\[|G|=\frac{2\pi}{a}\sqrt{h^2+k^2+l^2}\]
Variables
Gmagnitude of reciprocal lattice vector (1/m)
alattice parameter (m)
hMiller index h
kMiller index k
lMiller index l
Description
What is this formula?
This formula calculates the magnitude of the reciprocal lattice vector for cubic crystal systems using the lattice parameter and Miller indices.
When to use it
Use it in crystallography and solid-state physics when analyzing diffraction conditions, reciprocal space, and crystal momentum relationships.
Example
Data:
a = 4.00e-10 m
h = 1
k = 1
l = 0
Formula:
G = (2*pi*sqrt(h^2+k^2+l^2))/a
Substitution:
G = (2*pi*sqrt(1^2+1^2+0^2))/(4.00e-10)
Result:
G = 2.22e10 1/m
Applications
X-ray diffraction, reciprocal lattice analysis, semiconductor physics, Brillouin zone calculations, neutron diffraction, and solid-state physics.