Diffusion of hydrogen in self-stressed metals — transfer function spectroscopy approach

The transfer function spectroscopy approach to the diffusion of hydrogen in a self-stressed isotropic elastic metal matrix is proposed. The system should be close to equilibrium. It is perturbed by a sine-wave input signal applied at one surface of the thin-plate specimen. The magnitude of this signal, of varied frequency, is small enough to treat the system as linear. The response signal is measured at the opposite surface of the specimen. The transfer function is the ratio of steady-state response to input signals. The hydrogen concentration and hydrogen flux are the input and output signals, respectively. The diffusion equations are derived, and they are solved analytically. The resulting transfer function is discussed in terms of hydrogen permeation through a specimen of properties similar to palladium and Pd81Pt19 alloy, in a wide range of hydrogen concentrations in the metal matrix. It is demonstrated that at relatively high frequencies the transfer function is highly sensitive to the non-Fickian diffusion, resulting from the non-local effect of self-stress. In contrast, at infinitesimally low frequency, i.e. at steady-state, both local and non-local effects compensate. Hence, the self-stress is absent. Under the proposed experimental conditions the transfer function spectroscopy is more appropriate for studying the diffusion of hydrogen in self-stressed metals than the commonly used transient break-through method. It should allow the study of the diffusion coefficient of hydrogen in metals, and, moreover, of the elastic modulus of metal–hydrogen solids, both these quantities as function of hydrogen concentration in isotropic matrixes.