Physics ★★☆ Moderate

💎 Crystal Structures

Rotate and explore the seven fundamental crystal lattice types in real 3D (WebGL). See how atoms pack together in Simple Cubic, BCC, FCC, HCP, Diamond, NaCl and CsCl structures. Drag to orbit, scroll to zoom. Observe coordination numbers, atomic packing factors, and unit cell geometry.

Click and drag to orbit · Scroll to zoom

0.55
1×1×1
0.6
Structure
BCC
Atoms / unit cell
2
Coordination #
8
Packing fraction
0.68
Bravais lattice
Body-centred cubic
Examples
Fe, W, Cr

Body-Centred Cubic (BCC)

BCC has atoms at all 8 corners of the cube plus one in the centre. Each atom touches 8 neighbours along the body diagonal. Coordination number = 8. Atomic packing factor 0.68. Common in metals: iron (α-Fe), tungsten, chromium, molybdenum. Less dense than the close-packed FCC and HCP arrangements.

Comparing Crystal Structures

Simple Cubic (SC) — Atoms only at cube corners. CN = 6. Packing 0.52. Rare — only Polonium adopts this Bravais lattice.

BCC — Atoms at corners + body centre. CN = 8. Packing 0.68. Typical in Group 5/6 metals and iron below 912°C.

FCC — Atoms at corners + all face centres. CN = 12. Packing 0.74 (highest for equal spheres, close-packing). Al, Cu, Ni, Au, Ag.

HCP — Hexagonally close-packed. CN = 12, packing 0.74 — same density as FCC but different stacking (ABAB vs ABCABC). Mg, Ti, Zn, Co.

Diamond Cubic — FCC with basis: 2 atoms per lattice point (tetrahedral bonding, sp³). CN = 4. Packing only 0.34 but extremely rigid. Carbon, Si, Ge.

NaCl (Rock Salt) — Two interpenetrating FCC sub-lattices (Na⁺ and Cl⁻). Each ion surrounded by 6 of the opposite type. CN = 6. Very common for ionic compounds.

CsCl — Two interpenetrating simple-cubic sub-lattices (Cs⁺ and Cl⁻). Each ion has CN = 8. Distinct from BCC because the centre and corner atoms differ. CsCl, CsBr, NH₄Cl.

About Crystal Structures

This interactive 3D viewer lets you rotate and explore seven fundamental crystal lattice types — Simple Cubic, BCC, FCC, HCP, Diamond, NaCl, and CsCl — rendered in real time using WebGL. The simulation shows how atoms pack together in periodic arrangements and displays key crystallographic properties such as coordination number, atomic packing factor, and unit cell geometry. By switching between structures you can directly compare how atomic arrangements affect density and symmetry.

Crystal structure determines a material's mechanical strength, electrical conductivity, and melting point. Crystallographers and materials scientists use these lattice models to design alloys, semiconductors, ceramics, and pharmaceutical compounds, making crystallography one of the most practically important branches of solid-state physics and chemistry.

Frequently Asked Questions

What is a crystal structure?

A crystal structure is the periodic, three-dimensional arrangement of atoms, ions, or molecules in a solid material. Atoms occupy specific positions defined by a repeating unit called the unit cell, and the entire crystal is built by stacking that unit cell in all directions. The type of crystal structure determines almost all physical and chemical properties of the material.

How do I use this simulation?

Click one of the structure buttons (SC, BCC, FCC, HCP, Diamond, NaCl, CsCl) to switch lattices, then click and drag on the canvas to orbit the model. Scroll to zoom in or out. Use the toggles to show or hide the unit cell box, bonds, and an extended lattice replica. The Atom size and Unit cells/axis sliders let you adjust the visual appearance and see how cells tile in 3D.

What is the difference between FCC and HCP?

Both FCC (face-centred cubic) and HCP (hexagonal close-packed) achieve the maximum atomic packing factor of 0.74 and a coordination number of 12, meaning each atom touches 12 nearest neighbours. The difference lies in layer stacking: FCC follows an ABCABC sequence while HCP follows ABAB. Gold, aluminium, and copper adopt FCC; magnesium, titanium, and zinc adopt HCP.

What is the atomic packing factor (APF) and how is it calculated?

