Crystal Lattice Viewer

How the Crystal Lattice Viewer works

Crystal lattice viewer: the structures

Simple cubic puts an atom at each corner of a cube, which only polonium adopts because it wastes so much space. Body-centred cubic adds one in the middle, the structure of iron at room temperature, chromium and tungsten. Face-centred cubic adds an atom to each face instead and is the densest cubic packing, shared by copper, aluminium, gold, silver and nickel. Hexagonal close packing reaches the same density with a different stacking order (ABAB rather than ABCABC) and is the structure of magnesium, zinc and titanium; its cell is a rhombic prism rather than a cube, so the edges here are drawn on that shape. Diamond is face-centred cubic with a second, offset copy interleaved, giving each carbon or silicon atom four neighbours in a tetrahedron. The ionic structures place two or three species on separate sublattices: sodium and chloride ions each on their own face-centred lattice in rock salt, one of each in the cube for caesium chloride, the diamond arrangement with alternating elements in zinc blende, and the corner, body and face positions of perovskite filled by three different ions.

Reading the numbers

Atoms per cell counts the fractions: a corner atom is shared by eight cells and a face atom by two, so face-centred cubic has 8 × ⅛ + 6 × ½ = 4 atoms per cell. Coordination is the number of nearest neighbours around an atom, which is what the bonds drawn in the viewport join. The packing fraction is the share of the cell volume filled by touching spheres: 52 percent for simple cubic, 68 for body-centred, 74 for both close-packed structures and only 34 for diamond. For ionic structures the fraction depends on the two ion radii so it is not quoted, but the radius relation line gives the geometry that sets the lattice constant, for example a = 2(r₊ + r₋) in rock salt where cation and anion touch along a cell edge.

Atom size and bonds

At 100 percent the spheres are drawn at the radius where nearest neighbours touch, which shows how the structure packs and where the interstitial holes are; for ionic cells the two radii are in the ratio of the real ions. Smaller sizes turn the model into a ball-and-stick diagram where the geometry is easier to see. Bonds join every pair of nearest neighbours in the drawn block; in ionic structures only cation–anion pairs are joined, which makes the six-fold octahedra of rock salt and the four-fold tetrahedra of zinc blende stand out.

Repeats and edges

With one cell you see the textbook unit cell, including the atoms on all of its corners and faces even though most of each belongs to a neighbouring cell. Two to four repeats show how the cells tile into a lattice and make close-packed planes visible when you orbit to look along a body diagonal. Cell edges can be hidden for a cleaner picture of the packing alone.

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