J. Appl. Phys. 128, 245102 (2020); https://doi.org/10.1063/5.0035041 128, 245102

© 2020 Author(s).

Effects of mechanical constraint onthermally induced reverse martensitictransformation in granular shape memoryceramic packings

Cite as: J. Appl. Phys. 128, 245102 (2020); https://doi.org/10.1063/5.0035041Submitted: 25 October 2020 . Accepted: 04 December 2020 . Published Online: 22 December 2020

Hunter A. Rauch, and Hang Z. Yu

COLLECTIONS

This paper was selected as an Editor’s Pick

Effects of mechanical constraint on thermallyinduced reverse martensitic transformation ingranular shape memory ceramic packings

Cite as: J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041

View Online Export Citation CrossMarkSubmitted: 25 October 2020 · Accepted: 4 December 2020 ·Published Online: 22 December 2020

Hunter A. Rauch and Hang Z. Yua)

AFFILIATIONS

Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA

a)Author to whom correspondence should be addressed: hangyu@vt.edu

ABSTRACT

Zirconia-based ceramics exhibit shape memory and superelastic effects based on the reversible martensitic transformation between tetrago-nal and monoclinic crystal structures. In the form of granular packings, these shape memory ceramics can be scaled up for bulk applicationsdespite their intrinsic brittleness, while displaying drastically different transformation characteristics than the monolithic counterparts. Here,we present a comparative study to understand the thermally induced reverse martensitic transformation in granular packings and the influ-ence of mechanical constraints. This study employs ZrO2–CeO2 shape memory ceramics of the same composition but with different degreesof mechanical constraints. The explored material forms include loose and jammed granular packings, themselves consisting of polycrystal-line or single crystal particles, as well as sintered bulk polycrystals. Except for the latter, no endothermic peak is observed in the heat flowmeasurement of the reverse transformation process. This unusual behavior is shown to stem from the weak inter-particle mechanical con-straint and the transformation heterogeneity among individual particles, rather than stress relaxation or particle rearrangement. Tocompare, conspicuous endothermic peaks only appear in bursting-type transformations under a strong mechanical constraint. For granularpackings, the intra-particle mechanical constraint does not affect the presence of any endothermic peaks in thermal reversion but can influ-ence the austenite start temperature.

Published under license by AIP Publishing. https://doi.org/10.1063/5.0035041

I. INTRODUCTION

Shape memory ceramics are materials that have a martensitictransformation between two crystallographic phases as a response toeither stress or temperature. When a sufficiently high stress isapplied, a zirconia shape memory ceramic transforms from the tet-ragonal crystal structure to the monoclinic and adopts a new shape;upon heating the transformed zirconia above a critical temperature,the reverse transformation converts martensite back to austeniteand allows the original shape to be recovered. Compared to theestablished metallic shape memory alloys (e.g., NiTi, Cu–Al–Ni,etc.), shape memory ceramics in the zirconia family are burgeoningfunctional materials with several enticing properties, to wit: highactuation energy output, large operation temperature windows, andgood thermal and chemical stability.1,2 The reversible martensitictransformation of these ceramics was first compared to nucleation-dominated, shear-induced martensitic transformations in Fe–Ni

alloys by Wolten3 and has since drawn great scientific interest. Akey milestone in zirconia research was accomplished by Garvie andhis co-workers, who reported stress-induced transformation in tet-ragonal zirconia4 and created a new vision of “ceramic steels.”Afterward, zirconia was extensively exploited for transformationtoughened ceramics,5–8 wherein the metastable tetragonal zirconiaconstrained in a brittle matrix material could transform to themonoclinic phase during crack propagation, resulting in substantialenergy dissipation. This toughening effect has been exploitedfurther in recent works on cerium-stabilized zirconia ceramics fordental and medical applications9,10 and on bulk zirconia-containingceramics with plastic-like deformation behavior.11 More intrigu-ingly, monolithic zirconia enables shape memory and superelasticeffects and has tremendous potential for smart structures and appli-cations.12 The research on this topic has shed light on the linkagebetween the microstructure and functionalities of smart materials.In particular, mechanical constraint is found to be the origin of

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-1

Published under license by AIP Publishing.

several unique phenomena, such as autocatalysis and self-accommodation, which govern the kinetics of transformation. Astrong mechanical constraint can produce a characteristic “bursting”effect, which results in large regions of fully transformed martensite,often containing self-accommodating twins.2,12,13

The challenges in implementing zirconia-based smart applica-tions stem from the large volume change (∼5%) during transforma-tion between the tetragonal phase and the monoclinic phase. As aresult, bulk zirconia accumulates significant strain at grain boundariesand triple junctions, encountering failure at early stages of loading.1,14

Researchers have recently proposed solutions to the problembased on the “oligocrystal” concept by reducing the number ofgrain boundaries and triple junctions. Lai et al.1 first demon-strated the shape memory and superelastic effects with a singlecrystal (SC) micropillar of ZrO2–CeO2 and ZrO2–CeO2–Y2O3.Similar behavior was subsequently demonstrated with polycrystalline(PC) micropillars,15,16 poly- and single crystalline microparticles,17,18

micro-foams,19,20 millimeter-scale single crystals,21 and granularpackings.22,23 All these experiments capitalize the benefits of reduc-ing mechanical constraints, showing that oligocrystalline zirconia cantransform repeatedly without catastrophic failure in a manner consis-tent with the martensitic transformation theory.2

Among the aforementioned explored material forms, thegranular packing is of particular interest from both practical andfundamental perspectives. From a practical perspective, granularsuperelastic ceramic packings are characterized by a good energydissipation capability (∼2 J/g18,23). Solely based on contact fric-tion, non-transforming granular materials are already employedfor their energy absorbing ability in sandbags24 or as an additive inKevlar-based ballistic armor.25 Introducing reversible stress-inducedphase transformation to the particles (i.e., replacing silica withcerium-doped zirconia) would add an appreciable, reusable compo-nent to the medium’s energy dissipation capability. From a funda-mental perspective, granular packings are characterized by a lack ofinter-particle cohesion and a highly heterogeneous structure.22,26,27

In situ neutron diffraction22 shows that these features lead to apeculiar transformation behavior in stress-induced martensitictransformation, such as the absence of critical stress and the appear-ance of a continuous transformation mode. A similar continuousmode of stress-induced martensitic transformation has been pre-dicted in recent theoretical works by Wang and co-workers,28,29

who proposed that local composition modulation can allow NiTi totransform continuously with the applied stress.

