Section 1.3 states

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

Section 1.3 states, without showing the algebra, that adding a repulsion Ae−r/sAe^{-r/s} to the electrostatic energy −αMe2/(4πϵ0r)-\alpha_Me^2/(4\pi\epsilon_0r) and setting dE/dr=0\mathrm{d}E/\mathrm{d}r=0 at r=r0r=r_0 leaves E(r0)=−(αMe2/4πϵ0r0)(1−s/r0)E(r_0)=-(\alpha_Me^2/4\pi\epsilon_0r_0)(1-s/r_0). Derive this result, then apply it to potassium chloride, which has the rock salt structure with αM=1.7476\alpha_M=1.7476, nearest-neighbour separation r0=3.15 A˚r_0=3.15\,\mathrm{\mathring{A}}, and repulsion range s=0.33 A˚s=0.33\,\mathrm{\mathring{A}}.

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