Phase transition induced strain in ZnO under high pressure

Under high pressure, the phase transition mechanism and mechanical property of material are supposed to be largely associated with the transformation induced elastic strain. However, the experimental evidences for such strain are scanty. The elastic and plastic properties of ZnO, a leading material for applications in chemical sensor, catalyst, and optical thin coatings, were determined using in situ high pressure synchrotron axial and radial x-ray diffraction. The abnormal elastic behaviors of selected lattice planes of ZnO during phase transition revealed the existence of internal elastic strain, which arise from the lattice misfit between wurtzite and rocksalt phase. Furthermore, the strength decrease of ZnO during phase transition under non-hydrostatic pressure was observed and could be attributed to such internal elastic strain, unveiling the relationship between pressure induced internal strain and mechanical property of material. These findings are of fundamental importance to understanding the mechanism of phase transition and the properties of materials under pressure.

Under high pressure, the phase transition mechanism and mechanical property of material are supposed to be largely associated with the transformation induced elastic strain. However, the experimental evidences for such strain are scanty. The elastic and plastic properties of ZnO, a leading material for applications in chemical sensor, catalyst, and optical thin coatings, were determined using in situ high pressure synchrotron axial and radial x-ray diffraction. The abnormal elastic behaviors of selected lattice planes of ZnO during phase transition revealed the existence of internal elastic strain, which arise from the lattice misfit between wurtzite and rocksalt phase. Furthermore, the strength decrease of ZnO during phase transition under non-hydrostatic pressure was observed and could be attributed to such internal elastic strain, unveiling the relationship between pressure induced internal strain and mechanical property of material. These findings are of fundamental importance to understanding the mechanism of phase transition and the properties of materials under pressure.
Pressure induced phase transition has been considered as an important and extensively used approach in designing new materials [1][2][3][4][5] and in geoscientific research 6,7 . For instance, under high pressure and high temperature soft graphite and carbon transform into diamond, the hardest known bulk material 8,9 ; olivine in the deep earth transforms to spinel and result in the abnormal seismic velocity and the deep earthquake 10,11 . The phase transition mechanism of materials under high pressure has shown many unique features and is still under exploration [12][13][14] .
During a pressure induced first order solid-solid transformation, usually both phases can co-exist over a certain pressure range (transition zone). The crystal structure and lattice parameters of the new phase are different from the original phase, thus, theoretically speaking internal lattice strain should be generated during the nucleation and growth of new phase to accommodate the misfit between nucleus and matrix 15 . Especially, in a displacive phase transition there would be an orientation relationship between each phase and the new phase grows epitaxially on certain lattice plane of the matrix phase, thereby the lattices of each phase on the interface may be mismatched and internal strain arises 16 . The internal strain stemmed from lattice misfit enhances the transformation potential barrier. Thereby it affects the transformation kinetics and is assumed to be responsible for many important phenomena under pressure 14,[17][18][19] . In addition, the phase transition induced elastic strain is usually anisotropic, making the actual microscopic deviatoric stress on material higher than external applied stress and is expected to result in plastic deformation in material [19][20][21] . Namely, misfit strain could soften materials during phase transition. However, such phase transition induced elastic lattice strain has not yet been well examined experimentally under high pressure, therefore it is still an ambiguous explanation for related phenomena. Whether such internal strain exists, what are the characteristics of it, how it evolves during phase transition and how mechanical property is affected are all unresolved questions.
In the present work, using in situ high pressure synchrotron x-ray diffraction, we checked the compressibility of ZnO which experiences a wurtzite-rocksalt phase transition under pressure [22][23][24] , identifying the transformation induced elastic strain. Moreover, the expected strength softening during phase transition of ZnO was observed under non-hydrostatic pressure.

