Laue: Crystallography

Laue is a crystallography workshop for students, teachers and researchers: choose a space group, place atoms, and the app does the rest — exactly, from the symmetry operations themselves.

THE CRYSTAL
• All 230 space groups in their 530 settings of the International Tables, by number, Hermann-Mauguin or Hall symbol.
• Place atoms: Laue gives the Wyckoff position, multiplicity and site symmetry, and snaps them onto special positions.
• Symmetry elements with the symbols of the Tables: rotation and screw axes, mirror and glide planes, inversion centers — one axis order at a time if you wish.
• Turn the crystal, look along any symmetry element, or show the projection of the Tables. Stereograms of the point group and of each site.
• The Laue pattern of a single crystal: a white beam from 0.25 to 2.5 Å, on a film in transmission — the 1912 experiment — or in back-reflection, the one that orients crystals.

THE PLANE
• The 17 plane groups, the 7 frieze groups and the rosettes of mandalas (Cₙ, Dₙ, any order), with fundamental domain, symmetry elements and operations.
• Shapes, characters, your own pictures or freehand drawing: every stroke is repeated by the group.
• The 46 two-color groups, subgroups and supergroups, and a photograph under the motif to find its group.

POWDER
• The powder pattern of every crystal, with X-rays or neutrons, recomputed as an atom moves: indexed lines, absences explained, real atoms or identical points, and the Debye–Scherrer film.
• Your measurements: read a pattern (.xy, CSV, powder CIF, GSAS), refine the cell, zero shift, background and peak profile, with Rwp and χ².
• An unknown powder: Laue finds the peaks, indexes the cell (cubic to orthorhombic) and suggests the compatible space groups.

ELECTRONS AND LIGHT
• The electronic band structure by tight binding or pseudopotentials: band gap, density of states, absorption, refractive index and birefringence.
• Color centers: the red of ruby, the green of emerald, the blue of sapphire.

PHONONS
• Dispersion and density of states, from springs to rigid ions with the LO–TO splitting.
• Infrared and Raman modes, the reststrahlen band and the reflectivity.

DIFFRACTION
• The pattern of every tiling, its absences and its Laue class, to enlarge and export.
• Fourier synthesis: the motif rebuilt with the true phases, zero or random phases, or the Patterson map — the phase problem before your eyes.

QUASICRYSTALS
• Penrose, Ammann-Beenker and dodecagonal, by de Bruijn's multigrid or by inflation, with the perpendicular space and 10-, 8- or 12-fold peaks.
• Colored and decorated tiles: Penrose arcs, girih strapwork from Persian mosaics, or your own drawing on one tile, carried across the whole tiling.
• The visible points of a lattice and their exact diffraction.

FOR PRINT AND FABRIC
• The pattern alone at a physical size: PDF, SVG, PNG, TIFF.
• Seamless straight, half-drop or half-brick repeats; print-ready PDF with bleed and crop marks; separations for screen printing.

ON THE PRINTER
• The structure goes out to a 3D printer: one cell or a block up to 6 × 6 × 6, as 3MF — one part and one colour per element, so each gets its own filament — or as STL.

THE FORMATS OF THE FIELD
• Reads CIF, SHELX and POSCAR; writes CIF, SHELX, POSCAR, XYZ, PDB, and CGD for Systre.
• Documents in open JSON, with a published schema.

THE TUTOR
• 47 exercises where the engine checks every answer, explains a mistake and gives the solution, from Wyckoff positions to band gaps.

FOR THE LECTURE HALL
• Presentation mode, saved views, undo and redo, PNG and vector PDF export, and settings to suit your habits.

VALIDATED
Exact rational arithmetic. The 530 settings, their Wyckoff positions and symmetry elements are checked against spglib; the refinement against a real NIST measurement (LaB₆).

Mac and iPad, one purchase, in 24 languages. Only the plane? Laue Plan offers tilings, friezes and quasicrystals on their own.