Advanced Topic 284 of 1102 States of Matter & Solutions
Bravais Lattices
Fourteen distinct three-dimensional lattice types.
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In-depth explanation of Bravais Lattices
A Bravais lattice is one of the fourteen distinct three-dimensional arrangements of lattice points, each describing a unique translational symmetry. The fourteen lattice types arise by combining the seven crystal systems with the centring options of primitive, body-centred, face-centred and base-centred. Every point in a Bravais lattice has an identical environment, so every crystal structure is built on one of these lattices. Knowing which lattice applies is the first step in determining a crystal structure from diffraction data. The fact that only fourteen lattice types exist shows that the number of possible lattice arrangements is limited.
Going deeper: Bravais Lattices
Key ideas: Count: cubic 3, tetragonal 2, orthorhombic 4, monoclinic 2, triclinic 1, hexagonal 1, rhombohedral 1, total 14. Centering types P, I, F, C. Some combinations are redundant, for instance base-centred tetragonal is equivalent to primitive tetragonal with a smaller cell. Lattice points are mathematical, not necessarily atoms.
Common mistakes and connections: Students think each lattice point is one atom, but a point may represent a group of atoms called the basis. Another mistake is thinking diamond is a Bravais lattice; it is fcc with a two-atom basis. Also, hcp is not a Bravais lattice by itself. Links to crystal systems, unit cell and structures of real solids.
Visualization of Bravais Lattices
The seven crystal systems contain 14 Bravais lattices in total (P, I, F and C variants): cubic 3, tetragonal 2, orthorhombic 4, monoclinic 2 and others 1. The interactive lesson shows this as a live animation or chart.
Worked example and use case
The cubic system has three Bravais lattices: primitive cubic, body-centred cubic and face-centred cubic.
Frequently asked questions about Bravais Lattices
What is Bravais Lattices?
Fourteen distinct three-dimensional lattice types.
Is Bravais Lattices a beginner, intermediate or advanced topic?
Bravais Lattices is a advanced topic in States of Matter & Solutions. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Bravais Lattices?
Study these earlier topics in States of Matter & Solutions first: Packing Efficiency, Tetrahedral and Octahedral Voids, Crystal Systems.
What comes after Bravais Lattices?
The next topics in States of Matter & Solutions are X-ray Diffraction and Bragg's Law and Crystal Defects.
Can I practise Bravais Lattices with quizzes?
Yes. The interactive lesson includes a self-check question on Bravais Lattices, and the States of Matter & Solutions quiz draws on every topic in this area.
Where Bravais Lattices fits in States of Matter & Solutions
Bravais Lattices is topic 65 of 109 in States of Matter & Solutions.