1.6 typical crystal structure Body Centered Cubic Packing Space Group Im3m a=4r/(32 Atom Site x M 2a 0 0 0 *r=metallic radius Representative Examples Fe(a=2.8664A Cr(a=2.8846A) Mo(a=3.1469A W(a=3.1650A) Cubic or Hexagonal Close Packing Coordination Number =12 Ta(a=3.3026A) Packing Efficiency 74% Ba(a=5.019A) Body Centered Cubic Packing Coordination Number 8 Packing Efficiency 68%
1.6 typical crystal structure
1).bcc lattice (Li,Na,K,Rb,Cs.etc) One possible choice of primitive vectors lattice a constant a(+方-动 属-++头 A conventional unit cell, 属(-+头 (nonprimitive) Note:A bcc lattice is a simple lattice. But we can also treat it as a cubic lattice with a 2-point basis! (to take advantage of the cubic symmetry
Simple Hexagonal Bravais Lattice 60 lal=la=a The simple hexagonal Bravais lattice.Two-dimensional triangular nets (shown in inset)are stacked directly above one another,a distance c apart
Simple Hexagonal Bravais Lattice
Conventional Primitive Unit Cells Points of Primitive Cell Hexagonal Bravais Lattice w Primitive Cell Conventional Cell Fractional coordinates of lattice points in conventional cell: 100,010,110,101,011 111,000,001 b
Conventional & Primitive Unit Cells Hexagonal Bravais Lattice Primitive Cell = Conventional Cell Fractional coordinates of lattice points in conventional cell: 100, 010, 110, 101, 011 111, 000, 001 Points of Primitive Cell a b c
Hexagonal Close Packed (HCP)Structure: (A Simple Hexagonal Bravais Lattice with a 2 Atom Basis) Figure 22 The hexagonal close-packed struc- ture.The atom positions in this structure do The HCP lattice is not a Bravais not constitute a space lattice.The space lattice is simple hexagonal with a basis of two identi- lattice,because the orientation of cal atoms associated with each lattice point. the environment of a point varies The lattice parameters a and c are indicated, where a is in the basal plane and c is the mag- from layer to layer along the c-axis. nitude of the axis ag of Fig.14
Hexagonal Close Packed (HCP) Structure: (A Simple Hexagonal Bravais Lattice with a 2 Atom Basis) The HCP lattice is not a Bravais lattice, because the orientation of the environment of a point varies from layer to layer along the c-axis