Along with the peculiarities of stress-induced forward trans-formation, granular packings display interesting behavior in ther-mally driven reverse transformation, or simply thermal reversion.Differential scanning calorimetry (DSC) is known as an effectivetool to characterize phase transformation in situ and has beensuccessfully applied to bulk zirconia ceramics.30–33 However, thethermal reversion of a jammed granular ZrO2–CeO2 packing hasshown no peak indicating AS or AF in the heat flow measurementduring DSC,23 despite the occurrence of a first-order martensite toaustenite phase transformation. Moreover, from in situ neutron dif-fraction, thermal reversion of such jammed packings seems to occurwithin a broad temperature range.22 This again implies a macroscop-ically continuous mode of transformation, which has been postulatedto stem from multiple transformation domains or stress relaxation in

the jammed packing23 but lacks experimental corroboration. To date,a verifiable mechanistic description of thermal reversion in granularpackings that can explain these findings has remained elusive, pri-marily due to a lack of comparisons with other material formshaving different levels of mechanical constraints.

Here, we conduct a comparative study on thermal reversionbased on ZrO2–CeO2 granular packings with the same chemicalcomposition but having different levels of mechanical constraintsand different starting martensite phase fractions. The investigatedmaterial forms include loose and jammed granular packings consist-ing of single crystal or polycrystalline particles, along with sinteredbulk polycrystals. We show that the absence of an endothermic peakin DSC mainly originates from the heterogeneity among individualparticles and the weak inter-particle mechanical constraint. Whenthe mechanical constraint is strong, a bursting-type transformationcan occur in a single step or multiple steps involving conspicuousendothermic peaks. While the intra-particle mechanical constraintdoes not determine whether endothermic peak appears, it influencesthe transformation temperature of the granular packing and plays animportant role in cooling-induced forward transformation.

II. EXPERIMENTAL PROCEDURES

We fabricated granular packings of (Zr0.88Ce0.12)O2 byco-precipitation and calcination as detailed elsewhere,23,34 whichyielded several grams of ceramic particles per batch. 12% ceria wasadded to the zirconia because, at this chemical composition, themartensite phase (monoclinic crystal structure) and the austenitephase (tetragonal crystal structure) are both metastable at roomtemperature,22 allowing for ex situ characterization of the phasetransformation characteristics. The granular packings were pre-pared with either large, polycrystalline particles (PC; particle size∼100 μm or above) or small, single crystal particles (SC; particlesize ∼1–5 μm). For the latter, particle size reduction was performedusing a high energy ball mill (Retsch Emax, zirconia milling media)at 1300 RPM for 1 h, after which an annealing step was performedat 600 °C in air for 10 min. The particle size after ball milling wasassessed using dynamic light scattering (Horiba Partica LA-960).After preparation, all the packings were >90% austenite, i.e., of thetetragonal phase. These as-synthesized packings are denoted as“PC-As Synth” and “SC-As Synth,” respectively. The morphologyof the particles was characterized using scanning electron micros-copy (SEM, FEI Helios 600 NanoLab).

The synthesized PC and SC packings were then subjected totwo treatments. The first treatment was confined uniaxial compres-sion of the as-synthesized packings (0.8 g for each) in a lubricated13mm diameter steel die. Such a treatment is known to effectivelycause forward martensitic transformation in zirconia-based granularpackings.23,35 50 kN force was applied, equivalent to a compressivestress of 377MPa. After compression, the resulting pellet was care-fully removed from the die and was gently broken up using a spatulato reach the “loose packing” state before characterization. Such loosepackings are denoted as “PC-Stress” and “SC-Stress.” The secondtreatment was submersion of the as-synthesized packings (0.8 g foreach) in liquid nitrogen for 1 h. The consequential packings aredenoted as “PC-Cooling” and “SC-Cooling.” After both treatments, asubstantial fraction of the martensite (monoclinic phase) was present

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-2

Published under license by AIP Publishing.

in these materials. In addition, 0.8 g of single crystal (Zr0.88Ce0.12)O2

particles were pressed in the steel die to form a “jammed packing.”With the jammed packing sintered at 1500 °C for 2 h, we finallyobtained a “sintered pellet,” whose diameter was 12.0 mm andheight was 1.47 mm. These treatments were repeated to provide mul-tiple samples for each category. The sample treatment history forthis comparative study is delineated in Fig. 1, with the mass of eachprepared sample being 0.8 g.

To explore the thermally induced reverse martensitic transfor-mation, the prepared samples were subjected to heat treatment usinga box furnace in air (Lindberg/Blue M 1700) with a heating rate of8.28 K/min up to 400 °C. They were annealed at 400 °C for 5minand then cooled to room temperature. Noting that the presence ofoxygen vacancy may influence the martensitic transformation behav-ior of zirconia-based shape memory ceramics, we performed theannealing heat treatment in an oxygenated environment. As a result,the possible creation of aliovalent Ce ions that can introduce oxygendefects was suppressed.36 After these heat treatments, the size of themicrostructure in individual particles stayed the same as they were

beforehand, because the kinetic condition defined by the annealingtemperature and time was insufficient for grain growth in zirconia.The martensite phase fraction was measured using x-ray diffraction(Panalytical X’Pert Pro) before and after the heat treatment. The frac-tion of the martensite phase (monoclinic structure) was estimatedwith the polymorph method as described by Garvie and Nicholson.37

For each prepared sample, differential scanning calorimetry (DSC,TA Instruments Q-10) was simultaneously performed to examine theheat flow behavior. This only involved a very small amount of mate-rial, ∼20mg per sample, with the heating and cooling rates designedto match those in the furnace heat treatments.

