<i>Ab Initio</i>Study of Phase Equilibria in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>TiC</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

Korzhavyi, Pavel A.; Pourovskii, L. V.; Hugosson, Håkan Wilhelm; Ruban, Andrei V.; Johansson, Börje

doi:10.1103/physrevlett.88.015505

Cited by 70 publications

(51 citation statements)

References 26 publications

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“…For convenience the vacancy could be designated as a type "C" atom, an idea already expressed earlier in Refs. [30,34,48,49,53,54]. The occupation variable for every site i thus has vector components p (C) , p (B) , and p (A) .…”

Section: B Cluster Expansionmentioning

confidence: 99%

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

Zhang

Sluiter

2015

Phys. Rev. B

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Vacancy properties in concentrated alloys continue to be of great interest because nowadays ab initio supercell simulations reach a scale where even defect properties in disordered alloys appear to be within reach. We show that vacancy properties cannot generally be extracted from supercell total energies in a consistent manner without a statistical model. Essential features of such a model are knowledge of the chemical potential and imposition of invariants. In the present work, we derive the simplest model that satisfies these requirements and we compare it with models in the literature. As illustration we compute ab initio vacancy properties of fcc Cu-Ni alloys as a function of composition and temperature. Ab initio density functional calculations were performed for SQS supercells at various compositions with and without vacancies. Various methods of extracting alloy vacancy properties were examined. A ternary cluster expansion yielded effective cluster interactions (ECIs) for the Cu-Ni-Vac system. Composition and temperature dependent alloy vacancy concentrations were obtained using statistical thermodynamic models with the ab initio ECIs. An Arrhenius analysis showed that the heat of vacancy formation was well represented by a linear function of temperature. The positive slope of the temperature dependence implies a negative configurational entropy contribution to the vacancy formation free energy in the alloy. These findings can be understood by considering local coordination effects.

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Section: B Cluster Expansionmentioning

confidence: 99%

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

Zhang

Sluiter

2015

Phys. Rev. B

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“…Since the migration energy of a C vacancy is very high (our calculated value is about 4 eV), the vacancies are essentially immobile. Nevertheless, such a high substoichiometry may lead to a continuous network of interconnected vacancies 60,61 , from the interface to the interior of the precipitate, that can facilitate H diffusion and trapping (see Sec. V.B).…”

Section: E Interaction Of H With C Vacanciesmentioning

confidence: 99%

First-principles investigation of hydrogen interaction with TiC precipitates inα-Fe

et al. 2016

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A correct description of hydrogen diffusion and trapping is the prerequisite for an understanding of the phenomenon of hydrogen embrittlement. In this study, we carried out extensive first-principles calculations based on density functional theory to investigate the interaction of H with TiC precipitates that are assumed to be efficient trapping agents mitigating HE in advanced high-strength steels. We found that there exists a large variety of possible trapping sites for H associated with different types of interfaces between the TiC particle and the Fe matrix, with misfit dislocations and other defects at these interfaces, and with carbon vacancies in TiC. The most efficient trapping by more than 1 eV occurs at carbon vacancies in the interior of TiC particles. However, these traps are difficult to populate at ambient temperatures since the energy barrier for H entering the particles is high. H trapping at the semicoherent interfaces between the TiC particles and the Fe matrix is moderate, ranging from 0.3 to 0.5 eV. However, a sufficiently large concentration of the carbide particles can significantly reduce the amount of H segregated at dislocation cores in the Fe matrix. A systematic comparison of the obtained theoretical results with available experimental observations reveals a consistent picture of hydrogen trapping at the TiC particles that is expected to be qualitatively valid also for other carbide precipitates with the rock-salt crystal structure.

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“…[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] In the cluster-expansion method as applied to a binary system comprising of A and B, one selects an underlying parent lattice and defines a configuration by specifying the occupations of each of the n lattice sites by an A atom or a B atom. For each configuration, one assigns a set of spin variables, Ŝ i ͑i =1,2, ... ,n͒ to each of the n sites with Ŝ i = −1 or +1 depending on the site i being occupied by an A or B atom, respectively.…”

Section: A Cluster Expansion and Monte Carlo Simulationsmentioning

confidence: 99%

Cluster expansion Monte Carlo study of phase stability of vanadium nitrides

et al. 2010

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Phase stability of stable and metastable vanadium nitrides is studied using density functional theory ͑DFT͒ based total-energy calculations combined with cluster expansion Monte Carlo simulation and supercell methods. We have computed the formation enthalpy of the various stable and metastable vanadium nitride phases considering the available structural models and found that the formation enthalpies of the different phases decrease in the same order as they appear in the experimental aging sequence. DFT calculations are known to show stoichiometric V 2 N to be polymorphic in ⑀-Fe 2 N and -Fe 2 N structures within a few meV and VN to be more stable in WC͑B h ͒ phase than in the experimentally observed NaCl͑B1͒ structure. As these nitrides are known to be generally nonstoichiometric due to presence of nitrogen vacancies, we used cluster expansion and supercell methods for examining the effect of nitrogen vacancies on the phase stability. It is found that nitrogen vacancies, represented by ᮀ, stabilize ⑀-Fe 2 N phase of V 2 N 1−x ᮀ x and NaCl͑B1͒ phase of VN 1−x ᮀ x compared to -Fe 2 N and WC͑B h ͒ phases respectively, rendering the computed phase stability scenario to be in agreement with experiments. Analysis of supercell calculated electronic density of states ͑DOS͒ of VN 1−x ᮀ x with varying x, shows that the nitrogen vacancies increase the DOS at Fermi level in WC phase, whereas they decrease the DOS in NaCl phase. And this serves as the mechanism of enhancement of the stability of the NaCl phase. Monte Carlo simulations were used for computing the finite temperature formation enthalpies of these phases as a function of nitrogen-vacancy concentration and found close agreement for NaCl͑B1͒ phase of VN 1−x ᮀ x for which measured values are available.

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Ab InitioStudy of Phase Equilibria inTiCx

Cited by 70 publications

References 26 publications

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

First-principles investigation of hydrogen interaction with TiC precipitates inα-Fe

Cluster expansion Monte Carlo study of phase stability of vanadium nitrides

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