Pressure-induced phase transitions of lead iodide

Abstract

Pressure is a fundamental thermodynamic variable that can efficiently modify crystal or electronic structure leading to new material states of interest. Here we search the crystal structures of lead iodide (PbI₂) up to 200 GPa using the swarm-intelligent CALYPSO structure prediction method combined with ab initio calculations. Four new stable high-pressure phases (orthorhombic Pnma, tegragonal I4/mmm, orthorhombic Immm and monoclinic C2/c) have been uncovered. A layered to three-dimensional structure transition from the ambient-pressure 2H phase to the orthorhombic Pnma phase is proposed to be taking place at ∼2.5 GPa. The newly proposed Pnma phase is a semiconductor with an indirect band gap of 1.68 eV. It is isosymmetric to the well-known cotunnite phase but with a very different bonding pattern. The semiconductor–metal transition of PbI₂ occurs at ∼27.2 GPa, where the semiconducting Pnma phase transforms to the metallic I4/mmm phase due to pressure-induced broadening of both the valance and conduction bands. The metallic nature persists in the higher-pressure phases of Immm and C2/c up to about 169.1 GPa, above which PbI₂ decomposes to its constituent elements. The current results represent a significant step toward the understanding of structural and electronic properties of PbI₂ under compression.

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Introduction

Lead iodide (PbI₂) has received considerable research effort for more than several decades because of its important scientific and technological applications.¹ Being a typical layered semiconductor with a direct bandgap around 2.3–2.5 eV,² it is a prototypical system for investigating the fundamental properties of excitions^3,4 and has been traditionally used as a stable nuclear radiation detector,^5–7 which converts γ- and X-ray radiation directly into current carriers. Recently, inspired by the emergence and rapid growth of two-dimensional (2D) materials (such as graphene,^8,9 transition-metal dichalcogenides,^10,11 and phosphorene^12,13), single layered and ultrathin 2D PbI₂ crystals have also been intensively explored by both experiment and theory as potential complementary compounds of existing 2D materials, which show promising applications in nanoelectronics and optoelectronics.^14,15 In addition, PbI₂ can serve as a precursor for low-cost synthesis of hybrid organic-inorganic perovskites, which are recent super star materials for photovoltaics.^16,17 Due to the versatile applications, various forms of PbI₂ including nanoclusters, nanotubes and thin film have been intensively explored.^18–23

At ambient condition, PbI₂ adopts a layered crystalline structure with repeating units of [I–Pb–I] stacking along the z direction. Each [I–Pb–I] layer consists of a hexagonally closed-packed layer of lead ions sandwiched between two layers of iodine ions [Fig. 1(a) and (b)], which are tightly hold together by ionic or covalent bonding.²⁴ Adjacent layers are bound via the relatively weak van der Waals forces typical of many two dimensional materials (e.g., graphite). Different stacking pattern of the [I–Pb–I] layers lead to a series of polytypes, such as 2H, 4H, 6H, 6R, 12R, etc, among which the 2H phase with P3̄m1 symmetry (denote 2H-P3̄m1 below) is the most stable form.²⁴

Fig. 1 Crystal structures of various PbI₂ phases, (a) and (b) 2H-P3̄m1, (c) Pnma, (d) I4/mmm, (e) Immm and (f) C2/c.

It is known that pressure is a fundamental thermodynamic variable that can efficiently alter the binding pattern of compounds and thus leads to new phase with intriguing chemical and physical properties. Studies concerning behaviors of PbI₂ under compression have long been carried out since 1937 and 1948, where two phase transitions from 2H-P3̄m1 structure were observed at 0.4 GPa and 2.5 GPa by Bridgman as characterized by volume changes of 4% and 2%, respectively.^25,26 Later measurements on the optical absorption coefficient have also observed the first phase transition at 0.4 GPa.²⁷ Jayaraman et. al. performed Raman and optical absorbtion experiments, where the two phase transition was observed at 0.5 and 3 GPa, respectively.²⁸ They deduced that the first phase is likely to possess a three-dimensional (3D) structure. In 2000, Saitoh et. al. investigated the pressure dependence of the Raman and luminescence spectra of 2H-P3̄m1 structure up to 1.5 GPa.²⁹ Based on the systematical analysis of experimental data, they found that the first phase transition occurs at 0.56 GPa and the new phase is a 2 × 2 supercell of 2H-P3̄m1 with relative atom position and bondings hardly changed. Though pressure-induced phase transitions of PbI₂ have long been found for several decades, the detailed structural information of these high-pressure phases are still elusive, impeding further understanding of the physical and chemical properties. Therefore, it is highly desired to determine the crystal structure of PbI₂ at high pressure.