III. RESULTS

A. Characterization before reverse martensitictransformation

Figures 2(a)–2(c) show the particle morphology of the SC andPC packings. The PC packings are composed of a broad size distri-bution of particles ∼100–200 μm. Two of these representative

FIG. 1. Sample preparation flow chart and treatment history. Sample history starts from the co-precipitation process at the top, following one path at a time. The rectangularboxes explain treatments or processing steps and the round boxes name the (Zr0.88Ce0.12)O2 samples studied in this work.

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-3

Published under license by AIP Publishing.

particles are shown in Fig. 2(a). Each polycrystalline particle has acrystallite (grain) size on the order of 1–5 μm [Fig. 2(b)].Comparing the particle size and crystallite size, each polycrystallineparticle should contain ∼105–106 crystallites, and each crystallite isconstrained by grain boundaries. However, the inter-particle forces(i.e., electrostatic and van der Waals) and the friction forcesbetween impinging particles during loading are much less than thebonding between crystallites. Therefore, the PC packings are char-acterized by weak inter-particle mechanical constraints but strongintra-particle constraints.

In preparing single crystal particles from the large polycrystal-line particles, ball milling is used to promote intergranular fracture.Based on SEM, the majority of the particles are reduced to facetedsingle crystals of diameters ∼1–5 μm [Fig. 2(c)]. Particle size analy-sis by dynamic light scattering [Fig. 2(d)] confirms that the sizedistribution is comparatively uniform; less than 20 vol. % of theparticles are below 1 μm and less than 7 vol. % are larger than5 μm. Comparing the crystallite size before ball milling and thefinal particle size, we conclude that these are mostly single crystalparticles. Each single crystal (Zr0.88Ce0.12)O2 particle can accommo-date the volume and shape changes during both forward or reversemartensitic transformation without straining other particles. TheSC packings, therefore, experience very low intra-particle and inter-particle mechanical constraint during either the forward or reversemartensitic transformation.

As compared to the granular packings, the sintered pellet con-tains ∼1010 crystallites, each of which is constrained by grainboundaries. The microstructure of this pellet is similar to the PCparticle highlighted in Fig. 2(b). The entire sample is dominated bybonding forces, which are much stronger than the inter-particleforces responsible for the modicum of cohesion in the granularpackings. The sintered pellet thus features the strongest mechanicalconstraint among all prepared samples in this work. The jammedpackings and loose packings have slightly different constraint casesdue to the inter-particle adhesive forces, but the constraint affordedby grain boundaries in polycrystals is much more significant thanforces found additionally in the jammed packings. Overall, thereexists a qualitative hierarchy of mechanical constraints thatincreases as the polycrystallinity increases, from the SC packings, tothe PC packings, and finally to the sintered pellet.

Figures 2(e)–2(g) show the XRD diffraction patterns of allthe prepared (Zr0.88Ce0.12)O2 samples following the flow chart inFig. 1. A substantial fraction of the martensite phase is present ineach of the treated packings [Figs. 2(e)–2(f )] as well as in the sin-tered pellet [Fig. 2(g)]. While every sample has the same chemi-cal composition, the exact phase ratio depends on the materialform and processing history. For example, cooling causes moreforward transformation in PC packings (78% martensite) thanthe SC packings (40% martensite), while stress causes moreforward transformation in SC packings (49% martensite) thanthe PC packings (35% martensite). The origin of such differenceswill be discussed in Sec. IV B.

For the sintered pellet, although any martensite would trans-form to the austenite phase when heated to the sintering tempera-ture (1500 °C), cooling of the pellet to room temperature causesintergranular stresses due to the strong mechanical constraint. Thisresults in substantial martensite transformation on the pellet’s

surface as seen from the XRD pattern in Fig. 2(g). Additionally,crystallographic alignment is observed in the jammed packing andsintered pellet in that the ratio of the (11�1) and (111) monoclinicpeaks differs from the random polycrystals. The former stems fromconfined compression, while the latter is due to thermal stress andself-accommodation during cooling.38 It should also be noted thatXRD is a surface characterization technique, and the surfaces of thejammed packing are in direct contact with the die rams with highstress concentration, so the calculated martensite fraction of thejammed packing is slightly higher than the packing-wide phasefraction presented in the SC-Stress sample [Fig. 2(f )].

B. Thermally induced reverse martensitictransformation: A comparison of loose packing,jammed packing, and sintered pellet

All the packings and pellets (pieces taken from their surfaceregions) are subjected to DSC testing, with the scanning resultsdisplayed in Fig. 3. The endothermic peak is only seen in the sin-tered (Zr0.88Ce0.12)O2 pellet [Fig. 3(b), black solid line] but not inthe jammed packing [Fig. 3(b), blue dashed line], PC loose pack-ings [Fig. 3(a), red lines with solid squares], or SC loose packings[Fig. 3(a), blue lines with open circles]. For every case, no matterthe material form, constraint level, starting phase fraction, orforward transformation driving force (i.e., by cooling or stress), themartensite phase peaks are absent in XRD spectra after DSC, indi-cating that the thermally induced reverse martensitic transformationoccurs in all samples. Table I summarizes the thermal reversionbehavior for the investigated samples.

