikare the stoichiometric coefficients, and the reaction ratecoefficients kfk

and kbkfor the forward and backward

reactions are defined as

kfk~Afk

Tbfk Pgfk exp{Efk

RT

� �(23)

kbk~Abk

Tbbk Pgbk exp{Ebk

RT

� �(24)

where the coefficient A is the frequency, E is theactivation energy, R is the gas constant and T is thereacting temperature. Values of A and E were set to 1017

and 72 kJ mol21 based upon the requirement thatreaction is completed within a single travel of the shockwave. The coefficients T and P in equations (23) and (24)allow for a temperature and pressure dependence of thereaction rates, but were set to unity (b,g50). In addition,the backward reaction was ignored (kbk

50). Transportof the reactants through the product phase was alsoconsidered in order to avoid arresting of the reactiononce all reactant interfaces were consumed. Owing to thelack of experimental evidence that would suggestotherwise, no limits on the transport rate were specified,i.e. it was assumed that transport through the productlayer was not a rate limiting process for furtherreaction.

The evolution of reactant and product materialconfiguration following shock compression at Up5

1 km s21 is shown in Fig. 34. Reaction appears to beinitiated almost immediately behind the shock front,leaving a mixture of NbSi2 and residual Nb. Figure 35shows the particle velocity in the x direction averagedthrough the model height for both the inert and reactedcase. In the reacted mixture, a nearly twofold increase inparticle velocity was observed within a zone ofy100 mm in thickness behind the shock front. Alsoobvious is an apparent increase in the shock velocity,evident when comparing the half-max positions att50?3 ms. The Us–Up relationship determined througha range of initial particle velocities is shown in Fig. 36,which shows a deviation from inert behaviour above

33 Measure of the extent of reaction as a function of shear strain and strain rate in the a NbzSi and b NizAl systems.

Reaction in the NbzSi system at the higher strain rate is arrested following melting of Si (from Tamura and Horie111)



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Up50?5 km s21. The authors also examined the tem-perature, pressure and microkinetic energy profiles atthese same time intervals, noticing that each showed amarked increase near the shock front. Such observationsagree with the work of Boslough,76 Iyer et al.,37 Bensonet al.118 and Nesterenko.119 Based upon the irregularityin simulated pressure profiles and the relative precisionof shock velocity measurements, the authors suggestthat the latter is a more precise indicator of shockinduced reactions.

This work does well to approach an upper limit on theinfluence of shock induced reaction on materialresponse. The assumed reaction rate activation energyand frequency, infinite transport rate and ignoredbackward reaction ensure that reaction goes to comple-tion immediately behind the shock front, clearlyinfluencing the degree of mixing (microkinetic energy),pressure, temperature and particle/shock velocities. Thegeneral form of this model also provides flexibility toalter the chemistry (multiple product phases) andkinetics of reaction to reflect the results of additionalsets of experimental data.

Most simulations of the shock compression ofpowder mixtures employ idealised representations of

the simulated material microstructure. Particles aretypically represented as circles/squares (or spheres/polyhedra in three dimensions), and their distributionsare either close packed or pseudo-random.120–124 Realmicrostructures, as used in the studies of static defor-mation, crack propagation, and the shock studies ofBenson and Conley125 and Eakins and Thadhani,126,127

may contain highly irregularly shaped particles and non-uniform orientation/spatial distributions.128–131 It fol-lows that the micromechanical behaviour of powdersand their extent of mixing during shock compressionmay depend heavily on these irregularities.

Simulation of the shock compression of realisticNizAl powder mixtures was performed by Eakins andThadhani126,127 using imported experimentally obtainedSEM images. Micrometre scale mixtures of varyingdensity (45–80%TMD) and particle morphology (sphe-rical, flake) were imported into the CTH hydrocode as16206260 mm two-dimensional fields. The responses ofboth Ni and Al were governed by a Mie–Gruneisenequation of state and Steinberg–Guinan constitutivestrength model. Shock compression was simulated bythe movement of a Cu piston at several constantvelocities (Up50?5, 0?75 and 1 km s21), and the features

34 Time series of reactant and product material configuration in a mixture of NbzSi during shock compression at

Up51 km s21. Note that the shock and reaction fronts are hardly distinguishable from each other. The residual

unreacted material behind the fronts is excess Nb, due to the non-stoichiometric starting mixture (from Do and

Benson115)



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of void collapse, particle deformation and mixing werenoted.

