卤化物钙钛矿材料ABX₃ (A⁺ = Cs, CH₃NH₃, CH(NH₂)₂; B²⁺ = Pb, Sn, Ge; X^- = Cl, Br, I)由于可控的物理结构和优良的光电特性成为材料、物理、化学等多领域研究的热点之一，而其在发光二极管(LED)、激光器、光电探测器及太阳能电池等方面的应用基础也非常广泛。在过去的近十年中，大量的研究工作围绕着如何优化卤化物钙钛矿的光伏性能、提高其器件的稳定性以及材料制备中如何消除铅的毒性方面，而有关卤化物钙钛矿力学性能方面研究相对较少。卤化物钙钛矿薄膜的应力/应变在太阳能电池的制造和操作过程中不可避免地存在。在材料的制备工艺热退火过程中，钙钛矿薄膜和基底之间不匹配的热膨胀会引起明显的应力。应力的存在会显著地导致钙钛矿薄膜的内在不稳定性和降解。基于应力可以通过调节卤化物钙钛矿的带隙、相变和离子迁移进而极大地影响太阳能电池器件的性能。本论文通过第一性原理计算，研究全无机-铯基卤化物钙钛矿材料的化学成分、相变、结构维数、八面体层厚和八面体连通性对其力学性能的影响。论文中采用弹性常数C_ij和弹性模量(体积模量B、剪切模量G、杨氏模量E)来确定卤化物钙钛矿的弹性性质，以及通过几何因素（即离子半径、键长、容忍因子、相对原子质量）和电子因素（即电负性EN，核电荷数）来解释卤化物钙钛矿的弹性趋势。本文主要的研究结论如下：

(1) 研究了不同元素对全无机-铯基卤化物钙钛矿材料CsBX₃力学性能的影响。发现随着X位阴离子的离子半径增大[r (Cl^-) < r (Br^-)< r (I^-)]，材料的弹性常数(C₁₁, C₁₂, C₄₄)逐渐减小, 这是由于B-X的化学键强度降低所导致。固定X位阴离子不变，观察到C₁₁和C₁₂随着EN（从Sn到Pb再到Ge）的增加而降低，表明元素的电子结构对卤化物钙钛矿的弹性系数起着关键作用。

(2) 研究了光电性能优良的不同晶相的CsPbI₃对其力学性能的影响。对于立方相 (α) 和四方相 (β) CsPbI₃，晶体的主弹性常数(C₁₁, C₂₂, C₃₃)与其晶格常数(a, b, c)呈相反的趋势。对于正交相 (γ) CsPbI₃，三个晶格常数的顺序为b > a > c，而弹性常数的变化趋势为C₃₃ < C₁₁ < C₂₂。这可能是由于随着相结构对称性的降低，B-X键强度和结构畸变的竞争中，结构畸变更占优势。弹性模量B、G和E均随Pb-I键长的增加而减小，也随晶体结构对称性的减小而减小。并且卤化物钙钛矿的结构维度也可调节其力学各向异性。

(3) 研究了CsPbI₃（3D, 空间群Pm-3m）、Cs₂PbI₄（2D,空间群I4/mcm62）和Cs₄PbI₆（0D, 空间群R-3c63）结构维数对材料力学性能的影响。结果表明卤化物钙钛矿力学变化趋势和维度的关系为3D ((4.914 g/cm³) > 0D (4.564 g/cm³) > 2D ((4.450 g/cm³)，即卤化物钙钛矿力学变化趋势与其质量密度有关。

(4) 研究了层状钙钛矿[n = 1 (Cs₂PbI₄), n = 2 (Cs₃Pb₂I₇)和n = 3 (Cs₄Pb₃I₁₀)]八面体[PbI₆]的层数n对其力学性能的影响，层数可以提高弹性性能。当n从1增加到2再增加到3时，面内、面外弹性常数不仅增加，而且面内弹性常数比面外弹性常数高出约12Gpa，这是由于平面内是通过离子键或/和共价键结合的，而平面外是通过弱的范德瓦尔斯相互作用结合的。杨氏模量(E)的各向异性不随层厚n改变。

(5) 研究了八面体[PbI₆]的面共享的比例对卤化物钙钛矿力学性能的影响。表明增加[PbI₆]的面共享比例会增加相应化合物的弹性常数和弹性模量，这可能与其晶格的刚度增加有关。

(6) 双钙钛矿Cs₂AgBX₆ (B³⁺ = Bi, Sb, In; X^- = Cl, Br, I)的X位卤素原子半径越小或B位原子的核电荷数越小则相应的双钙钛矿越难被压缩；与单钙钛矿相比，双钙钛矿具有更好的柔韧性。

