### Abstract

Original language | English |
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Article number | 174116 |

Journal | Physical Review B (Condensed Matter and Materials Physics) |

Volume | 92 |

ISSN | 1098-0121 |

DOIs | |

Publication status | Published - 23 Nov 2015 |

### Cite this

*Physical Review B (Condensed Matter and Materials Physics)*,

*92*, [174116]. https://doi.org/10.1103/PhysRevB.92.174116

}

*Physical Review B (Condensed Matter and Materials Physics)*, vol. 92, 174116. https://doi.org/10.1103/PhysRevB.92.174116

**Hidden scale invariance of metals.** / Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.; Pedersen, Ulf Rørbæk.

Research output: Contribution to journal › Journal article › Research › peer-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

M3 - Journal article

VL - 92

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

M1 - 174116

ER -