ISSN 0021-3640, JETP Letters, 2017, Vol. 106, No. 10, pp. 662–666. © Pleiades Publishing, Inc., 2017. Original Russian Text © A.G. Ivanova, I.A. Troyan, D.A. Chareev, A.G. Gavriliuk, K.V. Frolov, S.S. Starchikov, A.O. Baskakov, M. Mezouar, I.S. Lyubutin, 2017, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 106, No. 10, pp. 637–641.
CONDENSED MATTER
Structural Phase Transitions and the Equation of State of SnTe at High Pressures up to 2 Mbar A. G. Ivanovaa, b, I. A. Troyana, b, c, D. A. Chareevd, A. G. Gavriliuka, b, c, K. V. Frolova, S. S. Starchikova, b, A. O. Baskakova, M. Mezouare, and I. S. Lyubutina, * a
Shubnikov Institute of Crystallography, Federal Research Center Crystallography and Photonics, Russian Academy of Sciences, Moscow, 119333 Russia b Institute for Nuclear Research, Russian Academy of Sciences, Moscow, 117312 Russia c Immanuel Kant Baltic Federal University, Kaliningrad, 236041 Russia d Institute of Experimental Mineralogy, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia e European Synchrotron Radiation Facility, CS40220, F-38043 Grenoble, France *e-mail:
[email protected] Received October 12, 2017
Synchrotron X-ray diffraction studies of the structure of SnTe have been performed at room temperature and high pressures under the conditions of quasihydrostatic compression up to 193.5 GPa created in diamond anvil cells. Two structural phase transitions have been detected at P ≈ 3 and 23 GPa. The first phase transition is accompanied by a stepwise decrease in the volume of the unit cell by 4% because of the orthorhombic distortion of the initial SnTe-B1 cubic structure of the NaCl type. It has been found that two intermediate rhombic phases of SnTe with the space groups Cmcm and Pnma coexist in the pressure range of 3–23 GPa. The second phase transition at 23 GPa occurs from the intermediate rhombic modification to the SnTe-B2 cubic phase with the CsCl structure type. This phase transition is accompanied by an abrupt decrease in the volume of the unit cell by 8%. The pressure dependence of the volumes per formula unit at room temperature has been determined. DOI: 10.1134/S0021364017220106
1. INTRODUCTION The properties of tin telluride SnTe at atmospheric pressures are studied in order to use this material in thermoelectric power sources. It was experimentally confirmed recently that tin telluride belongs to the class of crystal topological insulators [1–4]. According to the theoretical calculations [5] and experimental studies [6], SnTe undergoes a transition to a superconducting state at a critical temperature of 7.16 K under pressure. However, to reveal a mechanism of superconductivity and to find new superconducting phases, it is necessary to study the crystal structure of SnTe in a wide pressure range. Experimental studies of the structure and properties of SnTe at pressures up to 50 GPa were reported in [1, 3, 7–10]. In this work, we report the results of X-ray diffraction study of phase transitions in SnTe at pressures up to 193.5 GPa. 2. EXPERIMENTAL METHOD The SnTe polycrystalline samples were synthesized by the solid-phase reaction method. Initial Sn and Te powders were mixed in stoichiometric proportions, were pressed into bullets, and were sealed into evacu-
ated quartz ampoules. The ampoules were heated to 900°C at a rate of 10°C/min, were left under these conditions for 24 h, were then cooled to 600°C at a rate of 3°C/min, were left for 120 h, and were finally cooled to room temperature in 6 h. The synthesized samples were preliminarily studied by the X-ray diffraction method at atmospheric pressure and room temperature at the Structural Material Science station, Kurchatov Synchrotron Radiation Source (National Research Center Kurchatov Institute). Twodimensional X-ray diffraction images were recorded at radiation with the wavelength λ = 0.7702 Å using a FujiFilm Image Plate two-dimensional detector. Twodimensional diffraction patterns were recalculated to the one-dimensional form with the use of the Dioptas program [11]. It was confirmed that the initial compound SnTe has the NaCl (B1) crystal structure. The crystallographic parameters were refined by the Rietveld method in the JANA2006 software package [12]. Studies at high pressures were performed in diamond anvil cells. For these studies, the SnTe powder ground to a fine-powder state was pressed into plates 2–4 μm thick. The thickness of plates in the process of their compression between diamond anvils was con-
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Fig. 1. (Color online) (а) Rietveld refinement of the SnTe-B1 structure (NaCl type) of the initial synthesized sample and (b) the image of the SnTe sample in the diamond anvil cell at an initial pressure of 0.15 GPa.
