Ab initio investigations of the phase stability in group IVB and VB transition metal carbides

Yu, Xiaoxiang; Weinberger, Christopher R.; Thompson, Gregory B.

doi:10.1016/j.commatsci.2015.10.038

Cited by 83 publications

(51 citation statements)

References 42 publications

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“…stacking fault phases) can form near the ideal compositions of M 4 C 3 or M 3 C 2 . In the case of the vacancy‐ordered forms of the M 4 C 3 and M 3 C 2 , several structures related to the FCC metal stacking sequence are proposed, and for brevity, we will not go into detailed description of the specifics of these structures that are well described in references …”

Section: Overview Of the Crystal Structuresmentioning

confidence: 90%

“…In the Ti‐C system, Yu et al reported the equilibrium structures at 0 K using an evolutionary algorithm in conjunction with all the group IVB and VB TMCs. They found that 4 titanium carbides: a

Fd \bar{3} m

Ti 2 C phase, a C2/m Ti 3 C 2 phase, a

R \bar{3}

Ti 7 C 6 phase, and the standard

Fm \bar{3} m

TiC phase—along with HCP titanium and graphite—lying on the convex hull, with the Ti 2 C, Ti 3 C 2 , and Ti 7 C 6 phases being vacancy‐ordered forms of the B1 structure.…”

Section: Phase Stability Predictionsmentioning

confidence: 99%

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Review of phase stability in the group IVB and VB transition‐metal carbides

Weinberger

Thompson

2018

J Am Ceram Soc

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This review summarizes the phase stability in the group IVB (Ti‐C; Zr‐C; Hf‐C) and group VB (V‐C; Nb‐C; Ta‐C) transition‐metal carbides. The order parameter functional (OPF) method and density functional theory (DFT) method have been used to predict phase equilibria in these systems. Extensive experimental investigations have attempted to determine both phase stability as a function of composition as well the crystal structures present using X‐ray diffraction, neutron diffraction, electron backscatter detection, and selected area electron diffraction. These investigations have demonstrated that the structures that form are based on the close‐packing of the metal atoms and the arrangement of the carbon atoms in the octahedral interstices. In general, the rocksalt B1 phase is stable for all of the transition‐metal carbides, with their substoichiometry tolerance increasing with temperature; vanadium carbide is the exception due to its negative vacancy formation energy. Vacancy‐ordered M6C5 phases have been predicted and experimentally confirmed in both groups of carbides; however, kinetic limitations often inhibit the formation of vacancy‐ordered phases, which has contributed to controversy in phase identification. The vacancy‐ordered M4C3 phase has been predicted for select carbides and has only been observed in zirconium carbide. In contrast, the stacking fault phase ζ‐M4C3−x has been readily reported in the group VB carbides (but not in the group IVB carbides). The vacancy‐ordered M3C2 has been predicted by DFT for the group IVB carbides but not in the group VB carbides, whereas OPF predicts its stability in both carbides. Vacancy‐ordered M3C2 phases have been experimentally observed in the Ti‐C and Hf‐C systems. Finally, the M2C phase has been predicted in both group carbides, except for hafnium carbide, with an order‐disorder transition with temperature. These factors result in phase diagrams that are similar among all the carbides, but each phase diagram is unique due to subtle differences in bonding that result in slight differences in thermodynamically stable phases.

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Section: Overview Of the Crystal Structuresmentioning

confidence: 90%

Fd \bar{3} m

Ti 2 C phase, a C2/m Ti 3 C 2 phase, a

R \bar{3}

Ti 7 C 6 phase, and the standard

Fm \bar{3} m

TiC phase—along with HCP titanium and graphite—lying on the convex hull, with the Ti 2 C, Ti 3 C 2 , and Ti 7 C 6 phases being vacancy‐ordered forms of the B1 structure.…”

Section: Phase Stability Predictionsmentioning

confidence: 99%

Review of phase stability in the group IVB and VB transition‐metal carbides

Weinberger

Thompson

2018

J Am Ceram Soc

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“…Crystal structures of nonstoichiometric ZrC x have also been studied by computational methods, which predicted the stability of the Fd

\bar{3}

crystal structure at carbon stoichiometries as low as x = 0.5 using mixing enthalpy calculations . Phase stability of highly carbon‐deficient compositions (eg, x ≤ 0.5) has been studied using formation enthalpy calculations, which showed that the Fd

\bar{3}

structure, with ordered vacancies, was the most stable . However, not all of the carbides with the rock‐salt crystal structure have the same characteristic as ZrC x .…”

Section: Introductionmentioning

confidence: 99%

Carbon vacancy ordering in zirconium carbide powder

et al. 2019

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Ordered carbon vacancies were detected in zirconium carbide (ZrCx) powders that were synthesized by direct reaction. Zirconium hydride (ZrH2) and carbon black were used as starting powders with the molar ratio of ZrH2:C = 1:0.6. Powders were reacted at 1300°C or 2000°C. The major phase detected by x‐ray diffraction (XRD) was ZrCx. No excess carbon was observed by transmission electron microscopy (TEM) in powders synthesized at either temperature. Ordering of the carbon vacancies was identified by neutron powder diffraction (NPD) and further supported by selected area electron diffraction (SAED). The vacancies in carbon‐deficient ZrCx exhibited diamond cubic symmetry with a supercell that consisted of eight (2 × 2 × 2) ZrCx unit cells with the rock‐salt structure. Rietveld refinement of the neutron diffraction patterns revealed that the synthesis temperature did not have a significant effect on the degree of vacancy ordering in ZrCx powders. Direct synthesis of ZrC0.6 resulted in the partial ordering of carbon vacancies without the need for extended isothermal annealing as reported in previous experimental studies.

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“…With the depletion of the non-metal atoms, intermediate phases (between the metal atom and the rocksalt structure) are able to form. These include vacancy ordered and faulted phases [21]. At low non-metal vacancy concentrations (relative to the B1 structure), a vacancy ordered phase can be observed at the chemical composition of M 6 X 5 , where M denotes the metal atoms and X denotes the non-metal atoms [22].…”

Section: Introductionmentioning

confidence: 99%

A model for understanding the formation energies of nanolamellar phases in transition metal carbides and nitrides

Guziewski

Thompson

et al. 2016

Modelling Simul. Mater. Sci. Eng.

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Abstract. In this paper we introduce a stacking-fault based model to understand the energetics of formation of the nanolamellar-based metal carbide and nitride structures. The model is able to reproduce the cohesive energies of the stacking fault phases from Density Functional Theory calculations by fitting the energy of different stacking sequences of metal layers. The model demonstrates that the first and second nearest metal-metal neighbor interactions and the nearest metal-carbon/nitrogen interaction are the dominant terms in determining the cohesive energy of these structures. The model further demonstrates that above a metal to non-metal ratio of 75%, there is no energetic favorability for the stacking faults to form a long-range ordered structure. The model's applicability is demonstrated using the Ta-C system as its case study from which we report that the interfacial energy between ζ-Ta 4 C 3 and TaC or Ta 2 C is negligible. Our results suggest that the closed packed planes of these phases should be aligned and that precipitated phases should be thin, which is in agreement with experiments.

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Ab initio investigations of the phase stability in group IVB and VB transition metal carbides

Cited by 83 publications

References 42 publications

Review of phase stability in the group IVB and VB transition‐metal carbides

Review of phase stability in the group IVB and VB transition‐metal carbides

Carbon vacancy ordering in zirconium carbide powder

A model for understanding the formation energies of nanolamellar phases in transition metal carbides and nitrides

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