Hidden scale invariance of metals

Author(s)
Felix Hummel, Georg Kresse, Jeppe C. Dyre, Ulf R. Pedersen
Abstract

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 Grüneisen 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 Grüneisen equation of state and a number of well-known empirical melting and freezing rules.

Organisation(s)
Computational Materials Physics
External organisation(s)
Roskilde University, Technische Universität Wien
Journal
Physical Review B
Volume
92
No. of pages
12
ISSN
1098-0121
DOI
https://doi.org/10.1103/PhysRevB.92.174116
Publication date
11-2015
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics, 103036 Theoretical physics, 103015 Condensed matter, 103009 Solid state physics
Keywords
ASJC Scopus subject areas
Electronic, Optical and Magnetic Materials, Condensed Matter Physics
Portal url
https://ucris.univie.ac.at/portal/en/publications/hidden-scale-invariance-of-metals(81a06511-a836-4510-a087-069fee9c82f8).html