Answer to Question #109829 in Atomic and Nuclear Physics for Hiteshwar

Question #109829
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.
1
Expert's answer
2020-04-21T19:11:14-0400

For the fcc structure, the lattice sums A12A_{12} and A6A_6 are 12.132 and 14.454 respectively. Therefore, the lattice parameter of the crystal lattice can be found as


R0=(A12A6)1/6p=0.971p,R0=0.9712.82=2.74 A˚.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.


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