Universal binding energy relation for cleaved and structurally relaxed surfaces.
TL;DR: It is found that the cohesive law (stress-displacement relation) differs significantly in the case where cracked surfaces are allowed to relax, with lower peak stresses occurring at higher displacements.
Abstract: The universal binding energy relation (UBER), derived earlier to describe the cohesion between two rigid atomic planes, does not accurately capture the cohesive properties when the cleaved surfaces are allowed to relax. We suggest a modified functional form of UBER that is analytical and at the same time accurately models the properties of surfaces relaxed during cleavage. We demonstrate the generality as well as the validity of this modified UBER through first-principles density functional theory calculations of cleavage in a number of crystal systems. Our results show that the total energies of all the relaxed surfaces lie on a single (universal) energy surface, that is given by the proposed functional form which contains an additional length-scale associated with structural relaxation. This functional form could be used in modelling the cohesive zones in crack growth simulation studies. We find that the cohesive law (stress-displacement relation) differs significantly in the case where cracked surfaces are allowed to relax, with lower peak stresses occurring at higher displacements.
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TL;DR: In this paper, the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE) was extended to the CE and the correlation functions were stripped off of their asymptotic behaviour.
Abstract: Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE). However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in nanopore systems could certainly benefit from a mesoscopic DFT in the CE. The stumbling block is the fixed $N$ constraint which is responsible for the failure in proving the interchangeability of density profiles and external potentials as independent variables. Here we prove that, if in the CE the correlation functions are stripped off of their asymptotic behaviour (which is not in the form of a properly irreducible $n$-body function), the HKSM theorem can be extended to the CE. In proving that, we generate a new {\it hierarchy} of $N$-modified distribution and correlation functions which have the same formal structure that the more conventional ones have (but with the proper irreducible $n$-body behaviour) and show that, if they are employed, either a modified external field or the density profiles can indistinctly be used as independent variables. We also write down the $N$-modified free energy functional and prove that the thermodynamic potential is minimized by the equilibrium values of the new hierarchy.
79 citations
TL;DR: In this paper, an ab initio study of the influence of hydrogen filled vacancies on the mechanical properties of zirconium was carried out and the results of the modelling imply that the work of fracture and peak stress decrease as a result of the presence of hydrogen-filled vacancies.
27 citations
TL;DR: In this article, the authors have studied transgranular cleavage and fracture toughness of titanium hydrides by means of quantum mechanical calculations based on density functional theory, and they have shown that the fracture strength of the hydride can be improved by using a density functional model.
25 citations
TL;DR: The ratio between the frictional and cleavage strengths is provided as good indicator for the material failure mode – dislocation propagation versus crack nucleation.
Abstract: We present a comprehensive ab initio, high-throughput study of the frictional and cleavage strengths of interfaces of elemental crystals with different orientations. It is based on the detailed analysis of the adhesion energy as a function of lateral, γ(x, y), and perpendicular displacements, γ(z), with respect to the considered interface plane. We use the large amount of computed data to derive fundamental insight into the relation of the ideal strength of an interface plane with its adhesion. Moreover, the ratio between the frictional and cleavage strengths is provided as good indicator for the material failure mode – dislocation propagation versus crack nucleation. All raw and curated data are made available to be used as input parameters for continuum mechanic models, benchmarks, or further analysis.
17 citations
TL;DR: In this paper, the key properties of carbide-metal interfaces controlling the energy and critical stress of fracture, based on density functional theory (DFT) calculations, are determined, and the critical stresses of both intraprecipitate and interfacial fractures due to a tensile loading are estimated via the universal binding energy relation (UBER) model, parametrized on the DFT data.
