\[d_{hkl}=\frac{a}{\sqrt{h^2+k^2+l^2}}\]
Variables
d[d_hkl]interplanar spacing (m)
acubic lattice constant (m)
hMiller index h
kMiller index k
lMiller index l
Description
What is this formula?
The cubic lattice plane spacing formula calculates the distance between adjacent crystallographic planes in a cubic crystal structure using Miller indices.
When to use it
This formula is used in crystallography, solid state physics, materials science, and X-ray diffraction analysis to determine atomic plane spacing in cubic crystals.
Example
A cubic crystal has:
a = 5.64×10^-10 m
(hkl) = (111)
Using:
d_hkl = a / √(h²+k²+l²)
Substitution:
d = (5.64×10^-10) / √(1²+1²+1²)
Result:
d ≈ 3.26×10^-10 m
Applications
- X-ray diffraction analysis
- Crystal structure characterization
- Materials science
- Semiconductor crystallography
- Solid state physics
- Bragg diffraction calculations