10-Fold Structure in Bismuth ... - ACS Publications

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Stabilization of 9/10-Fold Structure in Bismuth Selenide at High Pressures Guangtao Liu,† Li Zhu,† Yanmei Ma,*,†,‡ Chuanlong Lin,§ Jing Liu,§ and Yanming Ma*,† †

State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China Department of Agronomy, Jilin University, Changchun 130062, China § Beijing Synchrotron Radiation Laboratory, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, China ‡

ABSTRACT: We report joint theoretical and experimental research on the high-pressure structures of bismuth selenide (Bi2Se3) up to 50 GPa. Our first-principles structure prediction via calypso methodology meets our high-pressure X-ray diffraction experiments performed in diamond anvil cell. We established that the ambient-pressure rhombohedral phase transforms to a monoclinic C2/m structure at 9.8 GPa, and then to a monoclinic C2/c structure at 12.4 GPa. Above 22.1 GPa, we were able to identify that Bi2Se3 develops into a novel 9/10-fold structure, which was not taken by its other family members Bi2Te3 and Sb2Te3. The large differences in atomic core and electronegativity of Bi and Se are suggested to be the physical origin of the stabilization of this 9/10-fold structure. Our research work allows us to reveal a rich chemistry of Bi in the formation of 6, 7, 8, and 9/10-fold covalent bond with Se at elevated pressures.

1. INTRODUCTION Bismuth selenide (Bi2Se3), a binary semiconductor with a narrow band gap formed between group V and VI elements, has attracted great attention due to its applications in thermoelectric devices.1 It has been established that Bi2Se3 crystallizes in a rhombohedral structure (phase I, space group: R3̅m, Z = 3)2 at ambient conditions and possesses high electrical conductivity and high thermal conductivity, similar to its other family members (e.g., Bi2Te33 and Sb2Te34). The ambient-pressure R3̅m structure contains alternating layers of Bi and Se atoms with the stacking order of Bi−Se−Bi−Se−Bi, and form the so-called quintuple layers linked by van der Waals forces. Intriguingly, Bi2Se3 has been found to be one of the simplest three-dimensional topological insulators.5,6 It is well-known that pressure can efficiently modify the electronic and atomic structures of materials, leading to the formation of novel materials with unusual physical properties. It has been verified that the thermoelectric properties of Bi2Te3, Bi2Se3, and Sb2Te3 can be improved under high pressures.7−10 High-pressure X-ray diffraction (XRD) experiments have established the pressure-induced superconductivities11−14 by accompanying structural phase transitions9,15−17 in Bi2Te3. The high pressure structures of Bi2Te3 remain unsolved for decades. And only recently, it was solved by employing a first-principles structure prediction technique based on CALYPSO algorithm.18−20 With increasing pressure, Bi2Te3 was found to transform in turn into two monoclinic high-pressure C2/m (βBi2Te3) and C2/c (γ-Bi2Te3) structures at 8.2 and 13.4 GPa, respectively. Above 25 GPa, the continuously monoclinic distortions lead to the eventual formation of substitutional alloy.21,22 Soon after, the similar phase transitions were observed in Sb2Te3.23−25 Raman studies observed pressure© 2013 American Chemical Society

induced electronic topological transitions around 3.5 GPa and three structural phase transitions at elevated pressures.25 Our high-pressure XRD experiments in combination with firstprinciples calculations24 demonstrated that Sb2Te3 adopts the same phase transition sequence with Bi2Te3. Another highpressure XRD experiment confirmed the formation of β-Bi2Te3 phase and the substitutional alloy phase, but a discrepancy was proposed on the second high-pressure structure, where a type of C2/m disordered substitutional alloy of Sb and Te atoms was proposed.23 Though Bi2Te3 and Sb2Te3 were extensively studied, Bi2Se3 remains less explored. The only known high-pressure research work reported the structural and vibrational properties of Bi2Se325 up to 30 GPa. Their XRD and Raman experiments confirmed that Bi2Se3 transforms to β-Bi2Te3 phase at 14.4 GPa and then to the other two phases at 20 and 28 GPa, respectively. These two additional phases remain unknown. Here, we have performed a joint theoretical and experimental research to explore the high pressure structures of Bi2Se3 up to 50 GPa. The theoretical research involves using our developed CALYPSO methodology on structure prediction, unbiased by any prior known structural information. We aimed to establish the room-temperature isothermal high-pressure phase diagram of Bi2Se3. Surprisingly, we uncovered for the first time that in contrast to that in Bi2Te3 and Sb2Te3, a 9/10-fold structure was stabilized in Bi2Se3 above 22.1 GPa. Received: March 18, 2013 Revised: April 23, 2013 Published: April 23, 2013 10045

dx.doi.org/10.1021/jp402697t | J. Phys. Chem. C 2013, 117, 10045−10050

The Journal of Physical Chemistry C

Article

Figure 1. Structures of (a) Pnma phase and (b) 9/10-fold phase in Bi2Se3. Large and small spheres represent Bi and Se atoms, respectively. Large black and brown spheres indicate Bi1 and Bi2 atoms, respectively.

