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Yuhei UMEDA, Yuma NAGAI, Naotaka TOMIOKA, Toshimori SEKINE, [Masashi MIYAKAWA](https://orcid.org/0000-0002-0838-8156), Takamichi KOBAYASHI, [Hitoshi YUSA](https://orcid.org/0000-0001-6980-9279), Takuo OKUCHI

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[Deformation microstructures in shock-compressed single crystal and powdered rutile](https://mdr.nims.go.jp/datasets/78beb0ab-2a9e-42bf-87ce-90aa45e7d933)

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Deformation microstructures in shock–compressed single crystal and powdered rutileDeformation microstructures in shock–compressed single crystaland powdered rutileYuhei UMEDA*,**, Yuma NAGAI**,*, Naotaka TOMIOKA***,*, Toshimori SEKINE†, Masashi MIYAKAWA‡,Takamichi KOBAYASHI‡, Hitoshi YUSA‡ and Takuo OKUCHI*,***Institute for Integrated Radiation and Nuclear Science, Kyoto University, Osaka 590–0494, Japan**Graduate School of Engineering, Kyoto University, Kyoto 615–8540, Japan***Kochi Institute for Core Sample Research, X–star, Japan Agency for Marine–Earth Science and Technology,Kochi 783–8502, Japan†Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China‡Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Ibaraki 305–0044, JapanShock recovery experiments on the single crystal rutile and the powdered rutile were performed using a single–stage propellant gun to investigate the effects of porosity (i.e., temperature effect) on the formation of shock–induced deformation microstructures. X–ray diffraction and transmission electron microscopy analyses of theshocked single crystal rutile revealed the occurrence of a high–density stacking fault in the {101} plane of rutile.This defect suggests that the dominant slip system causing the plastic deformation of the crystal was {101}<�101>at lower temperatures, forming stacking faults. Additionally, part of the crystal exhibited intergrowth with the α–PbO2 structure in a topotaxial relationship: <100>Rutile // <001>α–PbO2. Topological analysis suggests that thesingle crystal rutile transforms into the α–PbO2 structure concomitantly with the shear deformation via the fluo-rite structure. In contrast, the shocked powdered rutile primarily comprises particles with pervasive entangleddislocations and recrystallized particles, where the α–PbO2 structure was not observed at all. Considering theabsence of stacking faults, the dominant slip system in the shocked powdered rutile should have been{110}<001>, which is expected to work more actively at higher temperatures. These contrasting results onshocked rutile indicate that the shock heating effect and the initial porosity significantly influenced the defor-mation microstructures and high–pressure phase transformations of rutile in shocked meteorites as well as inimpact crater rocks.Keywords: Rutile, Shock recovery experiments, Deformation, Defect structuresINTRODUCTIONThe shock response of minerals is essential for under-standing the deformation properties of rocks during natu-ral impact events in the histories of the Earth and otherplanets. Shock compression experiments are the primarymethods used to simulate such deformation processes un-der the known conditions. Microstructural observations ofshock–recovered samples have provided valuable indica-tors for determining the levels of shock pressure and tem-perature in various types of minerals (Langenhorst, 2002;Fritz et al., 2017; Stöffler et al., 2018). These findingssuggested that features of brittle deformation, such as ir-regular fractures and planar fractures, were dominantunder relatively low shock pressures, whereas featuresof plastic deformation, such as undulatory extinctionand mosaicism, were dominant under higher shock pres-sures (Meyers, 1994; Stöffler et al., 2018). Plastic defor-mation also produces dislocations, stacking faults, andmechanical twins in shocked minerals, which are identi-fied by transmission electron microscopy (TEM) (Lan-genhorst, 2002).We note that shock temperatures differ between re-flected shock waves (multiple compressions: conventionalshock recovery experiments) and single shock wave (sin-gle compression: natural collisions) due to the differencein internal energy increase (Boslough and Asay, 1993). Inmost cases of shock recovery experiments, the sample issandwiched between high–impedance metals and subject-doi:10.2465/jmps.230706Y. Umeda, umeda.yuhei.2e@kyoto–u.ac.jp Corresponding author© 2024 Japan Association of Mineralogical SciencesJournal of Mineralogical and Petrological Sciences (2024) 119:001ed to multiple shock compressions generated by the reflec-tion of shock waves between the metals. As a result, theshock pressure and the shock temperature gradually in-crease (Figs. 16a and 16b in Tomeoka et al., 1999; Fig.7 in Sharp and DeCarli, 2006). Therefore, when the peakpressure reaches a certain value, the peak shock temper-ature in multiple shocks is relatively lower than that in asingle shock due to the difference in internal energy in-crease (Tomeoka et al., 1999; Sharp and DeCarli, 2006).In most cases of natural collisions, impactors and targetsare subjected to a single shock wave, which has a highershock temperature than the samples from the shock recov-ery experiments at the same peak pressure (Wünnemann etal., 2016; Winkler et al., 2018; Kurosawa et al., 2022).Titanium dioxide (TiO2) exhibits various crystalstructures depending on the pressure and the temperature.Rutile is a stable phase of TiO2 at the ambient pressure.In nature, the intergrowth of TiO2 polymorphs has beenfound in the suevite impactites from the Ries crater inGermany (El Goresy et al., 2001). Therefore, the poly-morphism of TiO2 is an important clue for understandingthe pressure and temperature histories of natural impacts(Liou et al., 1998; El Goresy et al., 2001). The α–PbO2structure of TiO2 forms under a wide range of high–pres-sure conditions, as reported by the static (above ~ 7 GPa)and the dynamic (above ~ 20 GPa) experiments (Kusabaet al., 1988; Nishio–Hamane et al., 2010). In the case ofdynamic compression, the phase transition boundary be-tween rutile and the α–PbO2 structure depends not only onthe pressure but also on the crystal orientation to the shockcompression axis (Syono et al., 1987; Kusaba et al.,1988). Despite the occurrence of TiO2 polymorphs in var-ious natural forms, their formation mechanisms, shocktemperature profiles, and origin of intergrowth texturesunder high–pressure conditions remain poorly under-stood, mostly because of such a complex transition behav-ior of TiO2. Furthermore, only a few studies have care-fully described shock deformation microstructures ofTiO2 polymorphs. In the previous study on the shock re-covery experiment of TiO2, stacking faults were observedin the shocked single crystal rutile (Kusaba et al., 1988).On the other hand, stacking faults were not observed inthe shocked powdered rutile, even at the similar pressures(Tan et al., 2018). Therefore, to understand the variabilityof microtextural evolution of TiO2 in the natural impactevents, it is very meaningful to compare the textural char-acteristics of the shock–compressed single crystal andpowdered rutile each other, which experience differenttemperatures at the same peak shock pressure.This study used a single–stage propellant gun to per-form the shock compression experiments on the non–po-rous (single crystal rutile) and the porous (powdered ru-tile) samples. The experimental design ensured that thesesamples experienced the same peak shock pressure. On theother hand, the shock temperature of the powdered rutilewas significantly higher than that of the single crystal ru-tile (Zel’Dovich and Raizer, 2002; Sekine, 2016). This isbecause the shock compression of the powdered samplesinvolves a large increase in internal energy due to a highdegree of the pore collapse and the frictional heating be-tween particle surfaces (Sekine, 2016). Our primary objec-tive was to evaluate potential variations by comparing thedeformation microstructure between the shock recoveredsamples that experienced the different temperatures. Forthat purpose, a (100) planar single crystal rutile and a pow-dered rutile were prepared, shock compressed, recovered,and characterized by X–ray diffraction (XRD) and TEM.EXPERIMENTAL METHODSShock recovery experimentsShock recovery experiments were performed using a sin-gle–stage propellant gun at the National Institute for Ma-terials Science, Japan (NIMS). Details of the gun used inthis study have been previously described (Sekine, 1997).As shown in Figure 1a, the projectile consists of a steel(SUS304) disk (29 mm in diameter and 3 mm thick) anda sabot (high–density polyethylene) comprising a mag-netic disc. The sample container was made of SUS304(30 mm in diameter and 30 mm in length) with a samplespace (18 mm in diameter and 1 mm thick) located 3 mmfrom the projectile side (Fig. 1a). The samples weresealed with a SUS 304 screw of 25.5 mm length. Theprojectile was accelerated to the required velocity (1.37km/s), and the velocity was measured using the magneticflyer method (Sekine, 1997). The peak shock pressure of30 GPa was estimated by the impedance mismatch meth-od. Shock recovery experiments were designed to gener-ate the peak pressure of 30 GPa, where the phase transi-tion from rutile to the α–PbO2 structure was reported tohave the highest yield (Kusaba et al., 1988).The starting material comprised a synthetic singlecrystal rutile (Crystal Base Co., Ltd., 10 mm × 10 mm ×0.5 mm, purity: 99.99%) or a powdered rutile reagent witha particle size of ~ 2 µm in diameter (Rare Metallic Co.,Ltd.). The single crystal was compressed perpendicular tothe (100) plane of rutile (Fig. 1b). The experimental setupfor compression of this crystal included a free space (thickblue area in Fig. 1b) surrounding the sample in a directionperpendicular to the compression axis. The powderedrutile was annealed at 950 °C for 3 hours to remove theremaining minor anatase. The complete absence of suchminor phases was confirmed by powder XRD. The pow-Y. Umeda, Y. Nagai, N. Tomioka, T. Sekine, M. Miyakawa, T. Kobayashi, H. Yusa and T. Okuchi2der pellet of 1.02 ± 0.05 mm in thickness and 17.99 ± 0.05mm in diameter, measured with a caliper, was preparedusing a pelletizer and then placed in the sample container(Fig. 1b). The pellet had a porosity of 28.3 ± 1.5%, whichwas determined from the volume and weight of the pellet,and the X–ray density of the annealed reagent determinedby fitting its XRD pattern. After the shock compressionexperiments, the shocked samples were recovered fromthe sample container by cutting a section parallel to theimpact plane using a cutting machine (Struers, Accutom–50).Analytical methodsPart of each recovered sample was ground into fine pow-der and subjected to XRD analysis for the phase identi-fication, using a Rigaku Ultima IV diffractometer withCuKα radiation driven at 40 mA and 40 kV, which isinstalled at the Institute for Integrated Radiation and Nu-clear Science, Kyoto University (KURNS).Then, another part of each sample was subjectedto TEM and scanning transmission electron microscopy(STEM) analyses. Several 150 nm thick sections forTEM and STEM analysis were prepared using focusedion beam (FIB) instruments FEI Quanta3D200i installedat KRUNS, and HITACHI SMI4050 installed at the Ja-pan Agency for Marine–Earth Science and Technology(JAMSTEC). Following the deposition of the carbon pro-tection layers, the sample surfaces were reduced to ~ 2µm thick sections and cut using a Ga–ion beam at anaccelerating voltage of 30 kV. Subsequently, the sectionswere mounted on Cu grids using a micromanipulatorequipped with FIBs and ultra–thinned. TEM and STEMobservations of the ultrathin sections were conductedusing a transmission electron microscope (JEOL JEM–ARM200F) at JAMSTEC, operating at an acceleratingvoltage of 200 kV. Crystallographic and microstructuralanalyses were performed using selected–area electron dif-fraction (SAED), bright–field TEM (BF–TEM), and low–angle annular dark–field STEM (LAADF–STEM).RESULTSThe geometry of the shock–recovered single crystal rutileexhibited ~ 10% length increase along the directions per-pendicular to the compression axis. The powder XRDprofile of the shocked single crystal rutile showed the co-existence of rutile (Rt) and the α–PbO2 (α) structures atthe peak shock pressure of 30 GPa (Fig. 2a). On the otherhand, the shock–recovered powdered rutile became awell–sintered aggregate of submicron–sized particles.The powder XRD profile of the shocked powdered rutileshowed only the peaks of rutile even at the same peakshock pressure (Fig. 2b).Figures 3a and 3b provide an overview of the micro-textures of the shocked single crystal rutile observed byTEM. The ultrathin foil sample displayed significant straincontrast and numerous intersecting lineations. The SAEDpatterns showed the diffraction spots of rutile with streaksalong the <011>*Rt direction (Fig. 3c). These streaks sug-gest that the lineations are stacking faults lying on two ofthe four equivalent planes on {101}Rt. The SAED patternsshowed the additional weak spots corresponding to thesingle crystal of the α–PbO2 structure. The observed crys-tallographic relationship between the rutile structure andthe α–PbO2 structure was identified as <100>Rt // <001>α.Owing to the complex microstructure with possible over-laps and a high density of stacking faults on the {101}Rtplanes, the lattice fringes of the α–PbO2 structure could notbe recognized in the high–resolution TEM images.Figure 4 shows the TEM images of the shocked pow-dered rutile. The direction of the compression axis re-mains unknown in the images because the particles losttheir original orientation after recovery. The powder wassintered with crystal sizes ranging from the sub–nanorange to ~ 2 µm (Fig. 4a). In contrast to the shocked singleFigure 1. (a) The common setup ofshock recovery experiments. (b)The sample setups for the singlecrystal rutile (top) and the pow-dered rutile (bottom), with topviews of the sample space in thesample container (perpendicular tothe collision plane). The samplesare shown in light blue.Shock deformation microstructures in