Chapter 3, Problem 3.32P

Interpretation Introduction

(a)

Interpretation:

The number of atoms of each type in the $\mathrm{CuAu}$ Unit cell is to be determined.

Concept Introduction:

$\mathrm{CuAu}$ crystal structure is a simple cubic lattice with coordinates of

  $\begin{array}{l}\text{Cu }–\left(0,0,0\right)\text{ and }\left(\mathrm{½},\mathrm{½},0\right)\text{ and,}\hfill \\ \text{Au }–\left(\mathrm{½},0,\mathrm{½}\right)\text{ and }\left(0,\mathrm{½},\mathrm{½}\right)\hfill \end{array}$

Interpretation Introduction

(b)

Interpretation:

A symbolic representation of the $\text{CuAu}$ Unit cell needs to be drawn with proper indication.

Concept Introduction:

$\text{CuAu}$ crystal structure is a simple cubic lattice with coordinates of

  $\begin{array}{l}\text{Cu }–\left(0,0,0\right)\text{ and }\left(\mathrm{½},\mathrm{½},0\right)\text{ and,}\hfill \\ \text{Au }–\left(\mathrm{½},0,\mathrm{½}\right)\text{ and }\left(0,\mathrm{½},\mathrm{½}\right)\hfill \end{array}$

Here, 0 represents origin.

Interpretation Introduction

(c)

Interpretation:

An alternative lattice representation of $\text{CuAu}$ needs to be determined, if one atom is Au(0,0,0).

Concept Introduction:

$\mathrm{CuAu}$ crystal structure is a simple cubic lattice with coordinates of

  $\begin{array}{l}\text{Cu }–\left(0,0,0\right)\text{ and }\left(\mathrm{½},\mathrm{½},0\right)\text{ and,}\hfill \\ \text{Au }–\left(\mathrm{½},0,\mathrm{½}\right)\text{ and }\left(0,\mathrm{½},\mathrm{½}\right)\hfill \end{array}$

If coordinates of atoms changes, the position of atoms in the unit cells changes.

Interpretation Introduction

(d)

Interpretation:

The crystal structure of ${\text{Cu}}_{\text{3}}\text{Au}$ is to be explained.

Concept Introduction:

${\text{Cu}}_{\text{3}}\text{Au}$ is similar to FCC Unit cell. A Gold element is at corner and the copper element is at face centered. $\mathrm{CuAu}$ has cubic structure with coordinates of Cu and Au as follows:

  $\begin{array}{l}\text{Cu }–\left(0,0,0\right)\text{ and }\left(\mathrm{½},\mathrm{½},0\right)\text{ and,}\hfill \\ \text{Au }–\left(\mathrm{½},0,\mathrm{½}\right)\text{ and }\left(0,\mathrm{½},\mathrm{½}\right)\hfill \end{array}$

Interpretation Introduction

(e)

Interpretation:

The reason for FCC structure of ${\text{Cu}}_{\text{3}}\text{Au}$ not having FCC lattice is to be explained.

Concept Introduction:

${\text{Cu}}_{\text{3}}\text{Au}$ is similar to FCC Unit cell. A Gold element is at corner and the copper element is at face centered. $\mathrm{CuAu}$ has cubic structure with coordinates of Cu and Au as follows:

  $\begin{array}{l}\text{Cu }–\left(0,0,0\right)\text{ and }\left(\mathrm{½},\mathrm{½},0\right)\text{ and,}\hfill \\ \text{Au }–\left(\mathrm{½},0,\mathrm{½}\right)\text{ and }\left(0,\mathrm{½},\mathrm{½}\right)\hfill \end{array}$