Predicted bismuth–tellurium under high pressures

ABSTRACT The high-pressure structures of the Bi–Te system were theoretically predicted by this work, which also clarified some ambiguous structures. Using variable-composition evolutionary algorithms, the crystal structures of the Bi–Te system at high pressures were searched, and one new stable structure BiTe-P-1 was proposed. BiTe-P-1 was discovered to be the experiment's undetected structure by comparing with the experimental XRD. Thereafter, the pressure-composition diagram of the Bi–Te system was calculated using the first-principles method. In contrast to previous reports, Bi2Te3 only had two high-pressure structures, R-3m and C2/m, and it would decompose into BiTe and Te at 13.4 GPa. The calculation of quasi-harmonic approximation shown that the BCC alloy phase of Bi2Te3 only could exist stably under high temperature and high pressure. For BiTe, The phase transition route was P-3m1 → P-1 → Pm-3m, and the transition pressure was 7.5 and 11.2 GPa, respectively.

discovered that Bi 2 Se 3 only had three stable high-pressure structures, R-3m, C2/m, and BCC alloy or I4/mmm, and that there was no C2/c phase.
Other compounds in the Bi-Te system exist in addition to Bi 2 Te 3 , including Bi 4 Te 3 , Bi 8 Te 9 , and BiTe. Under normal pressure, all of these compounds have a hexagonal layered structure. They do have high-pressure structures, although there aren't many reports on them. According to Loa I [20], who studied the cubic Bi-Te alloy phases at high pressures, the pressure required to generate the BCC alloy phase dropped as the Bi component was increased. Bi 4 Te 3 's high-pressure structures were explored by Jeffries J [21], who discovered that at 6.4 GPa and 12.6 GPa, respectively, the structure changed into the C2/m and BCC alloy phases. The space group and atom count for C2/m were the same as those for Bi-II [22]. Zhang JL [23] conducted an experimental search for BiTe high-pressure structures and discovered that ambient structure P-3m1 transitioned to phases II, III, and IV (BCC alloy) at pressures of around 8, 14, and 14.4 GPa, respectively. Crystal structures of Phase II and III, however, were still unknown. Then there are the unresolved high-pressure structures of the Bi-Te system or the ongoing debates.
Materials may synthesize or decompose at extreme pressure, as well as produce new chemicals and stable structures [24,25]. In order to thoroughly search the high-pressure structures of the Bi-Te system, this work used variable-composition evolutionary algorithms, which could simultaneously search many components and their structures while taking into account the potential responses of the Bi-Te system. As a result, it has distinct advantages over experimental and theoretical studies [9][10][11][13][14][15][16][17][18][19][20][21][22][23] that simply took into account one aspect of the Bi-Te system.

Computational methods
In the current paper, the first-principles method and the variable-composition evolutionary algorithms implemented in USPEX [26][27][28] were used to search for the crystal structures of the Bi-Te system at 0, 2, 5, 8, 10, 15, and 20 GPa, respectively. Enthalpy was selected as the fitness function in these predictions, and each generated Bi-Te structure has up to 20 atoms in the primitive cell. The first generation of the structure searches consists of 120 randomly generated structures, and each succeeding generation contains 100 structures that were generated, respectively, by heredity (40%) softmutation (20%) lattice mutation (10%) transmutation (10%), and random symmetric (20%) generator operations. The Vienna ab initio simulation package (VASP) [29] was used to carry out first-principles structural optimization and total energy calculation for each candidate structure produced by USPEX [26][27][28]. The convex-hull construction then predicted the stable structures (a compound was thermodynamically stable if the enthalpy of its decomposition into any other compounds was positive). The USPEX [26][27][28] search was terminated when the stable structures did not change for 20 generations or 50 generations had been searched.
Then for the stable high-pressure structures of Bi-Te system, geometric optimization was done again with more accuracy parameter based on density functional theory within the Perdew-Burke-Ernzerhof (PBE) [30] generalized gradient approximation (GGA) functional as implemented in VASP [29]. The all-electron projector-augmented wave (PAW) [31] method was used. The plane-wave kinetic-energy cutoff of 900 eV and the k-point mesh resolution in reciprocal space of 2π × 0.02 Å −1 was used. The geometry optimization was performed by minimizing the total energy together with the force on atoms and the stress of the lattice. The convergence criteria for energy and force were 10 −8 eV and 10 −3 eV/Å, respectively. Phonon spectra dispersion was calculated by DFPT method implemented in Phonopy code [32]. Crystal structures and synchrotron radiation X-ray diffraction patterns (XRD) were simulated by VESTA [33].

