Unraveling Convoluted Structural Transitions in SnTe at High Pressure

Article pubs.acs.org/JPCC

Unraveling Convoluted Structural Transitions in SnTe at High Pressure Dan Zhou,†,‡ Quan Li,*,†,‡ Yanming Ma,† Qiliang Cui,*,† and Changfeng Chen‡ †

State Key Laboratory of Superhard Materials, College of Materials Science and Engineering, Jilin University, Changchun 130012, China ‡ Department of Physics and HiPSEC, University of Nevada, Las Vegas, Nevada 89154, United States ABSTRACT: The longstanding uncertainty in high-pressure structural evolution of SnTe has greatly impeded the understanding of its complex electronic properties. Here we unravel the convoluted high-pressure phase transitions of SnTe using angle-dispersive synchrotron X-ray diffraction combined with first-principles structural search. We identify three coexisting intermediate phases of Pnma, Cmcm, and GeS type structure and establish the corresponding phase boundaries. We further unveil the intricate pressure-driven evolution of the energetics, kinetics, and lattice dynamics to elucidate its distinct phase-transition mechanisms. These findings resolve structures of SnTe, which have broad implications for other IV−VI semiconductors that likely harbor similar novel high-pressure phases.

1. INTRODUCTION Tin telluride (SnTe) is an exemplary case among IV−VI narrow-gap semiconductors that exhibit unusual thermodynamic, vibrational, and electronic properties, which find applications in phase-change memory devices, solar cells, thermoelectric generators, and infrared detectors.1−4 Recent discoveries of novel structural and electronic states5,6 and the latest realization of a new type of topological order in SnTe have reinvigorated strong interest in this fascinating material.7,8 It has long been known that SnTe undergoes pressure-driven phase transitions from the ambient-pressure Fm3̅m (B1) structure through an intermediate phase to the Pm3̅m (B2) structure.9−16 However, structural determination of the intermediate phase has remained an intriguing and longstanding mystery since X-ray diffraction (XRD) is often insufficient by itself to resolve complex phases, especially those with low symmetries. Previous work proposed conflicting structures such as an orthorhombic GeS structure or a pseudotetragonal structure.17 Similar uncertainties exist for other IV−VI compounds such as SnS, which was proposed to change under pressure from GeS to monoclinic structure, which is in contradiction to another prediction of transition to orthorhombic Cmcm structure.18 Meanwhile, several orthorhombic phases have been proposed for the intermediate phases of PbX (X = Te, Se, and S) without a consensus view.19−21 These structural uncertainties greatly impede further exploration of this important class of materials. In this work, we unravel the convoluted structural evolution of SnTe at high pressure using an integrated approach of angledispersive synchrotron XRD combined with a first-principles structural search method. A systematic analysis of the experimental XRD data and the calculated enthalpy, kinetic © 2013 American Chemical Society

barrier, and phonon modes leads to the identification of three orthorhombic structures of Pnma, Cmcm, and GeS type that dynamically coexist in the intermediate pressure range. Further investigation reveals distinct mechanisms for phase transitions that are driven by energetics and kinetics at the low-pressure phase boundary and by softening acoustic phonon modes at the high-pressure phase boundary. The present work establishes the first comprehensive understanding of the high-pressure evolution of the structural properties of SnTe and opens a promising avenue for further exploring many other IV−VI semiconductors that likely harbor new structural phases at high pressure.

2. EXPERIMENTAL SECTION High-pressure angle-dispersive XRD diffraction experiments were carried out at room temperature using a synchrotron Xray source (λ = 0.4859 Å) of the B2 High-Pressure Station of Cornell High Energy Synchrotron Source (CHESS). A MaoBell-type diamond-anvil cell with 400 μm culet diamond anvils was used to preindent the T-301 stainless steel gasket to 50 μm central thickness. A 120 μm diameter hole was drilled at the center of the gasket to form the sample chamber. Commercially available SnTe powder (Alfa Products, 99.999%) was loaded into the sample chamber with silicone oil as the pressuretransmitting medium. The pressure was determined from the frequency shift of the ruby R1 fluorescence line.22 The diffraction patterns were collected using a MAR165 image plate, and the average acquisition time was 300 s. The 2D XRD Received: January 25, 2013 Revised: February 20, 2013 Published: February 25, 2013 5352

dx.doi.org/10.1021/jp4008762 | J. Phys. Chem. C 2013, 117, 5352−5357

The Journal of Physical Chemistry C

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diffraction images were integrated using FIT2D software,23 which produces patterns of intensity versus diffraction angle 2θ.24 Diffraction patterns were fitted using Rietveld profile matching with GSAS+EXPGUI programs.25,26

