Power Laws and Scale Invariance in Physical Metallurgy

Physical metallurgy, and more generally materials science has a somewhat ambiguous status with respect to the topic of this school. On one hand materials scientists are defmitely interested in scale invariance and numerous power laws exist in physical metallurgy, either to describe microstructures, or to model the relations between microstructures and properties. By nature, the activity of a materials scientist is to build bridges between different scales, and to explain macroscopic behaviour using microscopic ingredients. On the other hand, universality is not precisely the aim of materials scientists, and they are more interested in knowing the macroscopic consequences of a microscopic phenomenon, or conversely to derive from macroscopic observations information about the micromechanisms. A characteristic and almost caricatural example of this difference in attitude between the two communities — physics and materials scienceoccured concerning the structure of fracture surfaces: when it became clear that the self affine structure was the same irrespectively of the fracture mechanisms, physicist were overexcited by the universality of the result, whereas materials scientist were very disappointed! However, beside the different status in the two fields of the “generic vs specific” distinction, materials science provides numerous examples of scaling or power law behaviours, for which materials scientists have derived explanations relying on detailed mechanisms, but which appear to be applicable in a much wider range of situation that the ones implied by the hypothesis used in their derivation. The purpose of this lecture is to provide an introduction to the field of physical metallurgy (§2), to illustrate the concepts of power laws and scale invariance by examples taken from the field (§3), and to outline open questions in physical metallurgy for which tools developed in statistical physics might be useful (§4).