Materials Science and Engineering: An Introduction

Published by Wiley
ISBN 10: 1118324579
ISBN 13: 978-1-11832-457-8

Chapter 3 - The Structure of Crystalline Solids - Questions and Problems - Page 98: 3.22


The percentage change in the unit cell is 97.6%.

Work Step by Step

Given $R_{bcc}=0.12584 nm$ and $R_{fcc}=0.12894 nm$ unit cell length: $a_{bcc}=\frac{4}{\sqrt{3}}R_{bcc}$ $a_{bcc}=\frac{4}{\sqrt{3}}\times 0.12584 $ unit cell length: $a_{fcc}=\frac{4}{\sqrt{2}}R_{bcc}$ $a_{fcc}={2\sqrt{2}}\times 0.12894 $ volume of bcc unit cell $(a_{bcc})^3=(\frac{4}{\sqrt{3}}\times 0.12584)^3 nm^3$ $(a_{bcc})^3=0.024545 nm^3$ volume of fcc unit cell $(a_{fcc})^3=(\frac{4}{\sqrt{3}}\times 0.12894)^3 nm^3$ $(a_{bcc})^3=0.048506 nm^3$ percentage change=$\frac{(a_{fcc})^3-(a_{bcc})^3}{(a_{bcc})^3}\times 100$ percentage change=$\frac{0.048506-0.024545}{0.024545}\times 100=97.6$ The percentage change in the unit cell is 97.6%.
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