The stability of CsGeX₃ (X = I, Br, Cl) selectively tuned by the crystal structures and halide ions as inferred from the calculated phonon spectrum

Abstract

In spite of the considerable advancements achieved in enhancing the power conversion efficiency (PCE) of lead-based all-inorganic perovskite solar cells, there persists a need for materials that are both more stable and environmentally friendly. This investigation systematically explores the structural and thermodynamic stability, and electronic properties of Ge-based all-inorganic perovskite CsGeX₃ (X = Cl, Br, I) in two space groups, Pm3̄m and R3m, utilizing first-principles calculations. Introducing the novel concept of the “imaginary frequency coefficient” alongside the tolerance factor and stabilizing the chemical potential window, we collectively characterize the stability of CsGeX₃ based on the phonon spectrum and phonon density of states calculations. The findings reveal that the stable phase of the Ge-based perovskite differs from that of lead-based systems, with the R3m structure of CsGeX₃ being the most stable in the rhombohedral phase. Moreover, the stability of R3m-CsGeX₃ can be manipulated by adjusting the halide composition with a gradual increase in stability observed as halogen atoms shift from I to Cl. This comprehensive approach, integrating the phonon spectrum, innovative measurement indicators, and tolerance factor, presents an effective strategy for designing materials that are both non-toxic and stable.

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1. Introduction

Organic–inorganic halide perovskite solar cells (PVSCs), denoted by the chemical formula ABX₃, represent a highly promising class of renewable energy materials, showcasing a remarkable power conversion efficiency (PCE) of up to 26.41%.^1–5 However, their thermal instability and light instability have always impeded the widespread commercialization of perovskite solar cells. A pivotal advancement in addressing this challenge emerged in 2015 when Eperon et al.⁶ pioneered the development of all-inorganic perovskite solar cells based on CsPbI₃. Subsequent investigations revealed that the incorporation of metal cations in lieu of organic cations at the A-site significantly enhances thermal and phase stability, propelling the rapid advancement of all-inorganic perovskite technology.^7–10 Notably, the most recent PCE milestone has surged to 21.15%,¹¹ positioning all-inorganic perovskite materials in structures like ABX₃ (A = Cs; B = Ge, Sn, Pb; X = Cl, Br, I) at a focal point of contemporary research. This achievement is particularly significant as it approaches the current highest photoelectric conversion rate of organic–inorganic hybrid perovskite solar cells. Moreover, in response to concerns regarding the toxicity of Pb and the susceptibility of Sn to oxidation,^12,13 researchers have turned their attention to Ge-based perovskites. This strategic shift has not only resulted in groundbreaking power conversion efficiency (PCE) surpassing 10% but has also demonstrated remarkable stability, enduring beyond 500 hours, which offers a promising avenue to overcome environmental and stability challenges associated with traditional perovskite materials.^14–16

Compared to the Pb-based perovskite systems, CsGeX₃ (X = Cl, Br, I) materials exhibit distinctive structural characteristics. It has been reported in the literature that the Pb-based inorganic perovskite CsPbI₃ manifests a tetragonal (β) phase under specific room temperature conditions and transforms into a cubic (α) phase at elevated temperatures.^17,18 The substitution of Pb with Ge introduces structural modifications to CsGeX₃, yet debates persist regarding the most stable configuration of Ge-based perovskites. In 1982, Guen et al.¹⁹ synthesized CsGeI₃ crystals with the Pmmm space group for the first time. Following this, Thiele et al.²⁰ synthesized CsGeX₃ (X = Cl, Br, I) crystals and observed their phase transition behavior. At low temperatures, they exhibited a rhombohedral phase structure with the R3m space group, which transitioned to a cubic phase structure with the Pm3̄m space group as the temperature increased.²⁰ In 2015, Sherburne et al.²¹ successfully synthesized CsGeI₃ crystals with a stable R3m configuration and confirmed the absence of phase transitions within the operational temperature range of the device. In 2018, Wu et al.²² synthesized R3m-phase CsGeI₃ perovskite nanocrystals and investigated their degradation mechanism in air, observing their eventual transformation into polycrystalline CsI. In 2021, Luo et al.²³ computationally confirmed the R3m phase as the stable structure for CsGeI₃, with the Pmmm phase being metastable. In the same year, Dias et al.'s²⁴ theoretical calculations indicated that for CsGeX₃ (X = Cl, Br, I), the Pm3̄m phase is not the lowest energy configuration, while the R3m phase demonstrates superior stability.

