With the reference to the figure below, electron microscopy indicates that the grain size of the milled powder $($a$)$ is in the range of $10-50nm$ and that of the consolidated powder $($b$)$ is $5m$ and above. On the basis that the increased broadening in $($a$)$ arises solely as a result of the fine crystallite size, show that the X$-$ray data is consistent with the microscopical data.

Fig. $10\mathrm{.}19.$ Diffractometer charts radiation, $\{$:$=1\mathrm{.}541)$ showing the first three reflections for a steel specimen $(-$Fe$,$ bcc$)$ in $($a$)$ the annealed condition and $($b$)$ after heavy surface abrasion giving broadened and shifted X$-$ray diffraction peaks which arise from residual stresses on the microand macroscale and a reduction in crystallite size. $($Data by courtesy of Mr D$.$ G$.$ Wright.$)$