trolled by interference of light transmitted between the surfaces of anvils. The experiment was performed with bevel anvils (anvils with an additional bevel) with the diameter of the working surface (culet) ~50 μm and the outer diameter ~300 μm and tungsten gaskets were used. The 15-μm sample plate was placed in the central hole of a gasket with a diameter of 30 μm. A chemically pure NaCl powder was used as a pressure-transmitting medium in order to ensure quasihydrostatic conditions of compression of the sample at ultrahigh megabar pressures. Pressures in the range P < 27 GPa were determined from the equation of state of NaCl-B1 [13], whereas pressures in the range P > 27 GPa were determined from the equation of state of NaCl-B2 [14]. X-ray diffraction patterns in the pressure range of 0–193.5 GPa were recorded on the ID27 beamline at the European Synchrotron Radiation Facility (ESRF, Grenoble, France). We used a focused (1.7 × 2.3 -μm) monochromatic beam (33 keV, λ = 0.3738 Å). A MAR CCD 165 two-dimensional detector was placed at a distance of 215.67 mm from the sample. The exposure time was 30–60 s. Two-dimensional X-ray diffraction patterns were analyzed and integrated into one-dimensional X-ray diffraction patterns in the Dioptas software package [11]. The full-profile refinement of the parameters of unit cells in the entire studied pressure range was performed by the Le Bail method [15] in the JANA2006 software package [12]. 3. EXPERIMENTAL RESULTS AND THEIR DISCUSSION We found that the synthesized SnTe sample at atmospheric pressure has the NaCl-B1 cubic structure with JETP LETTERS
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the parameters a = 6.3204(1) Å, V = 252.484 Å3 (space group Fm3m , Z = 4 ) (Fig. 1а). The image of the sample in the diamond anvil cell at an initial pressure of 0.15 GPa is shown in Fig. 1b.
Figure 2 shows the evolution of X-ray diffraction patterns of SnTe at pressures up to 193.5 GPa. At P = 2.9 GPa, in addition to reflections of the cubic phase SnTe-B1, numerous broadened reflections of the mixture of rhombic phases SnTe-Cmcm and SnTe-Pnma appear. In the pressure range of 13–20 GPa, the intensities of reflections are further broadened and redistributed (see Fig. 2). A change in the volumes of unit cells in this pressure range is probably due to several competing mechanisms of the structural rearrangements. As was described in [10], the cubic phase SnTeB1 can be transformed to the bcc phase SnTe-B2 with the CsCl structure through the mixture of intermediate rhombic phases. According to [10], the phase transition to the SnTe-B2 structure occurs at P = 18.1 GPa, but this transition was not observed up to 25 GPa in previous works. The crystal structures of the cubic SnTe-B1 and rhombic SnTe-Pnma phases are shown in Figs. 3a and 3b, respectively. The phase SnTe-Cmcm with the GeS structure was previously observed in [7, 9, 10] and the phase SnTe-Pnma was observed in [10]. According to our X-ray data, the formation of the cubic phase SnTe-B2 occurs at pressures above 20 GPa. However, the accurate determination of this phase transition pressure of the SnTe sample compressed in the NaCl medium is complicated because of the overlapping of the most intense (002) reflection of NaCl-B1 and (101) reflection of SnTe-B2 in the pressure range of 20–27 GPa.
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Fig. 2. (Color online) Evolution of X-ray diffraction patterns of SnTe in the pressure range of 0.15–193.5 GPa.
Fig. 3. (Color online) Crystal structures of polymorphic modifications of SnTe in the pressure range of 0–193.5 GPa: (а) SnTe-B1 phase with the NaCl structure type (0–3 GPa); (b) structure of the intermediate rhombic phases Cmcm and Pnma with different degrees of distortion (3–23 GPa); (c) SnTe-B2 phase with the CsCl structure type.