What distinguishes the sintered pellet from the loose andjammed granular packings is the strong mechanical constraintassociated with inter-particle bonding. Despite variations in theintra-particle constraint between the SC and PC packings, neithershows a peak. The findings in Fig. 3 thus suggest that the sharppeak in DSC results from the inter-particle rather than the intra-particle mechanical constraint. Moreover, the endothermic peaksare absent regardless of whether the forward transformation istriggered by compression or cooling, suggesting a minor influenceof the previous forward transformation history on the mode ofthermal reversion. By comparing the behavior of loose and jammedpackings, we conclude that the absence of endothermic peaks is notassociated with any stress relaxation or particle rearrangementduring heating of the jammed packing, which has been postulatedto be a potential mechanism.23

Overall, there is a distinction in the thermally inducedreverse transformation behavior between the commonly reportedmonolithic samples30,31 and granular packings due to the differentmechanical constraint conditions. Only possessing intra-particlemechanical constraint—as in the PC packings—is insufficient toproduce a sharp DSC peak; the greater and more homogeneousmechanical constraint in a monolithic sample (i.e., sintered pellet) isnecessary for a sharp endothermic peak to appear. In general,random microscopic samplings of broadly heterogeneous packingsare ill-described by the macroscopic martensite phase fraction. Aftercompression or cooling, the martensite phase fraction varies fromparticle to particle owing to either the heterogeneity of stress trans-mission (and therefore heterogeneity of the transformation driving

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-4

Published under license by AIP Publishing.

FIG. 2. Characterization results before reverse martensitic transformation. (a) A SEM micrograph of representative polycrystalline (PC) particles. (b) A high magnificationmicrograph of the PC particle surface clearly showing grain boundaries and triple junctions in individual particles. (c) A micrograph of single crystal (SC) particles. (d)Particle size distribution of SC particles obtained with dynamic light scattering, showing narrow size distribution corresponding to the observed particle size in SEM. XRDspectra and calculated martensite phase fractions of (e) PC packings, (f ) SC packings, and (g) the surface of a sintered pellet.

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-5

Published under license by AIP Publishing.

force)22 or some pre-existing heterogeneity in the nucleation barrierfrom local constraint conditions, dislocations, and other crystallo-graphic defects. Regardless of its origin, the phase fraction heteroge-neity is broad enough to widen the reverse transformationtemperature window upon heating. In short, the distribution of the

particles’ states in a granular packing results in a distribution oftemperatures at which the reverse transformation starts and ends.

Without strong mechanical constraint to force the transforma-tion to happen in large “bursts,” the macroscopic transformationbehavior of the whole loose or jammed packing is merely the sum ofthe concurrent behavior of each individual particle. During thermalreversion, millions of discrete transformations blend together into a“continuous mode” with no discernable DSC peaks. This view is sup-ported by the recent in situ neutron diffraction study,22 in which ther-mally driven reverse martensitic transformation in a jammed packingis found to occur over an extremely broad temperature window. Tocompare, the strong mechanical constraint in a sintered pellet canlead to bursting effects, wherein large regions transform near-simultaneously according to the strain energy nucleation barrier.8,12

Macroscopically, this leads to a discontinuous transformation modewith a narrow transformation window and a sharp DSC peak.

C. Thermally induced reverse martensitictransformation: A comparison of single crystal andpolycrystalline granular packings

While neither of the PC and SC packings shows endothermicpeaks during thermally induced reverse martensitic transformation,a closer comparison of their heat flow behavior reveals new physicalinsights into the effects of intra-particle mechanical constraint. InFigs. 4(a) and 4(b), the reported heat flow signal is converted tospecific heat capacity CP (J/gK) by dividing the heat flow rate (J/s)by the sample mass (g) and the heating rate (K/s). This rescales theabsorbed heat for better comparisons between samples. In additionto the prepared and treated SC and PC packings, we include thedata for the packing composed of freshly ball-milled single crystalparticles without annealing, which is characterized by a high mar-tensite phase fraction of ∼80%.

The measured CP values in Figs. 4(a) and 4(b) are in reason-able accordance with the reported values for cerium-doped zirco-nia,32 but the evolution of CP is quite abnormal. In all the CP vs Tplots, the curves are concave up with two noticeable regimes. Theheat capacity is seen to increase with temperature in both regimes;however, the CP increase rate (i.e., ∂CP/∂T) is lower in the low tem-perature regime (CP

Low) than the high temperature regime (CPHigh).

The transition of the two regimes implies either (i) the introductionof additional vibrational modes or (ii) an endothermic process(over a wide range of temperatures). Regarding possibility (i), theDebye temperature TD indicates a point where every availablevibrational mode (phonon, electron, etc.) is activated and ∂CP/∂Tdecreases, corresponding only to the entropy-driven point defectformation. This means that the CP curve should be concave downin the vicinity of TD, which is expected to fall between ∼230 and

FIG. 3. Thermally induced reverse martensitic transformation. DSC scans of (a)PC and SC packings and (b) a jammed packing and a sintered pellet.

TABLE I. Thermally induced martensitic transformation in various forms of (Zr0.88Ce0.12)O2.

Sample name SC-Stress SC-Cooling PC-Stress PC-Cooling Jammed packing Sintered pellet

Constraint None None Intra-particle Intra-particle Weak inter-particle Strong inter-particleTransforms back? Yes Yes Yes Yes Yes YesEndothermic peak in DSC? No No No No No Yes

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-6

Published under license by AIP Publishing.

350 °C for doped ZrO2.33 However, the measured CP curves are

concave up in this temperature range, making possibility (i) improb-able. Regarding possibility (ii), the slope transition in the Cp vs Tplots occurs within the transformation temperature range noted inthe previous in situ neutron diffraction work with (Zr0.88Ce0.12)O2

22

and is near the temperature that the endothermic peak appears inthe sintered pellet in Fig. 3(b) (∼220 °C). Therefore, possibility (ii)is reasonable and the CP

Low to CPHigh regime transition likely origi-

nates from the reverse transformation of martensite to austeniteaccompanied by heat absorption.

