MINDMAP 1
Crystal Structure
Unit Cell
Crystal Classes
Crystal Consists of
Crystal
Polycrystal
Amorphous
The positions of the atoms form a repeated periodic geometrical pattern without any variation in composition, dimension and orientation
Is characterised by the regular arrangement of the atoms or the molecules
Eg. metal, alloy, semiconductor
The arrangement of the atoms form the same pattern as in crystal but the orientation changes at the crystallite boundaries
Eg. metal, alloy, semiconductor
The arrangement of the atoms don't form repeated periodic pattern, Because it made of random oriented atoms, ions, molecules
Have order but only within a few atomic or molecular dimensions
Eg. amorphous silicon, plastic, ceramic, glasses
lattice
basis
Is the position of the basis
Has a translation symmetry
Is a group of atoms or molecules that are identical in composition, and describe the crystal structure
Is a 3D geometrical block
An atom in the unit cell forms 1 crystal basis
Determined by 6 lattice constants:
a
b
c
⍺
β
𝛄
Primitive & non primitive unit cell
primitive
non primitive
Single lattice point or single basis per cell
Smallest area in 2D
Smallest volume in 3D
Will fill the space by using the repetition of a suitable crystal translation vectors
Volume of a primitive unit cell is a^3
V=a1.(a2a3)
More than one lattice point per cell
Integral of multiple areas of the primitive cell
Example. SC
Example. BCC
Atom at
corner 1/8
edge 1/4
surface 1/2
inside 1
Wigner-Seitz unit cell
Designed with one lattice point located in the centre of the cell and every point is closer to the centre
Is a primitive unit cell with full symmetry
To construct this cell
- Choose one lattice point at the centre
- Draw a line from that point to its neighbour lattice
- Draw on each line a plane perpendicular to the each line, dividing it into half
The polyhedron or the smallest geometrical shape boundaried by these planes and centred by the lattice point is a Wigner-Seitz unit cell
Common unit cell in 3D:
SC
BCC
FCC
Lattice System
Lattice
Basis
A periodic array of points in space. The environment surrounding each lattice point is identical
Atom or group of atoms attached to each lattice point in order to generate the crystal structure
Lattice Parameters
includes dimensions of the sides of the unit cell
includes angles between the sides
lengths often given in nanometers or Angstrom
Bravais Lattices
simple cubic
face centred cubic
body centred cubic
simple tetragonal
body centred tetragonal
hexagonal
simple ortohombic
body centred ortohombic
base centred ortohombic
face centred ortohombic
trigonal
simple monoclinic
base centred monoclinic
triclinic
No of Atoms per Unit Cell
a unit cell has a specific number of unit cell
at each corner of the cell
at centre of the cell (bcc)
at each face of the cell (fcc)
Simple Cubic Structure
rare due to low packing density
close packed directions are cube edges
only Po has this structure
face centred cubic structure
all atoms are identical
atoms touch each other along face diagonals
Example. Al, Cu, Au
body centred cubic
atoms touch each other along cube diagonals
Example. Cr, W, Fe
Coordination Number
the number of atoms touching a particular atom
SC : 6
BCC : 8
FCC : 12
Packing Factor
(number of atoms/cell) x (vol of each atom) / (vol of unit cell)
SC : 0.52
BCc : 0.68
FCC : 0.74
HCP : 0.74
Theoretical density, p = (nA) / (VcNa)
Symmetry Operation
important factors in determining crystal structure
lattice arrangement
crystal axes
type of basis
set of symmetry operation
translation
point operatiom
combination operation
T = n1a + n2b + n3c
identity
n fold rotation
reflection
inversion
n = 360/theta
on horizontal plane
on vertical plane
diagonal
Plane Direction
miller indices for planes
specific crystallographic of plane, (hkl)
family of crystallographic plane, {hkl}
procedures
- identify the coordinate intercepts
- take reciprocals
- clear fractions
- cite specific planes in parenthesis, (hkl)
HCP crystallographic direction
[UVW] > [uvtw]
u = 1/3(2U -V)
v = 1/3(2V - U)
t = -(U + V)
w = W