过渡金属硼化物（TMBs）凭借其特殊的原子排列和强化学键合性质，具备较高的硬度，能够满足高磨损、高冲击等极端工况的需求。在航天器、核能反应堆以及石油勘探、高端精密机械制造等高科技领域得到广泛应用。过渡金属硼化物的晶体结构之间具有强的化学键，使得过渡金属硼化物相较于传统耐火陶瓷材料具有更高的热稳定性，例如部分过渡金属硼化物的熔点超过3000℃，远高于许多传统耐火陶瓷，这种优异的耐高温性能使得此类化合物在诸多方面（如航空航天领域的超燃冲压发动机、冶金工业的高温熔炼等）展现出竞争优势。此外，在过渡金属硼化物体系中，硼元素位于周期表金属与非金属的独特边界区域，这一特殊位置赋予了硼原子既可能捕获电子，也可能释放电子的双重特性，与此同时，过渡金属具备较高的电子密度和灵活的价电子层结构，硼与过渡金属结合时能够衍生出多种体相结构的硼化物，也使得硼化物体系具有复杂的成键模式与结构特征。

过渡金属二硼化物（TMB₂）由于其合成条件相对较低、合成原料相对廉价、制备条件不苛刻以及在高温环境下的优异性能，在近些年持续受到研究者们的关注。其中，作为典型的过渡金属二硼化物，MnB₂因其独特的晶体结构与丰富的物理性质，成为了功能材料方向的研究热点。然而，现有研究主要聚焦于在常压条件下MnB₂的物性表征，高压对其结构及物性的影响尚未得到系统探究。众所周知，高压环境能够诱导晶体结构重构和电子排布变化，进而产生常压条件下难以观测的新相态和新性能，因此探究此类材料在高压条件下的结构相变与物性具有非常重要的科学意义和应用价值。鉴于此，本文将基于密度泛函理论（DFT）并结合CALYPSO晶体结构预测方法，全面探究MnB₂在0~400 GPa压力范围内的结构稳定性、力学性能、弹性各向异性及最小热导率等特性，所得结果将有助于提升对此类材料动态响应行为的预测和控制能力。本文的研究内容和创新性成果主要包括：

（1）本研究通过密度泛函理论计算结合CALYPSO结构预测算法，系统研究了零压下MnB₂不同晶体结构的稳定性、弹性各向异性和最小热导率。结果表明hP6-MnB₂，hP3-MnB₂，oP6-MnB₂，hR3-MnB₂，oP12-MnB₂和oI18-MnB₂六种结构的形成焓均为负值，意味着它们在常压下均具有热力学稳定性。基于形成焓的大小，确定了MnB₂的结构稳定性顺序为hP6 > hR3 > oP6 > oI18 > oP12 > hP3。此外，弹性常数及声子色散曲线的计算结果表明，这六种结构在环境条件下均是力学和动力学稳定的，证实了它们作为亚稳结构存在的可能性。维氏硬度计算表明hP6-MnB₂，hR3-MnB₂，oP6-MnB₂和oI18-MnB₂均是硬质材料的潜在候选者。另外，本文通过各向异性指数A^U、A_comp、A_shear以及方向相关的体积模量B、剪切模量G和杨氏模量E量化了不同MnB₂结构的弹性各向异性特征。结果发现，MnB₂的体积模量B的各向异性顺序为oP12 > hP3 > hP6 > hR3 > oI18 > oP6，而杨氏模量的各向异性顺序为oP12 > hR3 > hP6 > oP6 > hP3 > oI18。利用Clarke模型和Cahill模型进一步研究了此类材料的最小热导率，结果表明六种MnB₂结构的最小热导率均高于1.25 Wm^-1K^-1，表明它们均不是潜在的热障涂层材料。

