Crystal_structure - Wikiparency

# Crystal structure ## Microsim (three.js) <div class="microsim-player">  <p class="wt-pending"><strong>Microsim staged, not yet on the CDN.</strong> <code>Crystal_structure.html</code> is built and deploy-ready in <code>Microsims for Dissemination/</code>, but the Netlify project still serves the geometry+spintronics set only. The player is disabled until the deploy lands; the explanatory text below is unchanged.</p>   </div> *Part of the REACTION chemistry hub: the ordered lattices here become the [[Cubic_crystal_system]], depart from ideality through Crystallographic defects, and are revealed by X-ray diffraction as the repeating pattern an Ionic bond holds in place.* > A crystal structure is the regular, repeating three-dimensional arrangement of atoms, ions, or molecules in a crystalline solid. It is built from a lattice — an infinite grid of equivalent points — decorated by a motif (basis) of atoms, and the smallest block that tiles space to reproduce the whole is the unit cell. This microsim lets you grow that unit cell into a lattice, swell or shrink the atoms to see how tightly they pack, and toggle between the abstract lattice points and the atomic motif that sits on them, so long-range order, coordination, and packing efficiency emerge from a single repeating cell. ## About this microsim Before any definition, drag the controls. Set the **Unit-cell grid N×N×N** to 1 and you see one bare unit cell; step it to 2 or 3 and the cell copies itself into a 3×3×3 block, so translational symmetry — the defining feature of a crystal — appears in front of you. Now sweep the **Atomic radius** from 8% toward 105% of the site: at small values the spheres shrink to a ball-and-stick skeleton exposing the lattice geometry; near full size they approach contact and fill space to the packing fraction. The **lattice/motif visualization** separates the two ideas the definition rests on — the lattice points versus the atoms (motif) that decorate each one — so "crystal = lattice + motif" becomes something you see rather than memorize. ## Related microsims - [[Cubic_crystal_system]] — the three cubic lattices (SC, BCC, FCC) whose packing this sim builds - Crystallographic defect — how real crystals depart from the ideal repeating cell - X-ray — diffraction is the primary tool for measuring these structures - Ionic bond — the bonding that holds ionic crystals such as NaCl in their lattice - [[Quasicrystal]] — ordered solids that lack the translational periodicity shown here - Crystal twinning — intergrowths where two orientations of the same structure meet - Electron diffraction — related REACTION microsim - Electron microscope — related REACTION microsim - [[Ion]] — related REACTION microsim - [[Molecular_dynamics]] — related REACTION microsim - Nanomaterials — related REACTION microsim - [[Neutron_diffraction]] — related REACTION microsim - Polymer chemistry — related REACTION microsim - Stacking fault — related REACTION microsim - Transmission electron microscopy — related REACTION microsim ## Links (Wikipedia order)  `Abnormal_grain_growth` · `Adsorption` · `Allotropy` · [[Alloy]] · `Alternating_group` · `American_Crystallographic_Association` · `Amorphous_solid` · `Aperiodic_crystal` · `Atom` · `Atomic_packing_factor` · `Axial_ratio` · `Bilbao_Crystallographic_Server` · `Bjerrum_defect` · `Bragg's_law` · `Bragg_plane` · `Bravais_lattice` · `Brillouin_zone` · `British_Crystallographic_Association` · `Burgers_vector` · `Cambridge_Structural_Database` · `Carl_Hermann_Medal` · `Ceramic` · [[Ceramic_engineering]] · `Characterization_(materials_science)` · `Chemical_crystallography_before_X-rays` · `Chemical_stability` · `Chirality_(chemistry)` · `Cleavage_(crystal)` · `Close-packing_of_equal_spheres` · `Coesite` · `Cold_working` · `Collaborative_Computational_Project_Number_4` · `Composite_material` · `Coordination_geometry` · `Coordination_number` · `Coot_(software)` · `Cottrell_atmosphere` · `Creep_(deformation)` · `Cristobalite` · `Cross_slip` · `Crystal` · `CrystalExplorer` · `Crystal_Growth_&_Design` · `Crystal_engineering` · `Crystal_growth` · `Crystal_habit` · `Crystal_optics` · `Crystal_polymorphism` · `Crystal_