2015/04/30 by Felix Hummel, Georg Kresse, Jeppe C. Dyre +1 · 1 citation
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Condensed matter physics #High-pressure geophysics and materials #Invariant (physics) #Material Dynamics and Properties #Materials science #Phase (matter) #Phase diagram #Physics #Quantum mechanics #Scale invariance #Scaling #Structure factor #Theoretical and Computational Physics #Thermodynamics #Virial theorem #cond-mat.mtrl-sci #cond-mat.stat-mech #physics.chem-ph #physics.comp-ph #physics.geo-ph
paper · pdf · doi:10.1103/physrevb.92.174116
published as Phys. Rev. B 92, 174116 (2015) · 12 pages, 11 figures
arxiv created 2015/10/22 · openalex publication_date 2015/11/23 · arxiv updated 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general ``hidden'' scale invariance of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Gr"uneisen parameter, are in good agreement with experimental values for the 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. The virial-energy correlation coefficients of iron and phosphorous are shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Gr"uneisen equation of state and a number of well-known empirical melting and freezing rules.