Phase transitions of alkaline-earth metal sulfides under pressure

Materials Research Express PAPER • OPEN ACCESS Phase transitions of alkaline-earth metal sulfides under pressure To cite this article: Yuefeng Wang et al 2021 Mater. Res. Express 8 065902 View the article online for updates and enhancements. You may also like On the search for the chiral anomaly in Weyl semimetals: the negative longitudinal magnetoresistance R D dos Reis, M O Ajeesh, N Kumar et al. - Thermopower and thermal conductivity in the Weyl semimetal NbP U Stockert, R D dos Reis, M O Ajeesh et al. - Comparative Raman study of Weyl semimetals TaAs, NbAs, TaP and NbP H W Liu, P Richard, L X Zhao et al. - This content was downloaded from IP address 161.111.10.229 on 27/01/2022 at 12:17 Mater. Res. Express 8(2021)065902 https://doi.org/10.1088/2053-1591/ac0a05 PAPER Phase transitions of alkaline-earth metal sulfides under pressure Yuefeng Wang 1 , Aitor Bergara 2,3,4 , Cancan Shao 1 , Lin Wang 1 , Xiaowei Liang 1 , Linyan Wang 1 , Rongxin Sun 1 , Xudong Wei 1 , Tiansheng Wang 1,5 , Guoying Gao 1 and Yongjun Tian 1 1 State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People’s Republic of China 2 Departmento de Física, Universidad del País Vasco, UPV/EHU, 48080 Bilbao, Spain 3 Donostia International Physics Center (DIPC), 20018 Donostia, Spain 4 Centro de Física de Materiales CFM, Centro Mixto CSIC-UPV/EHU, 20018 Donostia, Spain 5 National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, People’s Republic of China E-mail: [email protected] Keywords: alkaline-earth metal sulfides, structure searching, ab initio calculation, phase transition sequence, modulated structure Abstract We have systematically explored the crystal structures of alkaline-earth metal sulfides under pressure by using a swarm-intelligence structural prediction method. At low pressures we successfully reproduced their known structures and phase transition sequences. Under high pressure, MgS is predicted to transform from B28 to a β-NbP-type structure at 262 GPa. CaS and SrS present the same phase transition sequence, from B2 to a β-NbP-type structure, while BaS is predicted to transform to a Imma structure. The Imma structure is actually similar to the β-NbP-type structure, as it can be seen as a modulated distortion of the latter structure. The absence of any imaginary phonon mode for the predicted structures suggests that they are dynamically stable. The calculated electronic band structures and density of states reveal that all the predicted phases are metallic, except that MgS is a semiconductor. Subsequent electron-phonon coupling calculations suggest that Imma BaS is a superconductor with a low T c of 1.32 K, while β-NbP MgS, CaS and SrS are not superconductors. The current study provides a comprehensive analysis of phase transitions for alkaline-earth metal sulfides up to 300 GPa and might stimulate experimental studies in the future. 1. Introduction The alkaline-earth metal sulfides XS(X=Be, Mg, Ca, Sr, Ba)have recently attracted interest in science and technology because of their remarkable physical properties and wide applications, ranging from catalysis to microelectronics [1–3]. For example, due to their wide semiconducting band gaps, they can be used as excellent host materials to incorporate different impurities (e.g. rare earth ions, transition metal ions)for optical applications, such as multicolor thin film electroluminescent devices, thermoluminescence dosimetry, and cathode ray tubes [4–8]. Pressure is a powerful thermal dynamic parameter which is often used to manipulate the band gap and properties of semiconductors without doping [9–11]. The high-pressure behavior of alkaline-earth metal sulfides have been studied by many theoretical and experimental groups. Under ambient conditions, almost all alkaline-earth metal sulfides crystallize in the rocksalt (B1)structure, with sixfold coordination, except BeS, which presents a fourfold coordinated zinc-blende (B3)structure. At 51 GPa, BeS transforms to a NiAs-type (B8)structure and, then, at 196 GPa a further transition to an orthorhombic structure was predicted by Feng et al [12]using a swarm intelligence algorithm. MgS was experimentally observed to be stable in the B1 structure up to 