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Journal ArticleDOI

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.
Citations
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Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

References
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Journal ArticleDOI
TL;DR: In this article, the elastic constants of nickel have been determined by the pulsed ultrasonic method by combining wave velocity measurements on four nickel single crystals of general orientation which were magnetically saturated with the approximation method leading to values of C11=2.53, C12=1.52, C44= 1.24, all in units of 1012 dyne cm−2.
Abstract: The elastic constants of nickel have been determined by the pulsed ultrasonic method. Wave velocity measurements on four nickel single crystals of general orientation which were magnetically saturated were combined by the approximation method leading to values of the elastic constants C11=2.53, C12=1.52, C44=1.24, all in units of 1012 dyne cm−2.

86 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extend the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the CE to the CE and show that the correlation functions can be stripped of their asymptotic behaviour.
Abstract: Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble. 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 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 new hierarchies of N-modified distribution and correlation functions with 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, completing in this way the extension of the HKSM theorem to the CE.

82 citations

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this article, the authors used a modified pseudo-Voigt function with the average particle size as one of its fitting parameters to follow the evolution of particle size with temperature for the different hydrolysis catalysts.

68 citations

Journal ArticleDOI
TL;DR: In this article, a universal relation for crack surface cohesion including surface relaxation is presented, where the energy and opening displacement are scaled appropriately with respect to N, the uniaxial elastic constant, the relaxed surface energy, and the equilibrium interlayer spacing, all energydisplacement curves collapse onto a single universal curve.
Abstract: We present a universal relation for crack surface cohesion including surface relaxation. Specifically, we analyze how N atomic planes respond to an opening displacement at its boundary, producing structurally relaxed surfaces. Via density-functional theory, we verify universality for metals ~Al!, ceramics (a-Al2O3), and semiconductors ~Si!. When the energy and opening displacement are scaled appropriately with respect to N, the uniaxial elastic constant, the relaxed surface energy, and the equilibrium interlayer spacing, all energydisplacement curves collapse onto a single universal curve.

66 citations