Simulating Order Parameters for Phase Transitions in Alloys

When determining the structure of alloys using diffraction patterns, possible distortions that lower the symmetry of the parent phase can be limited by group-theoretical arguments as long as a group-subgroup relationship exists between the parent and distorted phases$^1$. Order parameters are vectors in representation space where each dimension corresponds to a specific superlattice vector in reciprocal space (e.g. L = [0.5,0.5,0.5] or X=[1,0,0]); such order parameters determine the distortions that may arise during a phase transition. By measuring the Fourier transform of the structure at each relevant superlattice vector during a Monte Carlo simulation for CuPt$_3$, we were able to extract these thermodynamic order parameters and qualitatively confirm distortions in the L and X order parameters observed in experiment$^2$. The methodology presents a highly effective avenue for comparing simulated phase transitions with experimental results. \\ \\ \mbox{[1]} Harold T. Stokes, Branton J. Campbell and Dorian M. Hatch. \textit{Order parameters for phase transitions to structures with one-dimensional incommensurate modulations} \\ \mbox{[2]} Rokuro Miida and Denjiro Watanabe. \textit{Electron Microscope and Diffraction Study on the Ordered Structures of Platinum-Rich Cu-Pt Alloys}