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

2018

A systematic electronic structure density functional theory search for the zeta phase in the tantalum carbon system has been conducted, demonstrating that the zeta phase does indeed lie on the convex hull, establishing low‐temperature thermodynamic stability, and is structurally stable. Even though the zeta phase is most oft reported as a R3¯m ζ‐Ta4C3‐x structure, these new computational results reveal that the perfectly ordered zeta phase occurs at the Ta3C2 composition and belongs to the C2/m space group. Furthermore, these results suggest that the R3¯m space group may be a result of an order‐disorder transition and potential deviations from ideal stoichiometry at higher temperatures. The structure of this Ta3C2 compound can be described as ordered strings of carbon vacancies on a single carbon plane, which is also the preferred plane where additional carbon vacancies or interstitials form. These defects have modest formation energies, which provides further explanation for the small homogeneity range in zeta phase.

Section: Resultsmentioning

confidence: 95%

“…The transformation method has been described through the expansion of carbon‐depleted stacking faults bounded by Shockley partials which are able convert TaC to ζ‐Ta 4 C 3. A similar mechanism could also transform Ta 2 C to ζ‐Ta 4 C 3 . The structure of the ζ‐Ta 3 C 2 found here does not impact this prior understanding.…”

Section: Resultsmentioning

confidence: 96%

A computational search for the zeta phase in the tantalum carbides

2018

“…However, it is equally important to ensure structural stability, ascertained through phonon dispersion curves generated from DFT. It is worth noting that this has been done for most of the phases discussed here in the Hf‐C system by Zeng et al, the Ta‐C system by Yu et al, the Zr‐C system by Zhang et al, and select structures in the remaining systems by Yu et al . In those studies, all of the thermodynamically stable phases were also dynamically stable.…”

Section: Phase Stability Predictionsmentioning

confidence: 88%

“…This relationship can be easily rationalized by the formation of the zeta phase from the stacking sequences discussed in Section 2.3. To provide further insight into this process and the associated microstructure, Yu et al demonstrated the energetic equivalence of the organized stoichiometric ζ‐Ta 4 C 3 phase and isolated stacking faults in the TaC structure, which helps explain these observed microstructures . The stability of this zeta phase and the associated microstructure in the tantalum carbides has garnered much of its attention from reports that it has a very high fracture toughness, ~15 MPa

\sqrt{m}

, in materials with high‐volume fractions of this phase …”

Section: Experimental Observations Of Specific Crystal Structuresmentioning

confidence: 99%

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

2018

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.

“…Notably, in the carbides, high fractions of metal-rich carbides have been shown to substantially increase the fracture toughness. [31][32][33][34][35] Although the intent of his paper is not to address mechanical properties, the phase stability and structure of these carbides was found to be instrumental to their properties 31,[35][36][37][38] ; therefore, as a first-step, the equilibrium and structure of the similar nitride structures must be established and is the intent of this work. For clarity, we wish to point out a nomenclature approach that we will follow in this paper to distinguish between the phases (zeta and eta) and the structures that we will searched for.…”

Section: Weinberger and Thompsonmentioning

confidence: 99%

A computational examination of the zeta and eta phases in the hafnium nitrides

2020

The hafnium nitrides are an interesting class of ceramics that have shown promise in a diversity of applications that include high temperature coatings, 1,2 uses in electronics, 3 solar cells, 4 and even hydrogen storage. 5 Despite decades of research and the wide applications of these materials, the stability of the phases that comprise the hafnium-nitrogen (Hf-N) system are still debated. 6-10 For the advancement of these materials in these and other emerging technologies, it is particularly important to concretely establish and understand the equilibrium phase diagram in the Hf-N system. One of the earliest phase equilibrium diagrams for the Hf-N system was described by Toth. 11 As with many ultrahigh temperature ceramics, this system has a rocksalt phase, δ-HfN, which can be found at nitrogen concentrations between 39 and 52 at.%, depending on temperature. In contrast to the transition metal carbides which also form the rocksalt structure, 12,13 δ-HfN is able to retain the rocksalt structure for a modest nonmetal-rich composition. 7,10 Thus, δ-HfN can be regarded as a strongly nonstoichiometric compound. With the depletion of nitrogen, Rudy 14 originally reported two specific subnitride phases, the-Hf 3 N 2−x (originally called the ε-Hf 3 N 2) and ζ-Hf 4 N 3−x phases. The former eta phase was identified to have a 9R metal atom stacking sequence, that is (hhc) 3 or ABABCBCAC. The latter zeta phase has a similar metal atom stacking sequence given as (hhcc) 3 or ABABCACABCBC, which is equivalent to the structure identified by Yvon and Parthe as the ζ-V 4 C 3−x phase. 15,16 The compositions of the eta and zeta phases were only identified for single samples at chemistries of HfN 0.56 and HfN 0.65 , respectively. However, Rudy was not able to identify either a composition range for the phases (and thus they were assumed to be line compounds) nor establish if or how much the nitrogen atoms were ordered in either structure. Rudy further identified the upper decomposition temperatures for these respective phases to be approximately 2000°C (eta) and 2300°C (zeta).