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Journal ArticleDOI

Universal binding energy relation for cleaved and structurally relaxed surfaces.

05 Feb 2014-Journal of Physics: Condensed Matter (IOP Publishing)-Vol. 26, Iss: 5, pp 055006-055006

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.

AbstractThe 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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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.
Abstract: In this work we report the results of an ab initio study of the influence of hydrogen filled vacancies on the mechanical properties of zirconium. The modelling shows that hydrogen filled vacancies contribute to a lowering of the surface energy and an increase in the unstable stacking fault energy, which implies a reduction in ductility. The increase in unstable stacking fault energy suggests that the defects promote a change in the dislocation glide mechanism from prismatic to basal slip. To investigate the cleavage energetics, we model the decohesion process. For describing the interplanar interaction we adopt an extended version of Rose's universal binding energy relation, which is found to reproduce the behaviour accurately. 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.

22 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.
Abstract: In this work we have studied transgranular cleavage and the fracture toughness of titanium hydrides by means of quantum mechanical calculations based on density functional theory. The calculations ...

16 citations

Journal ArticleDOI
TL;DR: This work studies the adhesion and decohesion of Cu(1 0 0) surfaces using density functional theory (DFT) calculations and finds that the transition occurs via a localization of bond strain in the vicinity of the cleavage plane, which resembles the strain localization at the tip of a sharp crack that is predicted by linear elastic fracture mechanics.
Abstract: In this work, we study the adhesion and decohesion of Cu(1 0 0) surfaces using density functional theory (DFT) calculations. An upper stress to surface decohesion is obtained via the universal binding energy relation (UBER), but the model is limited to rigid separation of bulk-terminated surfaces. When structural relaxations are included, an unphysical size effect arises if decohesion is considered to occur as soon as the strain energy equals the energy of the newly formed surfaces. We employ the nudged elastic band (NEB) method to show that this size effect is opposed by a size-dependency of the energy barriers involved in the transition. Further, we find that the transition occurs via a localization of bond strain in the vicinity of the cleavage plane, which resembles the strain localization at the tip of a sharp crack that is predicted by linear elastic fracture mechanics.

10 citations

Journal ArticleDOI
TL;DR: Several theoretical and computational approaches that have been used to better understand the fracture of both single-crystal and polycrystalline diamond at the atomic level are discussed.
Abstract: Discussed in this paper are several theoretical and computational approaches that have been used to better understand the fracture of both single-crystal and polycrystalline diamond at the atomic level. The studies, which include first principles calculations, analytic models and molecular simulations, have been chosen to illustrate the different ways in which this problem has been approached, the conclusions and their reliability that have been reached by these methods, and how these theory and modelling methods can be effectively used together.

9 citations


Cites background from "Universal binding energy relation f..."

  • ...Additional scaling relations have been proposed that reportedly provide a better description of ideal cleavage, for example by accounting for relaxation during deformation [28,29]....

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References
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19,831 citations

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Abstract: A new approach to the construction of first-principles pseudopotentials is described. The method allows transferability to be improved systematically while holding the cutoff radius fixed, even for large cutoff radii. Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced. The potentials have a separable form well suited for plane-wave solid-state calculations, and show promise for application to first-row and transition-metal systems.

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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). The acronym 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 interoperable 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.

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Journal ArticleDOI
John P. Perdew1
TL;DR: Numerical results for atoms, positive ions, and surfaces are close to the exact correlation energies, with major improvements over the original LM approximation for the ions and surfaces.
Abstract: Langreth and Mehl (LM) and co-workers have developed a useful spin-density functional for the correlation energy of an electronic system. Here the LM functional is improved in two ways: (1) The natural separation between exchange and correlation is made, so that the density-gradient expansion of each is recovered in the slowly varying limit. (2) Uniform-gas and inhomogeneity effects beyond the randomphase approximation are built in. Numerical results for atoms, positive ions, and surfaces are close to the exact correlation energies, with major improvements over the original LM approximation for the ions and surfaces.

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