Consequently, the transition temperature between the tworegimes can be taken as the austenite start temperature of theentire packing AS

Packing. This is distinct from the austenite starttemperature of a discrete particle AS

Particle because the packing is, asdescribed previously, a statistical sample of a distribution of parti-cles. For a given granular packing, AS

Packing is governed by the par-ticle with the lowest AS

Particle. Figure 4(c) diagrams a method ofdetermining AS

Packing using linear fits of the heat capacity at low(50 °C < T < 150 °C) and high (300 °C < T < 400 °C) temperatureranges, followed by calculating their intercept. Note that the heatcapacity curves in Fig. 4 are indeed continuous without sharp peaks,so this interpolation only serves for comparison rather than an ulti-mate statement on AS

Packing. This approach is similar to the techniquewidely used in DSC of both high and low temperature glass transi-tions, which also occur over relatively broad temperature rangeswithout a sharp peak.39 We note that an alternative way to determineASPacking is to use the temperature at which CP

Low becomes nonlinear.However, the heat flow curves are not well described by a straightline in the CP

Low regime, making it challenging to accurately and pre-cisely pick the transition point this way. The resolution of the DSCexperiment is also insufficient to truly distinguish the heat flowchange associated with a single particle transforming, so the inter-cept method of determining AS

Packing is more consistent.By applying this approach to the packings investigated in this

work, Fig. 5 plots ASPacking as a function of the initial martensite

fraction, from which interesting trends are revealed. First, for bothPC and SC packings, AS

Packing decreases with an increase in theinitial martensite fraction. This is because, at a given temperaturebetween AS and AF, the Gibbs free energy of a martensite–austenitesystem is minimized at a given martensite fraction. Higher mar-tensite fractions are thermodynamically stable closer to AS, andlower martensite fractions are stable as the temperature approachesAF. As a result, particles with high martensite phase fractions tendto have low AS

Particle. For a granular packing, the phase fractiondiffers among particles. If the packing has a higher measured mar-tensite phase fraction, it contains more particles with high martens-ite phase fractions and low AS

Particle. This shifts ASPacking to the lower

temperature side.Second, for the same or similar initial phase fraction, AS

Packing

is seen to be lower for the PC packings than SC packings. This isanother reflection of the mechanical constraint conditions that dif-ferentiate them. In a PC particle, the mechanical constraint ishigher at grain boundaries than in the grain (i.e., crystallite) inte-rior, even more so at triple junctions, but it is lower at the particlesurface, near any internal pores, and in the vicinity of cracks, whichlikely form due to the large volume expansion during forwardtransformation.2 Because of that, forward transformation leads to

FIG. 4. Estimation of the austenite start temperature in granular packings. Heatcapacity analysis for the (a) PC packings and (b) SC packings. The existence oftwo regimes is illustrated by dashed arrows. (c) Linear interpolation to find theaustenite start temperature.

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-7

Published under license by AIP Publishing.

an internal stress distribution in the PC particles. Given the largenumber of crystallites in each PC particle (∼105–106), martensite–austenite interfaces form in many different crystallites, and some ofthem are associated with high internal stresses. During thermalreversion, migration of these interfaces would likely significantlyrelease the local strain energy, so the required thermodynamicdriving force for transformation is lowered. This would promotethe thermal reversion by interface migration at a lower temperaturein the PC particle, thereby reducing AS

Particle and ASPacking. However,

such crystallite-scale mechanical constraint effects are absent fromthe SC particles by definition.

IV. DISCUSSION

A. Effects of mechanical constraint on thermallyinduced reverse transformation

From the experimental results of the PC and SC shapememory ceramic packings as well as the sintered bulk polycrystals,this comparative study provides new insights into the role ofmechanical constraints in thermal reversion.

When the mechanical constraint is weak between particles,like in loose granular packings, the macroscopic transformationbehavior of the whole packing is just a superposition of thebehavior of each individual particle. Any heterogeneity in com-position, phase, orientation, defect density, microstructure, andresidual stress state among the particles15,16,23,40–42 may thus leadto a broadband effect of the martensitic transformation. Forthermal reversion investigated in this work, each particle has aunique austenite start temperature AS

Particle that depends on theparticle shape, size, microstructure, and the initial martensitefraction. Some particles are more martensitic than the measured

value from XRD (which is simply a volume-weighted mean) andhave lower AS

Particle, and others are less martensitic than theaverage particle and have higher AS

Particle. The distribution ofmartensite phase fraction in each packing is broad enough that asthe temperature is raised above AS

Packing, at every finite step, thereare some particles in the transforming process—leading to thecontinuous heat flow curves without endothermic peaks. Thebroadband effect is noticeable even when the packings consist ofpure martensite phase particles. For example, (Zr0.90Ce0.10)O2

loose packings are of pure monoclinic phase (martensite) at roomtemperature. When such packings are subjected to heating inDSC, although the endothermic peak is present, it is significantlywidened (AS to AF∼ 80 °C).23

When the mechanical constraint is strong, as in the sinteredbulk polycrystals, bursting effects dominate the transformationkinetics. Transforming a small amount of material to a new phaseinside a highly constrained matrix creates a comparatively largeamount of strain energy that raises the energy barrier for transfor-mation, shifting the local energy minima toward a situation wheremore material tends to transform in a single burst in order toreduce the influence of the strain energy penalty. We note thatmultiple burst events can happen sequentially if multiple strainenergy minima occur. Illustrating this point, Fig. 6(a) shows aDSC scan from another sintered pellet of the same composition[(Zr0.88Ce0.12)O2], where four distinct endothermic peaks areprominent. Each peak is associated with a region of martensiterapidly transforming to austenite when the local strain energybarrier is overcome by the thermodynamic driving force. The AS

for each peak is sharply delineated while AF occurs after sometapering. As compared in Fig. 6(b), this is quite similar to theshape of the singular peak seen in the first sintered pellet. Thefirst three peaks occur at lower temperatures than the singularpeak shown for the first sintered pellet, while the fourth peak fallsat virtually the same temperature. Collectively, these discreteevents almost look like one broad peak, as in the packings. TheDSC scan of the second sintered pellet shows direct evidence thatthe heat flow curve during reverse transformation can manifest ina peak-to-peak blur if multiple transformation events occur overthe same interval.

