Chapter 21, Problem 130SCQ

Interpretation Introduction

Interpretation:

To determine the $\text{B}-\text{N}$ bond length in the given cubic lattice.

Concept introduction:

There are two types of the cubic lattice of $\text{ZnS}$, zinc-blende and wurtzite. Zinc blende is based on a face-centred cubic lattice of anions and cations occupying one-half of the tetrahedral holes. Each ion is four coordinate and has local tetrahedral geometry.

If one constituent particles lie at the centre of each face and the particles lying at the centre is known as a face-centred cubic lattice.

The density of unit-cell is expressed as,

$\text{D}=\frac{\text{n}\times \text{M}}{{\text{N}}_{\text{A}}\times {\text{a}}^{\text{3}}}\text{g}\cdot {\text{cm}}^{-3}$ (1)

Here,

The density of unit cell is denoted by $\text{D}$

The number of atoms is denoted by $\text{n}$

The molar mass of each atom in the unit-cell is denoted by $\text{M}$

The Avogadro number is denoted by ${\text{N}}_{\text{A}}$

The bond-length is denoted by $\text{a}$

Bond length is the distance between the nuclei in a bond and it is related to the sum of the covalent radii at the bonded atoms.