Crystal Diffraction (Bragg's Law) Simulator

Crystal Structure

Lattice constant a 3.2 Å

X-ray wavelength λ 1.54 Å

Grazing angle θ 20°

d-spacing

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1st-order θ_B

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Diffracted intensity

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Bragg order n

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How it works

An X-ray beam grazes a stack of atomic planes spaced d apart at angle θ. Rays reflecting off successive planes travel slightly different path lengths — the extra distance is 2d·sinθ. When that extra distance equals a whole number of wavelengths, the reflected waves arrive in phase and add up constructively; at any other angle they cancel out. Sweep θ and watch the diffracted beam brighten only at the discrete Bragg angles predicted by the law below.

n·λ = 2d·sinθ  (Bragg's law)
θ_B = arcsin(n·λ / 2d)
d(SC)=a, d(BCC)=a/√2, d(FCC)=a/√3

Crystal structure — simple-cubic, body-centered-cubic or face-centered-cubic; denser packings diffract off more closely spaced allowed planes, shrinking d and shifting the Bragg angles.
Lattice constant a — the size of the repeating unit cell; a larger crystal spacing lowers the Bragg angle needed for constructive interference.
Wavelength λ — the X-ray wavelength; matching typical lab sources (Cu Kα ≈ 1.54 Å) to typical interplanar spacings is why X-rays, not visible light, reveal atomic structure.
Grazing angle θ — the incidence angle measured from the plane itself; drag it manually or hit Sweep to scan continuously and find every allowed reflection order n = 1, 2, 3…

Real-world relevance: this exact geometry is X-ray crystallography — the technique used to determine the atomic structure of everything from table salt to DNA and proteins.

Atoms Incident beam Diffracted beam

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