54 GPa [13]. At higher pressures, some groups predicted a CsCl-type (B2)structure at 158–255.5 GPa [14–18], while Wu et al [19]suggested a FeSi-type (B28, space group P2 1 3)structure from 143 GPa to 350 GPa. On the other hand, CaS, SrS, and BaS were all observed to transform to the B2 structure at 40, 18, and 6.5 GPa, respectively [20–22]. OPEN ACCESS RECEIVED 19 May 2021 REVISED 8 June 2021 ACCEPTED FOR PUBLICATION 10 June 2021 PUBLISHED 21 June 2021 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s)and the title of the work, journal citation and DOI. © 2021 The Author(s). Published by IOP Publishing Ltd However, there is not yet complete analysis of MgS, CaS, SrS, and BaS phase transitions up to 300 GPa, which we explore in this article. We predict two new high-pressure structures and complete the phase transition sequence for alkaline-earth metal sulfides below 300 GPa. MgS is predicted to transform from B28 to a β-NbPtype structure, CaS and SrS from B2 to a β-NbP-type structure, while BaS is predicted to transform to a Imma structure. 2. Computational details Structure searches of XS(X=Mg, Ca, Sr, Ba)were performed at 1 atm, 10, 50, 100, 150, 200, 250, and 300 GPa, using the recently developed CALYPSO code, which requires only chemical compositions for the given compounds [23–29].The maximum formula units (f.u.)considered per simulation cell at each pressure is eight. Based on density functional theory, structural optimizations were performed using the generalized gradient approximation [30](within Perdew–Burke–Ernzerhof parametrization), as implemented in the Vienna ab initio simulation package [31]. The all-electron projector augmented-wave method [32]was used to describe the electron-ion interaction. For Mg, Ca, Sr, Ba and S, 3s 2 ,3s 2 3p 6 4s 2 ,4s 2 4p 6 5s 2 ,5s 2 5p 6 6s 2 and3s 2 3p 4 configurations are considered asvalence electrons, respectively. A kinetic energy cutoffof 600 eVand appropriate Monkhorst– Pack [33]kmeshes were chosen to ensure enthalpy convergence within 1 meV/f.u. A supercell approach [34] was used to calculate the phonon spectra with the PHONOPY code [35]. Electron-phonon coupling (EPC) calculations were done through the widely used Quantum-ESPRESSO code [36]. Ultrasoft pseudopotentials were employed and convergence tests gave a kinetic energy cutoff of 60 Ry. 7×7×7 and 6×6×6q-point meshes in the first Brillouin zone were used for β-NbP MgS, CaS, SrS and Imma BaS, respectively. Correspondingly, 28×28×28 and 24×24×24 Monkhorst-Pack grids were used to ensure k-point sampling convergence with Gaussians of width 0.02 Ry, respectively, which approximates the zero-width limit for calculating the EPC parameter λ.λcan be defined as the first reciprocal moment of the spectral function α 2 F(ω), òå law wwlw=» ¥Fdq2, 1 qj qj 0 2() () () where w(q)is the weight of a qpoint in the first Brillouin zone, and α 2 F(ω)is expressed by the phonon linewidth γ qj , owing to electron-phonon coupling [37–39]: å aw p g wdw w w=-FNq 1 2,2 fqj qj qj qj 2 () ( ) () () where N f is the electronic density of states at the Fermi level. The linewidth γ qj of a phonon mode jat wave vector q, arising from EPC is given by å gpw dede=++ g2,3 qj qj knm kn k qm jkn k qm , 2 ∣∣()() () where the sum is over the Brillouin zone, and ε kn are the energies of bands measured with respect to the Fermi level at point k, and + g kn k q m j ,is the electron-phonon matrix element. The critical temperature T c has been estimated from the Allen-Dynes modified McMillan equation [40]: wl lm l =-+ -+ T1.2 exp 1.04 1 10.62 ,4 C log * ⎡ ⎣ ⎢⎤ ⎦ ⎥ () () () Where μ∗is the Coulomb pseudopotential, and ω log is the logarithmic average of the phonon frequencies and can be expressed as ò ww l aw w w ww=Fdexp 2log . 