structure_prediction` · `Crystal_system` · `Crystal_twinning` · `Crystallite` · `Crystallographic_Information_File` · `Crystallographic_Society_of_Japan` · `Crystallographic_database` · `Crystallographic_defect` · `Crystallographic_defects_in_diamond` · `Crystallographic_point_group` · `Crystallographic_restriction_theorem` · `Crystallography` · `Crystallography_Open_Database` · `Crystallography_Reviews` · `Cube` · [[Cubic_crystal_system]] · `Cuboctahedron` · `Cyclic_group` · `Diamond` · `Diamond_cubic` · `Dielectric` · [[Diffusion]] · `Dihedral_group` · `Direct_methods_(crystallography)` · `Disclination` · `Dislocation` · `Disordered_Structure_Refinement` · `Electron_crystallography` · `Electron_diffraction` · `Electron_scattering` · `Electronic_band_structure` · `Equiaxed_crystal` · `European_Crystallographic_Association` · `Eutectic_system` · `Ewald's_sphere` · `Ewald_Prize` · `F-center` · `Ferromagnetism` · `Fiveling` · `Fractional_coordinates` · `Frank–Kasper_phases` · `Frank–Read_source` · `French_Crystallographic_Association` · `Frenkel_defect` · `Friedel's_law` · `Geometrical_crystallography_before_X-rays` · `Geometrically_necessary_dislocations` · `Gerchberg–Saxton_algorithm` · `German_Crystallographic_Society` · `German_Mineralogical_Society` · [[Germanium]] · `Glass` · `Grain_boundary` · `Grain_growth` · `Gregori_Aminoff_Prize` · `Group_theory` · `Guinier–Preston_zone` · `Hermann–Mauguin_notation` · `Hexagonal_crystal_family` · `Hexagonal_lattice` · `History_of_crystallography_before_X-rays` · `Improper_rotation` · `Inorganic_Crystal_Structure_Database` · `Integer` · `International_Centre_for_Diffraction_Data` · `International_Organization_for_Biological_Crystallization` · `International_Union_of_Crystallography` · `Interstitial_defect` · `Interstitial_site` · [[Ion]] · `Isomorphous_replacement` · `Journal_of_Chemical_Crystallography` · `Journal_of_Crystal_Growth` · `Kink_(materials_science)` · `Klein_four-group` · `Kristallografija` · `Laser-heated_pedestal_growth` · `Lattice_constant` · `Law_of_constancy_of_interfacial_angles` · `Law_of_rational_indices` · `Law_of_symmetry_(crystallography)` · `Linus_Pauling` · `Liquid_crystal` · `List_of_biophysically_important_macromolecular_crystal_structures` · `Lomer–Cottrell_junction` · `MTEX` · [[Materials_science]] · `Metadynamics` · `Metal` · [[Metallurgy]] · `Microstructure` · `Miller_index` · `Mineral` · `Miscibility_gap` · [[Molecular_dynamics]] · `Molecular_replacement` · `Molecule` · `Monoclinic_crystal_system` · `Neil_Ashcroft` · [[Neutron_diffraction]] · `Neutron_scattering` · `Nuclear_magnetic_resonance_crystallography` · `Oblique_lattice` · `OctaDist` · `Octahedron` · `Olex2` · `Optics` · `Orthorhombic_crystal_system` · `Ostwald_ripening` · `Parallelepiped` · `Partial_dislocation` · `Patterson_function` · `Pauling's_rules` · `Peierls_stress` · `Perfect_crystal` · `Periodic_table_(crystal_structure)` · `Perovskite_(structure)` · `Phase_diagram` · `Phase_retrieval` · `Phase_transformation_crystallography` · [[Phase_transition]] · `Physical_crystallography_before_X-rays` · `Piezoelectricity` · `Plane_(mathematics)` · `Plasticity_(physics)` · `Point_group` · `Point_reflection` · `Polar_point_group` · `Polymer` · `Precipitation_(chemistry)` · `Precipitation_hardening` · `Prism_(geometry)` · `Protein_Data_Bank` · `Protein_crystallization` · `Pyramid_(geometry)` · `Quartz` · [[Quasicrystal]] · `Reactivity_(chemistry)` · `Reciprocal_lattice` · `Rectangular_lattice` · `Reflection_(mathematics)` · `Refractive_index` · `Resonating_valence_bond_theory` · `Rita_G._Lerner` · `Rotation_(mathematics)` · `Rotational_symmetry` · `Schoenflies_notation` · `Schottky_defect` · `Seed_crystal` · `Segregation_(materials_science)` · `Semiconductor` · `Shear_stress` · `ShelXle` · `Shubnikov_Institute_of_Crystallography_RAS` · [[Silicon]] · `Silicon_dioxide` · `Single_crystal` · `Single_particle_analysis` · `Sintering` · `Slip_(materials_science)` · `Slip_bands_in_metals` · `Sodium_chloride` · `Space_group` · `Spinodal_decomposition` · `Square_lattice` · `Stacking_fault` · `Stishovite` · `Stone–Wales_defect` · `Structure_factor` · `Supercell_(crystal)` · `Supersaturation` · `Surface_tension` · `Symmetric_group` · `Symmetry` · `Symmetry_number` · `Tetragonal_crystal_system` · `Tetrahedron` · `Thermal_ellipsoid` · `Timeline_of_crystallography` · [[Tin]] · `Translation_(geometry)` · `Translational_symmetry` · `Triangular_orthobicupola` · `Triclinic_crystal_system` · `Tridymite` · `Unit_cell` · `Vacancy_defect` · `Wigner_effect` · `Wigner–Seitz_cell` · `X-ray_crystallography` · `X-ray_diffraction` · `Zeitschrift_für_Kristallographie_–_Crystalline_Materials` · `Zeitschrift_für_Kristallographie_–_New_Crystal_Structures` ## Overview