The atomic packing factor (APF) is the fraction of the unit cell volume occupied by atoms, calculated as APF = (N x V_atom) / V_cell, where N is the number of atoms per unit cell and V_atom is the volume of one atom treated as a sphere. Simple Cubic gives APF = 0.52, BCC = 0.68, FCC and HCP = 0.74 (the theoretical maximum for equal hard spheres, known as close-packing), and Diamond Cubic only 0.34 due to its open tetrahedral bonding.

Which real materials use each crystal structure?

Simple Cubic is extremely rare — only polonium adopts it. BCC is common in the transition metals iron (below 912 degrees C), tungsten, chromium, and molybdenum. FCC appears in aluminium, copper, gold, silver, and nickel. HCP is found in magnesium, titanium, zinc, and cobalt. The Diamond Cubic structure describes carbon (diamond), silicon, and germanium. The NaCl (rock-salt) structure is adopted by common salt, magnesium oxide, and iron(II) oxide, while CsCl applies to caesium chloride, caesium bromide, and ammonium chloride.

Why is diamond so hard if its packing factor is only 0.34?

Hardness in diamond does not come from dense packing but from the nature of the bonds. Each carbon atom forms four strong, directional covalent bonds (sp3 hybridisation) arranged in a perfect tetrahedron. Deforming the crystal requires breaking many of these bonds simultaneously throughout the three-dimensional network, which demands enormous energy. BCC iron has a higher packing factor but much weaker metallic bonds, making it far softer than diamond.

Who discovered X-ray crystallography and when?

Max von Laue demonstrated in 1912 that X-rays diffract through crystals, proving both the wave nature of X-rays and the periodic structure of crystals. William Henry Bragg and his son William Lawrence Bragg then derived Bragg's Law (n*lambda = 2d*sin(theta)) in 1913, enabling scientists to calculate atomic spacings from diffraction patterns. Both Braggs shared the 1915 Nobel Prize in Physics. X-ray crystallography later revealed the double helix structure of DNA in 1953.

How does crystal structure relate to other simulations?

Crystal structures are closely linked to topics such as phonons and lattice vibrations (heat conduction), electron band theory (why metals conduct and semiconductors do not), and materials failure (dislocation motion through BCC or FCC lattices governs ductility). Fluid simulations such as SPH Fluid are the complementary case where atoms lack long-range order. Phase transitions between crystal types, like iron switching from BCC to FCC at 912 degrees C, connect to thermodynamics simulations.

How are crystal structures used in semiconductor technology?

Silicon and germanium both adopt the Diamond Cubic structure, and their semiconductor properties arise directly from the sp3 tetrahedral bonding. Integrated circuits are fabricated on single-crystal silicon wafers cut along specific crystallographic planes (usually the (100) or (111) plane) because surface reactivity and electron mobility depend on orientation. Compound semiconductors like gallium arsenide (GaAs) use the closely related Zinc Blende structure, a variant of Diamond Cubic with two different atom types.

What is an active research frontier in crystal structure science?

Computational crystal structure prediction — using density functional theory and machine learning force fields to predict which structure a new compound will adopt before it is ever synthesised — is a rapidly growing field. The Cambridge Structural Database holds over one million experimentally determined crystal structures, and AI models trained on this data can now propose novel stable crystal phases for battery materials, pharmaceuticals, and high-entropy alloys. Quasicrystals, discovered by Dan Shechtman in 1982 (Nobel Prize 2011), also remain an active area; they show diffraction patterns with five-fold symmetry that is impossible in any conventional Bravais lattice.

💎 Crystal Structures

About this simulation

This viewer renders, in real 3D using WebGL, how atoms arrange themselves in the seven fundamental crystal lattices — Simple Cubic, BCC, FCC, HCP, Diamond, NaCl and CsCl. Crystal structure determines a material's strength, conductivity and melting point, so crystallographers use these models to design alloys, semiconductors and ceramics. It is fascinating that swapping the same atoms between FCC and BCC can change a metal from soft to brittle.

How it works

Key equations

APF = (N · V_atom) / V_cell — the atomic packing factor is the number of atoms per cell (N) times each atom's volume divided by the unit-cell volume; FCC and HCP reach the maximum 0.74 for equal spheres (close-packing), while ideal HCP has c/a = √(8/3) ≈ 1.633.

Controls

Did you know?

Diamond and graphite are both pure carbon — the only difference is the crystal structure. Diamond's rigid tetrahedral lattice makes it the hardest natural material, while graphite's stacked sheets slide past each other, which is why it works as a pencil and a lubricant.