广义Vegard定律和广义余氏定律

来源期刊：中南大学学报(自然科学版)1985年第3期

论文作者：谢佑卿 马柳莺

文章页码：1 - 10

关键词：定律； 价电子状态； 原子体积； 广义； 价电子结构； 二元合金； 无序固溶体； 晶格参数； 原子状态； 参量

摘    要：本文指出,Vegard定律与实际情况不符的根本原因在于它没有考虑到溶质和溶剂原子在固溶体中由于近邻原子的不同而引起原子电子结构状态的变化。 此文在考虑了原子状态的变化和确定的原子状态具有固有的特征晶格参量基础上,提出了广义Vegard定律和广义余氏定律。在Au-Cu合金中,Au和Cu原子的价电子状态向h态方向分裂,从而形成向上凸的a—c曲线。按新堤出的广义Vegard定律和广义余氏定律计算的a—c理论曲线与实验结果极为一致。

Abstract: The variation of lattice parmeters across a solid solution range between two isostructural elements has been expressed in Vegard’s law which is so seldom obeyed. Numerous attempts have been made to explain its failure, but the factor mainly responsible for deviations from the law has not yet been considered. In the present work, we have pointed out that the varia- tion of atomic states of solute and solvent with changes of nearest- neighbour environments is the predominating influence on the deviations from the law. According to the fact that there is an intrinsic characteris lattice parameter for a certain crystal structure and a certain composition of the hybridization state, we have established two laws calculating the lattic eparameter of a solid solution: 1) generalized Vegard’s law which means that the lattice parameter of a solid solution is equal to the sum of the products of the characteristic lattice parameters of the individual atomic hybridization states and their corresponding atomic concentrations, a = ∑_i∑_jC_i,j a_i,j . 2) generalized Yu’s law which means that the lattice parameter of a solid solution is equal to that of the average atomic hybridization state of the solute and solvent, a =∑_i∑_j 2 C_i,_j R_i,_j -β lg [∑_i∑_jC_i,jn^C_i,j/(A + Be^-Ea/β)]}. If the C_i,_j, R_i,j and n_i,j^C are hnown, the lattice parameter of a solid solution can be calculated at any concentration. We have calculated the lattice parameter curve of Au-Cu system as a function of the atomic concentration. It has been shown that the agreement between observed and calculated lattice parameters of Au-Cu alloys is good when two laws are used. The magnitude calculated by generalized Vegard’s law is slightly greater than that by generalized Yu’s law, but the maximum discrepance is less than 0.001 A. Because the atomic hybridization states of Au and Cu alloyed are splitted in the directions of h states which have relatively big characteristic lattice parameters as compared with their single subs- tances, the lattice parameter curve of the Au-Cu system as a function of composition is convex upward.