As a summary, Fig. 7 illustrates how the mechanical con-straint possibly affects the thermal reversion in various forms ofshape memory ceramics. We base these large-scale illustrationson the simulation and microscopy of martensite and austenitemorphologies in zirconia11,14,43–45 and steels,46,47 which are bothnucleation-dominated during martensitic transformation. Here,the transformation can progress rapidly via bursting transforma-tion modes, as in the case of a sintered pellet, which may involvea single [Fig. 7(a)] or multiple transformation steps [Fig. 7(b)].Alternatively, the bursts may be contained in discrete volumes, as inthe case of polycrystalline particles [Fig. 7(c)]. Without significantbursting transformation, the transformation may progress compara-tively slowly, as in the case of unconstrained single crystal particles[Fig. 7(d)]. Acoustic emissions occurring during the forward trans-formation have been used in the past to differentiate between burst-ing and non-bursting-type transformations,48–50 and future workutilizing similar approaches for the reverse transformation couldcorroborate these findings.

FIG. 5. Austenite start temperature as a function of martensite phase fractionwith a comparison between PC and SC packings. The ball-milled packingwithout annealing is included with the SC packings because it lacks intra-particle mechanical constraint.

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-8

Published under license by AIP Publishing.

B. Effects of mechanical constraint on stress- andcooling-induced forward martensitic transformation

Although the focus of this work is on the effects of mechanicalconstraints on thermal reversion, we find that a mechanical con-straint plays an important role in forward martensitic transforma-tion as well. As shown in Figs. 2(e) and 2(f ), in SC packings, themartensite fractions resulting from stress- and cooling-inducedforward transformation are comparable (49% vs 40%); however, inPC packings, stress leads to a much lower martensite phase fractionthan cooling (35% vs 78%).

For stress-induced forward martensitic transformation, let usconsider the unique loading mechanics that occur inside a granular

packing in tandem with the previously discussed conditions ofmechanical constraint and polycrystallinity. On the mesoscale, theapplied macroscopic force is distributed highly heterogeneously bya continuous network of load-bearing particles that form “forcechains”26,27 and shield non-load-bearing particles partially orentirely (these are called “rattlers”). Those particles that are in forcechains make up a minority of the volume and thus bear exceedinglyhigh load. On the microscale, the corresponding stresses at a load-bearing particle’s contact sites are amplified by Hertzian stress. Asa result, the contact regions between the particles in force chainscan transform at low macroscopic loads. For a packing of smallsingle crystal particles, this will most likely result in a backbone ofpartially martensitic particles as described in a previous work.23

For a packing of large, polycrystalline particles, the stress state andmartensite morphology are more complicated—the intra-particleconstraint (i.e., between crystallites) will promote bursting transfor-mation modes in the contact regions. Self-accommodating mar-tensite variants likely form in fully transformed crystallites tominimize the strain energy, while the strain of these transformingregions will autocatalytically promote the transformation of adja-cent crystallites, increasing the total transformed volume in a local-ized region. From our observation, the transformed volume causedby the applied stress is slightly higher in the SC packings than thePC packings, which is probably caused by the reduction in themartensite nucleation barrier in SC packings due to the lack ofintra-particle mechanical constraint.

For cooling-induced forward martensitic transformation, thetemperature is generally uniform, so cooling-induced transformationhas a much more homogenously distributed driving force comparedto stress-induced transformation. In PC packings, because of theanisotropic contraction among crystallites during cooling and thestrong intra-particle mechanical constraint from grain boundariesand triple junctions, thermal stresses develop inside each particle.The resulting stress distribution is more heterogeneous than the tem-perature distribution and can preferentially lead to forward transfor-mation around the grain boundaries or triple junctions and a moreheterogeneous distribution of the martensite phase than the SCpacking case. For PC-Cooling, the driving force for forward transfor-mation is effectively a combined mode of cooling and stress, whereasin SC-Cooling, there is no stress resulting from anisotropic contrac-tion among individual crystallites inside each particle. This explainswhy PC-Cooling has a considerably higher martensite phase fractionthan SC-Cooling. The martensite phase fraction in the sintered bulkpolycrystal, which similarly forms during cooling (from 1500 °C)under strong constraint, is also high [Fig. 2(g)].

By comparing the martensite fractions among PC-Stress,SC-Stress, PC-Cooling, and SC-Cooling, we conclude that themechanical constraint has more influences over the cooling-inducedthan stress-induced forward transformation. This is because, instress-induced transformation, the distribution of the driving force—the heterogeneous stresses resulting from force chain formation andparticle contact—is present in both PC and SC packings, whereasthe mechanical constraint more determines the nucleation barrier. Incooling-induced transformation, in contrast, the mechanical con-straint creates thermal stresses in PC packings that increase thedriving force and distinguish the transformation behavior betweenthe PC and SC packings.

FIG. 6. Thermal reversion with conspicuous endothermic peaks in heat flowmeasurement. (a) DSC scan of another batch of sintered bulk (Zr0.88Ce0.12)O2

pellet with multiple burst events. (b) A comparison of the endothermic peaksbetween the first and second sintered pellets in greater detail.

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-9

Published under license by AIP Publishing.

V. CONCLUSIONS

In this work, we investigate the thermally induced reversemartensitic transformation in zirconia-based shape memory ceram-ics of various material forms, including single crystal and polycrys-talline loose packings, jammed packings, and sintered bulkpolycrystals. Several salient conclusions can be drawn from thiscomparative study:

• Owing to intrinsic heterogeneity and weak inter-particle mechani-cal constraints, granular shape memory ceramic packings undergoreverse transformation over a broad temperature range. This mani-fests as a continuous transformation mode without a conspicuousendothermic peak in DSC.

• Conspicuous endothermic peaks only appear when bursting-typetransformation occurs, which may involve a single or multipletransformation steps. This requires a strong mechanical constraint.

• In both polycrystalline and single crystal packings, the austenitestart temperature is reduced when the martensite phase fractionincreases. For similar phase fractions, the austenite start temperatureis lower in polycrystalline packings than single crystal packings.

• In forward martensitic transformation, the intra-particlemechanical constraint is more influential in the cooling-inducedthan the stress-induced transformation.