A crystal structure is the ordered arrangement of matter that gives crystalline solids their flat faces, cleavage, and sharp diffraction. The idea that crystals are stacks of identical repeating units dates to René-Just Haüy in the 1780s; Auguste Bravais showed in 1848 that only 14 distinct lattices (the Bravais lattices) exist in three dimensions, grouped into 7 crystal systems. Modern determination began in 1912, when Max von Laue discovered X-ray diffraction from crystals, and W. H. and W. L. Bragg solved the first structures (including NaCl) using Bragg's law the following year. Structure governs nearly every solid-state property — density, stiffness, conductivity, reactivity — making it foundational to chemistry, physics, mineralogy, and materials science. Distances are conventionally reported in ångström (1 Å = 10⁻¹⁰ m = 0.1 nm). ## The physics A structure is specified by lattice parameters: edge lengths a, b, c and angles α, β, γ. How efficiently atoms fill the cell is the atomic packing factor, APF = (N · (4/3)πr³) / V_cell, where N is the number of atoms per cell and r the atomic radius. Atoms "touch" along specific directions, fixing r in terms of a and giving the classic close-packing limits. The Atomic radius control walks r from a small fraction of its contact value (8%) up to and just past touching (105%), so the packing factor rises toward these ideal values. | Structure | Atoms/cell N | Touch condition | Coordination | APF | |---|---|---|---|---| | Simple cubic | 1 | a = 2r | 6 | 0.52 | | Body-centered cubic | 2 | √3·a = 4r | 8 | 0.68 | | Face-centered cubic | 4 | √2·a = 4r | 12 | 0.74 | | Hexagonal close-packed | 6 | a = 2r | 12 | 0.74 | ## Controls → what each maps to | Control | Maps to (symbol) | Range / values | Physical meaning | |---|---|---|---| | Atomic radius | r (% of site) | 8–105% | Sphere size relative to contact radius; drives the atomic packing factor and switches between ball-and-stick and space-filling views | | Unit-cell grid | N (cells per edge) | 1–3 (N×N×N) | Number of unit-cell repeats; reveals translational periodicity and long-range order | | Lattice/motif visualization | lattice + basis | toggle | Separates the Bravais lattice points from the atomic motif that decorates each point | ## Learning objective After playing, a learner can predict how coordination number and packing fraction change with structure, and explain why a crystal is fully described by a repeating unit cell equal to a lattice plus a motif. ## Limits and connections The hard-sphere model here idealizes atoms as touching balls; real bonding is directional, thermal motion vibrates atoms about their sites, and no crystal is perfect. Missing or misplaced atoms, planar faults, and aperiodic order extend the picture toward defects and quasicrystals. ## Poster & source <div class="microsim-fallback">  <p><em>Live microsim · <a href="https://wikitube-3d-microsims.netlify.app/Crystal_structure.html">open full</a> · source: Microsims for Dissemination/REACTION/Crystal_structure.html</em></p> </div>  *Built to the [[WT!Three_js_Microsim_Master_Class|three.js Master Class]].*   **Microsim — three.js (Wikitube framework):** *Crystal structure* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Crystal_structure.html" data-title="Crystal structure"></div> *Built from `MICROSIM_GUIDE/specs/sims/Crystal_structure.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Crystal_structure) : [Wikitube](https://en.wikitube.io/wiki/Crystal_structure) ## Previous hub tags Tree parents: [[Helium]] · [[Hydrogen]] · [[Oxygen]] · [[Self-organization]]. Legacy hubs: `REACTION`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*