Calculation of the entropy of fusion for the group IVb metals titanium, zirconium, and hafnium by the vacancy theory

The vacancy theory for the description of the melting process of pure metal s is applied to the IVb group metals titanium, zirconium, and hafnium. The total entropy change of the solid-liquid transition is divided into contrib utions coming from the interactional, configurational, volume, and vibratio nal changes. In order to calculate the named contributions the following pr operties are used: the change in the molar volume at the melting point, the thermal volume expansion coefficient and the bulk modulus of the solid pha se, the enthalpy and entropy of vacancy formation, the coordination numbers in the solid and the liquid state, and finally, the enthalpy of fusion. Th e values obtained for the entropy of fusion in J . mol(-1).K-1 are: titaniu m 6.98; zirconium 7.86; hafnium 8.30. The results are in good agreement wit h experimental values obtained by enthalpy measurements on the solid and li quid phases of these metals by levitation drop calorimetry.