This is the flat-plate Debye-Scherrer powder camera — the 2D counterpart of the single-crystal Ewald sphere construction. A powder sample is millions of tiny crystallite grains at every possible random orientation. For a fixed lattice spacing a, each family of lattice planes {hkl} has a fixed spacing dhkl = a / √(h²+k²+l²), and Bragg's law fixes the scattering angle for that family regardless of which way an individual grain happens to be pointing:
Bragg's law: 2 d_hkl sin θ = λ
Scattering angle: Θ = 2θ
Ring radius on a flat plate at distance L:
r = L · tan(Θ)
Because grain orientation about the beam axis is random, the diffracted beams from all correctly-tilted grains sweep out a full cone of half-angle Θ = 2θ around the direct beam — which a flat detector sees as a ring of radius r = L·tan(2θ), not a single spot. Individual grains still flash at random azimuthal positions on that ring as the "exposure" accumulates, exactly like the speckled rings on a real photographic powder pattern before enough grains have fired to smooth it into a continuous circle.
- λ slider — Bragg's law only has a solution when λ ≤ 2d; shorter wavelengths let more, smaller-d families of planes reach a valid θ, so more rings appear.
- Lattice spacing a — scales every dhkl = a/√(h²+k²+l²), spreading or compressing the whole ring pattern.
- Detector distance L — the same angular pattern, but a larger L stretches ring radii (r = L·tan Θ) faster than the plate grows, pushing high-angle rings off the visible plate — a real trade-off in camera design between angular resolution and field of view.
- Lattice type — Simple Cubic allows every (hkl); FCC and BCC apply the real structure-factor extinction rules, so entire families vanish and the ring spacing pattern changes shape, not just scale — this is exactly how real powder patterns are used to identify a crystal structure.
- Move the mouse over the plate to read off the scattering angle 2θ at any radius and see which {hkl} family is nearest.
Real-world relevance: powder X-ray diffraction is the everyday workhorse technique for identifying unknown crystalline materials, measuring lattice strain, and quality-checking pharmaceuticals and battery electrodes — because it needs only a powder, not a single perfect crystal.