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The unusual properties of shape memory alloys (SMAs) are due to solid-to-solid martensitic phase transformations
(MPTs) which correspond to a lattice level instability of the crystal structure. The high temperature phase
is usually a high symmetry structure and is called the austenite phase whereas the low temperature phase has a
low symmetry and is called the martensite phase. Currently, there exists a shortage of material models of MPTs
based on the material's atomic composition and crystal structure that would lead to computational discovery
of new improved SMAs. The present work develops a lattice dynamics model using a first-order self-consistent
approach based on statistical perturbation theory that aims to capture the qualitative and ultimately quantitative
behavior of MPTs. In particular, the atomic interactions are modeled using Morse pair potentials. The
effects of atomic vibrations on the material properties are captured by 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 stress-free equilibrium paths with temperature as the loading parameter. These plots are generated
using branch-following and bifurcation techniques. A second-order phase transformation (PT) is predicted which
involves transformation from a high symmetry phase to a low symmetry phase as the temperature is decreased.
Thus, the current model is able to capture the important aspect in MPTs, i.e., transformation from high symmetry
phase to low symmetry phase as temperature is decreased. We believe that this model applied to three
dimensional structures will be able to capture first-order MPTs that occur in SMAs.
This qualitative prediction of a temperature-induced PT indicates the likely hood that the current model
can be used for the computational discovery of new shape memory alloys. 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.
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