Analyzing phonon vibrations and phase diagrams serves as a valuable methodology for assessing thermal stability and phase transitions. Within the phase diagram, the polyhedron region delineated by the exclusion of competing phases signifies the establishment of a stable state.²⁵ Concurrently, the presence of soft phonon modes in the phonon spectrum, characterized by imaginary frequencies, serves as a key indicator of structural instability.²⁶ For instance, Huang et al. conducted an extensive investigation into the relationship between soft phonon modes and phase transitions in CsSnX₃ (X = Cl, Br, I). They performed comprehensive calculations of the full phonon spectrum and the phonon density of states (PDOS) across various phases. Their findings revealed the exclusive manifestation of soft phonon modes in cubic and square phases, while their absence was noted in orthorhombic or monoclinic phases.²⁷ Similarly, Zhu et al.²⁸ demonstrated in 2019 that phonon calculations could unveil lattice instability resulting from dynamic disorder and anharmonicity of phonons in hybrid lead halide perovskites. Building upon these prior investigations, our study aims to explore the stable structure of all-inorganic Ge-based perovskites by analyzing the phase diagram and phonon dispersion of CsGeX₃ (X = Cl, Br, I) in different phases and scrutinizing trends related to soft phonon modes.

In this work, we systematically studied the structure, phonons, thermodynamic stability, and electronic properties of Ge-based all-inorganic perovskite CsGeX₃ (X = Cl, Br, I) in two space groups, Pm3̄m and R3m, using density functional theory (DFT) calculations. Firstly, we investigated the geometric structure and energy of both space groups and found that CsGeX₃ in the R3m space group had lower energy due to the displacement of Ge ions. Secondly, we computed the phonon spectrum and phonon density of states (PDOS) of both space groups using the density functional perturbation theory (DFPT) method. For the first time, we introduced the concept of the “imaginary frequency coefficient” to quantify the stability of CsGeX₃ in the two space groups, in conjunction with the tolerance factor value. The results indicated that CsGeX₃ in the R3m space group exhibited a smaller imaginary frequency coefficient, suggesting a more stable structure. The stability could be adjusted by changing the halogen composition. Additionally, we systematically investigated the stability chemical potential window and found that the halogen composition could significantly regulate the size of the chemical potential window, effectively tuning the thermodynamic stability of CsGeX₃. Lastly, we computed the electronic properties of CsGeX₃ in both space groups and observed similar electronic band structures, although the R3m space group had a wider bandgap. This study provided a novel perspective for characterizing the stability of Ge-based all-inorganic perovskite materials by combining the tolerance factor with other parameters, contributing to the research and design of stable materials.

2. Computational methods

All first-principles calculations were performed using the projector augmented wave (PAW)²⁹ method as implemented in the Vienna ab initio simulation (VASP)³⁰ package, based on density functional theory (DFT). We chose the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) as the exchange–correlation functional.³¹

For the calculation of the energy band structure, in the first Brillouin zone integration, we set the cut-off energy of the plane waves to 500 eV. We used a Γ-centered mesh with k-points set to 6 × 6 × 6.³² Highly symmetric k-points were introduced for the band structure calculation, including Γ(0,0,0), X(0,1/2,0), M(1/2,1/2,0), R/T(1/2,1/2,1/2), L(1/2,0,0), and F(1/2,0,1/2). All structures were relaxed using a conjugate-gradient algorithm until the energy on the ions was less than 1.0 × 10⁻⁵ eV and all forces were minimized to 0.02 eV Å⁻¹. The initial wave function was randomly generated, using the superposition of atomic charge densities. Finally, the projected band structure of the material was plotted.

In order to obtain accurate phonon dispersion curves, it is necessary to first perform high-precision optimization of the crystal structure. Set the convergence energy of the system to 10⁻⁶ eV and progressively refine the accuracy from low to high until the atomic force convergence criterion reaches 10⁻⁶ eV Å⁻¹. For the calculation of the phonon spectrum, we utilized the density functional perturbation theory (DFPT) method implemented in the PHONOPY code.^33,34 The supercell was set at 2 × 2 × 2, and VASP was used to calculate the forces on atoms in the reconstructed supercell generated by PHONOPY to obtain the phonon vibrational properties and the phonon density of states (PDOS). To ensure convergence, we reduced the k-point sampling for force calculation based on the increase in supercell volume, ultimately setting the Γ-centered mesh k-point at 3 × 3 × 3. Finally, the corresponding phonon spectra and phonon density of states images of the materials were plotted. The crystal structures were constructed using the VESTA³⁵ program.

