Libowitz method

Let us consider the compounds which show a small deviation from the stoichiometric composition and whose non-stoichiometry is derived from metal vacancies. The free energy of these compounds, which take the composition MX in the ideal or non-defect state, can be calculated by the method proposed by Libowitz. To readers who are well acquainted with the Fowler-Guggenheim style of statistical thermodynamics, the method here adopted may not be quite satisfactory however, the Libowitz method is understandable even to beginners who know only elementary thermodynamics and statistical mechanics. It goes without saying that the result calculated by the Libowitz method is essentially coincident with that calculated by the Fowler-Guggenheim method. 

Lacher and Anderson discussed this phase diagram from the viewpoint of statistical thermodynamics based on the Fowler-Guggenheim treatment. On the other hand, Libowitz and Simon and Flanagan also calculated this phase diagram based on Libowitz s method mentioned in Section 1.3.7. The result obtained by the latter is the same as eqn (1.124). 

The thermochemical properties of the lanthanide-hydride systems have been well-catalogued by Libowitz and Maeland (1979). Heats, entropies and free energies of formation have been tabulated for both the dihydrides and dideuterides, as well as data for the La through Nd trihydrides and also the hydrogen-deficient hexagonal phases. Methods are described for typical calculations and are not repeated here. Thermodynamic data and thermal functions are presented by Flotow et al. (1984) and by Ward (1985a and b) for the hydrides of Th through Am. Newer data are reviewed here, and the values in table 1 reflect these updates. 

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