The Ewald sphere is the geometric construction that turns Bragg's law into a simple "does a point touch a sphere?" test. Every possible reflection off a crystal lattice corresponds to a point G = ha* + kb* + lc* in reciprocal space, where a*, b*, c* are the reciprocal lattice vectors (for a cubic real-space lattice of spacing a, |a*| = 2π/a).
Diffraction condition (Laue form):
k_out − k_in = G, |k_out| = |k_in| = 2π/λ
Equivalent (Bragg form):
2 d_hkl sin θ = nλ
Draw a sphere of radius 2π/λ (the Ewald sphere) centered so that the incident wavevector k_in ends exactly at the origin of reciprocal space, at the sphere's surface. A reflection fires — a real diffracted beam k_out leaves the crystal — precisely when a reciprocal lattice point also lies on that same sphere's surface. Rotating the crystal (the ω slider, or Auto-Rotate) spins the reciprocal lattice rigidly through the fixed sphere; lattice points sweep in and out of contact one by one, exactly as they do in a real rotating-crystal X-ray experiment.
- λ slider — shorter wavelength → larger sphere radius (2π/λ) → more reciprocal points can reach the surface → more simultaneous reflections, mirroring real synchrotron vs. lab-source data.
- Lattice spacing a — sets the reciprocal lattice constant 2π/a; a smaller real-space cell spreads reciprocal points further apart.
- ω / Auto-Rotate — rotates the crystal (and its reciprocal lattice) about the vertical axis, the same motion used in rotation/oscillation X-ray photography and in a rotating-anode diffractometer.
- Lattice type — Simple Cubic keeps every hkl point; FCC and BCC apply the real structure-factor selection (extinction) rules, so only the physically allowed reflections are drawn.
- A lattice point glows gold and locks to the sphere surface when |distance to origin along k_out direction| is within a small tolerance — that tolerance stands in for a real crystal's finite mosaic spread and beam divergence.
This exact construction is how every modern diffractometer and synchrotron beamline decides, geometrically, which (hkl) planes are "in reflecting position" at a given crystal orientation.