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 article, a series of ab initio calculations were performed to determine the atomic structure, ideal work of adhesion, and bonding character of the Al and O terminations of the oxide.
Abstract: We have performed a series of ab initio calculations to determine the atomic structure, ideal work of adhesion $({\mathcal{W}}_{\mathrm{ad}\mathrm{}}),$ and bonding character of the $\mathrm{Al}(111)/\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}(0001)$ interface. Six candidate interface geometries were considered, including Al and O terminations of the oxide. Minimization of the Hellman-Feynman forces resulted in substantial changes to the atomic structure of the metal near the interface, wherein some atoms adopted positions consistent with a continuation of the oxide's Al-sublattice crystal structure across the interface. Consequently, the lowest-energy structures (i.e., having the largest ${\mathcal{W}}_{\mathrm{ad}\mathrm{}})$ are those that facilitate this ``oxide extension'' mechanism. By applying several methods of analysis we have thoroughly characterized the electronic structure and have determined that Al-O bonds constitute the primary interfacial bonding interaction. These bonds are very similar to the cation-anion bonds found in the oxide bulk and are mainly ionic, yet maintain a small amount of covalent character. In addition, there is evidence of metal-cation bonding at the optimal Al-terminated interface. Taking into account recent theoretical and experimental evidence suggesting an Al termination of the clean oxide surface, our calculations predict ${\mathcal{W}}_{\mathrm{ad}\mathrm{}}=1.36{\mathrm{J}/\mathrm{m}}^{2}$ [local density approximation (LDA)] and 1.06 ${\mathrm{J}/\mathrm{m}}^{2}$ [generalized gradient approximation (GGA)] for the optimal Al-terminated structure, which are in good agreement with the experimental value of 1.13 ${\mathrm{J}/\mathrm{m}}^{2}$ as scaled to 0 K. These values are approximately an order of magnitude smaller than what is found for the optimal O-terminated interface: 10.70 ${\mathrm{J}/\mathrm{m}}^{2}$ (LDA) and 9.73 ${\mathrm{J}/\mathrm{m}}^{2}$ (GGA). Although cleavage preferentially occurs at the interface for the Al termination, strong bonding at the O-terminated interface favors cleavage within the metal.
219 citations
TL;DR: The lattice constants of germanium, aluminum gallium arsenide, alpha - uranium, orthorhomhic sulfur, natural quartz, and synthetic sapphire were determined to six significant figures by a precision single crystal x-ray method as mentioned in this paper.
Abstract: The lattice constants of germanium, aluminum gallium arsenide, alpha - uranium, orthorhomhic sulfur, natural quartz, and synthetic sapphire were determined to six significant figures by a precision single crystal x-ray method. A comparison is made with previously determined values for these materials. (auth)
212 citations
IBM1
TL;DR: It is shown that the electronic wavefunction does not need to be fully optimized in the earlier stages of geometry optimization when using the partitioned rational function optimizer (P-RFO and L-BFGS).
168 citations
TL;DR: In this paper, it is shown that the density functional theory is suitable, in principle, for the analysis of complex atomic systems, but this method, being based on contemporary computer codes, is not suitable even for simple atomic systems such as heavy atoms or metal clusters.
Abstract: Configurational transitions in atomic systems, i.e., transitions that change the system's geometric structure, include chemical reactions in gases, transitions between aggregate states of a polyatomic system, i.e., the phase transitions, and nanocatalytic processes. These transitions are analyzed from the standpoint of the behavior of the system on its effective potential energy surface (PES), so that the transition results from passage between different local minima of the PES. It is shown that the density functional theory (DFT) is suitable, in principle, for the analysis of complex atomic systems, but this method, being based on contemporary computer codes, is not suitable even for simple atomic systems, such as heavy atoms or metal clusters. Next, a statical determination of the energetic parameters of atomic systems does not allow analyzing the dynamics of configurational transitions; in particular, the activation energy of a chemical process differs significantly from the height of a potential barrier which separates the atomic configurations of the initial and final states of the transition. Notably, the static models, including DFT, give a melting point for clusters with a pairwise atomic interaction that is twice that from dynamic models which account for the thermal motion of atoms. Hence, the optimal description of configurational transitions for complex atomic systems may be based on joining the DFT methods for determining the PES of this system with molecular dynamics to account for the thermal motion of atoms.
156 citations
01 Jan 1999
TL;DR: In this article, the structure, chemical bond, and structure of II-VI compounds are described.From the contents: II-V compounds. I-VI compound structures, chemical bonds, and structures.
Abstract: From the contents: II-VI compounds.- Structure. Beryllium compounds. Beryllium oxide (BeO). Beryllium sulfide (BeS). Beryllium selenide (BeSe). Beryllium telluride (BeTe). Magnesium oxide (MgO). Magnesium sulfide (MgS). Magnesium selenide (MgSe). Magnesium telluride (MgTe). Calcium oxide (CaO). Strontium oxide (SrO). Barium oxide (BaO). Zinc oxide (ZnO). Zinc sulfide (ZnS). Zinc selenide (ZnSe). Zinc telluride (ZnTe). Cadmium oxide (CdO). Cadmium sulfide (CdS). Cadmium selenide (CdSe). Cadmium telluride (CdTe). Mercury oxide (HgO). Mercury sulfide (HgS). Mercury selenide (HgSe). Mercury telluride (HgTe). Solid solutions. I-VII compounds.- Structure, chemical bond. Cuprous flouride (CuF). Cuprous chloride (y-CuCl). Cuprous bromide (y-CuBr). Cuprous iodide (y-CuI). Silver monofluoride (AgF). Silver chloride (AgCl). Silver bromide (AgBr). Silver iodide (AgI). Semimagnetic semiconductors.-
123 citations