Hidden scale invariance of metals

TL;DR

Most metals exhibit a hidden scale invariance at their triple point, simplifying their thermodynamic behavior and enabling predictions of structure, dynamics, and melting curves through scale-invariant principles.

Contribution

This study reveals the pervasive hidden scale invariance in metals, linking DFT calculations, experimental data, and theoretical models to explain thermodynamic properties and phase behavior.

Findings

Density fluctuations in metals are nearly proportional, indicating scale invariance.

DFT density scaling exponents agree with experimental Grüneisen parameters.

Melting curves follow invariant isomorphs, and structure factors can be predicted by scale invariance.

Abstract

Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between thermal fluctuations between virial and potential-energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the dense part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Gr{\"u}neisen parameter, are in good agreement with experimental values for 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W and Hg), most post-transition metals (Ga, In, Sn, and Tl) and the metalloids Si and Ge cannot be explained by the IPL assumption. Thus, hidden scale invariance can be present even when the IPL-approximation is inadequate. The virial-energy correlation coefficient of iron and phosphorous is shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Gr{\"u}neisen equation of state and a number of well-known empirical melting and freezing rules.