How this calculator works
Rays reflected by neighbouring crystal planes travel different distances. Constructive interference occurs when this path difference equals a whole number of wavelengths. The angle in Bragg law is measured from the planes; a diffractometer often reports twice that angle. A permitted geometric angle does not guarantee a visible reflection because the crystal structure factor can suppress it.
Formula
nλ = 2d sinθ; scattering angle = 2θ. n is a positive integer.
Worked example
For λ = 0.1 nm, d = 0.1 nm and first order, sinθ = 0.5. The glancing angle is 30 degrees and the scattering angle is 60 degrees.
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Frequently asked questions
Is θ measured from the normal?
No. Bragg θ is the glancing angle from the crystal plane.
Why can an order be impossible?
If nλ exceeds 2d, the required sine exceeds one.
Why does an expected peak disappear?
Atomic arrangement, absorption and experimental geometry affect intensity even when the path condition is satisfied.