Seven categories such as cubic, tetragonal and hexagonal classified by unit cell axes and angles.
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There are seven crystal systems: cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic and triclinic. They classify crystals according to the lengths of the unit cell axes and the angles between them. Each system has a characteristic set of symmetry elements, such as rotation axes and mirror planes. The symmetry of the lattice determines many physical properties, including optical behaviour and cleavage. In the cubic system all three axes are equal and all angles are 90°, while in the hexagonal system two axes are equal and the angle between them is 120°. Recognizing the system helps interpret X-ray diffraction results.
Key ideas: Remember by axes and angles: cubic a=b=c all 90; tetragonal a=b not c all 90; orthorhombic three unequal all 90; monoclinic one angle not 90; triclinic none equal; hexagonal a=b not c with gamma 120; rhombohedral a=b=c with equal non-90 angles. Examples: NaCl cubic, rutile tetragonal, sulfur orthorhombic, gypsum monoclinic.
Common mistakes and connections: Students mix up hexagonal and rhombohedral and think that the shape of a visible crystal always shows the system. A crystal habit can differ from its lattice. Another error is claiming seven systems means seven lattice types; there are fourteen Bravais lattices. Links to unit cells, symmetry and X-ray diffraction.
Seven crystal systems are classified by relative edge lengths and angles; cubic has a=b=c and 90 degrees, triclinic has none equal. The interactive lesson shows this as a live animation or chart.
Table salt is cubic, whereas quartz is trigonal, a system closely related to the hexagonal one.
Seven categories such as cubic, tetragonal and hexagonal classified by unit cell axes and angles.
Crystal Systems is a advanced topic in States of Matter & Solutions. It builds on beginner and intermediate topics, so review those first if needed.
Study these earlier topics in States of Matter & Solutions first: Hexagonal Close Packing, Packing Efficiency, Tetrahedral and Octahedral Voids.
The next topics in States of Matter & Solutions are Bravais Lattices and X-ray Diffraction and Bragg's Law.
Yes. The interactive lesson includes a self-check question on Crystal Systems, and the States of Matter & Solutions quiz draws on every topic in this area.
Crystal Systems is topic 64 of 109 in States of Matter & Solutions.