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

Au-Fe alloys are of immense interest due to their biocompatibility, anomalous hall conductivity, and applications in various medical treatment. 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 lattice dynamical properties of Au$_{1-x}$Fe$_x$ alloys using density functional theory methods, where, being a multisite property, reliable interatomic force constant (IFC) calculations in disordered alloys remain a challenge. We follow a two fold 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 thermo-physical 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 miscibility gap in the phase diagram. Our results match fairly well with reported data, wherever available.