Results showed that the simulations did well to matchthe experimental Us–Up data within the range of inertbehaviour, and that such measures of macroscopicmaterial response, while strongly influenced by mixturedensity, are quite insensitive to variations in particlemorphology, orientation distribution or constituentyield strength difference. The construction of pressuresurfaces and profiles for the 45%TMD spherical andflake shaped Nizspherical Al mixtures, as shown inFig. 37, revealed the role of large, consolidated voidspace in the mechanical stability and structure of shockfronts through granular materials. The delayed collapseof particle sized voids in the spherical mixture intro-duced release pockets within the rise to peak pressure,effectively dispersing the shock front (y74 ns rise time).On the other hand, the homogeneously distributed voidspace in the flake mixture ensured a highly planar, sharprise (y15 ns rise time), leading to a stable high pressurestate. As shown in the work by Yang et al.,105 shockinduced chemical reactions are critically dependent uponthe front width, and do not occur if the shock front is

too dispersed. The findings of these simulations are thusin agreement with the corresponding experimental work,which revealed shock induced reaction in only the flakeNi containing mixture, evidenced by increases in themeasured shock velocity and generation of expandedpressure–volume states.40

Scatter plots of pressure, strain and ‘nearest reactiveneighbour distance’ (NRND) were constructed to indi-cate the change in mixture configuration. As shown inFig. 38, the minimum distance separating reactivepartners, or NRND, is equivalent for Al and Ni in thespherical mixture (Fig. 38a), but is greatly reduced forAl in the flake mixture (Fig. 38b). Such change inNRND was shown to be due to a particular deformationevent known as ‘flattening’ (Fig. 39). Flattening of Alparticles served to rapidly increase the amount ofintimate Ni/Al interface, and was attributed to theincreased propensity of shock induced reaction in theflake mixture. Though the equiaxed mixtures alsounderwent severe modes of deformation, such as focusedflow and vortex formation, such events were highlylocalised and concentrated within the softer aluminiumphase. While these conditions could very well have led toshort range reactions, lack of widespread deformationand intermixing between the two phases prevented shockinduced reaction at the bulk scale.

The details of shock wave propagation, particledeformation and mass mixing uncovered in this workfor the NizAl system were used to expoundGraham’s106 CONMAH scheme, which again, attributesthe initiation of shock induced reactions to the pro-cesses of configuration change, mixing, shock activationand heating. As discussed previously, the acronymCONMAH is a general statement concerning the criticalprocesses for reaction, and does not describe themechanisms of mixing and mass transport particularto each system. The work on two distinct configurationsof NizAl powder mixtures reveals that the transitionzone is greatly affected by mixture configuration, leadingto unique shock wave structures, deformation modesand mixing extent (Fig. 40). This suggests that thereexists for every reactive powder mixture, a transitionzone of critical character for shock induced reaction,which is not only a function of the differences in the

35 Spatial particle x velocity profiles averaged through

the model height as a function of time for simulations

a with no chemistry and b with chemistry. Those with

reaction considered exhibit a nearly twofold increase

in the particle velocity at the shock front. Notice also

the increase in shock velocity, evidenced by the half-

max positions of the front at t50?30 ms (adapted from

Do and Benson116)

36 Simulated Us–Up data for the inert and reacted NbzSi

mixture. The reacted mixture shows a strong deviation

from the inert response. The equation of state for the

solid NbSi2 compound is also shown for comparison

(from Do and Benson116)



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intrinsic properties of the reactants, but can be produced(or controlled) through manipulation of starting powderconfiguration.

Design and control of shock inducedreactionsThe observations of the effects of intrinsic and extrinsicproperties on reactive powder mixtures from themesoscale computational investigations and experimentsinvolving time resolved measurements can be used todevelop guidelines or criteria for promoting reaction invarious intermetallic forming systems. Such guidelineswould be useful for the deliberate design of materialsystems based on desired mechanical, chemical andenergetic behaviour. The following section describes aproposed design schema, which maps the criteria forshock induced reactions in binary intermetallic formingsystems. As mentioned previously, mixing and reactionin the micrometre scale, spherical NizAl mixture issuppressed due to the limited deformation of the harder,denser nickel phase.126,127 This preferentialism is causedby the large differences in properties between the twocomponents, such as density, sound speed and yieldstrength. The results of experiments performed on theflake Ni and equiaxed Al mixture indicates that there isalso an effect of particle morphology.40 Qualifying thesefactors into a plausible schema requires consideration ofwork on other equiaxed mixtures, while also consideringthe reactivity of individual systems on the basis of theheats of reaction. As observed by Thadhani et al.,30,38

