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Asked Mar 20, 2020
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For a side centered cubic unit cell, determine coordination number (CN), number of atoms and atomic packing factor (APF).

3. For a side centered cubic unit cell, determine coordination number (CN), number
of atoms and atomic packing factor (APF).
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3. For a side centered cubic unit cell, determine coordination number (CN), number of atoms and atomic packing factor (APF).

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Expert Answer

Introduction

Side centered cubic (SCC) is the crystal structure which possesses eight atoms on the eight corners and one atom exists on two parallel opposite faces. In SCC unit cell, the "number of atoms" (Z) is 2. SCC unit cell also termed as "end-centered cubic cell"

Calculation

The given side centered cubic unit cell is shown below. 

Chemistry homework question answer, step 2, image 1

In the given centered cubic, 1 atom is surrounded by 6 adjacent atoms. For example, one corner atom is surrounded by  6 adjacent corner atoms.

Hence the coordination number of side centered cubic unit cell (SCC) is 6.

Calculation

The number of atoms (Z) present in the side centered cubic unit cell can be calculated as shown below.

Chemistry homework question answer, step 3, image 1

The contribution of corners in a unit cell is 1/8.

The contribution of ends (faces) in a unit cell is 1/2.

The total number of atoms in corners is 8 and the total number of atoms in two sides is 2.

 

Substitute the values in the above formula.

Chemistry homework question answer, step 3, image 2

Hence the number of atoms (Z) in the side centered cubic unit cell is 2.

 

 

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