Theory of the vibrations of the sodium chloride lattice
Theory of the vibrations of the sodium chloride lattice
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氯化钠晶格的振动理论
DOI：
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发表时间：
1940
期刊：
影响因子：
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通讯作者：
E. Kellermann
中科院分区：
文献类型：
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作者：
E. Kellermann
人们对晶体热振动频谱的兴趣主要是与晶体在低温下的比热问题联系在一起的。然而，德拜的比热理论是如此的成功，以至于玻恩和卡门（1912）对频谱的实际测定被推到了幕后。但是最近的研究，特别是布莱克曼（1935，1937 a，B，1938）的研究表明，按照正确的原子论处理，应该会出现与德拜理论明显的偏差。这些偏差似乎在温度的绝对零度附近最明显。因此，计算晶体的精确频谱似乎是可取的。第一次尝试计算晶体的频谱是由玻恩和卡门在他们的原始论文中提出的。他们只假设相邻粒子之间存在准弹性力。后来，我们对离子晶格进行了计算，我们对决定平衡位置及其振动的真实的力有了相当的了解。该计算的主要困难一直是库仑力的长范围，这使得不可能对所有格点进行直接求和。Born和Thompson（1934）利用Ewald（1921）提出的方法，提出了一种将这些和变换成更快收敛的表达式的方法，Thompson（1935）给出了运动方程中库仑力引起的耦合系数的最终公式，但在他的论文中，系数的定义出现了一个小错误，到目前为止，这些计算的数值结果还没有公布。Broch（1937）利用Epstein的Zeta函数给出了一维晶格的公式。Lyddane和Herzfeld（1938）使用了Madelung方法（1918）的一种扩展，他们给出了一些数值结果，但他们的公式相当复杂，因此不能指望用这种方法计算整个频谱。此外，离子晶格的热振荡问题不是一个纯粹的静电问题，这一点并没有被Lyddane和Herzfeld充分阐明。他们对剩余射线情况的处理是有异议的，并且从中获得耦合系数的势是否满足拉普拉斯方程或泊松方程的问题也不清楚。
The interest in the frequency spectrum of the thermal vibrations in a crystal arose chiefly in connexion with the problem of the specific heat of crystals at low temperatures. Debye’s theory of the specific heat, however, has been so successful that the actual determination of the frequency spectrum according to Born and v. Karman (1912) has been pushed into the background. But recent investigations, especially those of Blackman (1935,1937 a,b, 1938), have shown that appreciable deviations from Debye’s theory should occur according to the correct atomistic treatment. These deviations appear to be most pronounced near the absolute zero of temperature. It, therefore, seemed desirable to calculate the exact frequency spectrum of a crystal. The first attempt to calculate the frequency spectrum of a crystal was made by Born and v. Karman in their original paper. They assumed only quasi-elastic forces between neighbouring particles. Later calculations have been made for ionic lattices, for which we have a fair knowledge of the real forces which determine the equilibrium positions and the vibrations about them. The chief difficulty in that calculation has always been the long range of the Coulomb force which makes a direct summation over all lattice points impossible. Born and Thompson (1934), using a method developed by Ewald (1921), suggested a way of transforming these sums into more rapidly convergent expressions, and Thompson (1935) has given the final formulae for the coupling coefficients due to the Coulomb force in the equation of motion, but in his paper a slight mistake occurred in the definition of the coefficients, and so far no numerical results of these calculations have been published. Broch (1937) has given formulae for the case of a one-dimensional lattice making use of Epstein’s Zeta functions. Lyddane and Herzfeld (1938) have used an extension of Madelung’s method (1918) and they have given some numerical results, but their formulae are rather complicated, so that one cannot expect to compute the whole frequency spectrum by this method. Moreover, the problem of the thermal oscillations of an ionic lattice is not a purely electrostatic problem, and this point has not been made sufficiently clear by Lyddane and Herzfeld. Their treatment of the case of the residual rays is open to objection, and the question whether the potential, from which the coupling coefficients are obtained, satisfies the Laplace equation or Poisson’s equation is not clear.