Elastic Properties of ReN2 under High Pressure
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摘要: 超硬材料在工业上具有广泛的应用前景，如切割器具、研磨材料及耐磨涂层等。作为5d过渡金属双氮化合物之一的ReN2由共价键、离子键及金属键混合而成，因而具有诸多如高硬度、高熔点、耐腐蚀等优异的物理性质，进而具有潜在的研究价值。采用密度泛函理论中的平面波赝势法计算了零温零压下C2/m-ReN2的结构性质，并首次研究了高压下C2/m-ReN2的力学结构稳定性及弹性性质。研究得出了C2/m-ReN2的弹性常数、弹性模量、德拜温度、声速随压强的变化关系，除个别弹性常数，这些物理量皆随压强的增加而增加。还预测了C2/m-ReN2的韧脆性，并估算了C2/m-ReN2的维氏硬度。Abstract: Super hard materials have wide applications in industry, such as cutting tools, abrasive materials, wear resistant coatings. As one of the 5d transition metals double nitrogen compound, ReN2 contains both covalent bond, ionic bond and metallic bonding. In view of its many excellent physical properties, such as high hardness, high melting point and corrosion resistance, ReN2 earns much research interests. This article has calculated the structural properties of C2/m-ReN2 under zero temperature and zero pressure using the plane wave pseudo-potential method of density functional theory, and has studied the mechanical structure stability and elastic properties of C2/m-ReN2 under high pressure for the first time. The relations of the elastic constants, various modulus of elasticity, Debye temperature and the sound speed of C2/m-ReN2 with the pressure have obtained. In addition to the individual elastic constants, these quantities increase with the increase in pressure. In addition, we have also predicted the toughness and brittleness of C2/m-ReN2, and have estimated the Vickers hardness of C2/m-ReN2.
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Key words:
- ReN2 /
- mechanical structure /
- elastic property /
- hardness
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图 1 0 K条件下C2/m-ReN2的弹性常数与压强p的变化关系
Figure 1. Relationship between the elastic constants and the pressure p at 0 K
图 2 0 K条件下C2/m-ReN2的弹性模量（B、E、G）及德拜温度
${\varTheta}$ 与压强p的变化关系Figure 2. Pressure dependence of the bulk modulus B, Young’s modulus E, shear modulus G and Debye temperature
${\varTheta}$ for C2/m-ReN2 at 0 K
图 3 0 K条件下C2/m-ReN2的韧脆性与压强p的变化关系
Figure 3. Pressure dependence of the toughness and brittleness for C2/m-ReN2 at 0 K
图 4 0 K条件下C2/m-ReN2的各个声速（vp、vs、vm）与压强p的变化关系
Figure 4. The compressional wave velocity, shear wave velocity and averaged wave velocity for C2/m-ReN2 as a function of pressure at 0 K
表 1 在p=0 GPa和T=0 K下的平衡晶格参数a、b、c及
${\;\beta}$ ，平衡体积V0，体模量B0，体模量对压强的一阶导数${B_0'}$ 及其他理论值[13, 27]Table 1. Equilibrium lattice parameters a, b, c and
${\;\beta}$ , equilibrium volume V0, bulk modulus B0, and its pressure derivation${B_0'}$ at p=0 GPa and T=0 K, together with other theoretical results [13, 27]Method a/nm b/nm c/nm $\beta$/（°） V0/nm3 B0/GPa B0′/GPa This work 0.682 0.282 0.939 142.38 0.027 59 361 4.78 Ref. [13] 0.682 0.284 0.936 142.30 0.027 60 Ref. [27] 0.683 0.284 0.939 0.027 77 
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表 2 在p=0 GPa和T=0 K下的体模量B、剪切模量G、杨氏模量E、泊松比
$\sigma $ 、维氏硬度HV及其他理论值[13, 27]Table 2. Bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratio
$\sigma $ and Vickers hardness HV at p=0 GPa and T=0 K, together with other theoretical results[13, 27]Method B/GPa G/GPa E/GPa $\sigma $ Hv /GPa This work 370 242 596 0.23 27.66 Ref. [13] 369 217 Ref. [27] 376 210 531 0.26
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