On the stability of certain heteropolar crystals
On the stability of certain heteropolar crystals
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DOI：
10.1103/physrev.39.675
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发表时间：
1932-02-01
期刊：
影响因子：
--
通讯作者：
Evjen, HM
中科院分区：
文献类型：
--
作者：
Evjen, HM
在传统的模型的基础上的异极晶体，它示出了一个不规则的结晶行为是预期在该地区的指数，p，排斥能的小值。在这个演示过程中，马德隆的方法获得的库仑潜力的晶体的立方系统是合理的，并描述了一个新的，非常简单的方法计算马德隆常数。这种方法适用于立方系统的三个晶体和其他应用建议。在排斥指数的小值的区域中的晶体的不规则行为被示出为对晶格的几何形状被改变的各种变化的不稳定性。特别是，不稳定性的情况下，证明了“方解石家族”的晶体是由一个连续的过程从一个单一的参数φ。NaCl和CsCl型晶体是这个家族的成员，因此可以实现从一种晶体到另一种晶体的连续过渡。这两种类型的晶体，在一般情况下，是不稳定的变化，其中参数φ的变化，（φ-变化），并为小值的指数，p，所有成员的”方解石家族”被证明有一种倾向，分为一维晶体的马德隆型。这些考虑的另一个结果是，斜结构，如方解石的斜结构，可以在纯粹的中心力的基础上解释。最后计算了一维和二维晶体以及立方晶系晶体最稳定的区域。这些结果的轴承的二级结构的理论进行了简要讨论。
On the basis of the conventional model of heteropolar crystals it is shown that an irregular crystalline behaviour is to be expected in the region of small values of the exponent, p, of the repulsive energy. In the course of this demonstration Madelung's method of obtaining the Coulomb potential for the crystals of the cubical system is justified, and a new, very simple method of calculating the Madelung constant is described. This method is applied to the three crystals of the cubical system and other applications are suggested. The irregular behavior of crystals in the region of small values of the repulsive exponent is shown to be manifested as an instability against various variations by which the geometry of the lattice is altered. In particular, the instability is demonstrated in the case of the" calcite family" of crystals which is evolved by a continuous process from a single parameter φ. The NaCl-and CsCl-types of crystals are members of this family, and a continuous mode of transition from one to the other is thus available. These two types of crystals, in general, are unstable against a variation in which the parameter φ is changed,(φ-variation), and for small values of the exponent, p, all members of the" calcite family" are shown to have a tendency to fall apart into one-dimensional crystals of the Madelung type. Another result of these considerations is that a skew structure, such as that of calcite may be accounted for on the basis of purely central forces. Finally the regions in which respectively one-dimensional and two-dimensional crystals, and the crystals of the cubical system are most stable are calculated. The bearing of these results on the theory of the secondary structure is briefly discussed.