Abstract: It is known that microcrack initiation in metallic alloys containing second-phase particles may be caused by either an interfacial or an intraprecipitate fracture. So far, the dependence of these features on properties of the precipitate and the interface is not clearly known. The present study aims to determine the key properties of carbide-metal interfaces controlling the energy and critical stress of fracture, based on density functional theory (DFT) calculations. We address coherent interfaces between a fcc iron or nickel matrix and a frequently observed carbide, the ${M}_{23}{\mathrm{C}}_{6}$, for which a simplified chemical composition ${\mathrm{Cr}}_{23}{\mathrm{C}}_{6}$ is assumed. The interfacial properties such as the formation and Griffith energies, and the effective Young's modulus are analyzed as functions of the magnetic state of the metal lattice, including the paramagnetic phase of iron. Interestingly, a simpler antiferromagnetic phase is found to exhibit similar interfacial mechanical behavior to the paramagnetic phase. A linear dependence is determined between the surface (and interface) energy and the variation of the number of chemical bonds weighted by the respective bond strength, which can be used to predict the relative formation energy for the surface and interface with various chemical terminations. Finally, the critical stresses of both intraprecipitate and interfacial fractures due to a tensile loading are estimated via the universal binding energy relation (UBER) model, parametrized on the DFT data. The validity of this model is verified in the case of intraprecipitate fracture, against results from DFT tensile test simulations. In agreement with experimental evidences, we predict a much stronger tendency for an interfacial fracture for this carbide. In addition, the calculated interfacial critical stresses are fully compatible with available experimental data in steels, where the interfacial carbide-matrix fracture is only observed at incoherent interfaces.
14 citations
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TL;DR: In this paper, the self-interaction correction (SIC) of any density functional for the ground-state energy is discussed. But the exact density functional is strictly selfinteraction-free (i.e., orbitals demonstrably do not selfinteract), but many approximations to it, including the local spin-density (LSD) approximation for exchange and correlation, are not.
Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.
16,027 citations
TL;DR: Quantum ESPRESSO as discussed by the authors is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave).
Abstract: Quantum ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for "opEn Source Package for Research in Electronic Structure, Simulation, and Optimization". It is freely available to researchers around the world under the terms of the GNU General Public License. Quantum ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively-parallel architectures, and a great effort being devoted to user friendliness. Quantum ESPRESSO is evolving towards a distribution of independent and inter-operable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
13,052 citations
TL;DR: In this article, the authors investigated the effect of surface scratches on the mechanical strength of solids, and some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion.
Abstract: In the course of an investigation of the effect of surface scratches on the mechanical strength of solids, some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion. The original object of the work, which was carried out at the Royal Aircraft Establishment, was the discovery of the effect of surface treatment—such as, for instance, filing, grinding or polishing—on the strength of metallic machine parts subjected to alternating or repeated loads. In the case of steel, and some other metals in common use, the results of fatigue tests indicated that the range of alternating stress which could be permanently sustained by the material was smaller than the range within which it was sensibly elastic, after being subjected to a great number of reversals. Hence it was inferred that the safe range of loading of a part, having a scratched or grooved surface of a given type, should be capable of estimation with the help of one of the two hypotheses of rupture commonly used for solids which are elastic to fracture. According to these hypotheses rupture may be expected if (a) the maximum tensile stress, ( b ) the maximum extension, exceeds a certain critical value. Moreover, as the behaviour of the materials under consideration, within the safe range of alternating stress, shows very little departure from Hooke’s law, it was thought that the necessary stress and strain calculations could be performed by means of the mathematical theory of elasticity.
10,162 citations
TL;DR: The mating of Brazilian and Guatemalan flies is, therefore, selective rather than random; however, the particular type of selectivity here observed does not constitute a barrier to gene exchange.
6,273 citations
TL;DR: Presentation d'une methode d'echantillonnage pour l'integration de la zone de Brillouin qui converge exponentiellement avec le nombre de points d’echant Dillonnage, sans perte de precision des techniques d'elargissement (broadening).
Abstract: We present a sampling method for Brillouin-zone integration in metals which converges exponentially with the number of sampling points, without the loss of precision of normal broadening techniques. The scheme is based on smooth approximants to the \ensuremath{\delta} and step functions which are constructed to give the exact result when integrating polynomials of a prescribed degree. In applications to the simple-cubic tight-binding band as well as to band structures of simple and transition metals, we demonstrate significant improvement over existing methods. The method promises general applicability in the fields of total-energy calculations and many-body physics.
5,862 citations