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

Equation 1 · Materials Science

Materials Discovery and Degradation in Practice: An Advanced Technical Guide

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Powder X-ray diffraction (XRD) is usually the first structural measurement run on a new crystalline material, because it is fast, non-destructive, and statistically representative — a powder sample presents billions of randomly oriented crystallites to the beam, and the resulting pattern of peak positions and intensities is a fingerprint of the unit cell and its symmetry. Peak positions locate the lattice through Bragg’s law, $n\lambda = 2d\sin\theta$. where $\lambda$ is the known X-ray wavelength, d is the spacing between a family of lattice planes, and $\theta$ is half the scattering angle at which a peak appears. Peak positions alone give the lattice parameters; peak intensities and shapes carry…

Meanings in this article

• $\lambda$: the known X-ray wavelength.
• $d$: the spacing between a family of lattice planes.
• $\theta$: half the scattering angle at which a peak appears.

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