（2）利用粒子群优化算法结合密度泛函理论探究了MnB₂在0~400 GPa压力范围内的结构稳定性、力学性质、电子性质及磁性性质。结果表明，MnB₂在压力下的相变序列为hP6→oI18→oP12→oI12，相应的相变压力分别为35.9、62.4和137.3 GPa。其中高压相oI12是首次在MnB₂中被发现。状态方程的拟合表明，结构转变时体积分别减少了约3.14%，2.76%和0.14%，表明该材料中发生的压致相变应为一阶相变。高压相oI18-MnB₂、oP12-MnB₂和oI12-MnB₂在50、80和140 GPa压力下的硬度分别为24.1、13.9和16.2 GPa，表明它们都是潜在的硬质材料。此外，对高压稳定相oP12-MnB₂和oI12-MnB₂电子性质的研究发现，B-B键形成的强共价键是维持其结构稳定的关键因素。最后，高压相oI12-MnB₂在磁性条件下仍然保持结构稳定，并且Mn的3d电子在费米能级附近有显著的自旋极化，证实了该结构是稳定的铁磁性材料，这为设计具有特定磁性性能的器件提供了重要参考。

Transition metal borides (TMBs), with special atomic arrangements and strong chemical bonds, are highly hard and can meet the demands of extreme conditions like high wear and impact. They are widely used in high-tech fields such as spacecraft, nuclear reactors, petroleum exploration, and high-precision machinery manufacturing. The strong chemical bonds in the crystal structure of transition metal borides give them higher thermal stability than traditional refractory ceramics. Some TMBs have melting points exceeding 3000℃, much higher than many traditional refractory ceramics. This excellent high-temperature resistance gives these compounds a competitive edge in various applications, such as scramjets in aerospace and high-temperature smelting in metallurgy. In the TMB system, boron occupies a unique position at the boundary between metals and non-metals in the periodic table. This distinctive location endows boron atoms with the dual ability to either capture or release electrons. Meanwhile, transition metals possess high electronic density and flexible valence electron shell structures. When boron combines with transition metals, it can form a variety of bulk boride structures, which also contribute to the complex bonding patterns and structural characteristics of the boride system.

Transition metal diborides (TMB₂) have garnered sustained attention from researchers in recent years due to their relatively low synthesis conditions, inexpensive raw materials, non-stringent preparation requirements, and excellent performance under high-temperature conditions. Among them, MnB₂, as a typical diboride, has become a research hotspot in the field of functional materials because of its unique crystal structure and rich physical properties. However, most existing studies have primarily focused on the characterization of its physical properties under ambient pressure conditions, and the effects of high pressure on its structure and properties have not yet been systematically investigated. It is well-known that high-pressure environments can induce crystal structure reconstruction and changes in electronic distribution in materials, thereby generating new phases and properties that are difficult to observe under ambient pressure conditions. Therefore, exploring the structure and properties of these materials under high-pressure conditions holds significant scientific importance and application value. In light of this, this paper will comprehensively investigate the structural stability, mechanical properties, elastic anisotropy, and minimum thermal conductivity of MnB₂ within the pressure range of 0~400 GPa, based on density functional theory (DFT) in conjunction with the CALYPSO crystal structure prediction method. The research content and innovative achievements of this paper are mainly summarized as follows:

