First-Principles Calculation of Self-Diffusion Coefficients
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Abstract:
We demonstrate a first-principles method to compute all factors entering the vacancy-mediated self-diffusion coefficient. Using density functional theory calculations of fcc Al as an illustrative case, we determine the energetic and entropic contributions to vacancy formation and atomic migration. These results yield a quantitative description of the migration energy and vibrational prefactor via transition state theory. The calculated diffusion parameters and coefficients show remarkably good agreement with experiments. We provide a simple physical picture for the positive entropic contributions.Keywords:
Self-diffusion
Transition state theory
Diffusion theory
We demonstrate a first-principles method to compute all factors entering the vacancy-mediated self-diffusion coefficient. Using density functional theory calculations of fcc Al as an illustrative case, we determine the energetic and entropic contributions to vacancy formation and atomic migration. These results yield a quantitative description of the migration energy and vibrational prefactor via transition state theory. The calculated diffusion parameters and coefficients show remarkably good agreement with experiments. We provide a simple physical picture for the positive entropic contributions.
Self-diffusion
Transition state theory
Diffusion theory
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Crystal (programming language)
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A new model based on fluctuation theory is presented and used to calculate migration energies in self-diffusion for fcc metals. The agreement between the experimental results and results calculated using this model is very good.
Self-diffusion
Diffusion theory
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Self-diffusion
Diffusion theory
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An expression is given relating the exact self-diffusion coefficients for dense hard sphere systems, obtained by the method of molecular dynamics, to the molar volume. It is shown that this simple relationship gives an accurate description of the density dependence of the self-diffusion coefficients of dense gases and liquids and this provides further evidence that the molecular correlated motions observed in computer hard sphere studies occur in real fluids also.
Self-diffusion
Diffusion theory
Molecular diffusion
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Vacancy clusters in graphite have been investigated using Density Functional T heory (DFT) within B3LYP exchange-functional. The smallest size of vacancy clusters (V4) has been chosen to study the migration energy and aggregation mechanism. Two main types of V4 vacancy clusters have been modeled, the disc (V4d) and the line vacancy clusters; including boat vacancy (V4b) and zig-zag vacancy (V4z). The results show that the presence of unst able V3 vacancy may induce the mono-vacancy to migrate with low energy and vanish through forming stable V4 vacancy cluster. Also, the calculated energy barriers required to form the boat vacancy cluster (V4b), the zig-zag vacancy cluster (V4z) and disk vacancy cluster (V4d) support that the disc and the boat vacancy clusters co-exist. However the zig-zag type might only exist by knocking-out mechanism for highly irradiated graphite.
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Abstract The formation energy of the mono-vacancy and both the formation energy and binding energy of the di-and tri-vacancy in BCC alkali metals and transition metals have been calculated by using the modified analytical embedded-atom method (MAEAM). The formation energy of each type of configuration of the vacancies in the alkali metals is much lower than that in the transition metals. From minimum of the formation energy or maximum of the binding energy, the favorable configuration of the di-vacancy and tri-vacancy respectively is the first-nearest-neighbor (FN) or second-nearest-neighbor (SN) di-vacancy and the [112] tri-vacancy constructed by two first-and one second-nearest-neighbor vacancies. It is indicated that there is a concentration tendency for vacancies in BCC metals.
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Molecular dynamics simulation was performed to obtain the formation energy of vacancy clusters in silicon crystal and learn relevant factors,in which the influence laws and their mechanisms of model system size,configuration of vacancy cluster and vacancy number on the formation energy of vacancy cluster were revealed.The results show that the size of model system and configuration of vacancy cluster have little effect on the formation energy of vacancy cluster in general;the size of 3×3×3 model system is more suitable for the calculation and analysis of the formation energy;the minimum formation energy increases linearly as vacancy number increasing is less than 6;the formation energy of vacancy cluster in essence depends on the number of broken Si-Si bonds as well and energy.
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A semiempirical interatomic potential for Fe was used to calculate the diffusivity in bcc Fe assuming the vacancy and interstitial mechanisms of self-diffusion. Point-defect concentrations and diffusivities were obtained directly from molecular dynamics (MD) simulations. It was found that self-diffusion in bcc Fe is controlled by the vacancy mechanism at all temperatures. This result is due to the fact that the equilibrium vacancy concentration is always much larger than the equilibrium interstitial concentration. The predominance of the equilibrium vacancy concentration over the interstitial concentration is explained by the lower vacancy-formation energy at low temperatures and high vacancy-formation entropy at high temperatures. The calculated diffusivity is in good agreement with experimental data. The MD simulations were also used to test the quasiharmonic (QH) approximation for point-defect calculations. It was found that the QH approximation can considerably underestimate variations in point-defect characteristics with temperature.
Self-diffusion
Frenkel defect
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