Chapter 3, Problem 3.31P

Interpretation Introduction

(a)

Interpretation:

The number of atoms of element A per unit cell is to be calculated.

Concept Introduction:

The most basic repeating structure of any solid is said to be the unit cell consuming least volume. The repeating pattern of unit cells results in a network said to be a lattice.

An atom's coordination number in a unit cell is equal to the number of atoms it touches in the cell.

Interpretation Introduction

(b)

Interpretation:

The number of atoms of element B per unit cell is to be calculated.

Concept Introduction:

Most basic repeating structure of any solid is said to be the unit cell consuming least volume. The repeating pattern of unit cells results in a network said to be a lattice.

An atom's coordination number in a unit cell is equal to the number of atoms it touches in the cell.

Interpretation Introduction

(c)

Interpretation:

Whether the answer in part (b) related with the stoichiometry of AB₂ compound or not should be determined.

Concept Introduction:

Rutile crystal structure is in the form of PQ₂. Q is an oxygen atom and P is a metal atom. Coordinates of Q are: $\left(1/4,\mathrm{¼},0\right),\left(3/4,3/4,0\right),\left(3/4,1/4,1/2\right),\left(1/4,3/4,1/2\right)$

Interpretation Introduction

(d)

Interpretation:

The unit cell for rutile should be drawn by using different symbol for every atom and a legend should be provided that shows which symbol denotes which type of atom.

Concept Introduction:

Parameters of unit cell:

  $\begin{array}{l}a=b\ne cand\hfill \\ a,b>c\hfill \\ a=b=\lambda ={90}^0\hfill \end{array}$

Interpretation Introduction

(e)

Interpretation:

The rutile strcuture should be described as a simple tetragonal lattice with basis.

Concept Introduction:

Parameters of unit cell:

  $\begin{array}{l}a=b\ne cand\hfill \\ a,b>c\hfill \\ a=b=\lambda ={90}^0\hfill \end{array}$