3. Results and discussion

We investigated two crystal structures of CsGeX₃ (X = Cl, Br, I): cubic phase (Pm3̄m space group, no. 221) and rhombohedral phase (R3m space group, no. 160). They are referred to as Pm3̄m-CsGeX₃ and R3m-CsGeX₃ in this paper. Fig. 1(a) and (b) illustrate CsGeCl₃ as an example for comparing and explaining the differences between the two crystal structures of CsGeX₃ materials. The detailed crystal structure parameters and schematic diagrams for all materials are respectively presented in Table 1 and Fig. S1 (ESI†). In the Pm3̄m-CsGeX₃, the Ge ions occupy the geometric center of the GeX₆ octahedron (0.5, 0.5, 0.5). The Ge ions and X ions form the GeX₆ regular octahedral structure through shared angles, where the Ge–X bond lengths are equal (all six Ge–X bond lengths in CsGeCl₃ are 2.67 Å). However, in the R3m-CsGeX₃, the Ge ions undergo displacement in the direction of the body diagonal (0.516, 0.516, 0.516), resulting in distortion of the GeX₆ octahedra. Three Ge–X bonds are compressed, while the other three Ge–X bonds are elongated (e.g., the longer and shorter Ge–X bond lengths in CsGeCl₃ are 3.118 Å and 2.415 Å, respectively). Furthermore, in the Pm3̄m-CsGeX₃, the lattice parameters a, b, and c are equal, and the Bravais lattice angles α = β = γ = 90°. In contrast, the lattice parameters and cell volume in the R3m-CsGeX₃ are larger, and the Bravais lattice angles α = β = γ < 90°. We manipulated the positions of the Ge ions in the Pm3̄m-CsGeX₃ crystal along the 〈111〉 crystal plane to achieve initial crystal structures with varying Ge ion displacement distances, the optimization of atomic positions and unit cell shape was subsequently conducted. Based on the changes in the crystal structure and energy depicted in Fig. 1(c), we can infer that the displacement of Ge ions along the 〈111〉 crystal plane may be the primary cause of the phase transition from Pm3̄m-CsGeX₃ to R3m-CsGeX₃. The stereochemically active lone pair (4s²) of Ge(II) cations can play a central role in promoting the Ge off-centering displacement.³⁶ The parameters of these initial crystal structures are listed in Table S1 (ESI†). We further applied the static DFT method to calculate the relationship between the displacement of Ge along the 〈111〉 crystal plane from the geometric center of the octahedron and the relative energy ΔE, as shown in Fig. 1(d). The displacement of Ge resulted in a decrease in the total energy of the structure, with no energy barrier observed. This further supports the results in Fig. 1(c), indicating that the structural fluctuations caused by the displacement of Ge atoms lead to a transition of the Pm3̄m phase structure to a more stable configuration.

Fig. 1 The crystal structure of (a) Pm3̄m-CsGeCl₃ and (b) R3m-CsGeCl₃, (c) the relationship between the displacement of Ge ions along the 〈111〉 crystal plane direction and the energy. The left inset in the figure illustrates the crystal structure when the Ge ion displacement is equal to 0 Å and 0.02 Å. The right inset in the figure depicts the relationship between the displacement of Ge ions and the variation in cell volume. (d) The relationship between the displacement of Ge along the 〈111〉 crystal plane from the geometric center of the octahedra and the relative energy ΔE. Here, ΔE is defined as the energy difference between the structure after the displacement of Ge atoms and the initial state. This result was obtained through static DFT calculations.

Table 1 Tolerance factor and the lattice parameters, Bravais lattice angles, cell volume, Ge–X bond lengths, and energy of Pm3̄m-CsGeX₃ and R3m-CsGeX₃. The bold values in the table represent experimentally measured data²⁰

Space group	Material	a = b = c (Å)	α = β = γ (deg)	Volume (Å^^3)	D ^Ge-X s(l) Å	Energy (eV)	t G
Pm3̄m (cubic phase)	CsGeCl3	5.339	90	152.204	2.670	−17.56	0.969
		5.47		163.7	2.73
	CsGeBr3	5.610	90	176.600	2.805	−15.90	0.954
		5.69		184.2	2.84
	CsGeI3	6.001	90	216.108	3.001	−14.10	0.934
		6.05		221.4	3.02
R3m (rhombohedral phase)	CsGeCl3	5.522	89.085	168.328	2.415(3.118)	−17.76	0.969
		5.434	89.72	160.44	2.348(3.092)
	CsGeBr3	5.758	88.430	190.691	2.580(3.200)	−15.98	0.954
		5.635	88.74	178.65	2.534(3.116)
	CsGeI3	6.115	88.362	228.435	2.792(3.359)	−14.17	0.934
		5.983	88.61	213.84	2.745(3.263)

