Anomalous random correlations of force constants on the lattice dynamical properties of disordered Au-Fe alloys

Gold iron (Au-Fe) alloys are of immense interest due to their biocompatibility, anomalous Hall conductivity, and applications in various medical treatments. However, irrespective of the method of preparation, they often exhibit a high level of disorder with properties sensitive to the thermal or magnetic annealing temperatures. We calculate the lattice dynamical properties of ${\mathrm{Au}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}$ alloys using density functional theory methods where, being multisite properties, reliable interatomic force constant (IFC) calculations in disordered alloys remain a challenge. We follow a twofold approach: (1) an accurate IFC calculation in an environment with nominally zero chemical pair correlations to mimic the homogeneously disordered alloy and (2) a configurational averaging for the desired phonon properties (e.g., dispersion, density of states, and entropy). We find an anomalous change in the IFC's and phonon dispersion (split bands) near $x=0.19$, which is attributed to the local stiffening of the Au-Au bonds when Au is in the vicinity of Fe. Other results based on mechanical and thermophysical properties reflect a similar anomaly: Phonon entropy, e.g., becomes negative below $x=0.19$, suggesting a tendency for chemical unmixing, reflecting the onset of a miscibility gap in the phase diagram. Our results match fairly well with reported data wherever available.