Cubic_crystal_system - Wikiparency

# Cubic crystal system ## Microsim (three.js) <div class="microsim-player">  <p class="wt-pending"><strong>Microsim staged, not yet on the CDN.</strong> <code>Cubic_crystal_system.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 cubic crystal system is the friendliest doorway into [[Crystal_structure]] — the periodic packing that X-ray diffraction first decoded, that governs how ionically bonded solids like rock salt stack, and whose disruptions become crystallographic defects.* > The cubic crystal system is the family of crystals whose repeating unit cell is a perfect cube. Three ways of decorating that cube — simple, body-centered, and face-centered — give very different densities and coordination even though every edge stays the same length. In the microsim you build each lattice atom by atom, tile it into a larger block, and inflate the spheres until they touch — showing why face-centered packing fits the most atoms and a bare simple cube wastes the most space. ## About this microsim The sim renders one cubic unit cell as a cage of eight corner atoms and lets you rebuild it into any of the three cubic lattices. Switch the **Lattice type** between SC, BCC, and FCC to add the body-center or face-center atoms and watch the coordination number climb; raise the **Unit-cell grid N** from 1 to 3 to tile the cell into a 3×3×3 block that exposes long-range periodicity; and drag the **Atomic radius scale** to grow the hard spheres until they kiss along the close-packed direction — the condition that fixes the packing fraction. The **cell** and **atoms** toggles hide the cube edges or the spheres so you can inspect the lattice points or the packing alone. ## Related microsims - [[Crystal_structure]] — the general framework this is a special case of - Crystallographic defect — disruptions of the perfect cubic lattice - Stacking fault — errors in the FCC ABCABC stacking sequence - [[Quasicrystal]] — ordered solids that break periodicity - X-ray — diffraction that measures the lattice parameter a - Ionic bond — bonding behind FCC salts like NaCl - Crystal twinning — related REACTION microsim - Electron diffraction — related REACTION microsim - Nanomaterials — related REACTION microsim - [[Neutron_diffraction]] — related REACTION microsim ## Links (Wikipedia order)  `A15_phases` · `Acta_Crystallographica` · `Acta_Crystallographica_Section_A` · `Alkali_metal` · `Alkali_metal_halide` · `Alkaline_earth_metal` · [[Aluminium]] · `Aluminium_antimonide` · `Aluminium_arsenide` · `Aluminium_nitride` · `Aluminium_phosphide` · `Americium_nitride` · `Atomic_packing_factor` · `Atomium` · `Barium_oxide` · `Barium_selenide` · `Barium_sulfide` · [[Beryllium]] · `Beryllium_sulfide` · `Beryllium_telluride` · `Binary_phase` · `Boron_arsenide` · `Boron_group` · `Boron_nitride` · `Boron_phosphide` · `Bravais_lattice` · `Cadmium_oxide` · `Cadmium_selenide` · `Cadmium_sulfide` · `Cadmium_telluride` · `Caesium_chloride` · `Caesium_fluoride` · `Caesium_hydride` · `Calcium_oxide` · `Calcium_polonide` · `Calcium_selenide` · `Calcium_sulfide` · `Carbide` · [[Carbon]] · `Cation-anion_radius_ratio` · `Centrosymmetry` · `Cerium_monoselenide` · `Cerium_monosulfide` · `Cerium_nitride` · `Cerium_phosphide` · `Chalcogenide` · [[Chemistry]] · `Chirality_(chemistry)` · `Chirality_(mathematics)` · [[Chromium]] · `Chromium(II)_oxide` · `Chromium(IV)_silicide` · `Chromium_nitride` · `Clathrate_compound` · `Clathrate_hydrate` · `Close-packing_of_equal_spheres` · `Cobalt(II)_oxide` · `Cobalt_germanide` · `Cobalt_monosilicide` · `Coordination_number` · [[Copper]] · `Copper(I)_bromide` · `Copper(I)_chloride` · `Copper(I)_fluoride` · `Copper(I)_iodide` · `Coxeter_notation` · `Crystal` · [[Crystal_structure]] · `Crystal_system` · `Crystallographic_point_group` · `Crystallography` · `Cube` · `Cubic_honeycomb` · `Curium_nitride` · `Diamond_cubic` · `Dislocation` · `Dodecahedron` · `Dysprosium_antimonide` · `Dysprosium_arsenide` · `Dysprosium_bismuthide` · `Dysprosium_monosulfide` · `Dysprosium_nitride` · `Dysprosium_phosphide` · `Erbium_nitride` · `Erbium_phosphide` · `Europium_monoselenide` · `Facet` · `Fluorite_structure` · `Gadolinium_monosulfide` · `Gadolinium_phosphide` · `Galena` · `Gallium_antimonide` · `Gallium_arsenide` · `Gallium_nitride` · `Gallium_palladide` · `Gallium_phosphide` · [[Germanium]] · [[Gold]] · `Group_11_element` · `Group_12_element` · `Hafnium_carbide` · `Halide` · `Halite` · `Hermann–Mauguin_notation` · `Heusler_compound` · `Hexagonal_crystal_family` · `Hexagonal_lattice` · `Holmium_antimonide` · `Holmium_arsenide` · `Holmium_bismuthide` · `Holmium_monosulfide` · `Holmium_nitride` · `Holmium_phosphide` · `Hydride` · `Hydrogen_bond` · `II-VI_semiconductor_compound` · `Indium_antimonide` · `Indium_arsenide` · `Indium_nitride` · `Indium_phosphide` · `Interstitial_site` · [[Iron]] · `Iron(II)_oxide` · `Iron_germanide` · `Iron_monosilicide` · `Jmol` · `Lanthanum_monosulfide` · `Lanthanum_nitride` · `Lanthanum_phosphide` · `Lattice_(group)` · `Lead(II)_nitrate` · `Lithium_bromide` · `Lithium_chloride` · `Lithium_fluoride` · `Lithium_hydride` · `Lithium_iodide` · `Lutetium_nitride` · `Lutetium_phosphide` · [[Magnesium]] · `Magnesium_oxide` · `Magnesium_selenide` · `Magnesium_sulfide` · [[Manganese]] · `Manganese(II)_oxide` · `Manganese_germanide` · `Manganese_monosilicide` · `Mercury_selenide` · `Mercury_sulfide` · `Mercury_telluride` · `Miller_index` · `Mineral` · `Molecular_geometry` · `Monoclinic_crystal_system` · `Neodymium_bismuthide` · `Neodymium_monosulfide` · `Neodymium_phosphide` · `Neptunium_arsenide` · `Neptunium_nitride` · `Neptunium_phosphide` · `Nickel(II)_oxide` · [[Niobium]] · `Niobium_carbide` · `Niobium_nitride` · `Nitride` · `Norman_Greenwood` · `Oblique_lattice` · `Octahedral_symmetry` · `Octahedron` · `Orbifold` · `Orbital_hybridisation` · `Orthorhombic_crystal_system` · `Pearson_symbol` · `Pergamon_Press` · `Periodic_table_(crystal_structure)` · `Petzite` · `Plutonium_carbide` · `Plutonium_nitride` · [[Polonium]] · `Potassium_bromide` · `Potassium_chloride` · `Potassium_fluoride` · `Potassium_hydride` · `Potassium_iodide` · `Praseodymium_antimonide` · `Praseodymium_arsenide` · `Praseodymium_bismuthide` · `Praseodymium_monoselenide` · `Praseodymium_monosulfide` · `Pyrite` · `Rare-earth_element` · `Reciprocal_lattice` · `Rectangular_lattice` · `Rubidium_bromide` · `Rubidium_chloride` · `Rubidium_fluoride` · `Rubidium_hydride` · `Rubidium_iodide` · `Samarium_monosulfide` · `Scandium_monosulfide` · `Scandium_nitride` · `Scandium_phosphide` · `Schoenflies_notation` · [[Silicon]] · [[Silver]] · `Sodium_bromide` · `Sodium_chlorate` · `Sodium_chloride` · `Sodium_fluoride` · `Sodium_hydride` · `Sodium_iodide` · `Space_group` · `Sphalerite` · `Square_lattice` · `Strontium_oxide` · `Strontium_selenide` · `Strontium_sulfide` · `Strukturbericht_designation` · `Tantalum_carbide` · `Terbium_monosulfide` · `Terbium_nitride` · `Terbium_phosphide` · `Ternary_compound` · `Tetradecahedron` · `Tetragonal_crystal_system` · `Tetrahedral-octahedral_honeycomb` · `Tetrahedral_symmetry` · `Tetrahedron` · `Thulium_nitride` · `Thulium_phosphide` · [[Tin]] · `Titanium(II)_oxide` · `Titanium_carbide` · `Titanium_nitride` · `Transition_metal` · `Triclinic_crystal_system` · [[Tungsten]] · `Ullmannite` · `Unit_cell` · `University_of_Graz` · `Uranium_carbide` · `Uranium_monophosphide` · `Uranium_monosulfide` · `Vanadium(II)_oxide` · `Vanadium_carbide` · `Vanadium_nitride` · [[Wayback_Machine]] · `Weaire–Phelan_structure` · `Wyckoff_positions` · `Yttrium_nitride` · `Yttrium_phosphide` · `Zinc_selenide` · `Zinc_sulfide` · `Zinc_telluride` · `Zirconium_carbide` · `Zirconium_nitride` ## The