Refraction and reflection of diffusion fronts

Diffusion waves form the basis of several measurement technologies in materials science as well as in biological systems. They are, however, so heavily damped that their observation is a real challenge to the experimentalist. We show that accurate information about the refractionlike and reflectionlike behavior of diffusion waves can be obtained by studying diffusion fronts. For this we use hydrogen in a metal as a model system and visualize its 2D migration with an optical indicator. The similarities between classical optics and diffusion, in particular, the applicability of Snell’s law to diffusive systems are discussed. Our measurements are in good agreement with numerical simulations. Generally, a wave can be defined as a propagating imbalance. This imbalance may be the density fluctuation in an elastic medium that leads to acoustic waves. In the case of linear restoring forces, such as in an elastic medium, there is a periodic conversion of different forms of energy. In contrast, an imbalance in concentration does not lead to a concentration wave due to the lack of a restoring force. Such a system does not overshoot its equilibrium concentration and does not form a self-sustained concentration wave. Therefore, concentration waves occur only as a result of locally imposed forced oscillations. Forced oscillations of particles or energy in a diffusive medium are known as diffusion waves. Mathematically, they are solutions of the diffusion equation