Chapter 15, Problem 15.40P

Interpretation Introduction

Interpretation:

The Avogadro number for the chromium in bcc lattice has to be determined.

Concept Introduction:

A unit cell is smallest repeating unit of a crystal lattice. Unit cells are classified as primitive and non-primitive. Unit cells that have atoms at only corners are primitive and unit cells that have atoms at positions other than corners are non-primitive.

Unit cells that are non- primitive are of various types:

Face centered unit cell (fcc), body-centered unit cell (bcc), edge centered unit cell, end centered unit cell.

Contribution of an atom at a position is as follows:

  $\begin{array}{cc}\text{position in unit}\text{cell}& \text{contributions}\\ \text{center of body}& \text{1}\\ \text{center of face}& \text{1/2}\\ \text{center of edge}& \text{1/4}\\ \text{corners}& \text{1/8}\end{array}$

The number of particles per unit cell, also denoted by Z is as follows:

$\begin{array}{cc}\text{Unit}\text{cell}& Z\\ \text{scc}& \text{1}\\ \text{fcc}& \text{4}\\ \text{bcc}& \text{2}\\ \text{edge-centered}\text{cubic}& \text{4}\\ \text{end-centered}\text{cubic}& \text{2}\end{array}$