physics A cubic lattice has equal edges and right angles (a = b = c, α = β = γ = 90°), so one lattice parameter a describes the whole cell. Treating atoms as hard spheres of radius r that touch along the close-packed direction fixes r versus a, the atoms per cell, the coordination number, and the atomic packing factor (APF = atom volume ÷ cell volume). | Lattice | Atoms/cell | Coordination | a in terms of r | APF | |---|---|---|---|---| | Simple cubic (SC) | 1 | 6 | a = 2r | π/6 ≈ 0.524 | | Body-centered (BCC) | 2 | 8 | a = 4r/√3 | √3·π/8 ≈ 0.680 | | Face-centered (FCC) | 4 | 12 | a = 2√2·r | √2·π/6 ≈ 0.740 | FCC (along with hexagonal close packing) reaches the densest arrangement possible for equal spheres, ≈74%, which is why many ductile metals — aluminium, copper, gold, γ-iron — adopt it. ## Overview The cubic or isometric system is the most symmetric of the seven crystal systems, marked by four threefold rotation axes along the cube's body diagonals (the ⟨111⟩ directions). It holds three of the fourteen Bravais lattices — primitive (cP), body-centered (cI), and face-centered (cF), enumerated by Auguste Bravais in 1848 — and spans 5 point groups and 36 of the 230 space groups. α-polonium is the lone simple-cubic element; sodium, chromium, and tungsten are body-centered; copper, silver, and aluminium are face-centered; and sodium chloride is two interpenetrating FCC lattices. Because the lattice parameter a (e.g. 0.3615 nm for copper) is directly measurable by X-ray diffraction, cubic metals are textbook systems linking atomic geometry to bulk density. ## Controls → what each maps to | Control | Maps to (symbol) | Range / values | Physical meaning | |---|---|---|---| | Lattice type | Bravais lattice | SC / BCC / FCC | Chooses primitive, body-centered, or face-centered decoration of the cube | | Unit-cell grid | N (repeats per edge) | 1–3 | Tiles the cell into an N×N×N supercell to expose periodicity | | Atomic radius scale | r (sphere radius) | 0.2–1.15 | Scales the hard-sphere radius; contact sets the packing factor | | Show cell / atoms | visibility flags | on / off | Toggles the cube edges and the atom spheres independently | ## Learning objective After playing, a learner can predict how coordination number and packing factor rise from SC to BCC to FCC, and explain why FCC is close-packed. ## Limits and connections The sim treats atoms as identical hard spheres, so it captures metallic and monatomic lattices well but idealizes ionic and molecular crystals, where two ion sizes or directional bonds matter. Perfect lattices also hide the defects and interfaces that dominate real materials. ## Poster & source <div class="microsim-fallback">  <p><em>Live microsim · <a href="https://wikitube-3d-microsims.netlify.app/Cubic_crystal_system.html">open full</a> · source: Microsims for Dissemination/REACTION/Cubic_crystal_system.html</em></p> </div>  *Built to the [[WT!Three_js_Microsim_Master_Class|three.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Cubic_crystal_system) : [Wikitube](https://en.wikitube.io/wiki/Cubic_crystal_system) ## Previous hub tags Tree parents: [[Helium]] · [[Helium-3]] · [[Oxygen]]. Legacy hubs: `REACTION`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*