3. RESULTS AND DISCUSSION The XRD patterns for SnTe up to 31.3 GPa are shown in Figure 1a. Rietveld refinement shows an excellent agreement

Figure 2. Rietveld refinements of the XRD patterns for the low-, intermediate-, and high-pressure phases of SnTe at selected pressures.

phases of Pnma, Cmcm, and GeS structure in the intermediate pressure range. The Pnma structure has the lowest enthalpy, but the Cmcm and GeS structures are within 30 meV and thus are likely to coexist at the room temperature, a prospect supported by low (calculated) kinetic barriers and verified by a detailed comparison of the experimental and simulated XRD data (see more discussions below). We note that the three intermediate structures can be viewed as different distortions in the orthorhombic subgroups of the Fm3̅m structure (see insets of Figure 2). The Pnma, Cmcm, and GeS cells correspond to √2 × √2/2 × 1,√2/2 × 2 × √2/2, and 2 × √2/2 × √2/2 Fm3̅m unit cell, respectively. Both the GeS and Cmcm structures have the stacking of pseudo 2D layers formed by major shear movements of two adjacent (001) planes along the (001)[110] direction in the doubled Fm3̅m unit cell, while the Pnma structure can be obtained by modulated displacements of Sn and Te atoms along the [001] and [110] directions. Moreover, the Pnma can be also viewed as a distorted Cmcm or GeS structure through sliding and buckling in the adjacent planes along the c-axis. Guided by the theoretical search results, we performed Rietveld refinements at 13.3 GPa where the intermediate phases are well established, and the results (Figure 2b−d) show that all three structures provide a good fit to the main XRD peaks. It is noted that only the Pnma phase reproduces the small peaks at 8.8, 9.2, and 10.7° that initially emerge near the low-pressure phase boundary. The refinement results also show that only the Cmcm structure reproduces the experimental XRD peak at 18.7°, providing a revealing sign for the

Figure 1. (a) XRD patterns of SnTe with rising pressure and then decompression to ambient pressure (bottom to top). Asterisks and down triangles mark the appearance of peaks associated with the intermediate and B2 phase, respectively. (b) Amplified view of the diffraction patterns for the evolution of the intermediate phase. (c) Calculated enthalpy of the Fm3̅m (B1), Cmcm, GeS, and Pm-3m (B2) phases relative to that of the Pnma phase versus pressure.

with the cubic Fm3̅m structure at 1.9 GPa (Figure 2a). Five new diffraction peaks begin to emerge at 4.1 GPa, which indicates the appearance of the intermediate phase, and they become stronger under further compression. Meanwhile, the main peaks of the Fm3̅m phase decrease in intensity and eventually disappear above 11.0 GPa. The transition from the intermediate phase to the Pm3̅m phase starts at 18.1 GPa and completes at 23.9 GPa. The XRD pattern at 31.3 GPa is well refined using the space group Pm3̅m (Figure 2e). These results set the lowand high-pressure boundaries for the intermediate phase of SnTe at 4.1 and 18.1 GPa, respectively. We carried out a structural search using a global minimization of free energy surfaces based on the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) methodology27,28 within the Perdew-Burke-Ernzerh (PBE) generalized gradient approximation (GGA)29 as implemented in the VASP code.30,31 The calculations (see Figure 1c) identify the Fm3m ̅ and Pm3m ̅ structure as the low- and high-pressure phases and set the phase boundaries for the intermediate phases at 5.0 and 18.3 GPa, which are in excellent agreement with the experimental results. The search identifies three orthorhombic 5353



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Table 1. Lattice Parameters and Atomic Coordinates for SnTe at 1.9 (Fm3̅m), 13.3 (Pnma, Cmcm, and GeS), and 31.3 (Pm3̅m) GPa, Respectively x

y

z

phase

parameters (Å)

atom

Fm3̅m

a = 6.250(1)

Pnma

a = 7.860(9) b = 4.226(5) c = 6.080(8) a = 4.260(8) b = 11.414(9) c = 4.208(8) a = 11.409(7) b = 4.215(7) c = 4.248(6) a = 3.473(1)

Sn1(4a) Te2(4b) Sn1(4c) Te5(4c)

0 0.5 0.602(5) 0.844(6)

0 0.5 0.25 0.75

0 0.5 0.884(9) 0.888(9)

Sn1(4c) Te3(4c)

0 0

−0.099(7) −0.357(8)

−0.25 −0.25

Sn1(4c) Te5(4c)

0.395(4) −0.359(5)

0.25 0.25

−0.027(7) −0.510(9)

Sn1(1a) Te2(1b)

