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Atomistic simulation of the structure and elastic properties of gold nanowires. (English) Zbl 1115.74303
Summary: We performed atomistic simulations to study the effect of free surfaces on the structure and elastic properties of gold nanowires aligned in the $$\langle 1 0 0 \rangle$$ and $$\langle 1 1 1 \rangle$$ crystallographic directions. Computationally, we formed a nanowire by assembling gold atoms into a long wire with free sides by putting them in their bulk fcc lattice positions. We then performed a static relaxation on the assemblage. The tensile surface stresses on the sides of the wire cause the wire to contract along the length with respect to the original fcc lattice, and we characterize this deformation in terms of an equilibrium strain versus the cross-sectional area. While the surface stress causes wires of both orientations and all sizes to increasingly contract with decreasing cross-sectional area, when the cross-sectional area of a $$\langle 1 0 0 \rangle$$ nanowire is less than 1.83 nm$$\times$$1.83 nm, the wire undergoes a phase transformation from fcc to bct, and the equilibrium strain increases by an order of magnitude. We then applied a uniform uniaxial strain incrementally to 1.2% to the relaxed nanowires in a molecular statics framework. From the simulation results we computed the effective axial Young’s modulus and Poisson’s ratios of the nanowire as a function of cross-sectional area. We used two approaches to compute the effective elastic moduli, one based on a definition in terms of the strain derivative of the total energy and another in terms of the virial stress often used in atomistic simulations. Both give quantitatively similar results, showing an increase in Young’s modulus with a decrease of cross-sectional area in the nanowires that do not undergo a phase transformation. Those that undergo a phase transformation experience an increase of about a factor of three of Young’s modulus. The Poisson’s ratio of the $$\langle 1 0 0 \rangle$$ wires that do not undergo a phase transformation show little change with the cross-sectional area. Those wires that undergo a phase transformation experience an increase of about 10% in Poisson’s ratio. The $$\langle 1 1 1 \rangle$$ wires show, with a decrease of cross-sectional area, an increase in one of Poisson’s ratios and small change in the other.

##### MSC:
 74A25 Molecular, statistical, and kinetic theories in solid mechanics 74A60 Micromechanical theories 74S30 Other numerical methods in solid mechanics (MSC2010) 82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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