ON THE THERMAL EXPANSION OF METALS AT LOW TEMPERATURES

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Abstract
A theory is developed which correlates the thermal expansion of crystals to the anharmonicity introduced into Born's lattice dynamics by allowing the force constants of the crystal to vary with volume. This is achieved by identifying the force constants with the elastic constants of the crystal by the method of long waves. It is then assumed that it is primarily the volume dependence of the elastic constants that give rise to their temperature variation. A central force nearest and next-nearest neighbor force model analogous to Leighton's is applied to copper. The values of the lattice thermal expansion coefficient and of Grüneisen's parameter are given as a function of the temperature and found to agree quite well with the latest experimental results. It is pointed out that the description of the interionic potential in metals by a two-body central force is certainly a serious oversimplification and that the theory is likely to be more realistic for, say, the ideal inert solid gases, as soon as the experimental data becomes available.