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The crystal structure differences between the Pm3̄m-CsGeX₃ with the R3m-CsGeX₃ resulted in distinct variations in structural stability. The tolerability factor (t_G) is an important parameter for evaluating the structural stability of perovskite materials: , where r is the radius of the corresponding ion.^37,38 By varying the ion radii at the A, B, and X positions, the stability of perovskite materials can be adjusted. The commonly encountered ion radii for inorganic halide perovskites are Cs⁺ = 1.67 Å, Ge²⁺ = 0.73 Å, Cl⁻ = 1.81 Å, Br⁻ = 1.96 Å, I⁻ = 2.20 Å.³⁹ According to this formula, the t_G values for the six CsGeX₃ systems all fall within the range of 0.9–1.0, indicating that their crystal structures can stably exist in the perovskite structure. As the radius of the halide anions at the X position decreases (from I to Br to Cl), the t_G value increases and gradually approaches 1, indicating that as the halide ion radius at the X position decreases, the CsGeX₃ perovskite structure tends towards the ideal cubic perovskite structure. According to the results shown in Table 1, the R3m-CsGeX₃ exhibits lower energy compared to the Pm3̄m-CsGeX₃. This indicates that the R3m-CsGeX₃ is more structurally stable. Further observations reveal that R3m-CsGeX₃, as the radius of the halide anions at the X position decreases, the cell volume also decreases. The Bravais lattice angles gradually approach 90°, indicating a lattice contraction and a tendency towards a transformation from a lower symmetry to an ideal cubic cell structure. This crystal structure transformation aligns with the trend described by the tolerability factor regarding structural stability and contributes to the enhancement of stability. This strengthening may be linked to the strengthening of chemical bonding between the Ge ion and the X ion. As the electronegativity of the halide anions at the X position increases from I to Cl, the interaction between Ge and X becomes stronger, further enhancing the stability of the crystal structure. Therefore, halide ions play a significant role in regulating the stability of CsGeX₃ materials.

To investigate the dynamical stability of CsGeX₃ (X = Cl, Br, I), we calculated the phonon spectrum and phonon density of states for Pm3̄m-CsGeX₃ and R3m-CsGeX₃. The results are depicted in Fig. 2. Both Pm3̄m-CsGeX₃ and R3m-CsGeX₃ exhibit imaginary frequencies in their respective phonon spectrum. However, the difference lies in the distribution of the imaginary frequencies. In the Pm3̄m-CsGeX₃, imaginary frequencies are observed in the optical branches and are distributed within the high-symmetry points of the Brillouin zone, specifically within the range of Γ–X–M–Γ. In contrast, in the R3m-CsGeX₃, imaginary frequencies are only present in the acoustic branches and are located in the vicinity of two high-symmetry points, T and F. This demonstrates that both lattice structures in the two space groups show factors that lead to lattice instability. By analyzing the phonon density of states and the schematic representation of atomic vibration modes in Fig. S2 (ESI†), we observe that the lattice instability primarily originates from the GeX₆ octahedra. Specifically, the instability of the Pm3̄m-CsGeX₆ structure arises from the vibrations occurring in opposite directions between the Ge and halide atoms, while the instability of the R3m-CsGeX₃ structure is attributed to the collective “swinging” vibrations of the Ge and halide atoms as an integrated unit. On the other hand, in the Pm3̄m-CsGeX₃, as halide ions change from Cl to I, the absolute value of the imaginary frequency decreases. This factor explains the narrowing of the frequency distribution range in the phonon spectrum from CsGeCl₃ to CsGeI₃. For instance, the frequency distribution range for Pm3̄m-CsGeCl₃ materials is −150 to 225 cm⁻¹, while for Pm3̄m-CsGeI₃ materials, it is −75 to 125 cm⁻¹. Moreover, this indicates that Cs, as the heaviest atom, contributes solely to the phonon spectrum at lower frequencies.

Fig. 2 The phonon spectrums and phonon density of states (PDOS) for (a)–(c) Pm3̄m-CsGeX₃ (X = Cl, Br, I) and (d)–(f) R3m-CsGeX₃. The acoustic branches are highlighted in red, with the PDOS plot vertically aligned to correspond to the phonon dispersion curve frequencies on the left. The gray area indicates the total phonon density of states, and the colored lines represent the contributions of individual ions.

