Non-empirical phase equilibria in the Cr–Mo system: A combination of first-principles calculations, cluster expansion and Monte Carlo simulations

Chen, Wenzhou; Xu, Guanglong; Martín-Bragado, Ignacio; Cui, Yujie

doi:10.1016/j.solidstatesciences.2015.01.012

Cited by 11 publications

(5 citation statements)

References 48 publications

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“…The cluster expansion (CE) formalism (Connolly and Williams, 1983;De Fontaine, 1994;Ducastelle, 1991;Laks et al, 1992;Sanchez et al, 1984;Zunger, 1994) allows one to fit a series-type Hamiltonian to the formation energy values of a few supercell configurations as a set of effective cluster interactions (ECIs), pairs, triplets, quadruplets, and higher n-tuplets to allow faster energy evaluation. The energy to be fitted can be calculated with empirical potentials or electronic structure methods such as density functional theory (DFT) as demonstrated for alloys (Barabash et al, 2009;Chen et al, 2015;Gao et al, 2013;Ghosh et al, 2008;Liu and Zunger, 2009;Liu et al, 2005;Ravi et al, 2012;van de Walle et al, 2004), semiconductors (Burton et al, 2011Kumagai et al, 2012;Li et al, 2015;Usanmaz et al, 2015;Xue et al, 2014), ionic compounds (Burton and van de Walle, 2012a, 2012bBurton et al, 2012), and minerals including carbonates (Burton and van de Walle, 2003;Vinograd et al, 2009Vinograd et al, , 2007Vinograd et al, , 2006.…”

Section: Introductionmentioning

confidence: 99%

First-principles phase diagram calculations for the carbonate quasibinary systems CaCO3-ZnCO3, CdCO3-ZnCO3, CaCO3-CdCO3 and MgCO3-ZnCO3

et al. 2016

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Quasibinary solid solutions of calcite-structure carbonate minerals play an important role in rock formation. We have investigated solid solutions with cations Ca 2+ , Cd 2+ , Mg 2+ and Zn 2+ by performing first-principles phase diagram calculations for Ca 1-x Zn x CO 3 , Cd 1x Zn x CO 3 , Ca 1-x Cd x CO 3 and Mg 1-x Zn x CO 3 (0 ≤ x ≤ 1) with density functional theory, cluster expansion and Monte Carlo simulations. The end members and the dolomite structures were individually studied to analyze their structural parameters and bonding characteristics. Consolute temperatures and continuous order-disorder transition temperatures are 1450 K for Ca 1-x Zn x CO 3 and 1000 K for Cd 1-x Zn x CO 3 , but below 100 K for Ca 1-x Cd x CO 3 and Mg 1-x Zn x CO 3. In agreement with existing literature, consolute temperatures increase with increasing differences in cation radii. If the dolomite structures are assumed to be stable, the phase diagram calculations predict that they persist to 1150 K for Ca 1-x Zn x CO 3 , and 900 K for Cd 1-x Zn x CO 3 before decomposition at peritectoid points. This confirms the conjectured phase diagram for Ca 1-x Zn x CO 3 in (Goldsmith, 1983. Rev. Mineral. Geochemistry 11). In addition, formation energies of the dolomite structures were decomposed into two parts: first a volume change, then chemical exchange and relaxation. They were compared with the corresponding random solid solutions at the same bulk compositions. (Meta)stability of the dolomite structures was demonstrated by this analysis, and was also studied by examining the bond lengths and cation octahedral distortions.

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Section: Introductionmentioning

confidence: 99%

First-principles phase diagram calculations for the carbonate quasibinary systems CaCO3-ZnCO3, CdCO3-ZnCO3, CaCO3-CdCO3 and MgCO3-ZnCO3

et al. 2016

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“…The Zr–N and Hf–N bonds behave similarly with large values, ~5 eV Å −2 for the stretching term at 2.24 Å, contrasting Ti-N, ~1 eV Å −2 , likely because of the difference in ionic radii. Vibrational contributions reduce T C from 2400 K to 1400 K for Ti 1− x Zr x N, and from 900 K to 700 K for Ti 1− x Hf x N. The 42% drop in Ti 1− x Zr x N is large, but is also seen in ionic systems such as NaCl-KCl [19] and metallic systems such as Cr–Mo [7]. In comparison, Holleck [27, 85] estimated T C to be 1850 K for Ti 1− x Zr x N and 1300 K for Ti 1− x Hf x N, based on phenomenological thermodynamic models.…”

