Hidden scale invariance of metals

Felix Hummel, Georg Kresse, Jeppe C. Dyre, Ulf Rørbæk Pedersen

Research output: Contribution to journalJournal articleResearchpeer-review

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
Original languageEnglish
Article number174116
JournalPhysical Review B (Condensed Matter and Materials Physics)
Volume92
ISSN1098-0121
DOIs
Publication statusPublished - 23 Nov 2015

Cite this

@article{89d6da561cb94a489d45c2132af40790,
title = "Hidden scale invariance of metals",
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 Gr{\"u}neisen 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{\"u}neisen equation of state and a number of well-known empirical melting and freezing rules",
author = "Felix Hummel and Georg Kresse and Dyre, {Jeppe C.} and Pedersen, {Ulf R{\o}rb{\ae}k}",
year = "2015",
month = "11",
day = "23",
doi = "10.1103/PhysRevB.92.174116",
language = "English",
volume = "92",
journal = "Physical Review B",
issn = "2469-9950",
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Hidden scale invariance of metals. / Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.; Pedersen, Ulf Rørbæk.

In: Physical Review B (Condensed Matter and Materials Physics), Vol. 92, 174116, 23.11.2015.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Hidden scale invariance of metals

AU - Hummel, Felix

AU - Kresse, Georg

AU - Dyre, Jeppe C.

AU - Pedersen, Ulf Rørbæk

PY - 2015/11/23

Y1 - 2015/11/23

N2 - 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

AB - 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

U2 - 10.1103/PhysRevB.92.174116

DO - 10.1103/PhysRevB.92.174116

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JO - Physical Review B

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