\[d=\frac{a}{\sqrt{h^2+k^2+l^2}}\]
Variables
dinterplanar spacing (m)
acubic lattice parameter (m)
hMiller index h
kMiller index k
lMiller index l
Description
What is this formula?
This formula calculates the distance between parallel crystal planes in a cubic crystal lattice using the lattice parameter and Miller indices.
When to use it
Use it for cubic crystal systems when the lattice parameter and Miller indices of the plane are known.
Example
Data:
a = 4.05e-10 m
h = 1
k = 1
l = 1
Formula:
d = a/sqrt(h^2+k^2+l^2)
Substitution:
d = 4.05e-10/sqrt(1^2+1^2+1^2)
Result:
d = 2.34e-10 m
Applications
Crystallography, X-ray diffraction, materials science, semiconductor analysis, lattice structure calculations, and solid-state physics.