The diagram below shows a plan view of a structure of cubic

The diagram below shows a plan view of a structure of cubic ZnS (zincblende) looking down the 2 axis. The numbers attached to some atoms represent the heights of the atoms above the 2 = 0 plane expressed as a fractional of the cube edge length a. Unlabeled atoms are at 2 = 0 and 2 = a. What is the Bravais lattice type? Describe the basis. Given that a = 0.541 mu. calculate the nearest-neighbor Zn-Zn, Zn-S and S-S| distances.

Solution

a) this is a cubic Zinc Blend lattice,FCC Bravais lattice with each lattice point associated with two atoms. Zincblende is best thought of as a face-centered cubic array of anions cations occupying one half of the tetrahedral holes. Each ion is 4-coordinate and has local tetrahedral geometry.

1/2 of the tetrahedral sites (i.e. four of the eight octants of the cube) are occupied by Zn²⁺

c) Zn-Zn = 1a/1.414 =.382 nm

Zn-S = 1.732a/4 = .2342nm

S-S = a = .541nm