High-Pressure Structures and Superconductivity of Barium Iodide

Generally, pressure is a useful tool to modify the behavior of physical properties of materials due to the change in distance between atoms or molecules in the lattice. Barium iodide (BaI2), as one of the simplest and most prototypical iodine compounds, has substantial high pressure investigation value. In this work, we explored the crystal structures of BaI2 at a wide pressure range of 0–200 GPa using a global structure search methodology. A thermodynamical structure with tetragonal I4/mmm symmetry of BaI2 was predicted to be stable at 17.1 GPa. Further electronic calculations indicated that I4/mmm BaI2 exhibits the metallic feature via an indirect band gap closure under moderate pressure. We also found that the superconductivity of BaI2 at 30 GPa is much lower than that of CsI at 180 GPa based on our electron–phonon coupling simulations. Our current simulations provide a step toward the further understanding of the high-pressure behavior of iodine compounds at extreme conditions.


Introduction
A large number of interesting properties of iodine compounds have been reported such as optical properties, conduction characteristics, catalytic performance, medical application and the hypervalence phenomenon [1][2][3][4][5][6][7][8][9][10]. Barium iodide (BaI 2 ), as one of the simplest and most representative ionic iodine compounds, has attracted plentiful studies [11][12][13][14][15]. At ambient pressure, barium iodide (BaI 2 ) shares a cotunnite-type structure (orthorhombic Pnma, Z = 4) [11] with many other dihalides AX 2 (A = Ca, Ba, Pb, Sn) [16] Under high pressure, a new high-pressure phase of BaI 2 with monoclinic P112 1 /a (Z = 8) symmetry between 12 and 15 GPa was reported in 1995 [13]. Curiously, this previous work identified the monoclinic P112 1 /a phase at a pressure range of 20-40 GPa [13]. Moreover, the latest theoretical work in 2015 reported that BaI 2 maintains insulator characteristics at least up to 40 GPa [15]. The superconducting behavior of CsI has been reported by experimental and theoretical works [7,17,18], where the external pressure reached 180 GPa. BaI 2 , as one of the most representative iodine compounds, shares a similar prototype with CsI. According to the reported superconducting mechanism of CsI, the increasing number of electrons of Cs is responsible for superconductivity, and the Ba atom with more electrons is potentially superior to the Cs atom in the electron-phonon coupling. Thus, it is an interesting topic to investigate the conduction characteristics at lowering pressure, which implies much more application value. To the best of our knowledge, the highest pressure studied in previous work for BaI 2 was lower than 40 GPa, and the whole high-pressure structural transition sequence up to 200 GPa is still far from being clear and well established. These structural uncertainties impede the in-depth understanding and further exploration of the electronic properties of BaI 2 under compression.
Here, we present systematic structure searches for BaI 2 at high pressures using our developed CALYPSO method [19][20][21][22]. Our results show that BaI 2 adopts orthorhombic Pnma symmetry at 0 GPa, which is consistent with experimental work [11,13]. Furthermore, we identified one thermodynamically stable tetragonal I4/mmm phase for BaI 2 at high pressure which is energetically superior to the previously reported post-cotunnite phase (P112 1 /a, Z = 8) [13]. Further electronic calculations showed that BaI 2 becomes a metallic phase via indirect band gap closure at moderate compression. In addition, the simulations also suggest the superconductive feature of BaI 2 at 30 GPa [7].

Computational Details
To obtain stable high-pressure structures of BaI 2 , we carried out a global structure search by our developed CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method [19][20][21][22] within the first-principle electronic structure. This computational scheme was verified by many works [23][24][25][26][27]. We used Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) [28] exchange correlation for the simulations, where the VASP (Vienna ab initio simulation package) code was also employed [29]. Furthermore, we used the Phonopy code to investigate the dynamic properties of the predicted structures [30]. The Device Studio [31] program provides a number of functions for performing visualization, modeling and simulation. We used Bader's quantum theory of atoms in molecules (QTAIM) analysis [32] to investigate the charge properties of the predicted structures. Superconductivity was studied by density-functional perturbation theory [33,34], where the Quantum-ESPRESSO package [35,36] was used.

