### Microstructure in materials

### Solid-solid phase transformations in multi-component solids with a group/subgroup character

Many important multicomponent solids undergo phase transformations through diffusional redistribution of atoms leading to structural changes with group/subgroup relationships: a high symmetry phase transforms to several crystallographically equivalent low symmetry variants. One example is the cubic to tetragonal phase transformation of lithium manganese dioxide electrodes due to intercalation of lithium. Our collaborators (Anton van der Ven and his group) and we have demonstrated that this class of phase transformations is driven by a free energy density surface that is non-convex in the high-dimensional, strain-composition space. We have identified the phenomenon of *mechano-chemical spinodal decomposition* in these materials. It further emerges that, for physically meaningful solutions and mathematical well-posedness, the free energy description must be extended to include interface contributions via gradients of strain and composition. The formulation unites gradient elasticity at finite strain with phase field methods for the evolution of chemistry in a variational framework. Using a novel numerical treatment, we are probably the first group to become capable of a range of computations that unmask the subtleties of this complex multiphysics problem.

**Publications:**-
**Mechano-chemical spinodal decomposition: A phenomenological theory of phase transformations in multi-component, crystalline solids**

S. Rudraraju, A. Van der Ven, K. Garikipati

Nature npj Computational Materials

Article number: 16012, 2016, doi:10.1038/npjcompumats.2016.12

[available on arXiv]

Shown here are the free energy density functions in 2D and 3D, simulations of microstructure evolution and the movement of material points in the strain-compostion space.

[Click images to enlarge/play]