Learn / Structure & Transformations
Structure & Transformations

Lattices, symmetry,
and how structure changes.

Unit cells, symmetry, projections and reciprocal space, then the thermodynamics and kinetics that move a material from one structure to another.

Structure & Transformations
Start here

New to Structure? Read these first.

StoryTwo Bars, One Melt

A one-minute scrolling story: two bars from one melt, one heat treatment apart, and why one cracked. Grain boundaries,…

LabLattices & Point Groups

An interactive, fully rotatable 3D lab on basic crystallography: the 14 Bravais lattices with primitive-vs-conventional…

All topics

Lattices & symmetry2 pages
LabLattices & Point GroupsAn interactive, fully rotatable 3D lab on basic crystallography: the 14 Bravais lattices with…Foundation · 15 minLabSpace GroupsAn interactive 3D lab on space groups: explore Wyckoff positions, screw axes, and glide planes in four real…Foundation · 15 min
Planes, directions & reciprocal space1 page
LabStereographic ProjectionsAn interactive 3D lab on stereographic projection: watch the sphere-to-plane construction happen live,…Foundation · 15 min
Interfaces & orientation relationships2 pages
LabInterfaces & the Coincidence Site LatticeInteractive crystallography lab: misfit and tilt boundaries, coincidence site lattice (CSL) theory generated…Advanced · 15 minLabGrain Boundary MigrationPush a grain boundary by curvature or stored energy, see how its mobility can rise or fall with temperature,…Advanced · 12 min
Thermodynamics & phase diagrams2 pages
LabRegular Solution & Scheil-Gulliver LabInteractive binary phase diagram and tie-line lab from a regular-solution model (click for the lever rule, no…Foundation · 15 minLabHume-Rothery RulesCheck the four Hume-Rothery rules for any solute in copper or silver, see it on a Darken-Gurry map, and watch…Foundation · 10 min
Kinetics & transformations7 pages
LabSpinodal, Nucleation & Coarsening LabInteractive lab on spinodal decomposition vs. nucleation-and-growth, classical nucleation theory with a…Advanced · 15 minLabBragg-Williams Order-Disorder LabInteractive Bragg-Williams model of order-disorder transformations: the long-range order parameter S(T) from…Advanced · 15 minLabKinetics for Real Alloys LabInteractive TTT and CCT diagrams built from a real nucleation-barrier times Arrhenius-mobility C-curve, plus…Advanced · 15 minLabOrdered Intermetallic StructuresTurn L1₂, D0₂₂, D0₂₃, L1₀, B2, D0₃, L2₁ and D0₁₉ cells in 3D, build D0₂₂ and D0₂₃ from shifted L1₂ cubes, and…Advanced · 15 minLabShort-Range OrderWatch atoms swap on a live alloy lattice, read the Warren-Cowley short-range order parameters, and see how…Advanced · 12 minLabDiffusion Couples & Fick's LawsWatch atoms random-walk across an interface into the erf profile, recover D(c) with the Boltzmann-Matano…Foundation · 15 minLabGrain Growth & Zener PinningRun a live Potts simulation of grain growth, add particles until growth stops at the Zener limit, compare…Advanced · 15 min

Other chapters: TEM · EBSD · APT · Contact Mechanics · Mechanical Behavior · In-situ Testing.