Prediction of the material with highest known melting point from ab initio molecular dynamics calculations

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Prediction of the material with highest known melting point from ab initio molecular dynamics calculations

Qi-Jun Hong and Axel van de Walle

Phys. Rev. B 92, 020104(R) – Published 20 July 2015

Abstract

Using electronic structure calculations, we conduct an extensive investigation into the Hf-Ta-C system, which includes the compounds that have the highest melting points known to date. We identify three major chemical factors that contribute to the high melting temperatures. Based on these factors, we propose a class of materials that may possess even higher melting temperatures and explore it via efficient ab initio molecular dynamics calculations in order to identify the composition maximizing the melting point. This study demonstrates the feasibility of automated and high-throughput materials screening and discovery via ab initio calculations for the optimization of “higher-level” properties, such as melting points, whose determination requires extensive sampling of atomic configuration space.

Received 12 March 2015
Revised 20 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.020104

Authors & Affiliations

Qi-Jun Hong^*

School of Engineering, Brown University, Providence, Rhode Island 02912, USA and Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA

Axel van de Walle

School of Engineering, Brown University, Providence, Rhode Island 02912, USA

^*Corresponding author: qijun_hong@brown.edu

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Issue

Vol. 92, Iss. 2 — 1 July 2015

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Images

Figure 1
The Hf-C phase diagram. Prior experimental measurements of the melting points are compared with the present computational results (labelled “PBE” as they rely on the PBE functional). The temperatures where free energies of the liquid and of the solid intersect are marked by “+”. Also shown are the solidus and liquidus obtained via a calphad model [28] fitted to our calculated thermodynamic data. Our calculations successfully capture the location of the apex within 3 at. % of carbon content. The vertical shift in calculated temperature, relative to experimental data, is essentially composition-independent and mostly reflects DFT error (see discussion in text).
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Figure 2
Electronic density of states in HfC showing clear participation of both Hf and C in forming covalent bonds. Total density of states is shown in black. Projections on C and Hf are colored in red and blue, respectively. The Fermi level is at 0. Vertical lines are energy levels of atomic orbitals. Insets are wave functions illustrating the diversity of bond types in HfC with clear covalent character. From left to right, these figures represent Hf $5 d$ $σ$ bond, C $2 p$ $σ$ bond, and Hf $5 d - C$ $2 p$ $π$ bond. Surfaces of constant value of the real parts of the wave functions are represented. Hf and C atoms are colored in green and blue respectively.
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Figure 3
The electron transfer in HfC. The figure reports $ρ / ρ_{0} - 1$ , where $ρ$ is electronic charge density from DFT wave function and $ρ_{0}$ is initial overlapping atomic charge density. The sharp contrast clearly shows a charge transfer from Hf to C indicative of ionic interactions, although covalent character is still visible in the anisotropy of the charge density.
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Figure 4
Melting temperature of ${Ta}_{x} {Hf}_{1 - x} C_{0.875}$ as a function of $x$ . Agte's measurements [16] focused on the Ta-rich side, while the rest part of the phase diagram was extrapolated as dash lines. Our melting point calculations provide more details at the Hf-rich region. The calculated melting curve captures the cusp near ${Ta}_{4} {HfC}_{5}$ (as the melting points of ${Ta}_{0.75} {Hf}_{0.25} C_{0.875}$ and ${Ta}_{0.81} {Hf}_{0.19} C_{0.875}$ are evidently higher than those of ${Ta}_{0.5} {Hf}_{0.5} C_{0.875}$ and ${TaC}_{0.875})$ , which illustrates the effect of tuning the Fermi level via alloying, so that it lies precisely between the bonding and antibonding bands. The inset shows the effect on the Fermi level of the solid phase by tuning composition in ${Ta}_{x} {Hf}_{1 - x} C$ . Vertical lines are Fermi levels. Our calculation suggests that the melting temperature of ${HfTa}_{4} C_{5}$ , instead of being the highest, barely falls within the melting temperatures of the pure components, which corroborates Rudy's report [37].
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Figure 5
Melting temperatures of Ta-Hf-C-N alloys. Filled circles mark the calculated melting temperatures in the Hf-C and Hf-C-N systems while open circles show data from the Ta-Hf-C system for comparison. The melting temperature surface $T_{m} (x_{N}, x_{C})$ (shown as contour lines) was obtained via a regression analysis of the calculated melting temperatures based on a quadratic function of composition. See Table II in Ref. [25] for melting point data. A 2D version of the melting point surface is available in Fig. 1 in Ref. [25].
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Figure 6
Pair correlation function (normalized as $r \to \infty)$ in liquid-state ${Hf}_{32} C_{24} N_{7}$ . We find a remarkable difference between carbon and nitrogen: there is nearly no $N - N$ (yellow) “near neighbors” (first pair correlation peak), compared to a considerable amount of C–C (red). The inset shows compositions of near neighbors for C and N atoms in liquid-state ${Hf}_{32} C_{24} N_{7}$ (the compositions of Hf–C and Hf–N account for the rest and are omitted). N atom has significantly less tendency to couple with C (2.17% vs 7.15%) and N (0.02% vs 0.59%).
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