Bragg's Law Calculator

Bragg's law explains how X-rays reflect from the regularly spaced planes of atoms in a crystal, which is the basis of X-ray crystallography.

The Bragg angle is measured between the beam and the crystal plane. Two-theta is the total deflection of the beam and equals twice the Bragg angle.

Because sinθ = nλ ÷ (2d) cannot exceed 1, the smallest possible spacing that can diffract a given wavelength is d = nλ ÷ 2. If the wavelength is larger than twice the d-spacing, no diffraction peak of that order can form. This is why X-rays, with wavelengths near 0.1 nm comparable to atomic spacings, are used rather than visible light.

Lab diffractometers use characteristic X-rays from a metal target. Copper K-alpha (Cu Kα) at about 0.154 nm (1.54 Å) is by far the most common; molybdenum K-alpha (Mo Kα) at about 0.071 nm (0.71 Å) is used for smaller unit cells and single-crystal work. Both wavelengths are comparable to atomic spacings, which is exactly what Bragg's law needs for diffraction to occur.