The worked example on solid argon's bond kept only each atom's twelve nearest…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch What holds a solid together, and where its atoms sit

Problem

The worked example on solid argon's bond kept only each atom's twelve nearest neighbours and found

6\epsilon_{\rm LJ}=0.0624\,\mathrm{eV}

per atom, against a measured cohesive energy of

0.080\,\mathrm{eV}

. Solid argon is face-centred cubic, so each atom also has six second neighbours, one cube edge away. Keep the nearest-neighbour separation at

r_0=2^{1/6}\sigma_{\rm LJ}

and use the same Lennard-Jones potential, with

\epsilon_{\rm LJ}=0.0104\,\mathrm{eV}

. Find the energy of one second-neighbour pair as a multiple of

\epsilon_{\rm LJ}

, the second neighbours' contribution to the cohesive energy per atom, and the fraction of the gap between

0.0624

and

0.080\,\mathrm{eV}

that they close.

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