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17-05-2017 | Recent Advances on the Mechanics of Materials

Force constants of BN, SiC, AlN and GaN sheets through discrete homogenization

Authors: Alessandra Genoese, Andrea Genoese, Nicola Luigi Rizzi, Ginevra Salerno

Published in: Meccanica | Issue 3/2018

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Abstract

The force constants related to the bond stretching and angular variation of boron nitride, silicon carbide, aluminium nitride and gallium nitride nanosheets are directly evaluated from ab-initio reference solutions of the Young’s modulus and the Poisson’s ratio. To this end, the analytical expressions of the elastic constants of a generic monolayer hexagonal diatomic sheet are derived, starting from its sticks-and-springs molecular mechanics model, through proper tools of the homogenization of periodic discrete media. Numerical benchmark assessments are given.

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The effective charge of an atom is defined as the net positive nuclear charge acting on the valence electrons. Roughly speaking, the valence electrons are simultaneously attracted to the positive protons in the nucleus and repelled by the negatively charged inner-layer electrons. For this reason, the valence electrons do not feel the full positive charge of the nucleus.

Within the UFF model [80], the effective charges are used to account for the interactions between pairs of first and second nearest neighbouring atoms.

In what follows, when dealing with a rotational spring, index a identifies the spring, while indices 1 and 2 identify the elements of the pair of attached sticks (see Fig. 4b).

Equation (3c) provides a bond angle increase when \({\varvec{i}}_{2a}\cdot {\varvec{n}}_{1a}>0\) as in Fig. 4b.

It is hardly worth noting that the equilibrium equation against rotation of the stick 5 is a linear combination of the Eq. (12)

In the figures the balancing moments and not the equivalent moments to the external forces are reported.

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Title: Force constants of BN, SiC, AlN and GaN sheets through discrete homogenization
Authors: Alessandra Genoese
Andrea Genoese
Nicola Luigi Rizzi
Ginevra Salerno
Publication date: 17-05-2017
Publisher: Springer Netherlands
Published in: Meccanica / Issue 3/2018
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-017-0686-1

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