Bragg's Law Calculator

Bragg's law explains how crystals diffract X-rays, the basis of crystallography.

How the Math Works

Bragg's Law describes the condition for constructive interference of X-rays scattered by planes in a crystal. The formula n·λ = 2d·sinθ relates the wavelength of incident X-rays (λ), the spacing between crystal planes (d), the diffraction angle (θ), and the order of reflection (n). To find the angle, you rearrange the equation to solve for θ: θ = arcsin(n·λ / 2d). This trigonometric relationship reveals that only specific angles produce strong diffraction peaks, forming the foundation of X-ray crystallography analysis.

Practical Applications

To use this calculator, input the X-ray wavelength, crystal plane spacing, and desired reflection order. For example, when analyzing a crystal with 0.154 nm X-rays and (111) planes spaced 0.284 nm apart in the first order (n=1), the calculator determines the diffraction angle is approximately 15.5 degrees. Scientists use these angles to index diffraction patterns and determine crystal structures in materials science, chemistry, and biology research.

Day-to-Day Use

This calculation enables the development of life-saving medications by helping determine protein structures, as seen in COVID-19 vaccine development. It's essential for creating stronger aerospace alloys, more efficient solar panels, and computer chips. The technology also improves forensic analysis of materials and aids in quality control for manufacturing, ultimately contributing to safer, more efficient products in everyday items from smartphones to medical devices.

Worked example

λ = 0.154 nm, d = 0.282 nm, n = 1 → θ ≈ 15.86°.

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