Here, we have extensively explored the structures of PbI₂ at a wide pressure range of 0–200 GPa through elaborative swarm structure searching^30,31 combined with first-principles calculations. Four high pressure phases, orthorhombic Pnma, tetragonal I4/mmm, orthorhombic Immm and monoclinic C2/c, were uncovered to be stable at pressure intervals of 2.5–27.2, 27.2–74.5, 74.5–92.5 and 92.5–169.1 GPa, respectively. The predicted orthorhombic Pnma structure is a semiconductor with an intriguing 3D structure, which is isosymmetry to the well-known cotunnite structure for AB₂ compounds but with very different bonding patterns. The other three high pressure phases also adopt 3D structural patterns but show metallic nature. Above 169.1 GPa, PbI₂ is predicted to be unstable and dissociate into the constituent elements (Pb + 2I).

Computational method

Our structure searching simulations were performed through the swarm-intelligence CALYPSO method,^30,31 which enables a global minimization of free-energy (reduced to enthalpy at 0 K) surface merging first-principles total-energy calculations. The method is specially designed for global search of ground-state structures at given chemical composition and external condition (e.g. pressure) unbiased by any known structural information, and has been successfully applied to predictions of high-pressure phases of various system, such as Li,³² Bi₂Te₃,³³ Xe–Fe,³⁴ B₃NO³⁵ and mercury chalcogenides,³⁶ etc. The underlying ab initio structural relaxations and electronic band structure calculations were performed in the framework of density functional theory (DFT) using plane-wave pseudopotential method as implemented in the VASP code.³⁷ The electron–ion interaction is described by means of projector-augmented wave method.³⁸ Configurations of 6s²5d¹⁰6p² for Pb, 5s²5p⁵ for I are considered as valence electrons, respectively. We use the Perdew–Burke–Ernzerhof (PBE) parameterization of generalized gradient approximation as the exchange-correlation functional.³⁹ An energy cutoff of 400 eV for the plane-wave expansion and Monkhorst–Pack k-point meshes with spacing of 2π × 0.03 Å − 1 was used to sample the Brillouin zone, which is shown to yield excellent convergence for total energies. It is known that DFT-PBE approach seriously underestimates the band gaps of all the materials due to the self-interaction error. In order to given an accurate description of the electronic structures, the hybrid HSE06 functional⁴⁰ (with the standard 25% non-local Fock exchange) is used for band structure and density of states calculations. Furthermore, relativistic effect of spin–orbit coupling (SOC), which is especially important to high-Z element of Pb, is also included for band structure and density of states calculations. The phonon calculations were carried out by using a supercell approach as implemented in the PHONOPY code.⁴¹