(1) In this study, we systematically investigated the stability, elastic anisotropy, and minimum thermal conductivity of different crystal structures of MnB₂ at zero pressure using density functional theory calculations in conjunction with the CALYPSO structure prediction algorithm. The results indicate that the formation enthalpies of six structures, namely hP6-MnB₂, hP3-MnB₂, oP6-MnB₂, hR3-MnB₂, oP12-MnB₂, and oI18-MnB₂, are all negative, suggesting their thermodynamic stability under ambient conditions. Based on the magnitude of formation enthalpy, the stability sequence of MnB₂ structures was determined as hP6 > hR3 > oP6 > oI18 > oP12 > hP3. Furthermore, the calculations of elastic constants and phonon dispersion curves revealed that these structures are mechanically and dynamically stable under ambient conditions, confirming their potential existence as metastable phases. Additionally, the Vickers hardness calculations indicated that hP6, hR3, oP6, and oI18 structures of MnB₂ are potential candidates for hard materials. The elastic anisotropy characteristics of different MnB₂ structures were quantified using the anisotropy indices (A^U, A_comp, A_shear) and direction-dependent bulk modulus (B), shear modulus (G), and Young’s modulus (E). The results showed that the anisotropy sequence of the bulk modulus (B) is oP12 > hP3 > hP6 > hR3 > oI18 > oP6, while the anisotropy sequence of Young’s modulus (E) is oP12 > hR3 > hP6 > oP6 > hP3 > oI18. The minimum thermal conductivity of different MnB₂ structures was further investigated using the Clarke model and Cahill model. The results indicated that the minimum thermal conductivity of these materials is all above 1.25 Wm⁻¹K⁻¹, suggesting that they are not potential candidates for thermal barrier coating materials.

(2) The structural stability, electronic properties, mechanical properties, and magnetic properties of MnB₂ within the pressure range of 0~400 GPa were explored using the particle swarm optimization algorithm in combination with density functional theory. The results revealed that the phase transition sequence of MnB₂ under pressure is hP6→oI18→oP12→oI12, with phase transition pressures at 35.9, 62.4, and 137.3 GPa, respectively. Notably, the oI12 phase was discovered for the first time in MnB₂. Fitting of the equation of state shows that the volume decreases by approximately 3.14%, 2.76%, and 0.14% during the structural transitions, indicating that the pressure-induced structural transformations of MnB₂ should be first-order phase transitions. The hardness of the high-pressure stable phases oI18-MnB₂, oP12-MnB₂, and oI12-MnB₂ at pressures of 50, 80, and 140 GPa were 24.1, 13.9, and 16.2 GPa, respectively, indicating that they are potential hard materials. Furthermore, investigations into the electronic properties of the high-pressure stable phases oP12-MnB₂ and oI12-MnB₂ reveal that strong covalent B-B bonds are critical for maintaining structural stability. Finally, Furthermore, the oI12-MnB₂ phase remains structurally stable under magnetic conditions, with significant spin polarization of the Mn-3d electrons near the Fermi level, confirming that this structure is a stable ferromagnetic material. These findings provide important insights for designing devices with specific magnetic properties.

[1] Zheng X, Cui J, Gu C, et al. Superhard high-entropy dodecaboride with high electrical conductivity[J]. Scripta Materialia, 2022, 220: 114938.

[2] Solozhenko V L, Gregoryanz E. Synthesis of superhard materials[J]. Materials Today, 2005, 8(11): 44-51.

[3] 中国人民解放军第九十医院.一种眼科手术刀具:87212726.5[P]. 1987-10-20.

[4] 罗珊, 胡小月, 王成勇. 金刚石在医疗领域的应用[J].金刚石与磨料磨具工程, 2018(2).

[5] Xu B, Tian Y J. Superhard materials: recent research progress and prospects[J]. Science China Materials, 2015, 58(2): 132-142.

[6] Solozhenko V L, Andrault D, Fiquet G, et al. Synthesis of superhard cubic BC2N[J]. Applied Physics Letters, 2001, 78(10): 1385-1387.

[7] Azar-Kia B, Palacios E, Churchill R. Aqueductal stenosis and Parinaud’s syndrome[J]. IMJ. Illinois Medical Journal, 1975, 148(5): 532-533.

[8] Nagamatsu J, Nakagawa N, Muranaka T, et al. Superconductivity at 39 K in magnesium diboride[J]. Nature, 2001, 410(6824): 63-64.

[9] Cumberland R W, Weinberger M B, Gilman J J, et al. Osmium Diboride, an Ultra Incompressible, Hard Material[J]. ChemInform, 2005, 36(34).

[10] Chung H Y, Weinberger M B, Levine J B, et al. Synthesis of Ultra-Incompressible Superhard Rhenium Diboride at Ambient Pressure[J]. Science, 2007, 316(5823): 436-439.