5 log 0 2 0 ⎡ ⎣ ⎢⎤ ⎦ ⎥ () () 3. Results and discussion At ambient pressure, MgS, CaS, SrS, and BaS are all predicted to be stable in the B1 structure, which is in good agreement with the experimental results [13,20–22]. The calculated lattice parameters, elastic constants and formation energies of the predicted B1 MgS, CaS, SrS, and BaS together with experimental or previously theoretical results are shown in table 1, which are in good agreement with each other. For MgS, the B28 and βNbP-type structures (space group I4 1 /amd)with the lowest enthalpies are predicted at 150–200 and 300 GPa, 2 Mater. Res. Express 8(2021)065902 Y Wang et al respectively. For CaS, and SrS, the B2 and the β-NbP-type structures are predicted at 50–150 and 200–300GPa, respectively. The B2 structure is also predicted at 10–250 GPa for BaS, while a Imma structure at higher pressure. The B28 structure (group space P2 1 3, FeSi-type)for MgS, which is shown in figure 1(a), is a primitive-cubic structure with 8 atoms unit −1 cell. This structure is very simple and high-symmetry but with an unusual sevenfold coordination (see figure 1(b)) of both the Mg and S atoms. Each Mg atom is surrounded by seven S Figure 1. (a)and (b)are the predicted B28 structure and the corresponding histogram of Mg-S separations for MgS at 200 GPa, respectively. Mg’s are depicted as large orange spheres and S’s as small yellow ones. Figure 2. (a)and (b)are the predicted β-NbP-type structure and the corresponding histogram of Mg–S separations for MgS at 300 GPa, respectively. (c)One octahedron unit. Mg’s are depicted as large orange spheres and S’s as small yellow ones. Table 1. The calculated lattice parameters (Å), elastic constants (C11, C12, and C44, GPa) and formation energies (eV/atom)of the predicted B1 MgS, CaS, SrS, and BaS are compared with experimental or previously theoretical results. Compounds a C11 C12 C44 E form B1 MgS Present 5.21 137.9 42.8 51.1 −1.45 Others [41,42]5.19 140 42 54 −1.68 B1 CaS Present 5.72 123.3 23.7 33 −2.17 Others [41,42]5.68 123 24 33 −2.40 B1 SrS Present 6.06 107.8 18.9 25.8 −2.16 Others [41,42]6.01 106 17 26 −2.40 B1 BaS Present 6.45 90.2 16.9 18.7 −2.09 Others [42,43]6.37 91 17 19 −2.33 3 Mater. Res. Express 8(2021)065902 Y Wang et al atoms, and each S atom by seven Mg atoms, at distances of 2.38 Å, 2.12 (×3)Å, 2.20 (×3)Å of 200 GPa. In addition, each Mg atom has six next nearest Mg atoms with the same distance of 2.55 Å, whereas each S atom has six next nearest S atoms with 2.57 Å at 200 GPa. The β-NbP-type structure belongs to a tetragonal crystal system with 8 atoms unit −1 cell, as is shown in figure 2(a). In this structure, Mg and S form face-centered tetragonal sublattices, and the histogram of Mg–S separation is shown in figure 2(b). This histogram shows a clear gap between the shortest Mg–S distances of 2.1–2.23 Å, and the longer separations of 3.34–3.71 Å. According to this gap, we can easily conclude that the coordination number for β-NbP MgS is eight. In addition, each Mg atom is close to eight S atoms forming an octahedron which is composed of square-face-sharing two triangular prisms, where theMg atom locates at the center of the square-face (figure 2(c)), and vice versa. The predicted Imma structure for BaS is a body-centered orthorhombic structure with 8 atoms unit −1 cell and it can be seen as a modulated distortion of the β-NbP-type structure. The modulated distortion occurs with the change of atomic displacement in the XY plane, specifically, it is enlarging along the Xaxis and compressing along the Yaxis. These distortions cause highly distorted facecentered orthorhombic sublattices formed by Ba and S in the modulated structure, in which all S atoms and partial face-centered Ba atoms are displaced along the Zaxis (figures 3(a)and (b)). According to the histogram of Ba–S separations in Imma BaS (figure 3(c)), we can conclude that the coordination number for Imma BaS is also eight. Each Ba atom is also coordinated with eight S atoms forming an octahedron which is composed of facesharing two different triangular prisms, but Ba atom is not located on the face (figure 3(d)). Although pressureinduced modulated structures are not so common in simple binary compounds [12], this study provides such an example. Enthalpy calculations as a function of pressure for MgS, CaS, SrS and BaS are presented in figure 4. MgS is stable in the B1 structure below 140 GPa, above which the B28 structure becomes stable (figure 4(a)and its inset). At 262 GPa, a predicted β-NbP-type structure is then preferred. Figures 4(b)–(d)show that CaS, SrS, and Figure 3. (a)Predicted β-NbP-type structure for BaS at 100 GPa and its conventional unit cell is indicated by a dashed line. (b)and (c) are the predicted Imma structure and the corresponding histogram of Ba–S distances for BaS at 300 GPa, respectively. The displacements of Ba atoms and S atoms in the Imma structure relative to that in the β-NbP-type structure are parallel or anti-parallel with respect to the Zaxis in the XZ plane indicated by arrows in (b).