rutile 3crystal, stacking faults were rarely observed in theshocked powder, whereas several particles showed perva-sive entangled dislocations (Fig. 4b). The SAED patternsof the particles showed the distorted rutile diffractionspots (Fig. 4c). In contrast, some particles were nearlydislocation–free (Fig. 4d). The SAED patterns of theseparticles showed the sharp diffraction spots of rutile(Fig. 4e). These two particles existed in equal ratios andwere spatially and randomly distributed. Only a few par-ticles formed stacking faults (Fig. 4f). The SAED patternof the particles confirmed the presence of {101}Rt twinlamellae (Fig. 4g). In addition, the diffraction peaks wereaccompanied by weak streaks along the [101]* direction,similar to the shocked single crystal.DISCUSSIONEffect of heating on shock deformation microstruc-turesShock recovery experiments conducted on the singlecrystal rutile and the powdered rutile showed significantdifferences in their microstructural features, even if theywere shock–compressed at the identical peak pressure. Inthe shocked single crystal, stacking faults were prevailingon the {101}Rt planes throughout the thin section. In con-trast, only about half of the particles of the shocked pow-der exhibited a high density of entangled dislocations,whereas the stacking faults were rarely observed through-out the thin section (Fig. 4a). Such stark contrast in thedefect microstructures should have resulted from the dif-ferent plastic deformation process under the high–stressfields during shock compression. In the powder XRD pat-terns, all diffraction peaks of the shocked single crystal(Fig. 2a) were broadened, indicating that large strain re-mained even after the complete pressure release becauseof complex cross–cutting between the stacking faults.Meanwhile, smaller strain in the bulk shocked powderas shown by its much sharper diffraction peaks wouldbe caused by extensive stress relaxation due to the highershock temperature.A perfect dislocation is defined by the length of itsFigure 2. XRD profiles obtainedfrom (a) the shocked single crystalrutile at 30 GPa and (b) the shockedpowdered rutile at 30 GPa. Rt and αdenote the rutile structure and theα–PbO2 structure, respectively.Figure 3. TEM analysis of the shocked single crystal rutile at 30 GPa. (a) BF–TEM and (b) LAADF–STEM images showing stacking faultson the {011} planes of rutile (Rt). The direction of the compression axis [100]Rt perpendicular to the paper surface. (c) SAED pattern ofrutile along the [100] zone axis obtained from the area in the images (a) and (b). Weak diffraction patterns of the α–PbO2 structure (α) alongthe [001] zone axis were also observed.Y. Umeda, Y. Nagai, N. Tomioka, T. Sekine, M. Miyakawa, T. Kobayashi, H. Yusa and T. Okuchi4Burgers vector, an integer multiple of the translation vec-tor of the crystal lattice. In particular, a perfect dislocationsplits into partial dislocations to optimize thermodynamicconditions. The expanded interspace between two partialdislocations yields a stacking fault (Putnis, 1992). Theformation of the partial dislocations can be interpretedFigure 4. TEM analysis of the shocked powdered rutile at 30 GPa. The sample consisted only of rutile particles. (a) BF–TEM image showinga representative texture comprising deformed particles (indicated by black arrows) and undeformed particles (indicated by white arrows). (b)BF–TEM image of a particle with entangled dislocations. (c) SAED pattern obtained from the area in (b). (d) BF–TEM image of a particlewithout dislocations. The particle contained a vesicle in its rim (indicated by an arrow). (e) SAED pattern obtained from the area in (d). (f )BF–TEM image of a particle with the (101) twin lamellae (indicated by arrows). (g) SAED pattern obtained from the area in (f ). t denotestwin domain.Shock deformation microstructures in rutile 5in terms of the strain energy of the crystal lattice. Theenergy of dislocations is expressed as Kb2, where K isthe energy factor, and b is the magnitude of the Burgersvector. A perfect dislocation can be split into two partialdislocations with a stacking fault if the energy balanceisK1b12 > K2b22 þ K3b32where subscripts 1 denotes the perfect dislocation, and 2and 3 indicate partial dislocations.Two principal slip systems have been reported forrutile: (i) {101}<�101> and (ii) {110}<001> (Hirthe andBrittain, 1962; Ashbee and Smallman, 1963). Comparing(i) and (ii) slip systems, the perfect dislocation energiesfor (i) and (ii) were 0.45 (10−2 dyn/nm2) and 0.17 (10−2dyn/nm2), respectively (Motohashi et al., 1979). Conse-quently, the dislocations in the slip system (i) are morelikely to split into partial dislocations, forming stackingfaults. In contrast, the slip system (ii) is energeticallymore favorable for forming perfect dislocations. Theseresults are consistent with the present results, showingthat stacking faults dominate on {101}Rt planes only inthe single crystal rutile.Temperature affects the activity of slip systems ofrutile. Blanchin et al. (1990) suggests that the slip system(i) is predominantly active at ~ 1150 °C. It was observedthat the slip system (i) was the most active direction andwas able to move at a relatively lower temperature (Ash-bee and Smallman, 1963). In contrast, the slip system (ii)was active at temperatures as high as ~ 1450 °C. We es-timated the peak shock temperature of the single crystalrutile to be about 900 °C by evaluating the increase in theinternal energy (Meyers, 1994). We can assume that thepeak shock temperature of the powdered rutile surpassesthis temperature value attributed to the porosity effect(Zel’Dovich and Raizer, 2002). The fully annealed par-ticles without dislocation microstructures were identifiedin the shocked powdered rutile but not in the shockedsingle crystal rutile. Therefore, we propose that the sys-tem (i) was predominantly activated in the shocked singlecrystals, whereas the system (ii) was activated in theshocked powder. Our results, indicating the dominanceof slip system (ii) under high–temperature conditions,are consistent with those of Blanchin et al. (1990). How-ever, further investigation is necessary to explore the re-lationship between temperature and the slip system.The activation of the slip system is also dependenton the compression direction. In our shock experiment onthe single crystal rutile, the compression direction wasperpendicular to the [001] direction of rutile. Therefore,the slip system (ii) was unlikely to be activated, whereasthe slip system (i), as characterized by stacking faults,should have been dominant instead. Meanwhile, stackingfaults were rare in the powdered rutile, although the ran-dom crystal orientation allows many of the particles to bepreferentially oriented to the slip system (i). We concludethat the difference in the deformation microstructures be-tween non–porous and porous samples is more influencedby the shock temperature than the crystal orientation.High–pressure structural transformation of rutilethrough the shear mechanismThe formation of partial dislocations associated withstacking faults is essential in facilitating polymorphicstructural transitions via a shear mechanism. This mech-anism is expressed by the shear of the crystal lattice with-out atomic migration beyond the lattice dimensions. Asimilar mechanism has been proposed for high–pressuretransformations of metals and silicates (Poirier, 1981;Bassett and Huang, 1987; Tomioka, 2007).Both the ideal crystal structures of rutile and α–PbO2consist of hexagonal close–packed (hcp) oxygen anions(O’Keeffe, 1984). Meanwhile, the geometries of the tita-nium cation positions in these structures are different. Ifthe rutile structure is assumed to transform directly intothe α–PbO2 structure under shock compression, the tita-nium cations have to move a nontrivial distance in thehcp framework of the oxygen anions within ~ 1 micro-second as time scale for the shock experiments (Kusabaet al., 1988). To reconcile the above problem, a sheartransformation mechanism in the transition from rutileto the α–PbO2 structure via the fluorite structure was orig-inally proposed by Hyde et al. (1972). This pathway wasproposed because the positions of the titanium cations inthe fluorite structure are intermediate between rutile andthe α–PbO2 structure. Kusaba et al. (1988) found a top-otaxial relationship between rutile and the α–PbO2 struc-ture in their shock–compressed samples, supporting thetransformation model of Hyde et al. They proposed thatrutile transformed to the fluorite structure under shockcompression, and subsequently transformed to the α–PbO2 structure under decompression. In this study, thesame crystallographic relationship <100>Rt // <001>α re-ported by Kusaba et al. (1988) was observed in theshocked single crystal rutile. We will further developthe model for the above shear mechanism by introducingstacking faults and partial dislocations.This study presented a detailed shear deformationmodel of rutile forming the α–PbO2 structure via the flu-orite structure under shock compression to explain therelationship between defect structures and phase transfor-mations. Figures 5a and 5b show one oxygen layer andY. Umeda, Y. Nagai, N. Tomioka, T. Sekine, M. Miyakawa, T. Kobayashi, H. Yusa and T. Okuchi6one titanium layer of simplified rutile and fluorite struc-tures along the [010] and [001] directions, respectively.The rutile structure comprises a hcp of oxygen anions.Interstitial