[11] Chen Z Y, Xiang H J, Yang J, et al. Structural and electronic properties of OsB2 : A hard metallic material[J]. Physical Review B, 2006, 74(1): 012102.

[12] Hou G, Chen W, Sun Q, et al. Super wear-resistant WB4–B super-hard ceramic by in-situ formed lubrication film in high moisture[J]. Journal of Advanced Ceramics, 2024, 13(12): 1955-1964.

[13] Tao Q, Ma S L, Cui T, et al. Structures and properties of functional transition metal borides[J]. Acta Physica Sinica, 2017, 66(3): 036103-036103.

[14] Si J J, Yu J Q, Lan H H, et al. Chemical Potential-Modulated Ultrahigh-Phase-Purity Growth of Ultrathin Transition-Metal Boride Single Crystals[J]. Journal of the American Chemical Society, 2023, 145(7): 3994-4002.

[15] Pan Y, Chen S. Influence of alloying elements on the mechanical and thermodynamic properties of ZrB2 boride[J]. VACUUM, 2022, 198(110898).

[16] Beutler E, Kuhl W, Matsumoto F, et al. Acid hydrolases in leukocytes and platelets of normal subjects and in patients with Gaucher’s and Fabry’s disease[J]. The Journal of Experimental Medicine, 1976, 143(4): 975-980.

[17] Radziuk D, Möhwald H. Ultrasonically treated liquid interfaces for progress in cleaning and separation processes[J]. Physical Chemistry Chemical Physics, 2016, 18(1): 21-46.

[18] Ricci F, Chen W, Aydemir U, et al. An ab initio electronic transport database for inorganic materials[J]. Scientific Data, 2017, 4(1): 170085.

[19] Xu B, Tian B, Lv M Z, et al. Theoretical Study on the Mechanism of Direct Transformation from Graphite to Diamond at Ultra High-Pressure and High-Temperature[J]. Integrated Ferroelectrics, 2014, 151(1): 99-107.

[20] Ma Y, Eremets M, Oganov A R, et al. Transparent dense sodium[J]. Nature, 2009, 458(7235): 182-185.

[21] Kimoto T, Yonezawa Y. Current status and perspectives of ultrahigh voltage SiC power devices[J]. Materials Science in Semiconductor Processing, 2018, 78: 43-56.

[22] Wang Y, Lv J, Zhu L, et al. Crystal structure prediction via particle-swarm optimization[J]. Physical Review B, 2010, 82(9): 094116.

[23] Cely A, Tergenius L E, Lundstrom T. Microhardness measurements and phase analytical studies in the Mn-B system[J]. Journal of the Less Common Metals, 1978, 61(2): 193-198.

[24] Aydin S, Simsek M. First-principles calculations of MnB2, TcB2, and ReB2 within the ReB2-type structure[J]. Physical Review B, 2009, 80(13): 134107.

[25] Wang B, Li X, Wang Y X, et al. Phase Stability and Physical Properties of Manganese Borides: A First-Principles Study[J]. The Journal of Physical Chemistry C, 2011, 115(43): 21429-21435.

[26] Gou H, Steinle-Neumann G, Bykova E, et al. Stability of MnB2 with AlB2-type structure revealed by first-principles calculations and experiments[J]. Applied Physics Letters, 2013, 102(6): 061906.

[27] Niu H, Chen X Q, Ren W, et al. Variable-composition structural optimization and experimental verification of MnB3 and MnB4[J]. Physical Chemistry Chemical Physics, 2014, 16(30): 15866-15873.

[28] Fan J, Bao K, Jin X, et al. How to get superhard MnB2: a first-principles study[J]. Journal of Materials Chemistry, 2012, 22(34): 17630.

[29] Xu C, Bao K, Ma S, et al. A first-principles investigation of a new hard multi-layered MnB2 structure[J]. RSC Advances, 2017, 7(17): 10559-10563.