0 0.5

0 0.5

0 0.5

Cmcm

GeS

Pm3̅m

coexistence of the Cmcm structure with the Pnma structure. The experimental lattice parameters and atomic coordinates of the Pnma, Cmcm, and GeS phases at 13.3 GPa derived from Rietveld refinements are listed in Table 1. The pressure− volume data for the low-, intermedeiate-, and high-pressure phases have been fitted to the third-order Birch−Murnaghan (BM) equation of state.32 The calculated pressure−volume relationship agrees well with the experimental data over the entire measured pressure range (Figure 3). The abrupt volume

suggesting that all three structures exist in a very narrow energy range with low kinetic barriers (see below) that create a highly conducive environment for their coexistence. Moreover, the close XRD patterns of the three intermediate phases mean that the contributions from the Cmcm and GeS structures are expected to be masked by the already established Pnma peaks that started to appear at lower pressure. This makes it hard to separate peaks from different phases and renders the normal refinement procedure ineffective. We resolved this issue by a detailed comparison of the experimental and simulated XRD results that reveal that the relative peak intensity, profile, and their evolution with pressure can only be fully explained by the combined contributions from coexisting phases (Figure 4). (i) First, at 4.1 GPa, there is clear

Figure 3. Experimental and theoretical pressure−volume relationship of SnTe.

collapses of about 3% and 4% around 4.1 and 18.1 GPa, respectively, indicate the first-order nature of the phase transitions from the Fm3̅m to the intermediate phases (for clarity, only data for the Pnma phase are shown) and then from the intermediate phases to the Pm3̅m phase. With B0′ fixed at 4, the fitting yields experimental (theoretical) values of B0 = 50.14 (42.59) GPa and V0 = 63.25 (65.59) Å3/f.u. for the Fm3̅m phase. The high-pressure Pnma and Pm3m ̅ phases are also fitted, yielding experimental (theoretical) values of B0 = 49.79 (43.60) GPa and V0 = 60.88 (62.63) Å3/f.u. for the Pnma phase and B0 = 60.61 (58.43) GPa and V0 = 55.88 (56.38) Å3/f.u. for the Pm3m ̅ phase. All the theoretical values of B0 and V0 for the three phases are in excellent agreement with our experimental data. Among the identified intermediate phases, the Pnma structure provides the best fit to the experimental XRD results. We emphasize, however, that the Cmcm and GeS structures can not be ruled out simply because they produce somewhat inferior fits. First, there is compelling theoretical evidence

Figure 4. Comparison of experimental and simulated XRD patterns at selected pressure points.

evidence for the coexistence of the Fm3̅m and Pnma phases. The contribution from the Fm3m ̅ phase dominates here as expected since the Pnma phase is just emerging at this pressure according to our calculations. The significance of this result is that it confirms the reliability of our theoretical calculations that correctly predict the emerging (coexisting) appearance of the Pnma phase at the beginning of the phase transition. It builds confidence in the predicted appearance of the Cmcm and GeS phases that have similar energetics and kinetics at slightly 5354



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Figure 5. Crystal geometries and transition pathways to form Pnma (a), Cmcm (b), and GeS (c) structures starting from Fm3̅m phase at 5 GPa. The Sn and Te atoms are represented as large and small spheres, respectively.

higher pressure. (ii) At 7.6 GPa, where according to our calculations the Cmcm and GeS phases should appear, we indeed see clear signs of their presence. The experimental XRD peaks at 10.3 and 11.5° that are unambiguously assigned to the Pnma phase with nearly equal intensity at 4.1 GPa have now (at 7.6 GPa) developed very differently with the peak at 11.5° becoming much stronger that the peak at 10.3°. This can be explained by the contributions from the Cmcm and GeS phases that have a strong peak at 11.5°. A similar situation occurs for the peak near 13°: its intensity is similar to that of the peak at 11.5° but much higher than that of the peak at 10.3°, and its width is obviously broadened; both of these observations are consistent with the contributions from the Cmcm and GeS phases. Furthermore, the overall shape of the main peak around 9.5° has also broadened significantly, which can also be explained by the contributions from the Cmcm and GeS phases whose peaks with slightly different position and shape lead to the convoluted experimental XRD peak. (iii) At 11.0 GPa, the Fm3m ̅ phase has largely moved away due to its now higher enthalpy, and the GeS phase is no longer viable due to its lattice instability, leaving the Pnma and Cmcm phases as the coexisting structures, and indeed, the experimental XRD is consistent with this scenario: the profile and relative intensity of all the major peaks can only be explained by the combined contributions from both phases. The most prominent features include (a) the relative intensity of the main peak at 9.7° is obviously enhanced over that of the Pnma phase, (b) the large disparity between the peak intensity at 10.6 and 11.8° can only be explained by the contribution from the Cmcm phase at 11.8°, (c) the peak at