titanium cations are located at the oxygen 6–fold coordinated site (Fig. 5a). Meanwhile, the fluoritestructure comprises a primitive packing of oxygen anionsand interstitial titanium cations at the oxygen 8–fold co-ordinated site (Fig. 5b). The slip directions of the oxygenlayers in Figure 5a are [�101] on the (101) plane of rutile.The displacement vector of the oxygen layers is 1/4[�101],which is nearly equal to the radius of the oxygen anions.The titanium cations cooperating with the oxygen layersare displaced by vector 1/4[�101].In the case of deformation in the {101}<�101> slipsystem, the slip of the oxygen layers and the associateddisplacement of the titanium cations occurred randomlyon the (101) plane. These ionic movements are achievedby forming partial dislocations (Fig. 5c), and the inter-space between the two partials occurred as a stackingfault of the (101) plane. When the slip on the (101) planeoccurs on neighboring oxygen layers, oxygen anionsform primitive packing, and the titanium cations findtheir positions in the oxygen 8–fold coordinated site inthe sheared oxygen layers. The ionic arrangement corre-sponds to the fluorite structure (Fig. 5b). The fluorite andthe α–PbO2 structures have a similar arrangement of tita-nium cations. Therefore, the fluorite structure readilytransforms to the α–PbO2 structure through the slight dis-placement of the oxygen layers during decompression(Kusaba et al., 1988).This study showed that heating related to porositysignificantly affects the deformation mechanism, domi-nant slip systems, and structural phase transitions ofrutile. Because natural samples such as meteorites andcrater rocks are more or less porous, the effect of shockheating must also be considered for accurate evaluationof their shock stages. Finally, these findings may contrib-ute to the understanding of the formation histories of theRies and the Chicxulub impact craters, where shockedtitanium oxide minerals have been identified (El Goresyet al., 2001; Kring et al., 2020), although further system-atic experiments are necessary to investigate the effects ofporosity (i.e., shock temperature) on the mineral micro-structures as pressure indicators.CONCLUSIONS1. Nanometer–scale microstructural observations con-Figure 5. A model for the shear mechanism in the transition from rutile to the fluorite structure. (a) Arrangements of the titanium cations andthe oxygen anions in the ideal rutile structure and their displacements during the slip of the oxygen layers along the [�101] direction on the(101) plane to produce the fluorite structure. The titanium cations are displaced in the opposite direction to that of the oxygen layers. (b)Arrangements of the titanium cations and the oxygen anions in the fluorite structure. (c) Dissociation of the [�101] perfect dislocation intotwo partial dislocations to be promoted by the slip of the oxygen layers on the (101) plane.Shock deformation microstructures in rutile 7firmed the formation of stacking faults in the singlecrystal rutile and the formation of entangled dislo-cations in the powdered rutile.2. The single crystal rutile and the powdered rutileshowed the different dominant slip systems possiblyaffected by the different shock heating processes.3. Porosity difference to possibly induce the differentheating processes has potentially significant effectson the shock deformation microstructures and phasetransition mechanisms.ACKNOWLEDGMENTSThis study was supported by JSPS KAKENHIGrant Numbers JP22K14120 and JP21J01448 toY.U., JP21H04519 and JP20K20947 to T.O., andJP19H05790 to H.Y. The single–stage propellant gun ex-periments were supported by the National Institute ofMaterials Science (Grant No. QN3510). This study wassupported by the World Premier International ResearchCenter Initiative (WPI). The authors thank ProfessorsJun Kinomura and Takaaki Noguchi at Kyoto Universityfor their technical assistance. This study was partiallysupported by the Joint Usage/Research of the Institutefor Integrated Radiation and Nuclear Science, Kyoto Uni-versity (KURNS) (Nos. R4019, R5007, and R5073). Theauthors are grateful to two anonymous reviewers for theirconstructive reviews and comments.REFERENCESAshbee, K.H.G. and Smallman, R.E. (1963) The plastic deforma-tion of titanium dioxide single crystals. Proceedings of theRoyal Society of London. Series A. Mathematical and Phys-ical Sciences, 274, 195–205.Bassett, W.A. and Huang, E. (1987) Mechanism of the body–cen-tered cubic–hexagonal close–packed phase transition in iron.Science, 238, 780–783.Blanchin, M.G., Bursill, L.A. and Lafage, C. (1990) Deformationand microstructure of rutile. Proceedings of the Royal Societyof London. A. 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