systems in which the difference between intrinsic proper-ties of reactants is small, tend to show a greaterpropensity (implying lower threshold stress) to reactunder shock induced mechanisms, irrespective of thethermodynamic effects of the heat of reaction. Likewise,extrinsic properties can be used to facilitate reactionin otherwise difficult to react materials systems.Continuing this rationale, it is of particular interest toconstruct a diagram that graphically depicts thesedifferences for several intermetallic forming systems.Though the combination of properties is endless, anattempt was made to schematically represent the pro-pensity for a system to react based upon the differenceslisted above, namely, the density, sound speed and yieldstrength, i.e. resistance to plastic deformation. Shown inFig. 41 is an intrinsic–extrinsic property difference spacefor equiaxed mixtures, where the vertical axis is ameasure of the difference in mechanical impedance,which couples the effects of both density and soundspeed, and the horizontal axis shows the difference inyield strength. A number of binary exothermic alumi-nide and silicide forming systems are shown, where thesize of the datum is proportional to the maximum heatof formation for the given system.

It is revealing to note that the systems reported toundergo shock induced chemical reaction, e.g. NizTi,TizSi, NbzSi and NizSi (shown centre filled), areclustered near the origin, where the impedance and yieldstrength differences are least.33,36,38,39,87,100 On the otherhand, those systems that remain inert, NizAl, MozSiand TizAl (shown centre crossed), are far removed

37 Simulated spatial pressure surfaces and temporal pressure profiles for a 45%TMD a spherical NizAl and b flake

Nizspherical Al mixtures (adapted from Eakins and Thadhani127)



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from the origin, and are associated with large differencesin intrinsic properties.85,92,103,132 From the distributionof data, it appears that shock induced reaction will besuppressed above impedance and strength differences ofy175 and y200% respectively. Based on these limits, areaction zone can be prescribed through the differencespace, indicating where the differences in impedance andstrength satisfy the proposed conditions for shockinduced reaction at modest pressures, in the regime ofthe crush strength of the powder mixture systems.

The intrinsic–extrinsic difference map is a usefuldesign tool for selecting material systems based upontheir ability to exhibit shock induced chemical reactionsat modest pressures. From the distribution of data, theVzSi and ZrzSi systems are both associated with largeheats of reaction, and small combined differences inimpedance and strength. It follows that these systemswould be attractive alternatives for energetic materials,benefiting from both high exothermicity and ease ofreaction. On the other hand, the CozAl system, whichwould ordinarily be attractive based upon its exother-micity, may not react as easily due to its nearly 600%difference between component yield strengths.

Thus far, the systems shown in Fig. 41 comprise theresults of equiaxed, micrometre scale particles. Accord-ingly, the NizAl system is not expected to undergoshock induced chemical reaction at modest pressures.Work on the flake mixture, however, indicates thatreaction does indeed occur.40 The question remains ofhow to incorporate the influence of the extrinsic pro-perties such as particle morphology and initial density. Itis suggested that a reflection of the influence of particlemorphology can be captured by defining an additionalmeasure De, which is the difference in eccentricitybetween the particles of each component

De~eA{eB (25)

where eA and eB are the meridional eccentricities ofparticles of component A and B, defined for each by

e~(a2{b2)1=2

a(26)

where a and b are necessarily the longest and shortestof the three semiaxes respectively. For equivalentlyequiaxed particles, such as those in the systemsrepresented in Fig. 41, De50. In the case of the recentresults for the NizAl flake mixture, however, andassuming a semimajor and semiminor axis for the Niflakes of 12?5 and 0?175 mm respectively, De approaches1. It is proposed that an increase in De serves to shift theboundary of the reaction zone away from the origin(Fig. 42), allowing progressively greater differences inimpedance and yield strength to be tolerated.

Such a shift is believed to have accompanied thechange in nickel particle morphology from spherical toflake, moving the inhibited zone boundary to higher

39 Time sequence showing the flattening of aluminium particles in the 45%TMD flake Nizspherical Al mixture. Total time

is 45 ns, corresponding to a local particle strain rate of 56109 s21 (from Eakins and Thadhani127)

38 Nearest reactive neighbour distance (NRND), pressure

and strain scatter plots obtained 100 ns after shock

compression within a y200 mm window for each com-

ponent in 45%TMD mixtures of a spherical NizAl and

b flake Nizspherical Al. The change in Ni particle

morphology greatly reduces the scatter in pressure,

and the minimum distance separating Ni and Al

(NRND) (from Eakins and Thadhani127)



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difference limits, and allowing reaction in the otherwiseinert NizAl powder mixture system. The precise limitsas a function of particle eccentricity require additionalmorphology based studies on systems such as TazSi,MozSi and TizAl. Similarly, the initial powder densityalso influences the boundary of the inhibited zone. Asshown in the simulations, increases in starting density(45–80%TMD) result in decreased volume for particledeformation, mass flow and mixing. Accordingly,increases in starting mixture density will result in a shiftin the inhibited zone boundary towards the origin.