2. COMPUTATIONAL AND EXPERIMENTAL DETAILS We performed structure predictions through a global minimization of free energy surfaces merging ab initio totalenergy calculations via CALYPSO (crystal structure analysis by particle swarm optimization) methodology.18−20 Our method unbiased by any known structural information has been benchmarked on various known systems with various chemical bonds and has several successful predictions on high-pressure structures.26−30 The underlying ab initio structural relaxations were carried out using density functional theory within the Perdew−Burke−Ernzerh of exchange-correlation as implemented in the Vienna Ab Initio Simulation Package (VASP) code.31 The all electron projector augmented wave32,33 method was adopted with 6s26p3 and 4s24p4 treated as valence electrons for Bi and Se, respectively. The cutoff energy of 300 eV and appropriate Monkhorst−Pack k-meshes were chosen to ensure that all the enthalpy calculations were well converged to less than 2 meV/atom. The phonon calculations were carried out by using a finite displacement approach34 through the PHONOPY code.35 Studies on commercially available Bi2Se3 powder (Alfa Aesar Products, purity 99.99%) were performed using symmetric diamond anvil cell utilizing 400 μm anvil culet. A T301 stainless steel gasket of 250 μm was preindented to thickness of about 80 μm by the diamonds. The sample was loaded in a 120 μm diameter cavity, and a 4:1 mixture of methanol−ethanol was used as pressure transmitting medium. Pressure was determined by ruby fluorescence.36 We performed two different high pressure angle dispersive XRD experiments. The first was carried out at beamline X17B3 of the National Synchrotron Light Source at Brookhaven, using synchrotron source λ = 0.4066 Å. The second was performed at the 4W2 High Pressure Station of Beijing Synchrotron Radiation Facility (BSRF) with λ = 0.6199 Å. The Bragg diffraction rings were collected using an imaging plate detector. The acquisition time was 200 or 300 s. The twodimensional diffraction images were analyzed with the FIT2D software,37 yielding one-dimensional intensity versus diffraction angle 2θ patterns. The sample detector distance and geometric parameters were calibrated using a CeO2 standard from NIST. High pressure synchrotron X-ray patterns were fitted by Rietveld profile matching through the GSAS+EXPGUI programs.38,39 For every refinement cycle, the fractional coordinates, scale factors, background parameters, isotropic

thermal parameters, profile functions, and lattice parameters were optimized.

3. RESULTS AND DISCUSSION Structure predictions using CALYPSO code18−20 with simulation cell sizes up to 4 formula units (f.u.) were performed in the pressure range 0−50 GPa. With the only given information of chemical compositions, we were able to correctly reproduce the experimental ambient-pressure rhombohedral R3̅m structure, validating our method adopted here. At 15 GPa, besides the previously known β- and γ-Bi2Te3 structures (hereafter denoted as phases II and III), we predicted an orthorhombic structure (space group Pnma), having the lowest energy. This orthorhombic structure has a 7-fold coordination formed by BiSe7 octahedrons (Figure 1a), sharing the same building blocks with phase II. At 30 GPa, an intriguing C2/m structure (denoted as phase IV) was found as the most stable phase. In this high-pressure structure, Bi ions are in the center of approximate BiSe9 enneahedrons or BiSe10 dodecahedrons and form 9/10-fold chemical bonds with Se (Figure 1b). The structural information of all predicted phases is listed in Table 1. Our enthalpy calculations (Figure 2) confirmed the phase stabilities of our predicted structures. Below 6 GPa, the ambient-pressure R3̅m structure is the most stable, which is in good agreement with experiment. Above 6 GPa, the Pnma phase is more stable than any other phases in a large pressure range up to 24.8 GPa. This fact is dramatically different from the situations in Bi2Te3 and Sb2Te3, where such a structure is not stable at all. It is important to point out that our calculated result about enthalpy is robust with respect to various approximations. Particularly, we have estimated the entropic contribution at 300 K by calculating the phonon frequencies based on quasiharmonic approximation.35 At 20 GPa, the resultant vibrational energies are −0.225 eV/f.u. and −0.227 eV/f.u for Pnma phase and phase II, respectively. Their energy difference is extremely small at 2 meV/f.u.. Thus, the consideration of temperature effect cannot revise our conclusion on phase transition sequences. In order to confirm the theoretically predicted phase transitions under high pressures, we have subsequently performed high-pressure XRD experiments on Bi2Se3 in pressure steps of 1−2 GPa in two different runs. The first and second supplementary experiments were performed up to 30.1 and 50.3 GPa. The selected XRD patterns are shown in 10046