(d)One octahedron unit. Ba’s are depicted as large green spheres and S’s as small yellow ones. 4 Mater. Res. Express 8(2021)065902 Y Wang et al BaS have the same B1–B2 phase transition at 37, 19, and 8 GPa, respectively, which is in agreement with the corresponding experimental results of 40, 18, and 6.5 GPa [20–22]. The corresponding differences are 3, 1, and 1.5 GPa, respectively. Above 162 and 191 GPa, CaS and SrS will transform to the same β-NbP-type structure, respectively, while BaS will be stable in the Imma structure above 264 GPa. The specific structure information of the predicted structures is shown in table 2. The complete phase transition sequences of alkaline-earth metal sulfides up to 300 GPa are summarized in figure 5. The phase transition sequence of MgS is B1→B28→β-NbP under pressure. CaS and SrS present the same phase transition sequence of B1→B2→β-NbP, while BaS has a different one, B1→B2→Imma. At low pressures MgS, CaS, and SrS are all stable in the B1 structure and at very high pressures they stabilize in the βNbP-type structure. The main difference is that CaS and SrS transform into the β-NbP-type structure from the B2 structure, while in MgS it does so from the B28 structure. At low pressures CaS, SrS and BaS have the same phase transition sequence, B1→B2, while at high pressures it is predicted that CaS and SrS will transform into the β-NbP-type structure and BaS into a Imma structure. Taking into account that the Imma structure derives from a modulated distortion of the β-NbP-type structure, the phase transition sequence of BaS can be considered to be similar to that of CaS and SrS. However, Figure 4. Ground-state static enthalpy curves per f.u. for (a)MgS, (b)CaS, (c)SrS, and (d)BaS as a function of pressure, with respect to the B1 structure. The inset in (a)shows that the B28 structure for MgS has a lower enthalpy than the B1 structure above 140 GPa. Table 2. Lattice parameters of the predicted new structures of alkaline-earth metal sulfides. Compounds Pressure (GPa)Space group Lattice parameters (Å, degree)Atomic positions (fractional) MgS 200 P2 1 3a=b=c=4.104, Mg 0.413 0.413 0.413 (B28)α=β=γ=90°S 0.077 0.077 0.077 300 I4 1 /amd a=b=2.964, c =6.673, Mg 0.500 0.000 0.750 (β-NbP)α=β=γ=90°S 0.500 0.000 0.250 CaS 200 I4 1 /amd a=b=3.314, c =7.159, Ca 0.500 0.000 0.750 (β-NbP)α=β=γ=90°S 0.500 0.000 0.250 SrS 200 I4 1 /amd a=b=3.479, c =7.299, Sr 0.500 0.000 0.750 (β-NbP)α=β=γ=90°S 0.500 0.000 0.250 BaS 300 Imma a=4.033, b =2.728, Ba 0.000 0.750 0.143 c=8.009, α=β=γ=90°S 0.000 0.750 0.595 5 Mater. Res. Express 8(2021)065902 Y Wang et al Figure 5. Phase transition sequences for alkaline-earth metal sulfides up to 300 GPa. Figure 6. Calculated phonon dispersion curves of the predicted novel structures of the alkaline-earth metal sulfides at pressures corresponding to their thermodynamically stable range. 6 Mater. Res. Express 8(2021)065902 Y Wang et al the phase transition sequence of MgS is different. The reason of this difference can be due to the pressureinduced electronic sto dmixing observed in Ca, Sr and Ba, but not in Mg. For pure solids at 1atm, the energies of the unoccupied 3d,4d, and 5dstates in Ca, Sr, and Ba, are quite close to the occupied 4s,5s, and 6 sstates, respectively [1]. Under pressure, the selectrons get trapped between the nuclei and they are excluded from them due to the requirement of orthogonality with core electronic states and the decrease of the atomic volume. Thus, under pressure, the sband energy rises relative to the dband until these selectrons start to occupy the dband [44]. This stodmixing in CaS, SrS, and BaS explains why they present a similar phase transition sequence, which is different from that of MgS, since Mg does not show the above mentioned s/dmixing. Analyzing the phase transition sequences of alkaline-earth metal sulfides we can see that the B1–B2 transition pressure of the compounds decreases from CaS, SrS to BaS, while it increases in the B2–β-NbP (or