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Crystals 2019, 9(2), 86; https://doi.org/10.3390/cryst9020086

Generalization of the Unified Analytic Melt-Shear Model to Multi-Phase Materials: Molybdenum as an Example

1
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
2
Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3
Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
Author to whom correspondence should be addressed.
Received: 21 November 2018 / Revised: 23 January 2019 / Accepted: 24 January 2019 / Published: 6 February 2019
PDF [1150 KB, uploaded 6 February 2019]

Abstract

The unified analytic melt-shear model that we introduced a decade ago is generalized to multi-phase materials. A new scheme for calculating the values of the model parameters for both the cold ( T = 0 ) shear modulus ( G ) and the melting temperature at all densities ( ρ ) is developed. The generalized melt-shear model is applied to molybdenum, a multi-phase material with a body-centered cubic (bcc) structure at low ρ which loses its dynamical stability with increasing pressure (P) and is therefore replaced by another (dynamically stable) solid structure at high ρ . One of the candidates for the high- ρ structure of Mo is face-centered cubic (fcc). The model is compared to (i) our ab initio results on the cold shear modulus of both bcc-Mo and fcc-Mo as a function of ρ , and (ii) the available theoretical results on the melting of bcc-Mo and our own quantum molecular dynamics (QMD) simulations of one melting point of fcc-Mo. Our generalized model of G ( ρ , T ) is used to calculate the shear modulus of bcc-Mo along its principal Hugoniot. It predicts that G of bcc-Mo increases with P up to ∼240 GPa and then decreases at higher P. This behavior is intrinsic to bcc-Mo and does not require the introduction of another solid phase such as Phase II suggested by Errandonea et al. Generalized melt-shear models for Ta and W also predict an increase in G followed by a decrease along the principal Hugoniot, hence this behavior may be typical for transition metals with ambient bcc structure that dynamically destabilize at high P. Thus, we concur with the conclusion reached in several recent papers (Nguyen et al., Zhang et al., Wang et al.) that no solid-solid phase transition can be definitively inferred on the basis of sound velocity data from shock experiments on Mo. Finally, our QMD simulations support the validity of the phase diagram of Mo suggested by Zeng et al.
Keywords: quantum molecular dynamics; thermoelasticity; melting curve; multi-phase materials quantum molecular dynamics; thermoelasticity; melting curve; multi-phase materials
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Burakovsky, L.; Luscher, D.J.; Preston, D.; Sjue, S.; Vaughan, D. Generalization of the Unified Analytic Melt-Shear Model to Multi-Phase Materials: Molybdenum as an Example. Crystals 2019, 9, 86.

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