Question

The potential energy of an fcc latticw is described by expression
U(r)= -4€[(p०/r)^6-(p०/r)^12]
Where É=3.12×10-³ ev and p•= 2.82Å. Calculate the lattice parameter of the crystal lattice.

Answer 1

For the fcc structure, the lattice sums $A_{12}$ and $A_6$ are 12.132 and 14.454 respectively. Therefore, the lattice parameter of the crystal lattice can be found as

$$R_0=\bigg(\frac{A_{12}}{A_6}\bigg)^{1/6}p^\circ=0.971p^\circ,\\ R_0=0.971\cdot 2.82=2.74\text{ Å}.$$

Reference

Giuseppe Grosso, Giuseppe Pastori Parravicini (2013). Solid State Physics. Elsevier.