Imma)transition sequence. At low pressures, the decrease of the B1–B2 transition pressure for heavier metal atoms is mainly due to the chemical precompression. With increasing pressure, the role of the electrostatic interaction between the ions (Madelung energy)becomes more important and complicated [45]; so that the increase of the B2–β-NbP (or Imma)phase transition pressure from CaS, SrS to BaS at high pressures might be due to the enhancement of the Madelung energy with pressure. Figure 7. Calculated electronic band structure of B28 MgS at 200 GPa. Figure 8. Calculated electronic DOS per valence electron of β-NbP MgS, CaS and SrS, and Imma BaS at 300, 200, 200 and 300 GPa, respectively. All these sulfides are metallic. 7 Mater. Res. Express 8(2021)065902 Y Wang et al To explore the dynamical stability of the predicted B28 MgS, β-NbP MgS, CaS and SrS, and Imma BaS, we have calculated their phonon dispersion curves at the corresponding stable pressure ranges (figure 6). Due to there are no imaginary frequency in the whole Brillouin zone, these structures are all dynamically stable. Figures 7and 8present the calculated electronic band structure and density of states (DOS)for static B28 MgS, β-NbP MgS, CaS and SrS, and Imma BaS at 200, 300, 200, 200 and 300 GPa, respectively. Interestingly, as it is shown in figure 7, at 200 GPa MgS is a semiconductor with an indirect band gap of 2.48 eV (calculated with a HSE hybrid functional [46,47], which is reasonably reliable to estimate band gaps). However, the other alkaliearth metal sulfides are all metallic (figure 8). An analysis of the contributions of different atomic orbitals to the total electronic DOS indicates that at the Fermi level there is an important contributions from S 3porbitals, while in BaS there are more contributions from Ba 5dorbitals. To investigate the superconductivity of metallic β-NbP MgS, CaS, and SrS and Imma BaS, the T c values of these predicted phases were estimated by using the Allen-Dynes modified McMillan equation [40]. As shown in table 3, the estimated T c values of β-NbP MgS, CaS and SrS are close to 0 K, and the T c for Imma BaS is 1.32 K with μ * of 0.1. The weak EPC, small phonon vibration frequencies and low electronic DOS at the Fermi level (figure 8)lead to the very small T c in these systems. 4. Conclusions We have systematically studied the phase transitions of the alkaline-earth metal sulfides XS (X=Mg, Ca, Sr, Ba) under pressure. MgS first transforms from B1 to the B28 structure and then to the β-NbP-type structure. At low pressures CaS, SrS and BaS have the same phase transition sequence, B1→B2, while at high pressures it is predicted that CaS and SrS will transform into the β-NbP-type structure and BaS into a Imma structure, which is actually a modulated distortion of the β-NbP-type structure. All the predicted phases are dynamically stable and metallic, except MgS which is a semiconductor. Moreover, Imma BaS is estimated to be superconducting with a T c of 1.32 K. Acknowledgments The work was supported by National Natural Science Foundation of China (91963115, 52022089), the PhD Foundation by Yanshan University (B970), Science and Technology Project of Hebei Education Department (Grant No. QN2021136). A.B. acknowledges financial support from the Spanish Ministry of Science and Innovation (PID2019-105488GB-I00). Data availability statement All data that support the findings of this study are included within the article (and any supplementary files). ORCID iDs Guoying Gao https://orcid.org/0000-0003-3823-2942 References [1]Chakrabarti A 1999 Phys. Rev. B 62 1806–14 [2]Li Y, Ma Y, Cui T, Yan Y and Zou G 2008 Appl. Phys. Lett. 92 101907 [3]Rached D, Rabah M, Benkhettou N, khenata R, Soudini B, Al-Douri Y and Baltache H 2006 Comput. Mater. Sci. 37 292–9 [4]Yamashita N 1984 J. Phys. Soc. Jpn. 53 2400–6 Table 3. The calculated EPC parameter λ, phonon frequency logarithmic average ω log and critical temperature T c (μ * =0.1)from the Allen-Dynes modified McMillan equation for β-NbP MgS, CaS and SrS and Imma BaS. Compounds Pressure (GPa)λω log (K) T c (K) (μ * =0.1) β-NbP MgS 300 0.24 626 0.02 β-NbP CaS 200 0.25 451 0.03 β-NbP SrS 200 0.19 444 0.00 Imma BaS 300 0.37 498 1.32 8 Mater. Res. Express 8(2021)065902 Y Wang et al