The 14 Bravais Lattices

CT5812701 · Crystal Structure 晶體結構

The 14 Bravais Lattices十四種布拉維格子

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cP

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cPPrimitive

Simple cubic

簡單立方

System 晶系

Cubic 立方

Edges 邊長

a = b = c

Angles 夾角

α = β = γ = 90°

Examples 實例

α-Po

Lattice points per cell 每晶胞晶格點

8 × 1/8

1

7 crystal systems · 14 lattices　七大晶系．十四種格子

Why only 14? Seven crystal systems × four centring types (P, C, I, F) would suggest 28 lattices, but most combinations are redundant — they can be redrawn as a smaller cell of another system (a C-centred cubic cell, for example, is just a smaller tetragonal cell). Only 14 distinct lattices survive.
為何只有 14 種？七大晶系 × 四種心化方式 (P, C, I, F) 看似有 28 種，但多數組合是重複的 —— 它們可改畫成另一晶系的較小晶胞 （例如底心立方其實就是較小的正方晶胞），因此只剩下 14 種相異的格子。

AEML · Advanced Engineering Materials Laboratory, NTUST