Chapter 1b

10 1 Crystal StructureTwo-Dimensional Bravais LatticesThere are only five different types of two-dimensional Bravais lattices.1. Square lattice: primitive (P) one onlyIt has a = b and α = β = 90 o .2. Rectangular: primitive (P) and centered (C) onesThey have a ≠ b but α = β = 90 o .3. Hexagonal: primitive (P) one onlyIt has a = b and α = 120 o (β = 60 o ).4. Oblique: primitive (P) one onlyIt has a ≠ b and α ≠ 90 o .Three-Dimensional Bravais LatticesThere are fourteen different types of three-dimensional Bravais lattices.1. Cubic: primitive (P), body centered I), and face centered (F) onesFor all of these a = b = c and α = β = γ = 90 o .2. Tetragonal: primitive and body centered (I) onesFor these a = b ≠ c and α = β = γ = 90 o . One can think of them as cubiclattices that have been stretched (or compressed) along one of the cubeaxes.3. Orthorombic: primitive (P), body centered (I), face centered (F), and basecentered (C) onesFor all of these a ≠ b ≠ c but α = β = γ = 90 o . These can be thoughtof as cubic lattices that have been stretched (or compressed) by differentamounts along two of the cube axes.4. Monoclinic: primitive (P) and base centered (C) onesFor these a ≠ b ≠ c and α = β = 90 o ≠ γ. These can be thought of asorthorhombic lattices which have suffered shear distortion in one direction.5. Triclinic: primitive (P) oneThis has the lowest symmetry with a ≠ b ≠ c and α ≠ β ≠ γ.6. Trigonal:It has a = b = c and α = β = γ ≠ 90 o < 120 o . The primitive cell is arhombohedron. The trigonal lattice can be thought of as a cubic latticewhich has suffered shear distortion.7. Hexagonal: primitive (P) one onlyIt has a = b ≠ c and α = β = 90 o , γ = 120 o .1.2 Common Crystal Structures1. Cubic