Chapter 12, Problem 12.136MP

Interpretation Introduction

(a)

Interpretation:

The name of 3A metal should be identified.

Concept introduction:

A unit cell is the 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:

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

The elements or substances exist more in solid than liquid and gases. These solids can be of two types amorphous and crystalline. The crystalline solids are solids that contain their constituent particle in an arranged manner. While amorphous solids are solid in which constituent particles get arranged randomly such as rubber.

Interpretation Introduction

(b)

Interpretation:

The name of unit cell of 3A metal should be determined.

Concept introduction:

A unit cell is the 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:

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

The elements or substances exist more in solid than liquid and gases. These solids can be of two types amorphous and crystalline. The crystalline solids are solids that contain their constituent particle in an arranged manner. While amorphous solids are solid in which constituent particles get arranged randomly such as rubber.

Interpretation Introduction

(c)

Interpretation:

The radius of metal is to be calculated.

Concept introduction:

A unit cell is the 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:

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

The elements or substances exist more in solid than liquid and gases. These solids can be two types amorphous and crystalline. The crystalline solids are solids that contain their constituent particle in an arranged manner. While amorphous solids are solid in which constituent particles get arranged randomly such as rubber.

The relationship between the edge length ( a ) and a radius of cubic closest-packing or FCC unit cell is as follows:

$2a^2={\left(4r\right)}^2$

Where

• $a$ is the edge length of the unit cell.
• $r$ is the radius of the atom.

Rearrange above equation to calculate the radius of the atom as follows:

$r=\sqrt{\frac{{\left(a\right)}^2}{8}}$