Crystal systems
Choose a system or material. Drag the network to change the view.
Interticular distance and Bragg's law
The indices refer to the base displayed. The angle calculation does not predict a diffraction intensity.
Scientific benchmarks and references
The seven crystal systems are defined by the symmetry of the crystal; accidental equality of parameters is not enough to change this classification. The centering variants and the different choices of axes are not additional systems. The hP lattice appears in the hexagonal system and in some trigonal crystals. An hR network can be described in a primitive rhombohedral mesh or a hexagonal mesh centered R.
Network mode spheres represent translation nodes. Pattern mode, available for some documented simple structures, shows periodic atomic positions. Rays and colors are not a measure of atomic size; the segments are mesh edges, without chemical bonds. Orthographic projection and rotation relate to the view of the crystal.
Volumes, metrics, plans and distances are calculated from the six parameters. α=(b,c), β=(a,c), γ=(a,b). The reciprocal network is defined without factor 2π. A satisfied centering condition does not guarantee a reflection: the pattern and the space group can add extinctions. Indices are not automatically transformed when changing axes.
Material parameters are rounded and correspond to the specified phases. Historical mineralogical records sometimes use “hexagonal” for the entire family; the classification into systems here follows the IUCr nomenclature. The calculated density assumes the ideal composition, the Z number indicated and the usual rounded atomic masses. A manual modification switches to Educational Mesh mode.
References: IUCr · systems and networks ; IUCr · trigonal, hP and hR ; IUCr · mesh metric ; IUCr · compact structures ; Handbook of Mineralogy · parameters and phases ; IUPAC · atomic masses.