Application of operator-scaling anisotropic random fields to binary mixtures

Denis Anders (1) , Alexander Hoffmann (2) , Hans-Peter Scheffler (2) , Kerstin Weinberg (3)

1 Universität Siegen [Siegen]
2 Chair of Probability Theory and Analysis [Siegen]
3 Chair of Solid Mechanics

To understand the structural properties of multicomponent materials, it is important to capture the microstructure of these mixtures. Due to their vast range of applications multicomponent systems are subjected to microstructural changes as phase separation and coarsening. Therefore the ultimate microstructural arrangement depends on the system's configuration and on exterior driving forces. In addition to this, random physical imperfections within the material and random noises in the exterior thermodynamic fields influence in essence the microstructural evolution. Since all physical processes are subjected to a certain degree of random inhomogeneity under realistic conditions, the influence of random phenomena cannot be neglected in modern physical models. An advanced mathematical description and an implementation of these stochastic processes are required to adapt simulation results basing on deterministic mathematical models to experimental observations. In our contribution we will present an operator-scaling anisotropic random field embedded in the Cahn-Hilliard phase-field model to describe the phase evolution in a binary mixture. The arising non-linear diffusion equation will be solved numerically in the innovative framework of isogeometric finite element method. To illustrate the flexibility and versatility of our approach, numerical and experimental results for an eutectic Sn-Pb alloy are contraposed. It is the first time that the microstructural evolution in a multicomponent system is associated with operator-scaling anisotropic random fields. Due to its enormous potential as an essential ingredient in stochastic mathematical and physical modeling it is only a matter of time until these processes will become prevalent in engineering applications.

Mots clés: Physical Sciences

Domaines: Matière Condensée [cond-mat]

Denis Anders, Alexander Hoffmann, Hans-Peter Scheffler, Kerstin Weinberg. Application of operator-scaling anisotropic random fields to binary mixtures. Philosophical Magazine, 2011, pp.1. ⟨10.1080/14786435.2011.595378⟩. ⟨hal-00723593⟩