In order to compare the differences in dynamic stability between Pm3̄m-CsGeX₃ and R3m-CsGeX₃ and obtain quantitative results from the phonon spectrum and phonon density of states, we adopted the concept of the “imaginary frequency coefficient” to represent the imaginary frequency information in the phonon density of states. The imaginary frequency coefficient (referred to as I) was defined by integrating the portion corresponding to imaginary frequencies with the total phonon density of states curve.

f_Dos represents the phonon density of states as a function of frequency, while “a” represents the lowest imaginary frequency at which the density of states is non-zero. This definition of the imaginary frequency coefficient primarily takes into account two points. Firstly, the magnitude of the imaginary frequency is an important parameter for dynamic stability. Stronger imaginary frequencies indicate poorer stability. Secondly, considering that the density of states is also a crucial parameter for dynamic stability, a higher number of states occupied by the imaginary frequency implies greater instability of the material. Hence, a larger imaginary frequency coefficient indicates a worse structural stability of the material. We calculated the imaginary frequency coefficients of Pm3̄m-CsGeX₃ and R3m-CsGeX₃ combined with the tolerance factors, as shown in Fig. 3. The imaginary frequency coefficient of Pm3̄m-CsGeX₃ is significantly higher than that of R3m-CsGeX₃, indicating that R3m-CsGeX₃ exhibits stronger dynamic stability. It is noteworthy that in R3m-CsGeX₃, there is an increasing trend in the frequency coefficient as the halide ions change from Cl to I, leading to a decrease in the materials’ stability. This trend in variation is consistent with the trend observed when evaluating the material stability using the tolerance factor. Therefore, by considering both the frequency coefficient and the t_G, we can conclude that halide ions play a crucial role in regulating the stability of the material.

Fig. 3 The imaginary frequency coefficients and tolerance factors of CsGeX₃ (X = Cl, Br, I) in the Pm3̄m and R3m-CsGeX₃.

To further investigate the effective regulation of halide ions on the stability of CsGeX₃, computational phase diagram measurements were used to visualize the chemical potential stability regions for Pm3̄m-CsGeX₃ and R3m-CsGeX₃.^7,40,41 The physical implications of eqn (1)–(4) are as follows: the existence of a region that satisfies the specified inequality constraints indicates that, under certain conditions, it is feasible to synthesize single-phase crystals free of impurities, thereby suggesting that they are thermodynamically stable in essence. Conversely, the absence of such a region implies that the synthesis of crystals is challenging, and their phase stability is questionable.⁴² Taking R3m-CsGeCl₃ as an example, under thermodynamic equilibrium growth conditions, the existence of CsGeCl₃ should satisfy eqn (1). To exclude the possible secondary phases CsCl and GeCl₄, the following constraints must also be satisfied (2)–(4). The chemical potential of Cs and Ge satisfying eqn (1)–(4) are shown as the green region in Fig. 4(a). This chemical range indicates the growth conditions for synthesizing R3m-CsGeCl₃ under equilibrium conditions.

μ_Cs + μ_Ge + 3μ_Cl = ΔH_CsGeCl3 = −17.557 (1)

μ_Cs + μ_Cl < ΔH_CsCl = −6.639 (2)

μ_Cs + 4μ_Ge < ΔH_GeCl4 = −16.424 (3)

μ_i < 0 (i = Cs, Ge, Cl) (4)

where μ_Cs, μ_Ge, and μ_Cl represent the chemical potentials of each constituent element relative to its most stable phase, ΔH represents the formation enthalpy of the elemental material. Fig. S3 (ESI†) shows the constraints for Pm3̄m-CsGeX₃ and R3m-CsGeX₃. As illustrated in Fig. 4, R3m-CsGeCl₃ exhibits the largest stable chemical potential window, while the respective windows gradually decrease for the materials with halide ion variation from Cl to Br and then to I, indicating a weakening of thermodynamic stability. This trend is also observed for Pm3̄m-CsGeX₃. The chemical potential window of the same compound in the Pm3̄m space group is smaller than that in the R3m space group, suggesting that Pm3̄m-CsGeX₃ has lower thermodynamic stability than R3m-CsGeX₃. Pm3̄m-CsGeI₃ exhibits no chemical potential window, indicating the inability to form a stable Pm3̄m-CsGeI₃ material under these constraints.