Results and discussion
USPEX [26][27][28] was used in this study to search the high-pressure structures of the Bi-Te system. One new structure, BiTe-P-1, was observed in addition to the experimentally reported structures [11,13,23,[34][35][36][37][38][39][40][41][42][43]. The enthalpy convex-hulls from 0 to 20 GPa are shown in Figure 1(a,b). The following equation was used to determine the enthalpy of formation of Bi x Te y : As evident from Figure 1(a), only Bi 2 Te 3 was a stable structure when the pressure was higher than 5 GPa, while BiTe, Bi 2 Te 3 , Bi 4 Te 3 , and Bi 8 Te 9 were all stable when the pressure was lower than 2 GPa. Moreover, Figure 1(b) demonstrates that BiTe became stable at pressures greater than 10 GPa, and Bi 2 Te 3 became unstable at pressures greater than 15 GPa. The enthalpies of Bi-Te high-pressure structures were then calculated based on the density functional theory in order to determine the stability pressure domains of Bi-Te high-pressure structures. The phase transition paths of Bi and Te as well as the stable pressure domains of Bi 2 Te 3 , BiTe, Bi 4 Te 3 , and Bi 8 Te 9 were calculated based on the principle that 'the lowest energy structure is the most stable' and the convex-hull construction, as demonstrated in Table 1. The pressure-composition diagram for the Bi-Te system was then displayed in Figure 1(c), which was crucial in understanding how the Bi-Te system changed structurally and behaved under high pressures.
According to Zhu L [11] and Xiao G [13], Bi 2 Te 3 has four high-pressure structures: R-3m, C2/m, C2/c, and BCC alloy phases. The calculated phase transition pressure in this work was 10.2, 14, and 15 GPa, respectively, which was very similar to the findings of Zhu L [11] and Xiao G [13]. No new stable structure of Bi 2 Te 3 had been observed. However, as demonstrated in Figure 2(b), Bi 2 Te 3 would disintegrate into BiTe and Te at 13.4 GPa. The reaction enthalpy of Bi 2 Te 3 was calculated as follows: In other words, Bi 2 Te 3 had only two stable high-pressure structures and the BCC alloy phase (as shown in Figure 3), which was inconsistent with the experimental results [11,13] [13] only looked at Bi 2 Te 3 in their studies and disregarded the potential breakdown or synthesis of the Bi-Te system under high pressures. The simulated XRD of Bi 2 Te 3 -C2/c, Bi 2 Te 3 -C2/m, BiTe-P-1, and Te-III with λ = 0.3866 Å at 14.4 GPa is shown in Figure 2(c). Comparatively, it was observed that the strong diffraction peaks of BiTe-P-1 and Te-III had diffraction angles that were very similar to those of Bi 2 Te 3 -C2/c and Bi 2 Te 3 -C2/m, suggesting that the C2/c phase as presented by Zhu L [11] may have been the Te-III phase. Thereafter, using the quasiharmonic approximation (QHA) method at 15 GPa, the Gibbs free energies of Bi 2 Te 3 -C2/c, BiTe-Pm-3m, Te-III, and Bi-Im-3 m were calculated as a function of temperature. The convex-hulls of the Bi-Te system, as depicted in Figure 2(d) at temperatures between 0 and 960 K at 15 GPa, and Bi 2-Te 3 -C2/c were also unstable at high temperatures.  However, it needs to be demonstrated whether the stable of Bi 2 Te 3 BCC alloy phase could exist at high temperatures or not. In this research, the Gibbs free energies of Bi 2 Te 3 -C2/m(2), BiTe-Pm-3m, Te-III, and Bi-Im-3 m at 25 GPa, were also determined using the QHA method. In this work and Zhu L [11], Bi 2 Te 3 -C2/m(2) served as a representation of the BCC alloy phase of Bi 2 Te 3 . The convex-hulls of the Bi-Te system are depicted in Figure 3(a) at temperatures ranging from 0 to 960 K, and Bi 2 Te 3 -C2/m(2) would be stable above 500 K.
The reaction Gibbs free energy (ΔG r ) of Bi 2 Te 3 was then determined using the following equation: Additionally, it was discovered that the Bi 2 Te 3 BCC alloy phase could be stable above 330 K at 25 GPa, as depicted in Figure 3(b). Moreover, Zhang JL [23] examined the high-pressure structures of BiTe and observed four stable structures, however, only two structures were identified, i.e. BiTe-P-3m1 and BiTe-Pm-3m. One new stable structure, BiTe-P-1, was discovered for the first time in this work. Thereafter, enthalpies of BiTe high-pressure structures were calculated as a function of pressure. As shown in Figure 4(a), the phase transition path of BiTe was P-3m1 → P-1 → Pm-3m, and the transition pressure was 7.5 and 11.2 GPa, respectively.
Then, as shown in Figure 4(b), the simulated XRD of BiTe-P-3m1 and BiTe-P-1 was compared to the experimental XRD [23] with wave length λ = 0.6199 Å at 9.5 GPa. In experimental XRD [23], the strongest diffraction peaks of phases I and II were found to be in close proximity of one another, with diffraction angles of approximately 11.30°and 12.05°, respectively, while the second diffraction peak of phase II was found at approximately 14.80°. 2θ corresponding to the strongest peak for BiTe-P-3m1 and BiTe-P-1 from the simulated XRD was 11.45°and 12.05°, respectively, and the second strong diffraction peak of BiTe-P-1 was observed at 14.80°. Phase I was then determined to be BiTe-P-3m1, and phase II was determined to be BiTe-P-1. Since only a few diffraction peaks of phase III were observed, the phase III of BiTe may not even exist. The phase III of BiTe in XRD [23] always coexisted with phase II or IV.
The energy band structure and phonon spectrum curve of BiTe-P-1 were finally calculated using the first-principles method, as shown in Figure 4(c,d), respectively. Under high pressure, the structure was metallic and satisfied the conditions of lattice dynamics stability. The crystal structures of BiTe-P-3m1 and BiTe-P-1 are depicted in Figure 4(e,f). The similarity of their XRDs could be explained by considering the structure of BiTe-P-1 as a distortion of BiTe-P-3m1 along the caxis. The coordination number of Bi in the BiTe-P-1 structure was 6, which was higher than that of the BiTe-P-3m1.

Conclusions
The high-pressure structures of Bi-Te system were searched by evolutionary crystal structure prediction, and one new stable structure -BiTe-P-1 was found. Then we calculated the pressure-composition diagram of Bi-Te system. Bi 2 Te 3 had only two stable high-pressure structures and would decompose at 13.4 GPa, and the BCC alloy phase of Bi 2 Te 3 only could be stable at high temperature and high pressure. BiTe had three high-pressure structures, that is P-3m1, P-1 and Pm-3m, and the phase transition pressure was 7.5 and 11.2 GPa, respectively.

Disclosure statement
No potential conflict of interest was reported by the author(s).