[30] Dreizler R M, Gross E K U. Density Functional Theory[M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990.

[31] Ding F J, Zhang L F, Li G N. A charge-conserving approximation method for ab initio calculations[J]. Acta Chimica Sinica, 1989, 7(4): 311-316.

[32] Engel G, Pickett W. Density Functional Theories to predict both ground-state properties and band structures[M]. 1996.

[33] Dhara A K, Ghosh S K. Local-density approximation to the energy density functionals in a magnetic field[J]. Physical Review A, 1990, 41(9): 4653-4658.

[34] Durbin R P. Letter: Acid secretion by gastric mucous membrane[J]. The American Journal of Physiology, 1975, 229(6): 1726.

[35] Woodley S M, Battle P D, Gale J D, et al. The prediction of inorganic crystal structures using a genetic algorithm and energy minimization[J]. Physical Chemistry Chemical Physics, 1999, 1(10): 2535-2542.

[36] Pickard C J, Needs R J. High-Pressure Phases of Silane[J]. Physical Review Letters, 2006, 97(4): 045504.

[37] Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by Simulated Annealing[J]. Science, 1983, 220(4598): 671-680.

[38] Wang Y, Lv J, Zhu L, et al. CALYPSO: A method for crystal structure prediction[J]. Computer Physics Communications, 2012, 183(10): 2063-2070.

[39] Milman V, Winkler B, White J A, et al. Electronic structure, properties, and phase stability of inorganic crystals: A pseudopotential plane-wave study[J]. International Journal of Quantum Chemistry, 2000, 77(5): 895-910.

[40] Wang Y X, Wu H, Xie W N, et al. Pressure-induced evolution of structures and phase transition of technetium diboride[J]. Journal of Applied Physics, 2024, 135(20): 205901.

[41] Wang Y X, Yan Z X, Liu W, et al. Novel high pressure structures and mechanical properties of rhenium diboride[J]. Journal of Applied Physics, 2019, 126(13): 135901.

[42] Wang X F, Wang Y X, Wang Z, et al. Ab initio study of phase stability, elastic anisotropy, and minimum thermal conductivity of MnB2 in different crystal structures[J]. Chinese Physics B, 2024, 33(12): 422-431.

[43] Milman V, Winkler B, White J A, et al. Electronic structure, properties, and phase stability of inorganic crystals: A pseudopotential plane-wave study[J]. International Journal of Quantum Chemistry, 2000, 77(5): 895-910.

[44] Alfè D. PHON: A program to calculate phonons using the small displacement method[J]. Computer Physics Communications, 2009, 180(12): 2622-2633.

[45] Wang X F, Wang Y X, Wu H, et al. Theoretical prediction of phase transition, mechanical and electronic properties of manganese diboride under pressure[J]. Applied Physics A, 2024, 130(6): 414.

[46] Wu Z J, Zhao E J, Xiang H P, et al. Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles[J]. Physical Review B, 2007, 76(5): 054115.

[47] Liang Y, Zhang B. Mechanical and electronic properties of superhard ReB2[J]. Physical Review B, 2007, 76(13): 132101.

[48] Wang Y X, Liu Y Y, Yan Z X, et al. Ab initio study of elastic anisotropies and thermal conductivities of rhenium diborides in different crystal structures[J]. RSC Advances, 2020, 10(61): 37142-37152.

[49] Lazar P, Chen X Q, Podloucky R. First-principles modeling of hardness in transition-metal diborides[J]. Physical Review B, 2009, 80(1): 012103.

[50] Vogt T, Schneider G, Hriljac J A, et al. Compressibility and electronic structure of MgB2 up to 8 GPa[J]. Physical Review B, 2001, 63(22): 220505.

[51] Wang K, Wu X, Li W, et al. Third Order Elastic Constants and Debye Temperature of MgB2 Under Different Pressure: First-Principles Methods[J]. Journal of Superconductivity and Novel Magnetism, 2015, 28(5): 1483-1489.

