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.

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A variational treatment of interface motion and microstructural change as problems of evolving conigurations

Classical, quasi-static, nonlinear elasticity is an equilibrium problem; the displacement field minimizes the free energy of the solid. However, a number of other variables can be identified, some of which also parameterize the free energy, and with respect to which we may seek to minimize the free energy. We have considered configurational quantities in this setting. One example comes from sharp interfaces that define distinct phases of the material. The position of the interface, a vector quantity, describes the configuration of the solid. It varies independently of the standard displacement vector field. Another example is the configuration that specifies the crystal structure relative to a suitable reference state. The crystal can distort from one structure to another; e.g., from cubic to tetragonal, thus defining an evolving reference configuration, relative to which the standard displacement can be defined. We have developed a common variational framework for both these cases. Together, they allow us to model a range of phase transformation phenomena in crystals, including the transition from a diffuse/coherent to sharp/incoherent interface.


Publications:

A variational treatment of material configurations with application to interface motion and microstructural evolution
G. Teichert, S. Rudraraju, K. Garikipati
Journal of the Mechanics and Physics of Solids
Vol. 99: 338–356, 2017, doi:10.1016/j.jmps.2016.11.008
[available on arXiv]

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Representing chemical potential data with splines provides better fit and lower computation time when compared with classic Redlich-Kister polynomials

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. The partial differential equations (PDEs) that describe atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability and accuracy of the numerical methods that solve these PDEs can change depending on the type of functions used to representation the free energy. Redlich-Kister polynomials have traditionally been used to fit to chemical potential data, but they require high order terms to fit oscillations around phase transitions. We investigated the influence of different representations of chemical potential data on phase field computations. First-principles statistical mechanics methods were used by our collaborators (Anton van der Ven and his group) to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. We then obtained high fidelity fits to these rapidly fluctuating free energy data with cubic spline functions. The spline functions were many degrees lower than Redlich-Kister polynomials fit to the same data, and they provided equal or superior fits to the chemical potential data. When used in phase field computations, the spline fit resulted in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.


Publications:

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations
G. Teichert, H. Gunda, S. Rudraraju, A. Natarajan, B. Puchala, K. Garikipati, A. Van der Ven
Computational Materials Science
Vol. 128: 127-139, 2017, doi:10.1016/j.commatsci.2016.11.024
[available on arXiv]

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