Bragg's Law Calculator

What Is Bragg's Law?

Bragg's law relates X-ray wavelength, crystal plane spacing, and diffraction angle. It is the foundation of X-ray diffraction (XRD) used to determine crystal structures and lattice parameters.

Bragg's Law Formula

$$n\lambda = 2d\sin\theta$$

$n$ is the diffraction order (integer), $\lambda$ is wavelength, $d$ is interplanar spacing, and $\theta$ is the angle between the incident beam and the crystal plane (Bragg angle).

Example: Cu Kα radiation ($\lambda = 1.54$ Å) on planes with $d = 2.5$ Å at first order ($n = 1$) diffracts at $\theta = \arcsin(1.54 / 5) \approx 17.95°$.

Using Bragg's Law in XRD

Measuring diffraction peaks at known wavelength lets you calculate $d$-spacings. Conversely, knowing crystal structure predicts where peaks appear. Higher orders ($n = 2, 3, \ldots$) appear at larger angles.

Frequently Asked Questions

What does diffraction order n mean?

n is a positive integer representing which harmonic reflection is observed. First-order peaks use n = 1; second-order peaks use n = 2 at a larger angle.

What units are used for wavelength and d-spacing?

X-ray crystallography commonly uses angstroms (Å). This calculator accepts wavelength in nanometers and d-spacing in angstroms.

Why does arcsin fail for some inputs?

Bragg's law requires $|n\lambda / 2d| \leq 1$. If the ratio exceeds 1, no real diffraction angle exists for those values.

Is θ the same as the detector angle 2θ?

Bragg's law uses θ (half the total scattering angle). Many diffractometers report 2θ; divide by 2 to get θ for this formula.

What is a typical X-ray source?

Copper Kα ($\lambda \approx 1.54$ Å or 0.154 nm) is the most common laboratory X-ray source for powder and single-crystal diffraction.

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What Is Bragg's Law?

Bragg's Law Formula

Using Bragg's Law in XRD

Frequently Asked Questions

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