SOLID STATE PHYSICS - PowerPoint

							SOLID STATE PHYSICS




  Course Coordinator
   Dr. Dana A. Tahir
Unit Cell in 3D




                  Crystal Structure   2
Unit Cell in 3D




                  Crystal Structure   3
Three common Unit Cell in 3D




             Crystal Structure   4
                                   UNIT CELL


             Primitive                          Conventional & Non-primitive

  Single lattice point per cell
  Smallest area in 2D, or                      More than one lattice point per cell
 Smallest volume in 3D                         Integral multibles of the area of
                                                 primitive cell




     Simple cubic(sc)                          Body centered cubic(bcc)
Conventional = Primitive cell                 Conventional ≠ Primitive cell
                                     Crystal Structure                             5
The Conventional Unit Cell

              A unit cell just fills space when
               translated through a subset of
               Bravais lattice vectors.
              The conventional unit cell is
               chosen to be larger than the
               primitive cell, but with the full
               symmetry of the Bravais lattice.
              The size of the conventional cell
               is given by the lattice constant
               a.

                Crystal Structure              6
Primitive and conventional cells of FCC




                 Crystal Structure        7
Primitive and conventional cells of BCC

                    Primitive Translation Vectors:
                               1
                           a1  ( x  y  z )
                                  ˆ ˆ ˆ
                               2
                               1
                           a2  ( x  y  z )
                                    ˆ ˆ ˆ
                               2
                               1
                           a3  ( x  y  z )
                                  ˆ ˆ ˆ
                               2
Primitive and conventional cells
                Body centered cubic (bcc):
                conventional primitive cell
b   c
                Fractional coordinates of lattice points in
        a       conventional cell:
                000,100, 010, 001, 110,101, 011, 111, ½ ½ ½


                   Simple cubic (sc):
                   primitive cell=conventional cell
b       c          Fractional coordinates of lattice points:
                   000, 100, 010, 001, 110,101, 011, 111
            a
                           Crystal Structure                   9
    Primitive and conventional cells

                     Body centered cubic (bcc):
                 b
     c
                     primitive (rombohedron) conventional cell

             a       Fractional coordinates:
                     000, 100, 101, 110, 110,101, 011, 211, 200



                     Face centered cubic (fcc):
                     conventional primitive cell

b                    Fractional coordinates:
     c               000,100, 010, 001, 110,101, 011,111, ½ ½ 0, ½
                     0 ½, 0 ½ ½ ,½1 ½ , 1 ½ ½ , ½ ½ 1
         a
                            Crystal Structure                        10
Primitive and conventional cells-hcp
        points of primitive cell



                                   Hexagonal close packed cell (hcp):
                                   conventional primitive cell

                                   Fractional coordinates:
    c
                                   100, 010, 110, 101,011, 111,000, 001

        b

        a

                               Crystal Structure                    11