Figure 4 shows two-dimensional diffraction patterns in the transition regions at 20 GPa (Fig. 4а) and 23.2 GPa (Fig. 4b). At 20 GPa, a narrow and weak (002) reflection of NaCl-B1 at the angle 2Θ ≈ 8.5° (see Fig. 4а) indicates the absence of the (101) reflection of the phase SnTe-B2 at this pressure.
At 23.2 GPa (see Fig. 4b), the intensity of the reflection at the angle 2Θ ≈ 8.5° increases significantly because of the appearance of the (101) reflection of the phase SnTe-B2 with the CsCl structure. The rearrangement of SnTe crystal structure at 23 GPa is also confirmed by the appearance of diffuse traces JETP LETTERS
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where V0 is the volume of the unit cell at atmospheric pressure, B0 is the bulk modulus, and B' is the pressure derivative of the bulk modulus B0 . For the SnTe-B1 phase, fitted parameters are: B0 = (54 ± 5) GPa, B' = 4 (fixed), and V0 = 63.12 Å3 (the volume of the unit cell per formula unit). The pressure of the first phase transition is estimated as ≈ 2.8 GPa. The experimental dependence V (P ) in the pressure range 3 GPa < P < 23 GPa was approximated by the modified Birch–Murnaghan equation of state in the form
B
B
Fig. 4. (Color online) Diffraction patterns of the SnTe sample in the diamond anvil cell (a) before the phase transition at 20 GPa and (b) after the phase transition to the B2 phase at 23.2 GPa.
on the diffraction pattern near the (101) reflection of the phase SnTe-B2. The dependence V (P ) in the pressure range P < 3 GPa was approximated by the Birch–Murnaghan equation of state (Fig. 5) −35
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⎛ ⎛V ⎞ ⎞ ⎜1 − ⎜ ⎟ ⎟ ⎜ ⎝V0 ⎠ ⎟ ⎝ ⎠ 2 ⎡3 ⎛ ⎛ V ⎞− 3 ⎞ ⎤ × ⎢ (B' − 4) ⎜1 − ⎜ ⎟ ⎟ − 1⎥ , ⎜ ⎟ ⎣⎢4 ⎝ ⎝V0 ⎠ ⎠ ⎥⎦ ⎛ ⎞ P = 3 B0 ⎜ V ⎟ 2 ⎝V0 ⎠
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⎛ ⎞ P − 2.8 GPa = 3 B3 ⎜ V ⎟ 2 ⎝V3 ⎠
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⎛ ⎛ V ⎞− 3 ⎞ ⎜1 − ⎜ ⎟ ⎟ ⎜ ⎝V3 ⎠ ⎟ ⎝ ⎠ 2
⎡ ⎛ ⎛ ⎞− 3 ⎞ ⎤ × ⎢3 (B3' − 4) ⎜1 − ⎜ V ⎟ ⎟ − 1⎥ , ⎜ ⎝V3 ⎠ ⎟ ⎥ ⎢⎣4 ⎝ ⎠ ⎦ 2
where B3 = (61.5 ± 2.3) GPa, B3' = 5.14 , and V3 = 57.8 Å3 are the parameters obtained above the structural phase transition at 3 GPa. It is found that the volume of the unit cell per formula unit at the first phase transition at 3 GPa decreases by ~4%. The experimental dependence V (P ) in the pressure range 23 GPa < P < 190 GPa was approximated by the
B ' %
% B ' '
Fig. 5. (Color online) Pressure dependence of the volume V of the unit cell per formula unit (Z) in SnTe. Experimental points (circles for SnTe-B1, diamonds for the intermediate rhombic phases Pnma and Cmcm, and squares for SnTe-B2) are fitted by the Birch– Murnaghan equations of state. The first transition of SnTe from B1 to the intermediate orthorhombic phases (Pnma + Cmcm) was found to be at about 2.8 GPa with the volume drop by 4%. At the onset second transition to the cubic SnTe-B2 phase at 23 GPa, the volume drops by 8%. JETP LETTERS
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modified Birch–Murnaghan equation of state in the form
⎛ ⎛ V ⎞− 3 ⎞ ⎜1 − ⎜ ⎟ ⎟ ⎜ ⎝V23 ⎠ ⎟ ⎝ ⎠ (3) − 32 ⎡3 ⎛ ⎛V ⎞ ⎞ ⎤ ' − 4) ⎜1 − ⎜ ⎟ ⎟ − 1⎥ , × ⎢ (B23 ⎜ ⎝V23 ⎠ ⎟ ⎥ ⎢⎣4 ⎝ ⎠ ⎦ ' = 4.35, and V23 = where B23 = (123 ± 3.1) GPa, B23 43.5 Å3 are the parameters obtained above the structural phase transition at 23 GPa. It is found that the volume of the unit cell per formula unit at the second phase transition at 23 GPa drops by ~8%. ⎛ ⎞ P − 23 GPa = 3 B23 ⎜ V ⎟ 2 ⎝V23 ⎠
