Planes Into Points: Reciprocal Lattice | Crystallography 2.5

Copper's planes sit about 2 Å apart, the same size as the wavelength of its X-rays, but a crystal holds endless families of planes, each needing three Miller indices and a spacing. This episode replaces every family by one dot, placed on the plane normal at a distance 1/d, and watches the dots grow into a lattice of their own. It builds the recipe a* = (b × c)/V, proves that g is perpendicular to its planes and 1/d long, shows that FCC and BCC are each other's reciprocals, and ties up the zone law and Miller indices from the first season. Chapters 0:00 Too many families of planes 1:19 Miller, Bravais, Gibbs and Ewald 2:03 Building the dots in two dimensions 4:04 From lines to planes in 3D 4:43 A recipe for a*, b* and c* 6:00 Why g is perpendicular and 1/d long 7:49 Testing it on copper 8:26 FCC and BCC are each other's reciprocals 9:44 Hexagonal crystals 10:21 Zones and Miller indices, tied up 11:30 A note on 2π, and three takeaways 12:01 Next: which dots light up? Reference: M. Martínez-Ripoll (with the late F. Hernández Cano), Crystallography-Cristalografia, web course (CSIC, CC BY-NC 4.0, https://www.xtal.iqf.csic.es/Cristalo..., and university crystallography and diffraction lecture notes. Historical sources: Miller, A Treatise on Crystallography (1839): https://archive.org/details/treatiseo... · Fathi, History of the reciprocal lattice, Powder Diffraction 34, 260 (2019; abstract and reference list only): https://doi.org/10.1017/S088571561900... · Fathi, History of the reciprocal lattice (Cambridge Core page): https://www.cambridge.org/core/journa... Previous episode: 2.4 "Making X-Rays". Next episode: 2.6 "Bragg and Ewald". Narration: AI voice (ElevenLabs); music: AI-generated (Lyria) and original synthesized tracks.