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Open AccessArticle

Topological Equivalence of the Phase Diagrams of Molybdenum and Tungsten

by Samuel Baty 1,†, Leonid Burakovsky 2,*,† and Dean Preston 3,†
1
Analytics Intelligence and Technology, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
2
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3
Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Crystals 2020, 10(1), 20; https://doi.org/10.3390/cryst10010020
Received: 15 November 2019 / Revised: 21 December 2019 / Accepted: 26 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Pressure-Induced Phase Transformations)
We demonstrate the topological equivalence of the phase diagrams of molybdenum (Mo) and tungsten (W), Group 6B partners in the periodic table. The phase digram of Mo to 800 GPa from our earlier work is now extended to 2000 GPa. The phase diagram of W to 2500 GPa is obtained using a comprehensive ab initio approach that includes (i) the calculation of the T = 0 free energies (enthalpies) of different solid structures, (ii) the quantum molecular dynamics simulation of the melting curves of different solid structures, (iii) the derivation of the analytic form for the solid–solid phase transition boundary, and (iv) the simulations of the solidification of liquid W into the final solid states on both sides of the solid–solid phase transition boundary in order to confirm the corresponding analytic form. For both Mo and W, there are two solid structures confirmed to be present on their phase diagrams, the ambient body-centered cubic (bcc) and the high-pressure double hexagonal close-packed (dhcp), such that at T = 0 the bcc–dhcp transition occurs at 660 GPa in Mo and 1060 GPa in W. In either case, the transition boundary has a positive slope d T / d P . View Full-Text
Keywords: phase diagram; quantum molecular dynamics; melting curve; Z methodology; multi-phase materials phase diagram; quantum molecular dynamics; melting curve; Z methodology; multi-phase materials
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Baty, S.; Burakovsky, L.; Preston, D. Topological Equivalence of the Phase Diagrams of Molybdenum and Tungsten. Crystals 2020, 10, 20.

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