On the thermodynamics of phase transitions in metal hydrides

Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a particular phase transition in TiH _x , which can approximately be described as a second-order phase transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the density of H⁺ ions and of the distance between adjacent H⁺ ions. Moreover, as the system approaches the transition and the correlation radius increases, we show -with the help of statistical mechanics-that the statistical weight of modes involving a large number of H⁺ ions (‘collective modes’) increases sharply, in spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, the interaction of the H⁺ ions with collective modes makes a tiny suprathermal fraction of the H⁺ population appear. Our results hold for similar transitions in metal deuterides, too. A violation of an -insofar undisputed-upper bound on hydrogen loading follows.