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 ${\mathrm{Au}}_{1-x}{\mathrm{Fe}}_x$ 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.

Figure 1

(Left) Using force constants from the 32-atom SQS and phonon dispersion for ${\mathrm{Au}}_{1-x}{\mathrm{Fe}}_x$ along high-symmetry $\left[\zeta 00\right],\left[\zeta \zeta 0\right]$, and $\left[\zeta \zeta \zeta \right]$, where $\zeta =|\vec{k}|/|{\vec{k}}_{\max }|$ for reciprocal-space vector $\vec{k}$. Longitudinal ($L$) and transverse ($T$) modes are indicated. The bars indicate the calculated full width at half maxima (FWHM). (Right) Projected density of states (DOS).

Figure 2

Excess phonon entropy vs $x$ for ${\mathrm{Au}}_{1-x}{\mathrm{Fe}}_x$ at $T=300\mathrm{K}$ and configurational entropy of mixing $S_{\mathrm{config}}$ (blue curve). The inset shows $\mathrm{\Delta }{S}_{\mathrm{vib}}$ vs $T$ at various $x$'s.