Based on these projections, one can also makepredictions concerning the response of metal powderconfigurations not tested, e.g. a mixture of flakeNizflake Al. Such a system is likely to enjoy a planarand stable front, due to the stacking of flakes andhomogeneous distribution of particles and void space.The initiation of reaction, however, would suffer fromthe loss of the flattening process, as the softer aluminiumparticles are prethinned. In the reaction criteria map,this would be reflected by the difference in eccentricity,which would be zero, similar to the mixtures of equiaxedparticles. Thus, the extent of deformation for bothcomponents will be diminished, and the local shearinduced mixing processes will not occur.

All of these observations serve to illustrate thesignificant impact the reactant configuration can haveon the mechanical and chemical behaviour of a shock

compressed powder mixture. Through seemingly subtlechanges in the intrinsic properties and configurationof components (extrinsic effects), the behaviour ofmaterials can be widely affected. It follows that controlover the stability, and shape of the high amplitude frontcan be gained through deliberate manipulation of theparticle size, morphology and initial density. This pro-mises to be a particularly useful technique for intrinsicpulse shaping. Such activities have been pursued forsolid materials, in the form of density graded flyers.133

Furthermore, deliberate promotion of either shockinduced or shock assisted mechanisms of reaction allowscontrol over the time of reaction, from the tens ofnanoseconds (1028 s) timescale, to microsecond (1026 s)or even millisecond (1023 s) durations. This combinedunderstanding of the influence of intrinsic and extrinsicproperties, and effect of heterogeneity on front char-acter, level of ‘shock-like’ behaviour, and details ofmixing, can ultimately be used to guide the selection ofcomponent properties in the design of new materialswith predefined mechanical and chemical behaviour.

Summary and concluding remarksOur understanding of chemical reactions in shockcompressed reactive powder mixtures has maturedconsiderably since their discovery. Two classificationsof chemical response have been recognised, according to

40 Schematic illustrating Graham’s106 conceptual CONMAH model, which generalises the processes responsible for

shock induced chemical reactions. This model has been updated for the NizAl system with details of the transition

zone obtained from numerical simulation (from Eakins and Thadhani127)



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41 Schematic of an intrinsic–extrinsic difference space for several binary mixture systems of equiaxed particle morphol-

ogy. The size of the data points is proportional to the maximum heat of formation for any of the system’s stoichio-

metric compounds. Note that the data points for the W, Ta, Mo and Nb aluminides are indicated by closed circles

due to their small size. The systems represented by centre filled points have been reported to undergo shock

induced chemical reaction at modest pressures, while those represented by centre crossed points remain inert. The

proposed reaction zone corresponds to small differences in impedance and yield strength; systems that differ greatly

in these properties are predicted to remain inert at modest pressures. Note that the NizAl system is well outside the

reaction zone, and did not exhibit shock induced reaction (in the spherical mixtures) up to 6 GPa

42 Intrinsic–extrinsic difference space for several binary systems of silicide and aluminide forming mixtures. Changing

the particle morphology from uniformly equiaxed (De50) to a combination of equiaxed and flake-like (DeR1) serves

to shift the boundary separating reaction and inhibited zones from the origin. Such a mixture of spherical Al and

flake-like Ni particles exhibited shock induced chemical reaction above 3?5 GPa



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their initiation mechanisms (and timescales), followingyears of shock compression recovery and time resolvedexperimental work. Reactions initiated on the micro-second to millisecond timescale due to thermally assistedprocesses benefiting from the shock activated state of thematerial have been termed ‘shock assisted’ reactions, andhave been the subject of much of the recovery work.These reactions are controlled by the total internal energyincrease due to the shock process, reacting only when aminimum energy threshold has been surpassed.98