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Table 1. Lattice Parameters and Atomic Positions of Bi2Se3 in Different Structures lattice params

atoms

x

y

z

Bi1 (4c) Bi2 (4c) Se1 (4c) Se2 (4c) Se3 (4c)

0.1828 0.0199 0.2761 0.0550 0.3692

0.25 0.25 0.25 0.75 0.75

0.5336 0.1757 0.2191 0.3726 0.4371

Bi1 (4i) Bi2 (4i) Se1 (4i) Se2 (4i) Se3 (4i)

0.2776 0.4989 0.0631 0.8583 0.6956

0 0 0 0 0

0.3000 0.2748 0.8924 0.4957 0.1249

Bi1 (8f) Se1(8f) Se2(4e)

0.2390 0.0680 0

0.0750 0.8029 0.3735

0.3165 0.4520 0.25

Bi1 (4i) Bi2 (4i) Se1 (4i) Se2 (4i) Se3 (2c) Se3 (2a)

0.4038 0.1891 0.3969 0.7941 0 0

0 0 0 0 0 0

0.8605 0.6879 0.3839 0.8169 0.5 0

Pnma 20 GPa a = 10.916 Å b = 3.860 Å c = 10.522 Å C2/m 10 GPa a = 14.261 Å b = 3.897 Å c = 16.462 Å β = 148.290° C2/c 15 GPa a = 9.458 Å b = 7.024 Å c = 9.703 Å β = 135.348° C2/m 30 GPa a = 14.454 Å b = 4.825 Å c = 5.731 Å β = 105.236°

Figure 3. XRD patterns collected at various pressures for Bi2Se3 with two kinds of wavelength (λ = 0.4066 Å and 0.6199 Å). Background in XRD patterns was subtracted. The peaks marked as asterisks, solid circles, and solid triangles are the diffraction peaks for new phases II, III, and IV.

formation of phase III. Note that phase III can only stabilize in a narrow pressure range and coexist with either phase II or phase IV in the whole pressure range. Upon further compression, diffraction peaks denoted by solid triangles at 22.1 and 25.3 GPa appear, suggesting the formation of a new high-pressure phase IV. This phase remains stable with uploading pressure up to 50.3 GPa. After decompression, we observed the patterns of the ambient-pressure rhombohedral structure again, which suggests that the transition is reversible. We refined the observed XRD data by using our predicted structures. It is found that the experimental XRD patterns of phases II and III can be indexed to β- and γ-Bi2Te3 structures (Figure 4a,b), respectively. However, it is noteworthy that theory and experiment here have a serious discrepancy. βBi2Te3 structure is never stable with respect to Pnma structure in our calculation. In our two different high pressure experiments, we did not find any sign on the formation of the predicted Pnma phase. Moreover, our results on β-Bi2Te3 structure of phase II are in excellent agreement with the previous work.25 The only plausible explanation for this discrepancy is that the transformation into Pnma phase is kinetically hindered. High temperature conditions might be greatly helpful to synthesize such an intriguing Pnma phase. In fact, by a careful survey of the literature, we did find an experimental report on the synthesis of a high-temperature orthorhombic Pnma structure of Bi2Se3 by Atabaeva et al.40

Figure 2. Enthalpy curves (relative to ambient-pressure phase I) for various predicted structures as a function of pressure. Enthalpies are given per formula unit.

Figure 3. Three structural phase transitions were clearly observed with increasing pressure. At ambient pressure, all diffraction peaks can be indexed to the ambient-pressure rhombohedral phase I with lattice parameters of a = 4.221 Å and c = 28.659 Å by the Rietveld refinement. No obvious change in the diffraction patterns was observed at low pressures. However, with pressure increasing up to 9.8 GPa, the diffraction pattern suddenly experienced a large change with the emergence of new peaks as marked by asterisks, signifying the formation of high-pressure phase II. These peaks increase gradually in intensity, and those peaks for phase I disappear with pressure up to 11.5 GPa. When pressure reaches 12.4 GPa, new Bragg peaks marked as solid circles emerge, indicating the 10047



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Figure 5. (a) Lattice parameters and (b) volumes as a function of pressure for different phases. The symbols are experimental data. The solid lines are theoretical results.