Results and Discussion
To uncover stable structures of BaI 2 , we performed systematic structural predictions at a pressure range of 0-200 GPa without considering temperature effects, with the CALYPSO methodology [19][20][21][22]. According to our simulations, at ambient pressure, the cotunnitetype Pnma (Z = 4) phase of BaI 2 is the thermodynamically optimal structure (Figure 1). From Figure 1c, each barium atom was surrounded by nine iodine atoms, and all the atoms of the primitive cell were packed in an orthorhombic cage. The optimized lattice parameter of the Pnma phase takes a = 9.003 Å, b = 5.448 Å and c = 10.879 Å at ambient pressure, which is close to experiment data with a = 8.922 Å, b = 5.304 Å and c = 10.695 Å [11]. The agreement between our current simulations and experimental studies [11,13,15] provides a validation of the present simulation scheme.  Under high pressure, we found the stability of the Pnma structure at a pressure ra of 0-17 GPa, after which it undergoes a phase transition into the tetragonal I4/mmm ph (Z = 2), with nearly no volume collapse, as shown in Figure 1. Comparing with the Pn structure, the I4/mmm phase has a higher symmetry with a coordination of 10. We prov the lattice parameters and atomic coordinates in Table 1. Earlier experimental w showed the existence of a monoclinic P1121/a phase of BaI2 at a pressure range of 12 GPa at room temperature. 13 According to the lattice parameters and atomic position the current work, we calculated the enthalpy of the experimentally known monocl P1121/a structure, and our results indicate that this P1121/a structure has a higher entha than our predicted structure. The enthalpy curve of P1121/a is not shown due to its la number compared with the reference enthalpy lines. The P63/mmc and Cmcm phases underlying stable structures obtained during the structure prediction process, were a taken into account in the comparison (Figure 1a). We also provide the X-ray diffract patterns of these structures in Figure 2, and the future experiment is thus stimulated. O work shows that BaI2 follows the following structural progression: orthorhombic Pn (0-17.1 GPa) → tetragonal I4/mmm . Our simulations also suggest the namical stability feature of the predicted structures, as shown in Figure 2.  Under high pressure, we found the stability of the Pnma structure at a pressure range of 0-17 GPa, after which it undergoes a phase transition into the tetragonal I4/mmm phase (Z = 2), with nearly no volume collapse, as shown in Figure 1. Comparing with the Pnma structure, the I4/mmm phase has a higher symmetry with a coordination of 10. We provide the lattice parameters and atomic coordinates in Table 1. Earlier experimental work showed the existence of a monoclinic P112 1 /a phase of BaI 2 at a pressure range of 12-15 GPa at room temperature. 13 According to the lattice parameters and atomic positions in the current work, we calculated the enthalpy of the experimentally known monoclinic P112 1 /a structure, and our results indicate that this P112 1 /a structure has a higher enthalpy than our predicted structure. The enthalpy curve of P112 1 /a is not shown due to its large number compared with the reference enthalpy lines. The P6 3 /mmc and Cmcm phases, as underlying stable structures obtained during the structure prediction process, were also taken into account in the comparison (Figure 1a). We also provide the X-ray diffraction patterns of these structures in Figure 2, and the future experiment is thus stimulated. Our work shows that BaI 2 follows the following structural progression: orthorhombic Pnma (0-17.1 GPa) → tetragonal I4/mmm (17.1-200 GPa). Our simulations also suggest the dynamical stability feature of the predicted structures, as shown in Figure 2.  In this work, we also provide the Bader charge and the Ba-I bond distance in Figure  3. These simulations suggest the peculiar reverse of the charge transfer between Ba and I atoms. Previous studies suggested that CsCl, CsBr and CsI are metallic phases at high pressures [7,37]. At ambient conditions, BaI2 has a wide band gap between valance and conductive bands, with a value of 3.51 eV (Figure 4a). Interestingly, our studies also show the In this work, we also provide the Bader charge and the Ba-I bond distance in Figure 3. These simulations suggest the peculiar reverse of the charge transfer between Ba and I atoms.  