空位所引起的晶体弹性常数的改变

认为具有少量空位的晶体是一个均匀的晶体,把完整与不完整晶体的区别,归结为势函数的修改。应用Morse函数推导出弹性常数c₁₁和c₁₂的变化率与空位浓度的关系。因为空位邻近的原子有松弛,考虑了由松弛而改变了的相互作用对弹性常数的影响。首先求得铝中空位的第一和第二最近邻的位移百分率各为1.61和-0.32,这里的正号和负号各表示向空位移进和移出。其次,进行了具体的计算,在铜晶体中,估计1％的空位浓度使弹性常数减小1.3—1.4％。然而,铝晶体中的空位对弹性常数的影响

THE CHANGE OF THE ELASTIC CONSTANTS OF CRYSTALS DUE TO VACANCIES

Consider the crystal containing a small fraction of vacancies as a homogeneous crystal, and the difference between perfect and imperfect crystal reduces to the modification of the potential function. The relation between the rate of change of the elastic constants, c₁₁ and c₁₂, and concentration of vacancies is derived by the use of a Morse function. Owing to the relaxations of the neighbouring atoms, the effect of the elastic constants on the change of mutual interactions due to vacancy relaxation is taken into account. The first and second nearest-neighbour relaxations for Al are found to be (1.61, -0.32), expressed in percentage of normal distances. The positive sign indicates relaxation toward the vacancy and the negative sign indicates relaxation away from the vacancy. In the case of Cu, it is estimated that 1 per cent vacancy concentration would decrease the elastic constants by 1.3-1.4 per cent. However, the vacancy would have less effect on the elastic constants in Al than in Cu.