2. CRYSTAL
“A crystal is a solid in which atoms are arranged in
some regular repetition pattern in all directions.”
“Aggregation of molecules with a definite internal
structure and the external form of a solid enclosed
by symmetrically arranged plane faces.”
STRUCTURES
“Structure of anything is defined as the framework of
its body.”
3. Crystal = Lattice+Base
Motif or basis:
Typically an atom or a group of atoms associated with
each lattice point.
Lattice The underlying periodicity of the crystal
Basis Entity associated with each lattice points
Lattice Crystal
Translationally periodic Translationally periodic
arrangement of points. arrangement of motifs.
4. Crystal = Lattice (Where to repeat)
+
Motif (What to repeat)
Crystal
a
=
Lattice
a
+
Motif Note: all parts of the motif do not sit on the lattice
a point
2
5. Let us construct the crystal considered before starting with an
infinite array of points spaced a/2 apart
Put arrow marks pointing up and down alternately on the points:
What we get is a crystal of lattice parameter „a‟ and not „a/2‟!
And the
motif
is: +
6. A strict 1D crystal = 1D lattice + 1D motif
The only kind of 1D motif is a line segment.
An unit cell is a representative unit of the structure
(finite part of a infinite structure) .
Which when repeated gives the whole structure.
Lattice
+
Motif
=
Crystal
7. 2D crystal = 2D lattice + 2D motif
Lattice
+
Motif
b
a
9. 3D crystal = 3D lattice + 3D motifs
CRYSTAL OR SPACE LATTICE
It is defined as an array of points in 3 dimensions
in which every point has surroundings identical to
every other point in array.
According to BRAVAIS there are 14 possible types
of space lattice in 7 basic crystal system
11. a = b= c
= = = 90º
• Simple Cubic (P) - SC
• Body Centred Cubic (I) – BCC
• Face Centred Cubic (F) - FCC
Elements with Cubic structure →
SC: F, O
BCC: Cr, Fe, Nb, K, W
FCC: Al, Ar, Pb, Ni, Ge
12. SIMPLE CUBIC STRUCTURE
• Cubic unit cell is 3D repeat unit
• Rare (only Po has this structure)
• Coordination No. = 6
(# nearest neighbors)
13. a
R=0.5a
close-packed directions
contains 8 x 1/8 =
1 atom/unit cell
Adapted from Fig. 3.19,
Callister 6e.
0.52
Lattice constant
• APF for a simple cubic structure =
15. Unit cell c ontains:
1 + 8 x 1/8
= 2 atoms/unit cell
R
Adapted from a
Fig. 3.2,
Callister 6e.
• APF for a body-centered cubic structure = 3/8 = 0.68
16. FACE CENTERED CUBIC STRUCTURE
Atoms are arranged at the corners and center
of each cube face of the cell.
◦ Atoms are assumed to touch along face diagonals
18. Unit cell c ontains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
a
• APF for a body-centered cubic structure = /(3 2) = 0.74
19. • FCC Unit Cell
• ABCABC... Stacking Sequence
• 2D Projection
A
B B
C
A
A sites B B B
C C
B sites B B
C sites
20. Ideally, c/a = 1.633 for close packing
However, in most metals, c/a ratio deviates from this valu
21. • ABAB... Stacking Sequence
• 3D Projection • 2D Projection
A sites
B sites
A sites
• Coordination NO.= 12
• APF = 0.74, for ideal c/a ratio of 1.633
23. Close packed crystals
A plane
B plane
C plane
A plane
…ABCABCABC… packing …ABABAB… packing
[Face Centered Cubic (FCC)] [Hexagonal Close Packing (HCP)]
24. Examples of elements with Cubic Crystal Structure
Fe Cu
Po
n = 2 BCC n = 4 FCC/CCP
n = 1 SC
n = 8 DC
C (diamond)
25. a=b c
= = = 90º
Simple Tetragonal
Body Centred Tetragonal -BCT
Elements with Tetragonal structure → In, Sn
26. Example of an element with Body Centred Tetragonal Crystal Structure
B
C
T
27. a b c
= = = 90º
Simple Orthorhombic
Body Centred Orthorhombic
Face Centred Orthorhombic
End Centred Orthorhombic
Elements with Orthorhombic structure → Br, Cl, Ga
35. 14 Bravais Lattices divided into 7 Crystal Systems
A Symmetry based concept „Translation‟ based concept
Crystal System Shape of UC Bravais Lattices
P I F C
1 Cubic Cube
2 Tetragonal Square Prism (general height)
3 Orthorhombic Rectangular Prism (general height)
4 Hexagonal 120 Rhombic Prism
5 Trigonal Parallopiped (Equilateral, Equiangular)
6 Monoclinic Parallogramic Prism
7 Triclinic Parallopiped (general)
P Primitive
I Body Centred
F Face Centred
C A/B/C- Centred
36. Face Centred Cubic (FCC) Lattice Two Carbon atom Motif
(0,0,0) & (¼, ¼, ¼)
+
=
Diamond Cubic Crystal