Section: Resultsmentioning

confidence: 99%

“…The energies to be fitted can be calculated with empirical potentials or first-principles approach such as density functional theory (DFT). This approach has been used to study a diverse set of material systems including alloys [7][8][9][10][11][12][13][14], semiconductors [15][16][17][18], ionic compounds [19][20][21][22], and minerals [23][24][25][26] with satisfactory results that compare favorably with experiments.…”

Section: Introductionmentioning

confidence: 99%

First-principles phase diagram calculations for the rocksalt-structure quasibinary systems TiN–ZrN, TiN–HfN and ZrN–HfN

Liu¹,

Burton²,

Khare³

et al. 2016

J. Phys.: Condens. Matter

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We have studied the phase equilibria of three ceramic quasibinary systems Ti1−xZrxN, Ti1−xHfxN and Zr1−xHfxN (0 ≤ x ≤ 1) with density functional theory, cluster expansion and Monte Carlo simulations. We predict consolute temperatures (TC), at which miscibility gaps close, for Ti1−xZrxN to be 1400 K, for Ti1−xHfxN to be 700 K, and below 200 K for Zr1−xHfxN. The asymmetry of the formation energy ΔEf(x) is greater for Ti1−xHfxN than Ti1−xZrxN, with less solubility on the smaller cation TiN-side, and similar asymmetries were predicted for the corresponding phase diagrams. We also analyzed different energetic contributions: ΔEf of the random solid solutions were decomposed into a volume change term, ΔEvc, and a chemical exchange and relaxation term, ΔExc-rlx. These two energies partially cancel one another. We conclude that ΔEvc influences the magnitude of TC and ΔExc-rlx influences the asymmetry of ΔEf(x) and phase boundaries. We also conclude that the absence of experimentally observed phase separation in Ti1−xZrxN and Ti1−xHfxN is due to slow kinetics at low temperatures. In addition, elastic constants and mechanical properties of the random solid solutions were studied with the special quasirandom solution approach. Monotonic trends, in the composition dependence, of shear-related mechanical properties, such as Vickers hardness between 18 to 23 GPa, were predicted. Trends for Ti1−xZrxN and Ti1−xHfxN exhibit down-bowing (convexity). It shows that mixing nitrides of same group transition metals does not lead to hardness increase from an electronic origin, but through solution hardening mechanism. The mixed thin films show consistency and stability with little phase separation, making them desirable coating choices.

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“…Even though the vibrational entropy contribution is normally much smaller than the configurational one, it cannot be ignored in many cases to make accurate predictions of the stable phases as a function of temperature, the phase boundaries or the solubility [15][16][17][18]. A typical example is the stability of θ and θ' phases in the Al-Cu phase diagram.…”

Section: Introductionmentioning

confidence: 99%

First principles prediction of the Al-Li phase diagram including configurational and vibrational entropic contributions

Shao

Llorca

2023

Computational Materials Science

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Non-empirical phase equilibria in the Cr–Mo system: A combination of first-principles calculations, cluster expansion and Monte Carlo simulations

Cited by 11 publications

References 48 publications

First-principles phase diagram calculations for the carbonate quasibinary systems CaCO3-ZnCO3, CdCO3-ZnCO3, CaCO3-CdCO3 and MgCO3-ZnCO3

First-principles phase diagram calculations for the carbonate quasibinary systems CaCO3-ZnCO3, CdCO3-ZnCO3, CaCO3-CdCO3 and MgCO3-ZnCO3

First-principles phase diagram calculations for the rocksalt-structure quasibinary systems TiN–ZrN, TiN–HfN and ZrN–HfN

First principles prediction of the Al-Li phase diagram including configurational and vibrational entropic contributions

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