Bragg's Law Calculator
X-ray diffraction (XRD) follows nλ = 2d·sinθ: λ is the wavelength, d the interplanar crystal spacing (d-spacing), θ the Bragg angle between the beam and the crystal planes, n the diffraction order (integer ≥ 1). Diffractometers measure 2θ — the angle between the incident and diffracted beams.
Frequently asked questions
What is Bragg's law?
Bragg's law, nλ = 2d·sinθ, is the condition for constructive interference of X-rays scattered by parallel crystal planes. Diffraction occurs only at specific angles where the path difference between planes is exactly an integer multiple of the wavelength.
Why do diffractometers measure 2θ instead of θ?
θ is the angle between the incident X-ray beam and the crystal planes (the Bragg angle). The θ–2θ diffractometer geometry moves the detector at twice the sample angle, so the angle read between the incident and diffracted beams is 2θ.
When does no diffraction occur?
When nλ / (2d) > 1, no angle θ satisfies the equation — sin θ cannot exceed 1. That means the wavelength is too long for that interplanar spacing at that order; lower n or use a shorter λ.
Why is order n > 1 rarely used?
Higher-order diffraction (n = 2, 3, …) is generally far weaker in intensity than first order, so practical XRD analysis almost always uses n = 1.
What are common XRD anode wavelengths?
Cu Kα = 1.5406 Å (most common for powder diffraction), Mo Kα = 0.7107 Å (small-molecule crystallography), Co Kα = 1.7902 Å (iron-containing samples, avoids fluorescence).
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