搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

固溶体的位形配分函数

张宗燧

引用本文:
Citation:

固溶体的位形配分函数

张宗燧

THE CONFIGURATIONAL PARTITION FUNCTIONS OF SOLID SOLUTIONS

CHANG TSUNQ-SUI
PDF
导出引用
  • 这篇短文分二节,第一节是将王德懋,许永焕及作者所合写的一篇论文中的求固溶体的配分函数的方法,应用到各种固溶体上。我们处理了二种不同晶体结构的情形,处理了有长程秩及无长程秩的情形,处理了只有最近邻作用而无其他邻作用的情形及既有最近邻作用又有次最近邻作用的情形。在各种不同情形下,这个方法都被证明是合用的。第二节是用同一方法讨论准化学公式。我们证明了在保留了这个方法中所谓结构常数中的最低一个时,准化学公式是成立的,不论固溶体中有多少种原子。其次,我们指出,在保留较高级的结构常数后,寻常的准化学公式应如何的改进。最后我们直接写下三个互为近邻的原子所构成的各种不同的集团的数目的准化学公式,讨论了与此相应的组合数,并指出这样的理论与我们的理论是不同的。
    This short papper applies a method for studying the configurational partition function of regular solutions developed by Wang, Hsu and the author to a number of special cases. In sucb concrete calculations it is seen that the method is applicable to almcst every type of solid solutions. In fact, its applicability is independent of the type of lattice which atoms of the solution inhabit, of the existence of the long distance order, of the existence of interactions between atoms more distant than nearest neighbours, and of the number of components in the solution. Since the method is actually an expansion of the configurational free energy in terms of certain coordination numbers of the lattice, the results of the calculations after ignoring the higher coordination numbers become closed expressions in terms of the Boltzmann factors and thus avoids expansions in kT or in (kT)-1. Needless to say, expansion of the results obtained here in (kT)-1 gives results identical with those obtained by Kirkwocd's method. Next we discuss quasi-chemical formulas based on the above method. We point out that if we neglect all the coordination numbers except the lowest, we obtain the usual quasichemical formula, quite independently of the number of components in the solution, (A corresponding combinatory formula is derived.) On including higher coordination numbers, we get natural extensions of the quasi-chemical formula. Thus for a binary solid solution on a face centred cubic system, the quasi-chemical formula after including the next higher coordination number becomes In the above, NθA, NθB denote the numbers of A, B atoms, X′AA, X′AB,…,X",… are numbers determined by (2), (3), (4), and their substitution into the right hand sides of (1) gives the numbers XAA XAB, XBB of AA, AB, BB pairs of nearest neighbours. It may be noted that X′ may be negative and they do not bear any direct physical significance.It is also pointed out that instead of considering the numbers of pairs of nearest neighbours, we may consider directly the numbers of pairs of triplets (ie. 3 atoms forming mutually nearest neighbours) and write down by analogy (to the usual quasi-chemical formula) new quasi-chemical equations for the different numbers of triplets. (From this, a combinatory formula is easily derived). It is shown that such a theory differs from (1)-(4) given above.
  • [1]
计量
  • 文章访问数:  7549
  • PDF下载量:  464
  • 被引次数: 0
出版历程
  • 收稿日期:  1958-11-08
  • 刊出日期:  1959-01-20

/

返回文章
返回