Example:Particle spacing from peak position

Consider the case of trying to measure the particle-particle spacing from the q-value of a particular peak. The interpretation of the q value of course depends upon the packing of the particles; i.e. the unit cell. Consider a cubic unit cell (SC, BCC, FCC). Note that in general:

${\begin{alignedat}{2}\left({\frac {1}{d_{hkl}}}\right)^{2}=\left({\frac {h}{a}}\right)^{2}+\left({\frac {k}{b}}\right)^{2}+\left({\frac {l}{c}}\right)^{2}\end{alignedat}}$

Since $q=2\pi /d$, and since $a=b=c$, the realspace spacing of planes is:

${\begin{alignedat}{2}d_{hkl}&={\frac {a}{\sqrt {h^{2}+k^{2}+l^{2}}}}\end{alignedat}}$

BCC 110

${\begin{alignedat}{2}d_{hkl}&={\frac {a}{\sqrt {1^{2}+1^{2}+0^{2}}}}\\&={\frac {a}{\sqrt {2}}}\end{alignedat}}$