[52] Zhong M M, Huang C, Tian C L. Phase stability, Debye temperature and hardness of semiconducting manganese tetraboride MnB4: First-principles investigations[J]. International Journal of Modern Physics B, 2017, 31(20): 1750131.

[53] Steinki N, Winter J L, Grachtrup D S, et al. Electronic and magnetic ground state of MnB4[J]. Journal of Alloys and Compounds, 2017, 695: 2149-2153.

[54] Pei C, Zhang J, Gong C, et al. Distinct superconducting behaviors of pressurized WB2 and ReB2 with different local B layers[J]. Science China Physics, Mechanics Astronomy, 2022, 65(8): 287412.

[55] Liu D, Duan Y X, Bao W Z, et al. Structural properties, electronic structures and optical properties of WB2 with different structures: a theoretical investigation[J]. Ceramics International 2018, 44(10): 11438-11447.

[56] Mohn P, Pettifor D G. The calculated electronic and structural properties of the transition-metal monoborides[J]. Journal of Physics C: Solid State Physics, 1988, 21(15): 2829.

[57] Ma S, Bao K, Tao Q, et al. Manganese mono-boride, an inexpensive room temperature ferromagnetic hard material[J]. Scientific Reports, 2017, 7(1): 43759.

[58] Meng X X, Bao K, Zhu P, et al. Manganese borides synthesized at high pressure and high temperature[J]. Journal of Applied Physics, 2012, 111(11): 112616.

[59] Qu Z, Han F, Yu T, et al. Boron kagome-layer induced intrinsic superconductivity in a MnB3 monolayer with a high critical temperature[J]. Physical Review B, 2020, 102(7): 075431.

[60] Ishii T, Shimada M, Koizumi M. Exchange striction of ferromagnetic solid solution of (Mn1−xTax)3B4[J]. Journal of Applied Physics, 1983, 54(12): 6907-6911.

[61] Gou H, Tsirlin A A, Bykova E, et al. Peierls distortion, magnetism, and high hardness of manganese tetraboride[J]. Physical Review B, 2014, 89(6): 064108.

[62] Sun Y, Duan Y, Li X, et al. Intrinsic magnetism with high critical temperatures and piezoelectricity in 2D transition metal tetraborides[J]. International Journal of Quantum Chemistry, 2023, 123(13): e27117.

[63] Liang Y, Xu M, Qu Z, et al. A cage boron allotrope with high superconductivity at ambient pressure[J]. Journal of Materials Chemistry C, 2021, 9(26): 8258-8264.

[64] Asokamani R S, Vajeeston P R and Ravindra P, The Crystal Structure of MnB4 [J]. Acta Chemica Scandinavica, 1970, 24: 1791-1799.

[65] Lyakhov A O, Oganov A R, Stokes H T, et al. New developments in evolutionary structure prediction algorithm USPEX[J]. Computer Physics Communications, 2013, 184(4): 1172-1182.

[66] Gao B, Gao P, Lu S, et al. Interface structure prediction via CALYPSO method[J]. Science Bulletin, 2019, 64(5): 301-309.

[67] Zhang G, Zhao Y X, Zhu J, et al. Structural, elastic, electronic and thermodynamic properties of ZrB2 under high-pressure: First-principal study[J]. International Journal of Modern Physics B, 2018, 32(16): 1850200.

[68] Kresse G, Furthmüller J. Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set[J]. Computational Materials Science, 1996, 6(1): 15-50.

[69] Perdew J P, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple[J]. Physical Review Letters, 1996, 77(18): 3865-3868.

[70] Rose Y, MacWhinney B, Byrne R, et al. Introducing Phon: A Software Solution for the Study of Phonological Acquisition[C]. Proceedings of the Annual Boston University Conference on Language Development, 2006, 2006: 489-500.

[71] Łepkowski S P. First-principles calculation of higher order elastic constants using exact deformation-gradient tensors[J]. Physical Review B, 2020, 102(13): 134116.

