Relative magnetization and a Face Centered Cubic lattice

[LagrangeEuler]

In case of simple cubic lattice relative magnetization is given by

$$\sigma=1-\frac{1}{S}\frac{v}{(2\pi)^3}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\mbox{d} k_x\mbox{d} k_y\mbox{d}k_z(\mbox{e}^{\frac{E(\vec{k})}{kT}}-1)^{-1}$$
where $v$ is volume of elementary cell, $a$ is parameter of elementary cell, and integration from $-\frac{\pi}{a}$ to $\frac{\pi}{a}$ is integration over first Brillouin zone.

How relation for relative magnetization looks in case of face cubic centered lattice. What is $v$ and what are integral boundaries in that case? Thanks a lot for the answer.

 

[Chandra Prayaga]

In case of simple cubic lattice relative magnetization is given by

$$\sigma=1-\frac{1}{S}\frac{v}{(2\pi)^3}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\mbox{d} k_x\mbox{d} k_y\mbox{d}k_z(\mbox{e}^{\frac{E(\vec{k})}{kT}}-1)^{-1}$$
where $v$ is volume of elementary cell, $a$ is parameter of elementary cell, and integration from $-\frac{\pi}{a}$ to $\frac{\pi}{a}$ is integration over first Brillouin zone.

How relation for relative magnetization looks in case of face cubic centered lattice. What is $v$ and what are integral boundaries in that case? Thanks a lot for the answer.

Could you give us a reference for this equation?