Lattice Classification 晶体晶格种类.ppt

1、Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,Classification of lattice The Seven Crystal System And The Fourteen Bravais Lattices,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,7 crystal Systems,SystemUnit Cell Shape 1.Cubica=b=c, =90,Shiv K. Gupta Department of Applied Mechani

2、cs, IIT Delhi,7 crystal Systems,SystemUnit Cell Shape 2.Tetragonala=bc, =90,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,7 crystal Systems,SystemUnit Cell Shape 3 Orthorhombicabc, =90,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,7 crystal Systems,SystemUnit Cell Shape 4. Hexa

3、gonala=bc, = 90, =120 5. Rhombohedrala=b=c, =90 6. Monoclinicabc, =90 7. Triclinicabc, ,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,14 Bravais lattices divided into seven crystal systems,Crystal systemBravais lattices CubicPIF,Simple cubicPrimitive cubicCubic P,Body-centred cubicCubic I

4、,Face-centred cubicCubic F,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,14 Bravais lattices divided into seven crystal systems,Crystal systemBravais lattices CubicPIF TetragonalPI OrthorhombicPIFC HexagonalP TrigonalP MonoclinicPC TriclinicP,Shiv K. Gupta Department of Applied Mechanics,

5、 IIT Delhi,Orthorhombic CEnd-centred orthorhombicBase-centred orthorhombic,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,14 Bravais lattices divided into seven crystal systems,Crystal systemBravais lattices CubicPIF TetragonalPI OrthorhombicPIFC HexagonalP TrigonalP MonoclinicPC Triclinic

6、P,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,End-centred cubic not in the Bravais list ?,End-centred cubic = Simple Tetragonal,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,14 Bravais lattices divided into seven crystal systems,Crystal systemBravais lattices CubicPIFC Tetrag

7、onalPI OrthorhombicPIFC HexagonalP TrigonalP MonoclinicPC TriclinicP,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,Face-centred cubic in the Bravais list ?,Cubic F = Tetragonal I,Problem 3.1,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,14 Bravais lattices divided into seven cr

8、ystal systems,Crystal systemBravais lattices CubicPIFC TetragonalPI OrthorhombicPIFC HexagonalP TrigonalP MonoclinicPC TriclinicP,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,What is the basis for classification of lattices into 7

9、crystal systems and 14 Bravais lattices?,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,Lattices are classified on the basis of their symmetry,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,What is symmetry?,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,If an object is

10、 brought into self-coincidence after some operation it said to possess symmetry with respect to that operation.,Symmetry,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,Rotational symmetry,A rectangle comes into self-coincidence by 180 degrees rotation,Shiv K. Gupta Department of Applied Me

11、chanics, IIT Delhi,If an object come into self-coincidence through smallest non-zero rotation angle of then it is said to have an n-fold rotation axis where,=180,=90,Rotation Axis,n=2,2-fold rotation axis,n=4,4-fold rotation axis,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,Reflection (o

12、r 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

13、 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 complete symmetry, i.e., rotational, reflection and translational symmetry 14 types of lattices 14 Bravais lattice

14、s,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,7 crystal Systems,SystemRequired symmetry CubicThree 4-fold axis Tetragonalone 4-fold axis Orthorhombicthree 2-fold axis Hexagonalone 6-fold axis Rhombohedralone 3-fold axis Monoclinicone 2-fold axis Triclinicnone,Shiv K. Gupta Department of

15、 Applied Mechanics, IIT Delhi,Tetragonal symmetry,Cubic symmetry,Cubic C = Tetragonal P,Cubic F Tetragonal I,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,The three Bravais lattices in the cubic crystal system have the same rotational symmetry but different translational symmetry.,Simple

16、cubicPrimitive cubicCubic P,Body-centred cubicCubic I,Face-centred cubicCubic F,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 complete symmetry, i.e., rotat

17、ional, reflection and translational symmetry 14 types of lattices 14 Bravais lattices,Shiv K. Gupta Department of Applied Mechanics, IIT Delhi,Notation P: Primitive (lattice points only at the corners of the unit cell) I: Body-centred (lattice points at the corners + one lattice point at the centre of the unit cell) F: Face-centred (lattice points at the corners + lattice points at centres of all faces of the unit cell) C: End-centred or base-centred (lattice points a