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2
4. CONCLUSIONS The phase composition of the promising superconductor SnTe has been studied at ultrahigh pressures up to 193.5 GPa. Under the conditions of quasi-hydrostatic compression, two structural phase transitions have been revealed at 3 and 23 GPa. The first phase transition is a first-order phase transition with an abrupt decrease in the volume of the unit cell by 4% caused by the orthorhombic distortion of the initial SnTe-B1 cubic structure. After the first phase transition, the compound SnTe has a mixed phase state consisting of several phases, which requires additional indepth analysis. In the first approximation, the structural state of SnTe in the pressure range of 3–23 GPa can be considered as coexistence of two intermediate rhombic phases of SnTe with the space groups Cmcm and Pnma. The second phase transition in SnTe at 23 GPa occurs from the mixture of intermediate rhombic structures to the SnTe-B2 cubic phase with the CsCl structure type. This phase transition is also a first-order phase transition with the drop of the unit cell volume by 8%. The equations of state of all three phases have been constructed in the Birch–Murnaghan form and their parameters have been obtained. The results obtained in this work are very important for the interpretation of future experimental studies of the electronic properties of SnTe and for the search for a possible superconducting state.
This work was supported by the Ministry of Education and Science of the Russian Federation (contract no. 14.616.21.0068). The sample mounts were prepared using the facilities of the Center for Collective Usage “Accelerator Center for Neutron Research of the Structure of Matter and Nuclear Medicine,” Institute for Nuclear Research, Russian Academy of Sciences. REFERENCES 1. Y. Tanaka, Z. Ren, T. Sato, K. Nakayama, S. Souma, T. Takahashi, K. Segawa, and Y. Ando, Nat. Phys. 8, 800 (2012). 2. T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nat. Commun. 3, 982 (2012). 3. L. Fu, Phys. Rev. Lett. 106, 106802 (2011). 4. R.-J. Slager, A. Mesaros, V. Juričić, and J. Zaanen, Nat. Phys. 9, 98 (2012). 5. D. Zhou, Q. Li, Y. Ma, Q. Cui, and C. Chen, J. Phys. Chem. C 117, 12266 (2013). 6. Y. A. Timofeev, B. V. Vinogradov, E. N. Yakovlev, E. V. Kapitanov, and R. O. Kyzyan, Sov. Phys. Solid State 24, 1780 (1982). 7. A. N. Mariano and K. L. Chopra, Appl. Phys. Lett. 10, 282 (1967). 8. R. A. Hein, Phys. Lett. 23, 435 (1966). 9. J. A. Kafalas and A. N. Mariano, Science 143, 952 (1964). 10. D. Zhou, Q. Li, Y. Ma, Q. Cui, and C. Chen, J. Phys. Chem. C 117, 5352 (2013). 11. C. Prescher and V. B. Prakapenka, High Press. Res. 35, 223 (2015). 12. V. Petřiček, M. Dušek, and L. Palatinus, Z. Kristallogr.—Cryst. Mater. 229, 345 (2014). 13. P. I. Dorogokupets and A. Dewaele, High Press. Res. 27, 431 (2007). 14. Y. Fei, A. Ricolleau, M. Frank, K. Mibe, G. Shen, and V. Prakapenka, Proc. Natl. Acad. Sci. U.S.A. 104, 9182 (2007). 15. A. le Bail, Powder Diffract. 20, 316 (2005).
Translated by R. Tyapaev
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