13.1° is broad and has a higher intensity than the peak at 10.6°, which again can only be explained by the contribution from the Cmcm phase. Meanwhile, the signatures of the Pnma phase, especially the small peaks at 8.7, 9.2, and 10.6° are clearly visible. These subtle but distinctive signs clearly point to a dynamic (i.e., evolving with pressure) coexistence of the intermediate phases that produces the convoluted experimental XRD data. Since energetics alone cannot establish the stability of a crystal, we calculated the phonon dispersion of SnTe using the direct method33 as implemented in the PHONOPY code34,35 to check for its possible dynamical instability under pressure. The results show that the phonon frequency of the Fm3m ̅ structure increases with rising pressure up to the phase boundary, which suggests that the transition to the intermediate phases is not driven by phonon instability. We thus focus on the energetics (viz., results in Figure 1c) and kinetics (i.e., enthalpy barrier) of the transition. We calculated the enthalpy barriers using the climbing image nudged elastic band (CINEB) method.36−39 The crystal geometries and transition pathways to form Pnma, Cmcm, and GeS structures starting from Fm3̅m phase have been shown in Figure 5. Figure 6a shows the enthalpy change along the transformation pathway toward the Pnma, Cmcm, and GeS phases near the phase boundary at 5, 6, and 7 GPa. The enthalpy barriers are very low (62−73 meV/ SnTe at 5 GPa and 54−61 meV/SnTe at 7 GPa) and therefore easy to overcome at the experimental (room) temperature, which explains why elevated temperature is not needed in the experiment for these phase transitions. This behavior is rooted 5355



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experimental exploration of high-pressure evolution of crystal and electronic structures and phase-transition mechanisms in SnTe and other IV−VI compounds.

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AUTHOR INFORMATION

Corresponding Author

*(Q.L.) Tel: +1-702-895-1714. Fax: +1-702-895-0804. E-mail: [email protected]. (Q.C.) Tel: +86-431-8516-8346. Fax: +86-431-8516-8883. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by DOE (DE-FC52-06NA26274) at UNLV and by NSFC (No. 11074089, 51172087, 51202084, 11025418, and 91022029) and NBRP of China (2011CB808204) at Jilin University. CHESS is supported by NSF and NIH/NIGMS through NSF award DMR-0936384.

Figure 6. Calculated enthalpy change relative to the value for Fm3̅m along the pathway for the phase transformation to Pnma, Cmcm, and GeS structures at 5, 6, and 7 GPa. (b) Calculated squared phonon frequency ω2 as a function of pressure.

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in the close structural relationship between the Fm3̅m phase and the three intermediate phases as discussed above. These results establish the energetic and kinetic origin for the phase transition of SnTe at the low-pressure phase boundary. The close energetics and low kinetic barriers of the three intermediate phases also suggest the likelihood of their dynamic coexistence, viz., thermal fluctuation and equilibrium among these structural forms. Our phonon calculations at higher pressures reveal a strikingly different mechanism for the structural transition in SnTe. All three intermediate phases develop pressure-driven transverse acoustic (TA) phonon softening at high symmetry points L (0.5, 0.5, 0.5), R (0, 0.5, 0.5), and X (0, 0.5, 0) in GeS, Cmcm, and Pnma phases, respectively. In Figure 6b, the squared phonon frequency ω2 versus pressure plot clearly shows that the TA modes for GeS, Cmcm, and Pnma phases turn imaginary at 9.7, 19.5, and 21.5 GPa, respectively. We analyzed the atomic displacement along the soft-mode vibration eigenvector and found that the GeS structure spontaneously transforms to the Cmcm structure as pressure approaches 9.7 GPa. It indicates that the GeS phase may only exist briefly (even transiently given the fast descent of its TA phonon frequency) in a narrow pressure range between 7 and 9.7 GPa. Meanwhile, the atomic displacements along the soft-mode vibration eigenvectors for the Cmcm and Pnma phases do not have straightforward connections to the reconstructive transition to the Pm3̅m phase, but the TA phonon softening and the accompanying large anharmonicity that occur near the high-pressure phase boundary provide the driving force for their transition toward the Pm3̅m phase.

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4. CONCLUSIONS In summary, we have resolved the high-pressure structural evolution of SnTe using an integrated approach of angledispersive X-ray diffraction combined with first-principles structural search. We identify reversible phase transitions of B1 → orthorhombic mixed phases → B2, where the intermediate phases of Pnma, Cmcm, and GeS type dynamically coexist. The transition from the B1 to the orthorhombic phases is driven by energetics and kinetics, but further transitions to the B2 phase are induced by softening TA phonon modes. These results will likely stimulate further theoretical and 5356



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Unraveling Convoluted Structural Transitions in SnTe at High Pressure

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