In this work, we also provide the Bader charge and the Ba-I bond distance in Figure  3. These simulations suggest the peculiar reverse of the charge transfer between Ba and I atoms. Previous studies suggested that CsCl, CsBr and CsI are metallic phases at high pressures [7,37]. At ambient conditions, BaI2 has a wide band gap between valance and conductive bands, with a value of 3.51 eV (Figure 4a). Interestingly, our studies also show the Previous studies suggested that CsCl, CsBr and CsI are metallic phases at high pressures [7,37]. At ambient conditions, BaI 2 has a wide band gap between valance and conductive bands, with a value of 3.51 eV (Figure 4a). Interestingly, our studies also show the metallic feature of BaI 2 at a moderate pressure of 30 GPa (Figure 4), which is quite different from the direct band gap closure in the CsCl and CsBr systems [37]. The latest theoretical work in 2015 reported that BaI 2 maintains its insulating feature up to 40 GPa [15]. It is noteworthy that it adopts the ambient orthorhombic Pnma structure, which is obviously not accurate without considering high-pressure phases. Therefore, the newly Materials 2022, 15, 522 5 of 8 predicted tetragonal phase with I4/mmm symmetry is responsible for this pressure-induced metallization. metallic feature of BaI2 at a moderate pressure of 30 GPa (Figure 4), which is quite different from the direct band gap closure in the CsCl and CsBr systems [37]. The latest theoretical work in 2015 reported that BaI2 maintains its insulating feature up to 40 GPa [15]. It is noteworthy that it adopts the ambient orthorhombic Pnma structure, which is obviously not accurate without considering high-pressure phases. Therefore, the newly predicted tetragonal phase with I4/mmm symmetry is responsible for this pressure-induced metallization. The superconducting behavior of CsI has been extensively explored by experimental and theoretical methods [7,[17][18][19]. Therefore, it is noteworthy to study the superconductivity of BaI2 at high pressure. In this work, we performed electron-phonon coupling calculations for BaI2. We provide the Eliashberg spectral function α 2 F(ω) [38] (Figure 5) and the phonon density of states (PHDOS) of BaI2 at 30 GPa. It is clearly seen that α 2 F(ω) can be roughly divided into three parts: low (0.49-1.25 THz), medium (1.25-5.78 THz) and high frequency (5.78-6.51 THz). We employed the Allen-Dynes modified McMillan equation [39] = . exp − to estimate the superconductivity of the predicted structures, where ωlog is the logarithmic average frequency, and μ* is the Coulomb pseudopotential. At 30 GPa, ωlog was 132.62 K, while at 200 GPa, it was 207.23 K. Furthermore, we found that the estimated superconducting critical temperature TC for BaI2 was 1.27 K at 30 GPa and 0.35 K at 200 GPa. Moreover, two recent studies reported non-adiabatic superconductivity in sibling BKBO [40] and low-dimensional LiC6 [41]. These studies presented a coherent interpretation of the superconductivity. In our work, the relatively lower bottom of the conduction band of BaI2 implies the potential influence of non-adiabatic effects, and this may be an interesting orientation in future work. The superconducting behavior of CsI has been extensively explored by experimental and theoretical methods [7,[17][18][19]. Therefore, it is noteworthy to study the superconductivity of BaI 2 at high pressure. In this work, we performed electron-phonon coupling calculations for BaI 2 . We provide the Eliashberg spectral function α 2 F(ω) [38] (Figure 5) and the phonon density of states (PHDOS) of BaI 2 at 30 GPa. It is clearly seen that α 2 F(ω) can be roughly divided into three parts: low (0.49-1.25 THz), medium (1.25-5.78 THz) and high frequency (5.78-6.51 THz). We employed the Allen-Dynes modified McMillan equa- λ−µ * (1+0.62λ) to estimate the superconductivity of the predicted structures, where ω log is the logarithmic average frequency, and µ* is the Coulomb pseudopotential. At 30 GPa, ω log was 132.62 K, while at 200 GPa, it was 207.23 K. Furthermore, we found that the estimated superconducting critical temperature T C for BaI 2 was 1.27 K at 30 GPa and 0.35 K at 200 GPa. Moreover, two recent studies reported non-adiabatic superconductivity in sibling BKBO [40] and low-dimensional LiC 6 [41]. These studies presented a coherent interpretation of the superconductivity. In our work, the relatively lower bottom of the conduction band of BaI 2 implies the potential influence of non-adiabatic effects, and this may be an interesting orientation in future work.

Conclusions
We investigated the high-pressure crystal structures and electronic properties of BaI2 up to 200 GPa. Our results suggest a thermodynamically stable tetragonal I4/mmm symmetry of BaI2 identified at 17.1 GPa. The systematic increase in the coordination number from 9 to 10 should be seen in many AX2 compounds. Furthermore, we uncovered that I4/mmm BaI2 becomes a metallic phase at moderate pressure, which is different to Pbam CsCl and Pmma CsBr (via direct band gap closure at the Γ point) [37]. Our simulations suggest the superconducting feature of the predicted structure for BaI2 at 30 GPa. Comparing with CsI, cesium xenide and barium xenide have a similar composition with more electrons, making them good subjects for study, with great potential to exhibit superconductivity at moderate pressure. Our work clarifies the high-pressure phase transition sequence of BaI2 up to 200 GPa, which represents a step toward the understanding of the behavior of AX2-type iodine compounds under extreme conditions.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.