Results and discussions

Structure predictions through the CALYPSO code were performed with 1–4 formula unit (f.u.) per simulation cell at 0, 50, 80, 100, 150, 200 GPa and 1–8 f.u. at 10 GPa. The detailed structure information and calculated enthalpies of low-lying structures from the structure searches are given in Table SI–IV in the ESI.† It is seen that the energy differences between these low-lying structures is usually several or several tens meV, which is substantial enough to identify the lowest-energy structures. At 0 GPa, our simulations readily reproduced the experimental 2H-P3̄m1 structure as the global minimum structure for PbI₂, validating the method adopted here. At higher pressures, we uncovered a group of new structures. Among them, four structures were found to be most stable at certain pressure range. At 10 GPa, simulations revealed an orthorhombic Pnma structure with 4 f.u. per unit cell (Z = 4). As depicted in Fig. 1(c), this structure is 3-dimensional, which is in stark contrast to that of layered 2H-P3̄m1 [Fig. 1(a) and (b)]. It contains one crystallographically distinct Pb atom and two I atoms, all of which locate on the fourfold 4c site. The Pb atom is coordinated to eight I atoms, while each I atom is coordinated to four Pb atoms. It should be noteworthy that the current orthorhombic Pnma phase is different from the isosymmetric cotunnite phase (α-PbCl₂ phase), which is commonly adopted for many AB₂ compounds.⁴¹ As seen in Fig. 2, the structural topology of the Pb–I network in the two phases are essentially different, and the cations are 9-coordinated in the well-known cotunnite phase.⁴² It should be further notice that another Pnma structure has also been found for the high-pressure phases of FeF₂ and CoF₂ previously.^43,44 However, this structure is different from the current one, since it is about 415 meV higher in energy the current one for PbI₂ at 10 GPa (Table SI in the ESI†). To the best of our knowledge, the current orthorhombic Pnma phase has not been observed in AB₂ compounds previously. At 50 GPa, a tetragonal I4/mmm structure with Z = 2 was uncovered. As shown in Fig. 1(d), this structure is also a 3-dimensional structure composed of one crystallographically distinct Pb atom occupying 2b site and one I atom occupying 4e site. Within this structure, each Pb atom is coordinated to ten I atoms forming a double-capped square prism and each I atom is five-coordinated. The distance between central Pb atom and I atom at the vertex of the prism is 3.015 Å, and the distance between central Pb atom and capped I atoms is 3.311 Å. The double-capped square prisms stacked along the c axis and share the triangular facets each other. The structure uncovered at 80 GPa through the CALYPSO searches adopts an orthorhombic Immm symmetry with Z = 2 [Fig. 1(e)], which can be derived from symmetry lowing of the lower-pressure I4/mmm structure. As a result, on pair of facets of the prism formed by I atoms change from regular square to rectangle, but the coordination number of the Pb and I atoms are same as those in I4/mmm structure. Upon increasing pressure to 100 and 150 GPa, a monoclinic C2/c structure with Z = 4 is found as show in Fig. 1(f). This structure contains one distinct Pb atom and two I atoms, all of which occupy the 4e site. Within this structure, Pb atoms is still 10-coordinated, but the coordination number of the two distinct I atoms increase to 5 and 7, respectively.

Fig. 2 Frameworks of (a) current orthorhombic Pnma structure and (b) the cotunnite structure (α-PbCl₂ structure).

The calculated enthalpies of various phases of PbI₂ relative to Pb + 2I are plotted as a function of pressure in Fig. 3(a), which confirm the energetic stability of our predicted structures. The experimental 2H-P3̄m1 structure is most stable up to around 2.5 GPa, beyond which orthorhombic Pnma structure becomes energetically most favorable. In the pressure range 27.2–74.5 GPa, the tetragonal I4/mmm structure has the lowest enthalpies, while orthorhombic Immm structure is stable between 74.5 GPa and 92.5 GPa, the monoclinic C2/c structure is found to be stable up to 169.1 GPa, above which PbI₂ becomes unstable against decomposition to constituent elements (Pb + 2I). Our phonon calculations have verified the dynamical stabilities of all these predicted structures by evidence of the absence of any imaginary frequency in the whole Brillouin zone [Fig. 4]. Thus, the current results suggest PbI₂ takes the phase transition sequence of 2H-P3̄m1 → Pnma → I4/mmm → Immm → C2/c under compression.

Fig. 3 (a) Calculated enthalpies per formula unit as functions of pressure with respect to Pb + 2I and (b) calculated equation of states of various phases of PbI₂.

Fig. 4 Calculated phonon-dispersion curves for (a) Pnma, (b) I4/mmm, (c) Immm and (d) C2/c phases of PbI₂. The 2 × 2 × 2, 4 × 4 × 4, 4 × 4 × 4 and 3 × 3 × 3 supercells were used for the calculations.

It is known that experiments have observed two phase transitions of PbI₂, which occur at ∼0.5 and ∼3 GPa as characterized by volume changes of 4% and 2%, respectively.^25–29 The current results indicate one of the high-pressure phases adopts the 3D orthorhombic Pnma structure stable above 2.5 GPa. This phase is most likely corresponding to the second one observed in experiments as evidenced by the calculated equation of states of PbI₂ [Fig. 3(b)], where the volume decrease of 5.6% from the 2H-P3̄m1 to Pnma structure at 2.5 GPa is in good agreement with that of 6% (2% + 4%) observed by experiments.^25,26 The stability field of the first high-pressure phase that do not found in the current work covers only a very narrow pressure range of about 1–2 GPa. In fact, there are some discrepancies between experiments. While Raman and optical measurements in 1986 deduce the first high-pressure phase possesses a 3D structure,²⁸ later Raman and luminescence spectra study in 2000 suggests this phase is a 2 × 2 supercell of 2H-P3̄m1 structure with relative atom position and bondings hardly changed.²⁹ Nevertheless, the first high-pressure phase should be an intermediate phase account for the layered to 3D structural transition. Thus, the complete phase transition sequence of PbI₂ under compression should be 2H-P3̄m1 → intermediate phase → Pnma → I4/mmm → Immm → C2/c. Determination of the detailed crystal structure of such an intermediate phase in a narrow pressure range is challenging. Intensively theoretical structure search simulations with high level of accuracy or in situ X-ray diffraction experiments are needed.

