The full 3D Ewald sphere construction, sliced flat: a sphere of radius k = 2π/λ intersects the horizontal reciprocal-lattice layer y = n·a* (the "n-th Laue zone") in a circle of radius rn = √(k² − (n·a*)²) — real only while |n·a*| < k. That circle, drawn here in the main panel together with the rotating (h, n, l) lattice points of that layer, is exactly the textbook 2D Ewald-circle diagram used to read Weissenberg and precession photographs.
Sphere: x² + y² + (z+k)² = k²
Layer y = n·a*: x² + (z+k)² = k² − (n·a*)² = r_n²
Bragg law: λ = 2·d_hkl·sinθ, d_hkl = 2π/|G_hnl|
A reflection "fires" only when a lattice point sits within Δk of the circle's radius — the finite width models real mosaic spread / crystallite-size broadening (an idealized point crystal would need Δk → 0).
- Wavelength λ — shrinks or grows the circle (k = 2π/λ); shorter λ reaches more distant reciprocal points.
- Lattice constant a — sets a* = 2π/a; a larger real cell packs reciprocal points closer together.
- Crystal rotation γ — spins the lattice layer about the vertical axis, sweeping points through the circle.
- Laue zone n — picks which horizontal layer of the reciprocal lattice you are slicing; the side panel shows every layer's circle and whether it can reach the sphere at all for the current λ.
- Reflection width Δk — the shell tolerance; wider Δk reflects the broadening from a smaller or more mosaic crystal.
- Drag the main view to pan, scroll/pinch to zoom — the geometry is exact at any zoom level.
Real-world relevance: crystallographers pick λ and the rotation range from exactly this construction so enough (h n l) points sweep through the sphere to solve a structure — from table salt to protein crystals.