Institute of Metals Division - Estimation of the Entropy of NaCl-Type Compounds

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski's method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6'7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6'7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann' suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in 'K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1' values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This