Understanding Anharmonicity in fcc Materials: From its Origin to ab initio Strategies beyond the Quasiharmonic Approximation

We derive the Gibbs energy including the anharmonic contribution due to phonon-phonon interactions for an extensive set of unary fcc metals (Al, Ag, Au, Cu, Ir, Ni, Pb, Pd, Pt, Rh) by combining density-functional-theory (DFT) calculations with efficient statistical sampling approaches. We show that the anharmonicity of the macroscopic system can be traced back to the anharmonicity in local pairwise interactions. Using this insight, we derive and benchmark a highly efficient approach which allows the computation of anharmonic contributions using a few $T=0\mathrm{K}$ DFT calculations only.

Figure 1

(a) DFT heat capacity of Ag [quasiharmonic (qh), electronic (el), anharmonic (ah)] up to melting temperature $T^{\text{melt}}$, in comparison to experiment [27, 28, 29, 30, 31] and calphad data [32]. (b) GGA heat capacity and (c) Gibbs energy contributions as a function of homologous temperature. In (b) and (c), the qh data represent only the contribution beyond the purely harmonic part.

Figure 2

Results from an MD run for Ag at the melting temperature. (a) QH and fully DFT-based distribution of the projected nearest-neighbor vector ${\overrightarrow{d}}_{1\mathrm{NN}}$ with the center of reference at (0,0) (red quadrant). (b) Gauss-broadened first nearest-neighbor distribution functions ${\rho }_{1\mathrm{NN}}$ (dashed lines; broadening parameter $0.04{\AA }^{-1}$) and corresponding effective potentials $v^{\mathrm{eff}}$ (solid lines) obtained from full DFT (red) and QH (black) MD runs as a function of the first nearest-neighbor distance $d_{1\mathrm{NN}}$ around the effective equilibrium $d_{1\mathrm{NN}}^{\text{eq},\text{eff}}$ corresponding to the minimum of $v^{\mathrm{eff}}$.

Figure 3

Application of the local anharmonic (LA) approximation to Ag. (a) Longitudinal $T=0\mathrm{K}$ DFT forces (open red circles) obtained by displacing an atom from its $T=0\mathrm{K}$ equilibrium position, $d_{1\mathrm{NN}}^{\text{eq},0\mathrm{K}}$, towards and away from its next-nearest neighbor. The red solid line shows a fit according to the LA approximation and the black solid line using the QH approach. The necessary displacement range at $T=0\mathrm{K}$ is dictated by the shown distance distribution at the melting temperature (red dashed line and shaded area). (b) Comparison between full DFT and LA forces (red dots), and between full DFT and QH forces (black dots) for configurations obtained from a fully DFT-based MD run at the melting temperature.