$18\mathrm{.}23$ The energy $($per unit volume$)$ required to magnetize a ferromagnetic material to saturation$(E_s)$is defined by the following equation:

$E_s={\displaystyle \underset{0}{\overset{M_s}{}}}{}_{0}HdM$

That is$,E_s$ is equal to the product of ${}_0$ and the area under an $M-$versus$-H$ curve, to the point of saturation referenced to the ordinate $($or $M)$ axis$-$for example, in Figure $18\mathrm{.}17,$ the area between the vertical axis and the magnetization curve to $M_s.$

Estimate $E_s$ values $($in $\frac{J}{m^3})$ for single$-$crystal iron in $[100],[110],$ and $[111]$ directions.