【正文】
?=180? ?=90? Rotation Axis n=2 2fold rotation axis n=4 4fold rotation axis Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Reflection (or mirror symmetry) Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Lattices also have translational symmetry Translational symmetry Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Symmetry of lattices Lattices have Rotational symmetry Reflection symmetry Translational symmetry Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Symmetry classification of lattices Based on rotational and reflection symmetry alone ? 7 types of lattices ? 7 crystal systems Based on plete symmetry, ., rotational, reflection and translational symmetry ? 14 types of lattices ? 14 Bravais lattices Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 7 crystal Systems System Required symmetry ? Cubic Three 4fold axis ? Tetragonal one 4fold axis ? Orthorhombic three 2fold axis ? Hexagonal one 6fold axis ? Rhombohedral one 3fold axis ? Monoclinic one 2fold axis ? Triclinic none Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Tetragonal symmetry Cubic symmetry Cubic C = Tetragonal P Cubic F ? Tetragonal I Shiv K