The findings of this work further indicate that the mechanical con-straint in shape memory ceramics can be controlled to tune the

characteristics of martensitic transformation. Extending this conceptto the “continuous mode” of transformation, the correspondingshape memory or superelastic devices can be designed to operateat a wide range of load and temperature for optimal performance,wherein the dissipation of mechanical energy or exertion ofmechanical force can be robustly manipulated. Metal matrix com-posites are a particularly promising application for these granularshape memory ceramics; an intimately bonded matrix phase mayprovide intermediate mechanical constraint to widely tune thetransformation behavior.

ACKNOWLEDGMENTS

The authors would like to acknowledge the support from theNational Science Foundation (NSF) (No. CMMI-1853893) and theCollege of Engineering at Virginia Tech.

DATA AVAILABILITY

The data that support the findings of this study are availablefrom the corresponding author upon reasonable request.

REFERENCES1A. Lai et al., “Shape memory and superelastic ceramics at small scales,” Science341(6153), 1505–1508 (2013).2P. M. Kelly and L. R. F. Rose, “The martensitic transformation in ceramics—Itsrole in transformation toughening,” Prog. Mater. Sci. 47(5), 463–557 (2002).

FIG. 7. Schematics of thermally induced reverse transformation mechanism under different conditions. Green indicates martensite (monoclinic phase), and yellow indicatesaustenite (tetragonal phase). The hexagonal mesh feature is used to denote crystallites in a polycrystal. Each sequential illustration is at a higher temperature. (a) A singleburst of reverse transformation in a sintered pellet, where a large volume of martensite rapidly transforms. This corresponds to the heat flow signal in Fig. 3(b). (b) Multiplebursting-type transformation steps with discrete nucleation in a sintered pellet. This corresponds to the heat flow signal in Fig. 6(a). (c) Burst-like reverse transformation ina polycrystalline particle. Many of such particles transform at distributed temperatures in the PC packings. (d) Reverse transformation in a single crystal particle. Many ofsuch particles transforming at distributed temperatures compose the SC packings.

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-10

Published under license by AIP Publishing.

3G. M. Wolten, “Diffusionless phase transformations in zirconia and hafnia,”J. Am. Ceram. Soc. 46(9), 418–422 (1963).4R. C. Garvie, R. H. Hannink, and R. T. Pascoe, “Ceramic steel?,” Nature 258,703–704 (1975).5W. M. Kriven, “Martensitic toughening of ceramics,” Mater. Sci. Eng. A 127(2),249–255 (1990).6A. G. Evans, N. Burlingame, M. Drory, and W. M. Kriven, “Martensitic trans-formations in zirconia-particle size effects and toughening,” Acta Metall. 29(2),447–456 (1981).7J. C. Lambropoulos, “Shear, shape and orientation effects in transformationtoughening,” Int. J. Solids Struct. 22(10), 1083–1106 (1986).8R. C. Garvie, “Stabilization of the tetragonal structure in zirconia microcrystals,”J. Phys. Chem. 82(2), 218–224 (1978).9J. Chevalier, L. Gremillard, and S. Deville, “Low-temperature degradation of zir-conia and implications for biomedical implants,” Annu. Rev. Mater. Res. 37(1),1–32 (2007).10J. Chevalier and L. Gremillard, “Ceramics for medical applications: A picturefor the next 20 years,” J. Eur. Ceram. Soc. 29(7), 1245–1255 (2009).11A. Liens et al., “Phase transformation induces plasticity with negligibledamage in ceria-stabilized zirconia-based ceramics,” Acta Mater. 183, 261–273(2020).12P. E. Reyes-Morel and I.-W. Chen, “Transformation plasticity ofCeO2-stabilized tetragonal zirconia polycrystals: I, Stress assistance and autoca-talysis,” J. Am. Ceram. Soc. 71(5), 343–353 (1988).13E. S. Machlin and M. Cohen, “Burst phenomenon in the martensitic transfor-mation,” J. Met. 3(11), 1019–1029 (1951).14M. Mamivand, M. Asle Zaeem, and H. El Kadiri, “Shape memory effect andpseudoelasticity behavior in tetragonal zirconia polycrystals: A phase fieldstudy,” Int. J. Plast. 60, 71–86 (2014).15Z. Du et al., “Size effects and shape memory properties in ZrO2ceramicmicro- and nano-pillars,” Scr. Mater. 101, 40–43 (2015).16X. M. Zeng, A. Lai, C. L. Gan, and C. A. Schuh, “Crystal orientation depen-dence of the stress-induced martensitic transformation in zirconia-based shapememory ceramics,” Acta Mater. 116, 124–135 (2016).17Z. Du et al., “Synthesis of monodisperse CeO2–ZrO2 particles exhibiting cyclicsuperelasticity over hundreds of cycles,” J. Am. Ceram. Soc. 100(9), 4199–4208(2017).18Z. Du, X. M. Zeng, Q. Liu, C. A. Schuh, and C. L. Gan, “Superelasticity inmicro-scale shape memory ceramic particles,” Acta Mater. 123, 255–263(2017).19X. Zhao, A. Lai, and C. A. Schuh, “Shape memory zirconia foams through icetemplating,” Scr. Mater. 135, 50–53 (2017).20X. Zeng, N. Arai, and K. T. Faber, “Robust cellular shape-memory ceramicsvia gradient-controlled freeze casting,” Adv. Eng. Mater. 21(12), 1900398(2019).21I. R. Crystal, A. Lai, and C. A. Schuh, “Cyclic martensitic transformations anddamage evolution in shape memory zirconia: Single crystals vs. polycrystals,”J. Am. Ceram. Soc. 103(8), 1–13 (2020).22H. A. Rauch, Y. Chen, K. An, and H. Z. Yu, “In situ investigation ofstress-induced martensitic transformation in granular shape memory ceramicpackings,” Acta Mater. 168, 362–375 (2019).23H. Z. Yu, M. Hassani-Gangaraj, Z. Du, C. L. Gan, and C. A. Schuh, “Granularshape memory ceramic packings,” Acta Mater. 132, 455–466 (2017).24H. Luo, H. Lu, W. L. Cooper, and R. Komanduri, “Effect of mass density onthe compressive behavior of dry sand under confinement at high strain rates,”Exp. Mech. 51(9), 1499–1510 (2011).25M. Jabbar, M. Karahan, Y. Nawab, M. Ashraf, and T. Hussain, “Effect of silicananoparticles on mechanical properties of Kevlar/epoxy hybrid composites,”J. Text. Inst. 110(4), 606–613 (2019).26F. Göncü, O. Durán, and S. Luding, “Constitutive relations for the isotropicdeformation of frictionless packings of polydisperse spheres,” C. R. Mec.338(10–11), 570–586 (2010).

