Chapter 12, Problem 12.42QP

(a)

Interpretation Introduction

Interpretation: The minimum radius for the host metal for a $\text{B}$ atom to fit in a octahedral hole of an fcc unit cell and the value of $x$ if an average of one octahedral hole is occupied per unit cell is to be calculated.

Concept introduction: The atomic radius ratio range for octahedral holes is $0.41-0.73$. Metal borides ( ${\text{MB}}_x$) exists for many transition metals.

To determine: The minimum radius for the host metal for a $\text{B}$ atom to fit in a octahedral hole of an fcc unit cell.

(b)

Interpretation Introduction

To determine: The value of $x$ if an average of one octahedral hole is occupied per unit cell.