Ultrafast chemical reactions, labelled ‘shock induced’reactions, which register as increases in shock velocity(and perhaps pressure) in time resolved traces, haveinstead been proven sensitive to powder configuration,which in turn is influenced by differences in intrinsic andextrinsic properties of the reactants.36–40,87,104 Timeresolved studies of the effect of particle size, particlemorphology and powder pretreatment have shown thatextrinsic properties, specifically those that influence thelocal particle scale mechanics of deformation, can greatlyalter the propensity of a powder mixture to undergoshock induced chemical reaction, even in the case ofsystems with larger differences in intrinsic proper-ties.38,40,66,39 Several thermodynamic models have beenproposed over the years to explain the effect of ultrafastchemical reactions on the high pressure state, and aid inthe interpretation of experimental data.35,36,97,109 Owingto the lack of appreciable gas evolution in intermetallicreactions, isobaric methods of constructing the reactionproduct Hugoniot have taken favour.36 One such model(Ballotechnic) has been used with fair success to matchexperimental data in the work on NizTi powdermixtures.39,109 Additionally, a limited attempt has beenmade to apply the Ballotechnic model to infer theproducts formed and their extent from time resolveddata in the NizAl system, and has even been successfulin characterising the spatial distribution of reaction(heterogeneous).40 Despite these developments, themicromechanical details of particle scale deformationand mass mixing leading to shock induced reaction arestill beyond the reach of current experimental diagnostics.To fill this void, computational methods have beenemployed to investigate the shock compression process attemporal and spatial scales unreachable through experi-ment. Discrete element models by Yano and Horie110 andTamura and Horie111 have shown that mass mixingthrough particle velocity dispersion and shear bands areboth plausible transport mechanisms.35,84 Particle scalecontinuum simulations by Do and Benson116 usingassumed kinetics have demonstrated that ultrafastchemical reactions can indeed cause increases in shockand particle velocities. Mesoscale simulations onimported microstructures have revealed the uniquedeformation modes contributing to reaction initiation ina particular morphology of NizAl powders.127

Through the coupling of experimental, theoretical andnumerical work, it has become clear that the response ofreactive powders to shock compression is not easilygeneralised for all powder systems. There are as yet noglobal cutoffs or thresholds that can be applied toguarantee shock induced reaction to a given product orextent. What has developed, however, is a trend ofbehaviour, that when considered carefully suggests thatthere is an inextricable link between the propensity for amixture to react and its intrinsic/extrinsic material

properties. The more similar the starting componentsare in density, sound speed and yield strength, the moreeffective the mixing process during crush-up to fulldensity. Recent work has also shown that the config-uration of reactants can be used to alter the thresholdpressure for reaction, i.e. inhibiting reaction by changingthe relative particle size in TizSi mixtures, or promot-ing reaction through changes in particle morphology ina NizAl mixture.38,40 Continued investigation of theinfluence of component configuration on shock inducedreactivity is needed to further develop these trends, andestablish the design methodology needed to control thetimescale, extent and exothermicity of chemical reac-tions in shock loaded powder mixtures. This will requirea forward path which focuses future work aimed ataddressing challenges involving

(i) multiscale modelling incorporating moleculardynamics with particle level simulations toclearly elucidate mechanisms of bond break-age/formation in the highly turbulent transitionzone whose states are defined by mesolevelsimulations accounting for effects of intrinsicand extrinsic properties of reactants

(ii) innovative experimental methods in which thespatial and temporal scales of experiments andsimulations are comparable, for example,employing laser generated shocks, combinedwith instrumentation/diagnostic techniques thatprovide more direct inference of the progressionof reaction, such as ultrafast XRD, Ramanspectroscopy or even electrical conductivitymeasurements

(iii) coupling with first principles calculations forphase formation and preservation in the non-equilibrium state so as to allow the possibility ofsynthesising novel phases/compounds or evenproviding predictions of what non-equilibriumstructures can potentially be formed underextreme conditions

(iv) designing reactive systems that can potentiallybe employed as structural reactive materialswith tuneable mechanical properties and energyrelease characteristics.

Acknowledgments

The authors wish to acknowledge the various fundingagencies and program monitors for the continuedsupport of the research during the course of which thisreview article has been compiled. These include AFOSR(Craig Hartley), DTRA (Bill Wilson and Suhithi Paris),and ONR (Cliff Bedford and Judah Goldwasser). TheNational Defense Science and Engineering GraduateFellowship and the LANL Director’s Post-doctoralFellowship awarded to one of the authors (DE) arealso acknowledged. We are also grateful for the manycollaborations and consultations with researchersincluding Ron Armstrong, Bob Graham, Yuki Horie,Marc Meyers, Vitali Nesterenko, and Tim Weihs. Thecontributions of past and present students are alsoacknowledged.

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D. E. Eakins and N. N. Thadhani- Shock compression of reactive powder mixtures