Simulation · Condensed Matter Physics

Bragg's Law Diffraction Simulation

Reading time: 6 minConfidence: HighLast verified: August 2026

This simulation lets you adjust the X-ray wavelength, the incidence angle, and the crystal lattice plane spacing to see, visually, when the path-length difference between X-rays reflecting off successive atomic planes satisfies Bragg's Law and produces constructive interference.

Interactive simulation

Wavelength λ (Å)1.50 Plane spacing d (Å)2.50 Angle θ (degrees)30.0

Path difference: — Å

nλ (nearest order): — Å

Interference: —

The physics behind this simulation

Bragg's Law states that constructive interference occurs when the extra path length travelled by X-rays reflecting off a deeper atomic plane, compared to the plane above it, equals a whole number of wavelengths:

nλ = 2d sinθ

The extra path length is exactly 2d sinθ — twice the plane spacing times the sine of the incidence angle. Whenever this quantity matches a whole-number multiple of the wavelength, the reflected waves from successive planes arrive in phase and reinforce each other, producing a strong diffracted beam; at all other angles, the waves fall out of phase and largely cancel.

Common mistakeBragg's Law gives the angles at which constructive interference is possible, but real diffraction intensity also depends on the crystal's specific atomic arrangement (via the "structure factor") — some Bragg angles that satisfy the basic geometric condition can still show weak or zero intensity for certain crystal structures, due to additional destructive interference between atoms within the unit cell itself. This simulation illustrates the basic geometric condition only, not the full structure-factor calculation.

Sources

Bragg, W.H., Bragg, W.L. (1913). Proceedings of the Royal Society A, 88(605), 428–438.

Last verified: August 2026 · Source: Bragg & Bragg (1913) · Confidence: high

Interactive simulation

The physics behind this simulation

Sources

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