Å), Sb (1.45 Å), and Te atoms (1.40 Å) are similar at ambient conditions.41 With increasing pressure, the atomic radii in Bi2Te3 and Sb2Te3 become approximately equal,21 making it possible to be substitutional alloy at high pressures (Hume− Rothery rules42). Whereas Bi is much heavier than Se, the atomic radii of Bi and Se (1.15 Å)41 atoms are quite different even under high pressures; this might be a significant factor to hinder the formation of a substitutional alloy in Bi2Se3. On the other hand, according to the Pauling scale, Bi, Sb, and Te with similar electronegativity values of 2.02, 2.05, and 2.10, respectively, are favorable to form substitutional alloy in Bi2Te3 and Sb2Te3. However, the electronegativity value of Se is much larger (2.55), even approaching typical nonmetallic sulfur (2.58). More electrons of Bi are thus expected to be transferring to Se. As a result, the stabilization of ordered 9/10fold structure is preferable, rather than the formation of disordered substitutional alloy.

Figure 4. Diffraction profiles of high-pressure phases of Bi2Se3 at (a) 11.5 GPa, (b) 20.1 GPa, and (c) 41.0 GPa, respectively. The solid lines and open circles represent the Rietveld fits and observed data, respectively, and the solid lines at the bottom are the residual intensities. The vertical bars indicate the peak positions. Diffraction patterns in part b are a mixture of phases II and III, whose XRD peaks are indicated by the first and second row vertical bars, respectively.

Though it is not conclusive whether they have synthesized the same Pnma as we have predicted, the measured lattice parameters and crystal symmetry of their phase are rather similar with our theoretical results. It is worth mentioning that our predicted 9/10-fold C2/m structure was previously reported by us for Bi2Te3.21 However, this structure cannot account for the experimental patterns of Bi2Te3, the same as Sb2Te3.23,24 Here, the experimental XRD patterns of phase IV in Bi2Se3 are much more complex than those in Bi2Te3 and Sb2Te3. We failed to apply the structural model of disordered bcc-like alloy to the structural solution of phase IV of Bi2Se3. It is remarkable that once the 9/10-fold C2/ m structure was adopted as the fitting mode to perform the Rietveld refinement on the observed XRD data, an excellent fitting is evidenced as shown in Figure 4c. This strongly supports the correctness of 9/10-fold C2/m structure for phase IV. Figure 5a,b shows the experimental and theoretical lattice parameters and volumes as a function of pressures for phases I, II, III, and IV, respectively. There is excellent agreement between the theoretical and experimental data. It is obvious that the phase transitions can be characterized by first-order transitions accompanying 4% and 6% volume drops in the phase transitions, respectively. For Bi2Te3, Sb2Te3 and Bi2Se3, they share the common coordination numbers of six, seven, and eight in phases I, II, and III, respectively. The observation of 9/10-fold phase IV in Bi2Se3 is quite unexpected, because it does not follow the sequence of phase transitions in Bi2Te3 and Sb2Te3 at high pressures. We attribute this discrepancy to the differences in atomic size and electronegativity. The atomic radii of Bi (1.60

4. CONCLUSIONS In summary, by making use of CALYPSO technique on structure prediction and high pressure XRD experiments, we have solved two unknown high-pressure phases III and IV of Bi2Se3. Besides, we attribute our predicted Pnma structure to a high-temperature experimental phase. The particular importance in our study is the first demonstration of the formation of the 9/10-fold structure in Bi2Se3. The discovery of this novel 9/ 10-fold structure provides the first structural prototype in A2B3type materials and allows us to identify the high chemical ability of Bi in formation of 6, 7, 8, and 9/10 chemical bond with Se at elevated pressures. This work represents a significant step forward in understanding the high-pressure behaviors of Bi2Se3. We hope that our study will contribute to other research on high-pressure structures of A2B3-type materials.

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AUTHOR INFORMATION

Corresponding Author

*Contact information for Yanming Ma: e-mail [email protected]. cn, phone 86-431-85168276, fax 86-431-85168276. For Yanmei Ma: e-mail [email protected], phone 86-431-87836474, fax 86431-87836474. Notes

The authors declare no competing financial interest. 10048



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ACKNOWLEDGMENTS The authors acknowledge the funding supports from China 973 Program under Grant 2011CB808200; National Natural Science Foundation of China under Grants 11274136, 11025418, and 91022029; 2012 Changjiang Scholar of Ministry of Education, Changjiang Scholar and Innovative Research Team in University (No. IRT1132); and open project (No. 201006) of SKLSHM and basic research funding (No. 450060323071) in Jilin University. Part of the calculations were performed in high performance computing center of Jilin University. Part of this experimental work was performed at 4W2 beamline, Beijing Synchrotron Radiation Facility (BSRF), which is supported by Chinese Academy of Sciences (No. KJCX2-SW-N20, KJCX2-SWN03).

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