Learn / Crystallography
Crystallography
Lattices, symmetry,
and orientation.
Build intuition for unit cells, reciprocal space, symmetry, zone axes, plane/direction notation, and how crystallography connects across diffraction, microscopy, and mechanics.
1 · Start here
Build the foundation
LabLattices & Point GroupsAn interactive, fully rotatable 3D lab on basic crystallography: the 14 Bravais lattices with primitive-vs-conventional cells, Miller indices and the Weiss zone law, and a point-group identifier covering all 32 crystallographic point groups.LabStereographic ProjectionsAn interactive 3D lab on stereographic projection: watch the sphere-to-plane construction happen live, generate the standard stereogram for any of the 32 crystallographic point groups, and convert hexagonal Miller-Bravais indices with an interplanar-angle calculator.LabSpace GroupsAn interactive 3D lab on space groups: explore Wyckoff positions, screw axes, and glide planes in four real structures (diamond, zinc blende, cuprite, cementite), then compute how many crystallographically equivalent orientation variants a precipitate can form in a matrix.
2 · Learn the core
Master the key concepts
3 · Use a tool
Work with your data
ToolCBED Symmetry Tableswhole-pattern and bright-field symmetry → point group candidatesBuxton diffraction-group tables in the browser: pick a point group and a zone axis to read the whole-pattern, bright-field and dark-field symmetries a CBED pattern must show, or enter the symmetries you observed and list every point group and zone-axis class consistent with them. All 31 diffraction groups derived from the 32 point groups, not typed in.ToolKikuchi Map Navigatororientation → band to follow, tilt anglesFree in-browser Kikuchi map for any crystal: see which zone axes sit on which Kikuchi bands, which band to follow to reach a zone axis, how far to tilt, and the double-tilt holder settings that get you there. fcc, bcc, hcp, diamond and ordered alloys built in, or load a CIF.ToolSAED Zone-Axis Indexerpattern → zone-axis candidatesFree online SAED indexing tool: upload a TEM selected-area electron diffraction pattern, click the transmitted beam and two spots, and identify the zone axis: calibration-free, for FCC, BCC, SC, diamond, HCP and custom lattices.ToolSAED Pattern Simulatorstructure + zone axis → kinematic, Bloch or multislice patternFree in-browser electron diffraction simulator: 604 built-in structures or your CIF, any zone axis, kinematical or many-beam dynamical intensities with a thickness slider, precession, CBED discs, Kikuchi lines, the Ewald-sphere section, your own pattern with a residual fit and off-zone estimate, symmetry readout, CTF and partially coherent HRTEM tableau, HOLZ lines, Bloch-wave STEM images with thermal diffuse scattering (BF, ABF, ADF, HAADF), and a WebGPU frozen-phonon multislice engine (PRISM S-matrix or scanned probe) for supercells with dislocations, stacking faults and column substitutions.ToolEBSD Pattern Simulatorcrystal + orientation + detector → dynamical Kikuchi patternSimulate electron backscatter diffraction patterns in the browser: a Monte Carlo of the primary beam in the tilted sample gives the energy, depth and exit direction of the backscattered electrons, a many-beam Bloch-wave calculation on a symmetry-reduced Lambert grid gives the master pattern, and the detector geometry with Bunge Euler angles puts it on the phosphor, with kinematic band edges and zone-axis labels drawn over it. 604 crystals or a CIF, WebGPU with a JavaScript fallback, band profiles against the Bragg angle.LabLattices & Point GroupsAn interactive, fully rotatable 3D lab on basic crystallography: the 14 Bravais lattices with primitive-vs-conventional cells, Miller indices and the Weiss zone law, and a point-group identifier covering all 32 crystallographic point groups.
4 · Solve a problem
Troubleshoot real data
5 · Go deeper
Research-level topics
6 · All resources
Every Crystallography page
- LabLattices & Point GroupsAn interactive, fully rotatable 3D lab on basic crystallography: the 14 Bravais lattices with primitive-vs-conventional cells, Miller indices and the Weiss zone law, and a point-group identifier covering all 32 crystallographic point groups.
- LabStereographic ProjectionsAn interactive 3D lab on stereographic projection: watch the sphere-to-plane construction happen live, generate the standard stereogram for any of the 32 crystallographic point groups, and convert hexagonal Miller-Bravais indices with an interplanar-angle calculator.
- LabSpace GroupsAn interactive 3D lab on space groups: explore Wyckoff positions, screw axes, and glide planes in four real structures (diamond, zinc blende, cuprite, cementite), then compute how many crystallographically equivalent orientation variants a precipitate can form in a matrix.
- LabInterfaces & the Coincidence Site LatticeInteractive crystallography lab: misfit and tilt boundaries, coincidence site lattice (CSL) theory generated live from Ranganathan's relation, Bollmann's O-lattice construction, and secondary dislocations at the DSC lattice.
Other fields: TEM & STEM · EBSD & TKD · Atom Probe · Phase Transformations · Tribology · Nanoindentation · Scratch Testing · In-situ / FIB.