Grüneisen's Rule and the Thermal Expansion of Metals

Abstract

GRÜNEISEN¹ arrived at an empirical rule connecting the volume expansion of solids due to rise in temperature with the atomic heat of the solid and its compressibility at absolute zero. This rule has been stated in various forms, and Hume-Rothery², after a comparative study of the various forms, has recommended the form due to Simon and Vohsen³, namely: where V _T and V ₀ are the volumes of the solid at T° K. and 0° K. respectively, E _T is the total heat content of the solid at T° K. and Q and K are constants. Thus may be substituted by 3 , where a _T and a ₀ are lattice parameters of a cubic crystal at T° K. and 0° K., respectively. Similarly, we may write for E _T the Debye expression 9 RTD (θ/T). Substituting these values in equation 1, it becomes evident that the curve of vs. will become a straightline. Fischmeister⁴ has drawn these curves for ionic crystals such as sodium and potassium chlorides, potassium and cæsium bromides, potassium and cæsium iodides and lithium fluoride, and in each of these cases has obtained a straight-line curve. The present work was undertaken to find out if the same linear relation is obeyed for pure metals. For this purpose, the cell edges of pure copper, aluminium, silver and platinum at various temperatures were studied by the X-ray diffraction method. Measurements were carried out with the help of a 19-cm. camera and filtered X-rays were used. The cell edges were determined by the extrapolation technique due to Sinclair and Taylor⁵. Extrapolation to absolute zero was carried out by the technique described by Fischmeister⁴. The resultant curves are shown in Fig. 1. Unlike the curves for ionic crystals obtained by Fischmeister⁴ for metallic crystals, these are non-linear. Further work is being carried out to find the nature of these curves for other metals and alloys.