   Chapter 12, Problem 29PS

Chapter
Section
Textbook Problem

A diamond unit cell is shown here. Unit cell of diamond (a) How many carbon atoms are in one unit cell? (b) The unit cell can be considered as a cubic unit cell of C atoms with other C atoms in holes in the lattice. What type of unit cell is this (pc, bcc, fcc)? In what holes are other C atoms located, octahedral or tetrahedral holes?

(a)

Interpretation Introduction

Interpretation:

Number of carbon atoms has to be identified.

Concept introduction:

The face-centered cubic system:

It has lattice points on the faces of the cube, that each gives exactly one half contributions, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell

Explanation

There are eight carbon atoms per unit cell. Because, Number of atoms per unit is given below,

It has 8 atoms in the corner, 6 atom in the face, 4 internal carbon atoms in the body.

Number of atoms per unit=(8corneratoms×1/8+6

(b)

Interpretation Introduction

Interpretation:

The type of the unit cell and arrangement of carbon atoms has to be identified.

Concept introduction:

The face-centered cubic system:

It has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell

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