利用第一原理计算研究了共价晶体和离子晶体的单晶弹性常数及机械硬度.结果表明,对材料硬度起主导作用的是最软的弹性形变模式,而非普遍认为弹性模量的平均值.这体现了力学稳定性及各向异性在决定材料硬度时的重要作用.以碳化钨为例展示了上述理念在材料设计中的应用.通过氮或铼的合金化调节费米能级,从而强化最软的弹性模式,可以进一步提高这种硬质材料的硬度. The first-principles calculations of the single-crystal elastic constants and mechanical hardness of covalent and ionic crystals have been performed. The results show that the softest elastic deformation mode is dominant for the hardness of the material, rather than the average value of the elastic modulus This shows the important role of mechanical stability and anisotropy in the determination of material hardness.With tungsten carbide as an example, the application of the above concept in material design is illustrated.The Fermi level can be adjusted by the alloying of nitrogen or rhenium Strengthen the most flexible mode of elasticity, can further improve the hardness of this hard material.