# 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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### 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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^{1}, National Research Council

^{2}, International School for Advanced Studies

^{3}, Massachusetts Institute of Technology

^{4}, University of Paris

^{5}, Princeton University

^{6}, University of Minnesota

^{7}, ParisTech

^{8}, University of Milan

^{9}, International Centre for Theoretical Physics

^{10}, University of Paderborn

^{11}, ETH Zurich

^{12}, École Polytechnique Fédérale de Lausanne

^{13}

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