Equation for the multi-plateau isotherm of hydrogen + transition metal systems

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Abstract
A model for multi-plateau isotherms is developed with emphasis on the role of the lattice expansion which the parent metal always undergoes with hydrogen absorption. The contribution of the allotropic order–order phase transition of the parent metal itself or the formation of non-equilibrium phases is not considered in the model. Unlike Rees' equation, the equation, derived on the basis of statistical thermodynamics with the aid of continuum mechanics, is obtained as a combination of the component isotherms with their cross-effects. With the help of a computer the validity of the model is tested by comparison with the isotherm of the hydrogen + zirconium system as an example. The state parameters contained in the equation are determined by numerical comparison. The model is sufficient to explain the characteristic phase-pattern which the system displays in the phase diagram. There are two conditions under each of which the equation provided for double-plateau isotherms gives single-plateau isotherm curves. One of the conditions is required by the principle of thermodynamic stability and the other is concerned with the physical situation of the system.

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