The halide perovskite material ABX₃ (A⁺ = Cs，CH₃NH₃，CH(NH₂)₂；B²⁺ = Pb，Sn，Ge； X^- = Cl，Br，I) has become one of the research hotspots in many fields such as materials, physics, and chemistry due to its controllable physical structure and excellent optoelectronic properties. And its application in light-emitting diodes (LEDs), lasers, photodetectors and solar cells is also very extensive. In the past nearly ten years, a lot of research work has revolved around how to optimize the photovoltaic performance of halide perovskites, how to improve the stability of their devices, and how to eliminate lead toxicity in material preparation. However, there are relatively few studies on the mechanical properties of halide perovskites. Stress/strain in halide perovskite thin films inevitably exists during the fabrication and operation of solar cells. The mismatched thermal expansion between the perovskite film and the substrate can cause significant stress during the thermal annealing of the material's fabrication process. The presence of stress can significantly lead to intrinsic instability and degradation of perovskite films. Based on stress, the performance of solar cell devices can be greatly affected by tuning the band gap, phase transition and ion migration of halide perovskites. In this thesis, first-principles calculations are used to investigate the effects of chemical composition, phase transition, structural dimension, octahedral layer thickness and octahedral connectivity on the mechanical properties of all-inorganic-cesium-based halide perovskite materials. The elastic constant C_ij and elastic modulus (bulk modulus B, shear modulus G, Young's modulus E) are used in the paper to determine the elastic properties of halide perovskites, and the geometric factors (i.e., ionic radius, bond length, etc.), tolerance factor, relative atomic mass) and electronic factor (i.e., electronegativity EN, nuclear charge number) to explain the elastic tendency of halide perovskites. The main conclusions of this study are as follows:

(1) The effects of different elements on the mechanical properties of the all-inorganic-cesium-based halide perovskite material CsBX₃ were studied. It is found that the elastic constants (C₁₁, C₁₂, C₄₄) of the material decrease gradually as the ionic radius of the X-site anion increases [r (Cl^-) < r (Br^-)< r (I^-)], which is due to the decrease in the chemical bond strength of B-X. With the fixed X-site anion unchanged, C₁₁ and C₁₂ were observed to decrease with increasing EN (from Sn to Pb to Ge), suggesting that the electronic structure of the element plays a key role in the elastic modulus of halide perovskites.

(2) The effects of different crystal phases of CsPbI₃ with excellent optoelectronic properties on their mechanical properties were studied. For cubic (α) and tetragonal (β) CsPbI₃, the principal elastic constants (C₁₁, C₂₂, C₃₃) of the crystals show opposite trends to their lattice constants (a, b, c). For orthorhombic (γ) CsPbI₃, the order of the three lattice constants is b > a > c, while the trend of the elastic constants is C₃₃ < C₁₁ < C₂₂. This may be since as the symmetry of the phase structure decreases, the structural distortion becomes more dominant in the competition between the B-X bond strength and the structural distortion. The elastic moduli B, G and E all decrease with the increase of the Pb-I bond length, and decrease with the decrease of the symmetry of the crystal structure. In addition, it was found that the structural dimension of halide perovskites can also tune their mechanical anisotropy.

(3) The effects of the structural dimensions of CsPbI₃ (3D, space group Pm-3m), Cs₂PbI₄ (2D, space group I4/mcm62) and Cs₄PbBr₆ (0D, space group R-3c63) on the mechanical properties of materials were studied. The results show that the relationship between the mechanical change trend of halide perovskite and the dimension is 3D ((4.914 g/cm³) > 0D (4.564 g/cm³) > 2D ((4.450 g/cm³), that is, the mechanical change trend of halide perovskite related to its mass density. 

(4) The effect of layer number n of layered perovskite [n = 1 (Cs₂PbI₄), n = 2 (Cs₃Pb₂I₇) and n = 3 (Cs₄Pb₃I₁₀)] octahedral [PbI₆] on its mechanical properties was investigated and it was found that the number of layers n can improve their elastic properties. Specifically, when n increases from 1 to 2 to 3, the in-plane and out-of-plane elastic constants not only increase, but also the in-plane elastic constants is about 12 GPa higher than the out-of-plane elastic constants, which is due to in-plane bonding by ionic or/and covalent bonding, while out-of-plane bonding is by weak van der Waals interactions. And the anisotropy of Young's modulus (E) does not change with the layer thickness n.

(5) The effect of the ratio of face sharing of the octahedral [PbI₆] on the mechanical properties of halide perovskites was investigated. The results show that increasing the face-sharing ratio of [PbI₆] increases the principal elastic constants and elastic moduli of the corresponding compounds, which may be related to the increased stiffness of their lattices.

(6) The smaller the radius of the X-site halogen atom of the double perovskite Cs₂AgBX₆ (B³⁺ = Bi, Sb, In; X^- = Cl, Br, I) or the smaller the nuclear charge number of the B-site, the more difficult the double perovskite to be compressed; And compared with single perovskites, double perovskites have better flexibility.