On the Relationship Between the Coefficient of Expansion and the Melting Temperature

In 1950 and 1951, reports appeared in print[^1] on the discovery of a relationship between the melting temperature and the coefficient of expansion of a solid. The authors of these works ascribed to themselves the honor of finding a rather interesting relation that had been discovered more than 20 years ago. The relation in question had been undeservedly forgotten. In light of the new data obtained in recent works, it is worth recall—

...to revise the old results and to discuss the whole body of experimental facts from a new point of view.

The integral

\[ \int_{0}^{T_{\mathrm{m}}} \alpha\,dT = \bar{\alpha}T_{\mathrm{m}} \]

(where \(\alpha\) is the coefficient of expansion), taken over the temperature range from absolute zero to the melting temperature, characterizes the maximum possible expansion of a given solid. The quantity \(\bar{\alpha}T_{\mathrm{m}}\) was measured for a small number of substances; it is especially unfortunate that the temperature interval was usually not taken in full.

Nevertheless, the small fluctuations of this quantity are striking. The first to draw attention to this circumstance was probably Grüneisen, who indicated that the mean percentage increase in volume is equal to \(7.5\%\) (and consequently the mean linear increase is about \(2.5\%\)).

In 1928 a paper\(^2\) appeared in which it was shown that this product is equal to \(9\%\) for halides with a molecular lattice, \(8\%\) for alkali metals, \(7\%\) for divalent and trivalent metals, and \(1\)—\(2\%\) for tetravalent metals.

Interesting data on series of isomorphous substances whose crystals have a molecular lattice were given\(^3\) in 1930 (the number is \(\alpha T\) in percent).

Table I

It is quite probable that the differences in the values of \(\alpha T\) are due to differences in the types of lattice, i.e., to differences in the mutual arrangement of the molecules. In particular, in the group of monocarboxylic acids the molecules are arranged in a similar way in the compounds \(C_4\), \(C_8\), \(C_{10}\), and \(C_{12}\), and also in the compounds \(C_3\), \(C_5\), and \(C_9\).

Table II, borrowed from the latest work of 1951, shows quite clearly the dependence of the product \(\frac{1}{3}\alpha T\) on the type of lattice.

Table II

The data presented indicate the unquestionable advisability of searching for a relationship between the magnitude of the maximum expansion \(\overline{\alpha}T\) and the symmetry of the lattice and the character of the bonding of atoms. It is possible that, in the case of anisotropic crystals, a more characteristic quantity is \(\overline{\beta}_{\max}T\), where \(\overline{\beta}_{\max}\) is the temperature-averaged value of the maximum linear coefficient of expansion.

A. K.

References

1. G. Bonfiglioli and G. Montalenti, J. Appl. Phys. 22, 1089 (1951).
2. W. Klemm, Zeits. Elektrochem. 34, 526 (1928).
3. W. Biltz, Phys. Chem. A 151, 27 (1930).