Results and Discussions
In the axial x-ray diffraction (AXRD) experiments, the wurtzite-to-rocksalt transition starts from 10.1 GPa with increasing pressure. These two phases coexist over a pressure range of 10.1 GPa to 16.75 GPa, in good agreement with previous reports [23][24][25] . A typical XRD pattern and its Rietveld refinements of both wurtzite and rocksalt phases at 12.7 GPa are shown in Fig. 1. Figure    To explore the compression behavior of each lattice plane during phase transition, we take the (111) d-spacing of Au (d ) 111 Au as a reference, and the ratio d /d hkl ZnO 111 Au is used to represent the relative value of (h k l) d-spacing of ZnO compared to the (111) d-spacing of Au. As a common pressure standard, Au is believed to display no abnormal compression discontinuity in the pressure range in this work, so any discontinuities of the variation of d /d hkl ZnO 111 Au should be attributed to the unusual compression behavior of ZnO itself. Figure 3 shows the pressure evolution of ratio d /d Au deviates to larger values from the normal linear relationship, indicating an enlarged (100) d-spacing of wurtzite phase, which result in that the ratio d 100 /d 002 deviates to larger values, as seen in Fig. 2 Au , as a result the ratio d 200 /d 220 of rocksalt phase deviates to smaller values, as seen in Fig. 2(b). Limpijumnong et al. 26 proposed that the wurtzite-rocksalt phase transition should follow the hexagonal path, in which the c/a ratio decreased first, and then the hexagonal angle opens up while the atoms in the center of the triangle move horizontally to the center of the square, the rocksalt phase then occurs. In this model, wurtzite phase ( Fig. 5(a)) can continuously transform into rocksalt phase (Fig. 5(b)) along a simple homogeneous orthorhombic shear strain path, consequently the relative crystallographic orientation of the wurtzite and rocksalt phases with (001) wurtzite || (001) rocksalt is expected 26 . This phase transition model is also believed to apply to nanocrystals 27 and has been validated by experimental observations 28,29 .
At the onset of the phase transition, the rocksalt phase grows epitaxially on the matrix of the wurtzite phase because of the crystallographic relationship of these two phases. When wurtzite and rocksalt phases occur as intimately mixed phases with an epitaxial relationship between them, each phase is subjected to a stress imposed by the other phase. As a result, each phase would be elastically deformed with respect to what it would be when the other phase were absent. As a result of the crystallographic relationship with (001) wurtzite || (001) rocksalt , the (001) plane of rocksalt phase is expected to grow epitaxially on the (001) plane of wurtzite phase. In the wurtzite-rocksalt phase transition, the rhombus-shaped unit cell projection along the [001] direction in wurtzite phase transforms to a square in rocksalt phase (Fig. 5) 26 . In this process the d-spacing of (100) plane of wurtzite phase needs to increase to match the (110) plane of rocksalt phase, as d 110 of rocksalt phase is larger than d 100 of wurtzite phase. Therefore, d 100 of wurtzite phase would be stretched by the larger lattice dimension of (110) plane of rocksalt phase, while accordingly d 110 (or d 220 ) of rocksalt phase would be compressed to match the smaller lattice dimension of (100) plane of wurtzite phase. Owing to the symmetry of rocksalt phase, d 200 equals to 2d 220 and thus shows more obvious unusual compression behavior than d 220 (Fig. 4), therefore the d 200 /d 220 of rocksalt phase deviates to smaller values, as seen in Fig. 2(b).
In the initial stage of transformation, the amount of rocksalt phase is small. The lattice parameter of wurtzite phase does not deviate significantly (Fig. 3(a)) due to the relative small strained interface compared to the whole detected volume, while the deviation of lattice parameters of rocksalt phase is large (Fig. 4). For a similar reason, as the amount of the rocksalt phase is dominant near the end of transition, the deviation of lattice parameter of wurtzite phase increases and the lattice parameter deviation in rocksalt phase decreases.
To check the influence of internal strain on the plastic property of ZnO, we derive differential elastic lattice strains for both phases of ZnO from line shifts in radial X-ray diffraction (RXRD) data collected at pressure 30 (Fig. 6(a)). The RXRD measurements were performed under non-hydrostatic conditions. Before the wurtzite-rocksalt phase transition, the average differential strain <Q (hkl)>, which refer the arithmetic average of measured differential strains of all lattice planes, increases with pressure. The differential strain of rocksalt ZnO also increases with pressure when the phase transition finished. But during the phase transition, <Q (hkl)> of each phase ZnO decreases steeply with pressure, indicating that plastic flow is achieved 31 (Fig. 6(b)) and the strength of each phase ZnO decreases.  As indicated in Figs 3 and 4, the internal strain on different lattice planes vary considerably, implying that the internal strain in ZnO is significantly anisotropic and leads to the development of localized shear stress. Such internal shear stress could make the actual shear stress in ZnO reach its yield strength, resulting in the deformation of ZnO. In the perspective of energy, the strain energy resulted from the lattice misfit accompanying transformation inhibits the phase transition by counteracting the chemical free energy driving force for growth. The plastic flow may relax this internal strain and enable the growth of rocksalt phase to continue 19,20 . Thereby, the anisotropic internal strain during phase transition could lead to the decrease of strength.
In summary, in situ synchrotron XRD measurements under quasi-hydrostatic conditions reveal unusual compression behaviors in ZnO during the wurtzite-rocksalt phase transition, indicating the internal elastic strain on selected lattice planes. Combined with the established phase transition model of ZnO, the observed elastic strain is believed to be caused by the lattice misfit between wurtzite phase and rocksalt phase during phase transition. Additionally, the internal elastic strain is supposed to give rise to strength softening of each phase ZnO during phase transition, which is observed in the present RXRD measurements at non-hydrostatic conditions. These results supply a strong evidence for the existence of phase transition induced elastic lattice strain under pressure and indicate that such strain could have significant affect on the physical property of material.

Methods
In situ high pressure AXRD experiments were performed at room temperature, and designed to generate quasi-hydrostatic conditions by using neon as a pressure transmitting medium. Polycrystalline ZnO powder (inset in Fig. 1) with a purity of 99.99% (Aladdin Company) was pressed to a pellet with thickness about 10 μm, and then loaded into a 120-μm-diameter sample hole drilled in a rhenium gasket with 40 μm in thickness. Fine Au powder was mixed with the sample while a tiny ruby ball was loaded near the sample. The equation of state of Au 32 and the ruby fluorescence shift 33 were used for pressure calibrations. In the RXRD experiments an x-ray transparent boron-epoxy disc with 40 μm in thickness was used as gasket. The mixture of ZnO and gold powder was loaded into a 40-μm-diameter sample hole and the equation of state of Au 32 was used for pressure calibrations. No pressure medium was used in the RXRD measurements.
The AXRD experiments were performed at the 4W2 beamline of the Beijing Synchrotron Radiation Facility (BSRF) with a wavelength of 0.6199 Å. The RXRD measurements were carried out at 16-BMD station of the High-Pressure Collaborative Access Team (HPCAT), Advanced Photon Source, Argonne National Laboratory, with a wavelength of 0.3101 Å. Diffraction patterns at various pressures were recorded with a Mar345 imaging plate detector. Collected data were analyzed for lattice parameters and differential elastic lattice strains using the programs FIT2D 34 and MAUD 35 .