physics

Crystallography & Crystal Structure

The science of crystal structures — unit cell geometry, Miller indices for plane notation, reciprocal lattice construction, symmetry operations, and point defects in crystalline solids.

crystallographycrystal structureunit cellMiller indicesreciprocal latticesymmetrydefectssolid state physics

Crystallography is the study of how atoms arrange themselves in periodic three-dimensional lattices. From the diamond structure of carbon to the body-centered cubic lattice of iron, crystal geometry governs material properties including hardness, conductivity, and optical behavior. X-ray diffraction reveals these hidden symmetries, connecting atomic-scale order to macroscopic material performance.

These simulations let you build unit cells, index crystal planes with Miller indices, construct reciprocal lattices, explore symmetry operations, and introduce point defects — all with real-time interactive controls and physically accurate crystallographic models.

5 interactive simulations

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Crystal Symmetry Operations

Explore crystal symmetry — apply rotation, mirror, inversion, and glide operations to a 2D motif and watch how symmetry generates the full pattern from a single asymmetric unit

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Crystal Defect Structure

Simulate point defects in crystals — adjust vacancy concentration, interstitial fraction, temperature, and substitutional impurity level to see how defects affect lattice energy and diffusion

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Miller Indices & Crystal Planes

Visualize crystal planes using Miller indices — adjust h, k, l values and lattice parameter to see how planes slice through the unit cell and calculate interplanar spacing

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Reciprocal Lattice Construction

Build and explore the reciprocal lattice — adjust real-space lattice parameters and angle to see how the reciprocal lattice transforms, with Ewald sphere visualization

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Unit Cell Geometry Explorer

Explore unit cell structures — adjust lattice parameters, crystal system type, atomic radius, and packing to visualize cubic, tetragonal, and hexagonal unit cells in real time