## Research Abstracts Online

January - December 2011

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### University of Minnesota Twin Cities

College of Science and Engineering

Department
of Aerospace Engineering and Mechanics

# PI: Ryan S. Elliott, Associate Fellow

### Self-Consistent Lattice Dynamics for Prediction of Martensitic Tranformations

The unusual properties of shape memory alloys (SMAs) are due to solid-to-solid martensitic transformations (MTs) that correspond to a lattice-level instability of the crystal structure. Currently, there are a shortage of material models of MTs based on the material’s atomic composition and crystal structure. This project aims to develop a model using first-order self-consistent lattice dynamics (SCLD) that captures the qualitative and quantitative behavior of MTs. The effects of atomic vibrations on the material properties are captured by renormalizing the frequencies of atomic vibrations using self-consistent equations. These renormalized frequencies are dependent on both configuration and temperature. The model has already been applied for the case of a one-dimensional bi-atomic chain. The resulting model is evaluated by generating equilibrium paths with temperature and mechanical load as the loading parameters. In both types of loading, a first-order entropically stabilized MT is predicted indicating that the current model is able to capture the first-order MTs that occur in SMAs. This qualitative prediction of a first-order MT indicates the likely-hood that the current model can be used for the computational design and discovery of SMAs with better properties. This undertaking will involve, first, determining the potential parameters of new alloys from first-principles calculations and, second, using these parameter values with the current self-consistent model to evaluate the shape memory behavior of the new previously unstudied materials. These tasks will require extensive computations with both electronic structure DFT simulations and the SCLD method itself. In both cases the resources being requested from the MSI are critical for the project's advancement and success.

### Group Members

Nathaniel Beaver, Supercomputing Institute Undergraduate Intern

Venkata Guthikonda, Graduate Student

Vincent Jusuf, Graduate Student

Dan S. Karls, Graduate Student