Thermodynamic modeling of martensitic transformations in shape memory alloys

The unusual properties of shape memory alloys (SMAs) are due to solid-to-solid martensitic transformations (MTs) which correspond to a lattice level instability of the crystal structure. Currently, there exists a shortage of material models that can capture the details of lattice level MTs occurring in SMAs.;In the first part of this work, an effective interaction potential (EIP) model is developed for the SMA AuCd. EIPs are atomic interaction potentials that are explicit functions of temperature. In particular, the Morse pair potential is used and its adjustable coefficients are taken to be temperature dependent. A hysteretic temperature-induced MT between the B2 cubic and B19 orthorhombic crystal structures is predicted. This is the behavior that is observed in the real material. The model predicts, to reasonable accuracy, the transformation strain tensor and captures the latent heat and thermal hysteresis to within an order of magnitude.;The second part of this work consists of developing a lattice dynamics model to simulate the MTs. The atomic interactions are modeled using temperature independent Morse pair potentials. The effects of atomic vibrations on the material properties are captured using the first-order self-consistent approach which consists of renormalizing the frequencies of atomic vibration using self-consistent equations. These renormalized frequencies are dependent on both configuration and temperature. The model is applied for the case of a one-dimensional bi-atomic chain. The constant Morse pair potential parameters are chosen to demonstrate the usefulness of the current model. 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 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. Such an undertaking would 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.