The interpretation of hydrogen isotope effects and their relation to microscopic energy related parameters by simplified statistical thermodynamic models

Abstract

Utilizing simplified statistical thermodynamic treatments, analytical expressions for the pressure-composition (p–c) isotherms of hydrogen-metal systems can be derived. Fitting a set of experimental isotherms for a given hydrogen isotope, A (A = H, D or T), to the model-derived functions, two energy-related parameters can be evaluated. These parameters are the pairwise A–A nearest neighbors interaction, ηAA, and an effective A-lattice interaction parameter, εAeff, which includes both, the non-vibrational (electronic and elastic) contributions and the vibrational contribution. Comparing εAeff for two hydrogen isotope systems (e.g. H and D) it is possible to estimate the corresponding zero-point vibrational energies of the isotopes in the hydride. This type of analysis has been performed for the Pd–H2(D2) system as well as for a series of the Laves phase TiCr2-XMnX (X = 0, 0.5 and 1) hydrides. For each system, experimental p–c isotherms of the two hydrogen isotopes (i.e. H and D) were obtained over a wide temperature and pressure range. This included the super-critical range (i.e. above the critical temperatures of the systems) for which the model-derived p–c isotherms better represent the experimental ones. A set of microscopic energy-related parameters were evaluated for these systems. A procedure which enabled the estimation of the average zero-point vibrational energies of the isotopes in the corresponding hydride is outlined. A comparison was made between the results obtained by this procedure and corresponding reported vibrational energies measured by some vibrational spectroscopy methods. The accuracy of the model-calculated results seems to be of the order of 15–50 %. A relation was obtained between the zero-point vibrational energies and the temperature where a transition occurs from a "positive" to a "negative" isotope effect.