27Y. Zhang and R. Behringer, “Pulling an intruder from a granular material : Anovel depinning experiment,” Powders Grains 03040, 4–7 (2017).28J. Zhu, D. Wang, Y. Gao, T.-Y. Zhang, and Y. Wang, “Linear-superelasticmetals by controlled strain release via nanoscale concentration-gradient engi-neering,” Mater. Today 33, 17–23 (2020).29J. Zhu, Y. Gao, D. Wang, T.-Y. Zhang, and Y. Wang, “Taming martensitic transfor-mation via concentration modulation at nanoscale,” Acta Mater. 130, 196–207 (2017).30X. Luo, W. Zhou, S. V. Ushakov, A. Navrotsky, and A. A. Demkov,“Monoclinic to tetragonal transformations in hafnia and zirconia: A combinedcalorimetric and density functional study,” Phys. Rev. B 80(13), 1–13 (2009).31X. Huang, A. Zakurdaev, and D. Wang, “Microstructure and phase transfor-mation of zirconia-based ternary oxides for thermal barrier coating applications,”J. Mater. Sci. 43(8), 2631–2641 (2008).32A. Zakurdaev and X. Huang, “Experimental study of phase transformationand specific heat of ternary zirconia-based oxides using differential scanning cal-orimetry,” J. Alloys Compd. 488(1), 469–478 (2009).33C. Degueldre, P. Tissot, H. Lartigue, and M. Pouchon, “Specific heat capacityand Debye temperature of zirconia and its solid solution,” Thermochim. Acta403(2), 267–273 (2003).34Z. Du, H. Z. Yu, C. A. Schuh, and C. L. Gan, “Shape memory ceramic particlesand structures formed thereof,” U.S. patent 2019/0039959 (7 February 2019).35V. S. Raut, T. S. Glen, H. A. Rauch, H. Z. Yu, and S. T. Boles, “Stress-inducedphase transformation in shape memory ceramic nanoparticles,” J. Appl. Phys.126(21), 215109 (2019).36R. F. Reidy and G. Simkovich, “Electrical conductivity and point defect behav-ior in ceria-stabilized zirconia,” Solid State Ionics 62(1–2), 85–97 (1993).37R. C. Garvie and P. S. Nicholson, “Phase analysis in zirconia systems,” J. Am.Ceram. Soc. 55(6), 303–305 (1972).38P. Scardi, R. Di Maggio, L. Lutterotti, U. Trento, P. Maistrelli, and D. Fisica,“Thermal expansion anisotropy,” J. Am. Ceram. Soc. 75(10), 2828–2832 (1992).39J. E. Shelby, Introduction to Glass Science and Technology (The Royal Societyof Chemistry, 2005).40X. M. Zeng, Z. Du, N. Tamura, Q. Liu, C. A. Schuh, and C. L. Gan, “In-situstudies on martensitic transformation and high-temperature shape memory insmall volume zirconia,” Acta Mater. 134, 257–266 (2017).41J. P. Hirth and R. C. Pond, “Compatibility and accommodation in displacivephase transformations,” Prog. Mater. Sci. 56(6), 586–636 (2011).42B. Y. Sukharevsky, B. G. Alapin, and A. M. Gavrish, “Some features of ZrO2

polymorphous transformation kinetics upon cooling,” Reports USSR Acad. Sci.156(3), 677–680 (1964).43M. Mamivand, M. A. Zaeem, H. El Kadiri, and L. Q. Chen, “Phase field mod-eling of the tetragonal-to-monoclinic phase transformation in zirconia,” ActaMater. 61(14), 5223–5235 (2013).44S. Deville, H. El Attaoui, and J. Chevalier, “Atomic force microscopy of trans-formation toughening in ceria-stabilized zirconia,” J. Eur. Ceram. Soc. 25(13),3089–3096 (2005).45S. Deville, G. Guénin, and J. Chevalier, “Martensitic transformation in zirconiapart I. Nanometer scale prediction and measurement of transformation inducedrelief,” Acta Mater. 52(19), 5697–5707 (2004).46H. Shirazi, G. Miyamoto, S. Hossein Nedjad, T. Chiba, M. Nili Ahmadabadi,and T. Furuhara, “Microstructure evolution during austenite reversion in Fe-Nimartensitic alloys,” Acta Mater. 144, 269–280 (2018).47N. Nakada, “Direct observation of martensitic reversion from lenticular mar-tensite to austenite in Fe-Ni alloy,” Mater. Lett. 187, 166–169 (2017).48M. Rühle, N. Claussen, A. H. Arthur, and H. Heuer, American CeramicSociety., Science and Technology of Zirconia II (American Ceramic Society, 1984).49G. Rauchs, T. Fett, D. Munz, and R. Oberacker, “Tetragonal-to-monoclinicphase transformation in CeO2-stabilised zirconia under uniaxial loading,” J. Eur.Ceram. Soc. 21(12), 2229–2241 (2001).50G. Rauchs, T. Fett, D. Munz, and R. Oberacker, “Tetragonal-to-monoclinicphase transformation in CeO2-stabilized zirconia under multiaxial loading,”J. Eur. Ceram. Soc. 22(6), 841–849 (2002).

Journal ofApplied Physics ARTICLE scitation.org/journal/jap

J. Appl. Phys. 128, 245102 (2020); doi: 10.1063/5.0035041 128, 245102-11

Published under license by AIP Publishing.