To gain insight into the electronic properties of PbI₂ under compression, the electronic band structures and partial density of states (PDOS) of various phases are calculated and shown in Fig. 5. For 2H-P3̄m1 structure, the calculated HSE + SOC band structure shows a direct bandgap of 2.15 eV at the A point of the Brillouin zone [Fig. 5(a)], which is in reasonable agreement with the experimental value of 2.3–2.5 eV.² For the high-Z element Pb, the Pb-6s state moves down in energy (forming lone-pair states), separating from Pb-6p state (mass-Darwin relativistic effect).⁴⁵ For +2 low oxidation state of Pb in PbI₂, there exists charge transfer form Pb-6p to I-5p. Thus the valence band (VB) edge is mainly formed by anti-bonding hybridization of the Pb-6s and I-5p states, while the conduction band (CB) edge is derived from anti-bonding hybridization of the Pb-6p and I-5p states. This situation can be clear seen form the PDOS as show in Fig. 5(f). The existence of Pb-6s lone-pair states renders the VB edges broaden and dispersive, leading to a small hole effective mass at the VB maximum. This is in contrast to the oxides having a rather narrow VB due to localized O-2p states, or the transition metal compounds where the narrow VB reflects localized d states, both of which show large hole effective masses. This type of physics has been elucidated earlier for binary lead chalcogenides.⁴⁶ For the orthorhombic Pnma structure, the band structure [Fig. 5(b)] calculated at 10 GPa shows an indirect bandgap of 1.68 eV formed by the VB maximum at U point and CB minimum at G point of the Brillouin zone. Through the structural topology is dramatically changed, the bonding character is essentially same as that of the 2H-P3̄m1 structure, e.g. VB edge formed by anti-bonding hybridization of Pb-6s and I-5p states, and CB edge formed by anti-bonding hybridization of Pb-6p and I-5p states [Fig. 5(g)]. PbI₂ is still a semiconductor at the stable field of Pnma phase (2.5–27.2 GPa). Band structure of the tetragonal I4/mmm structure [Fig. 5(c)] calculated at 50 GPa shows that both the VB and CB are broadened and pass through the Fermi level, indicating electron delocalization and pressure-induced metallization occurs. In higher pressure phases, Immm and C2/c, the metallic nature of PbI₂ persists [Fig. 5(d) and (e)] up to the decomposition pressure of ∼169.1 GPa.

Fig. 5 Electronic band structures (top row) and partial density of states (bottom row) for 2H-P3̄m1 [(a) and (f)], Pnma [(b) and (g)], I4/mmm [(c) and (h)], Immm [(d) and (i)] and C2/c [(e) and (j)] phases of PbI₂, respectively.

Conclusions

In summary, through systematic swarm-intelligent CALYSPO structure searches combined with first-principles calculations, we report the phase transition sequence of 2H-P3̄m1 → intermediate phase → Pnma → I4/mmm → Immm → C2/c for PbI₂ under compression, in which four new stable high-pressure phases have been uncovered. Within this phase transition sequence, layered to 3D structure transition was proposed to be taking place at 2.5 GPa from the 2H-P3̄m1 structure to an intriguing orthorhombic Pnma structure that have not been seen in other AB₂ compounds. Pressure-induced metallization is observed at the phase transition from Pnma to I4/mmm (27.1 GPa). The metallicity of PbI₂ persists in higher-pressure phases of Immm and C2/c up to about 169.1 GPa, above which PbI₂ decomposes to constituent elements. The current work presents significant results of fundamental structural and electronic properties of PbI₂ under compression and will inevitably stimulate future experimental and theoretical study of PbI₂ at high pressure.

Acknowledgements

The authors appreciate the financial supports form the National Natural Science Foundation of China (51272084, 61225018, 61475062), the Jilin Province Key Fund (20140204079GX) and the Postdoctoral Science Foundation of China (2015M571360).

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Footnote

† Electronic supplementary information (ESI) available: The detailed structure information and calculated enthalpies of ground-state and low-lying structures form the structure searches. See DOI: 10.1039/c6ra16487k

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