Fig. 4 The thermodynamic stability diagrams of (a)–(c) CsGeX₃ (X = Cl, Br, I) in the R3m-CsGeX₃ as functions of the chemical potentials of μ_Cs and μ_Ge.

Finally, we calculated the electronic band structures and density of states (DOS) for CsGeX₃ (X = Cl, Br, I) to understand their electronic properties. Fig. 5 illustrates the projected band structures and DOS. Firstly, we observe that the band structures of Pm3̄m-CsGeX₃ and R3m-CsGeX₃ are highly similar, with the main distinction being the splitting of the threefold degenerate CBM in the R3m-CsGeX₃ due to crystal field splitting or reduced symmetry,⁴³ and the degree of splitting becomes more pronounced as the halide ion at the X-site changes from Cl to I. Both Pm3̄m-CsGeX₃ and R3m-CsGeX₃ are direct band gap semiconductors, with the valence band maximum (VBM) and conduction band minimum (CBM) located at the T point (0.5, 0.5, 0.5). The VBM is mainly contributed by Ge-s and X-p orbitals, while the CBM is largely influenced by Ge-p orbitals. The band gap of Pm3̄m-CsGeX₃ is smaller than that of R3m-CsGeX₃, and their band gaps decrease with increasing halide ion radius.

Fig. 5 Electronic projected band structures and density of states (DOS) of (a)–(c) Pm3̄m-CsGeX₃ (X = Cl, Br, I) and (d)–(f) R3m-CsGeX₃. The Ge-p, Ge-s, and X-p orbitals were represented by the colors blue, red, and green, respectively. The value of E_g indicated the magnitude of the band gap in the material.

4. Conclusions

In this comprehensive study, we systematically explored the structural, phononic, thermodynamic, and electronic properties of Ge-based all-inorganic perovskites CsGeX₃ (X = Cl, Br, I) in the Pm3̄m and R3m space groups through rigorous first-principles calculations. The stability assessment of CsGeX₃ was conducted utilizing a multifaceted approach, incorporating the tolerance factor coefficient (t_G), imaginary frequency coefficient (I), and a stable chemical potential window. Our theoretical analysis discerned the stability disparity in CsGeX₃ in the two space groups, revealing that R3m-CsGeX₃ possesses heightened stability characterized by lower energy, a reduced imaginary frequency coefficient, and a broader stable chemical potential window. Additionally, we observed that the stability of R3m-CsGeX₃ can be modulated by varying the halide composition, exhibiting a gradual increase in stability as the halogen atom transitions from I to Cl. This innovative approach, amalgamating novel measurement indicators such as phonon spectra with tolerance factors, serves as an effective strategy for designing materials with enhanced stability and reduced toxicity.

Author contributions

The supervision of this research project was undertaken by Tingting Shi, Weiguang Xie, and Pengyi Liu, who provided essential computational resources to support the project. The conceptualization of the project theme and the determination of the research approach were collaboratively accomplished by Tingting Shi, Tengcheng Huang, and Zheyu Zhang. Tengcheng Huang and Zheyu Zhang also undertook the literature review and organization, as well as the computation, graphical representation, and analysis of the research findings, and participated in the drafting and revision of the initial manuscript. Tingting Shi offered professional guidance in the writing process and played a significant role in the construction of the paper's structure and theoretical guidance throughout the research process. Baoyun Liang and Ang Li contributed to the literature review and organization, as well as the graphical representation and analysis of the experimental results. Xin Xu and Yujia Gao engaged in the analysis and discussion of the phonon spectrum computational results. Zhuxia Wu, Haiyan Li, and Fei Yuan participated in the analysis and discussion of the structural characteristics and electronic structure computational results of the materials. All authors have reviewed and approved the final manuscript.

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

Tengcheng Huang and Zheyu Zhang contributed equally to this work. This work was supported by the National Natural Science Foundation of China (Grants No. 61674070, 62174072, 11804117 and 21973034), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019B151502049 and 2022A1515010276), and the Uniqueness and Innovation Projects for the Universities in Guangdong Province (Grant No. 2022KTSCX010). Computer time at the National Supercomputer Center in Guangzhou (NSCCGZ) and the High-Performance Computing Platform of Jinan University is gratefully acknowledged. T. S. and P. L. also acknowledge the Guangzhou Key Laboratory of Vacuum Coating Technologies and New Energy Materials (No. 201605030008).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4cp02988g

‡ Tengcheng Huang and Zheyu Zhang are co-first authors.

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