[72] Xie W N, Wang Y X, Yan Z X, et al. Mechanical properties, thermal conductivity, and optical properties of a novel layered compound Bi3O2S2Cl under pressure[J]. The European Physical Journal B, 2023, 96(5): 64.

[73] Zhang M, Yin S, Chang J, et al. Structural, mechanical, electronic and bonding properties of TMB2 (TM=Y, Sc, Ti) under pressure: a DFT investigation[J]. Philosophical Magazine, 2022, 102(12): 1136-1151.

[74] Liu Y Y, Wang Y X, Yan Z X, et al. Pressure effects on structure, mechanical properties and thermal conductivity of V2SnC: a first-principles study[J]. Philosophical Magazine, 2022, 102(3): 228-243.

[75] Li P, Ma L, Peng M, et al. Elastic anisotropies and thermal conductivities of WB2 diborides in different crystal structures: A first-principles calculation[J]. Journal of Alloys and Compounds, 2018, 747: 905-915.

[76] Lech A T, Turner C L, Mohammadi R, et al. Structure of superhard tungsten tetraboride: A missing link between MB2 and MB12 higher borides[J]. Proceedings of the National Academy of Sciences, 2015, 112(11): 3223-3228.

[77] Kaiwart R, Dwivedi A, Shukla R, et al. High pressure structural evolution of cubic solid solution YbInO3[J]. Journal of Applied Physics, 2021, 130(3): 035902.

[78] Chen L, Zhang M, Chang J, et al. Theoretical investigation on vanadium dinitrides from first-principles calculations[J]. Ceramics International, 2019, 45(2): 2457-2465.

[79] R Hill. The Elastic Behaviour of a Crystalline Aggregate[J]. Proceedings of the Physical Society. Section A, 1952, 65(5): 349.

[80] Pugh S F. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals[J]. Philosophical Magazine, 1954, 45(367): 823-843.

[81] Qu D, Li C, Bao L, et al. Structural, electronic, and elastic properties of orthorhombic, hexagonal, and cubic Cu3Sn intermetallic compounds in Sn-Cu lead-free solder[J]. Journal of Physics and Chemistry of Solids, 2020, 138: 109253.

[82] Schneider J M, Bigerelle M, et al. Statistical analysis of the Vickers hardness[J]. Materials Science and Engineering: A, 1999, 262(1-2): 256-263.

[83] Levine J B, Tolbert S H, Kaner R B. Advancements in the Search for Superhard Ultra‐Incompressible Metal Borides[J]. Advanced Functional Materials, 2009, 19(22): 3519-3533.

[84] Ranganathan S I, Ostoja S M. Universal Elastic Anisotropy Index[J]. Physical Review Letters, 2008, 101(5): 055504.

[85] Lv Y, Zhang X, Jiang W. Phase stability, elastic, anisotropic properties, lattice dynamical and thermodynamic properties of B12M (M=Th, U, Np, Pu) dodecaborides[J]. Ceramics International, 2018, 44(1): 128-135.

[86] Fan Q, Chai C, Wei Q, et al. Elastic anisotropy and electronic properties of Si3N4 under pressures[J]. AIP Advances, 2016, 6(8): 085207.

[87] Katz J L, Spencer P, Wang Y, et al. On the anisotropic elastic properties of woods[J]. Journal of Materials Science, 2008, 43(1): 139-145.

[88] Duan Y H, Sun Y, Peng M J, et al. Anisotropic elastic properties of the Ca-Pb compounds[J]. Journal of Alloys and Compounds, 2014, 595: 14-21.

[89] Vahldiek F W, Mersol S A. Anisotropy in Single-Crystal Refractory Compounds: Proceedings of an International Symposium on Anisotropy in Single-Crystal Refractory Compounds, held on June 13-15, 1967, in Dayton Ohio. Sponsored by the Ceramics and Branch of the air Force Materials Laboratory, United States Air Force[M]. Boston, MA: Springer US, 1968.

[90] Ravindran P, Fast L, Korzhavyi P A, et al. Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2[J]. Journal of Applied Physics, 1998, 84(9): 4891-4904.

[91] Ma Y, Zhang X, Ma H, et al. The elasticity, anisotropy and thermodynamic properties of binary and ternary B-Sc compounds: First-principles calculations[J]. Solid State Communications, 2022, 353: 114869.

[92] Watt J P, Davies G F, O'Connell R J, et al. The elastic properties of composite materials[J]. Reviews of Geophysics and Space Physics, 1976, 14(4): 541-563.

[93] Anderson O L. A simplified method for calculating the debye temperature from elastic constants[J]. Journal of Physics and Chemistry of Solids, 1963, 24(7): 909-917.

[94] Siethoff H, Ahlborn K. The Dependence of the Debye Temperature on the Elastic Constants[J]. Physica Status Solidi B, 1995, 190(1): 179-191.

[95] Panda K B, Ravi Chandran K S. Determination of elastic constants of titanium diboride (TiB2) from first principles using FLAPW implementation of the density functional theory[J]. Computational Materials Science, 2006, 35(2): 134-150.

[96] Pei Y L, He J, et al. High thermoelectric performance of oxyselenides: intrinsically low thermal conductivity of Ca-doped BiCuSeO[J]. NPG Asia Materials, 2013, 5(5): e47.

[97] Xiao Y, Chang C, Pei Y, et al. Origin of low thermal conductivity in SnSe[J]. Physical Review B, 2016, 94(12): 125203.

[98] David, G, Cahill, et al. Lower limit to the thermal conductivity of disordered crystals[J]. Physical Review B, 1992, 46(10): 6131-6140.

[99] Clarke D R. Materials selection guidelines for low thermal conductivity thermal barrier coatings[J]. Surface Coatings Technology, 2003, 163: 67-74.

[100] Sun M, Qian Q, Tang G, et al. Enhanced thermoelectric properties of polycrystalline Bi2Te3 core fibers with preferentially oriented nanosheets[J]. APL Materials, 2018, 6(3): 036103.

[101] Chen S, Luo T, Yang Z, et al. Regulation of dynamic recrystallization in p-type Bi2Te3 based compounds leads to high thermoelectric performance and robust mechanical properties[J]. Materials Today Physics, 2024, 46: 101524.

[102] Abuova A, Merali N, Abuova F, et al. Electronic Properties and Chemical Bonding in V2FeSi and Fe2VSi Heusler Alloys[J]. Crystals, 2022, 12(11): 1546.

[103] Dronskowski R, Bloechl P E. Crystal orbital Hamilton populations (COHP): energy resolved visualization of chemical bonding in solids based on density-functional calculations[J]. The Journal of Physical Chemistry, 1993, 97(33): 8617-8624.

[104] Steinberg S, Dronskowski R. The Crystal Orbital Hamilton Population (COHP) Method as a Tool to Visualize and Analyze Chemical Bonding in Intermetallic Compounds[J]. Crystals, 2018, 8(5): 225.

[105] Hempelmann J, Müller P C, Konze P M, et al. Long-Range Forces in Rock-Salt-Type Tellurides and How they Mirror the Underlying Chemical Bonding[J]. Advanced Materials, 2021, 33(37): 2100163.

[106] Liao P K, Spear K E. The B−Mn (Boron-Manganese) system[J]. Bulletin of Alloy Phase Diagrams, 1986, 7(6): 543-549.

[107] Vinet P, Rose J H, Ferrante J, et al. Universal features of the equation of state of solids[J]. Journal of Physics: Condensed Matter, 1989, 1(11): 1941-1963.

[108] Vajeeston P, Ravindran P, Ravi C, et al. Electronic structure, bonding, and ground-state properties of AlB2-type transition-metal diborides[J]. Physical Review B, 2001, 63(4): 045115.