crystal structure

1. Venue:
Presented
By
Dr. Walmik Sadashiv Rathod
Department of Mechanical Engineering,
V. J. T. I., Matunga, Mumbai-400019
Contact Numbers:
Cell - # 91 – 9892201145 Office - # 91 - 22 - 2419 8229
wsrathod@vjti.org.in
wsrathod@me.vjti.ac.in
Friday, 21st, Aug-2020.
GOOGLE MEET
CRYSTAL STRUCTURE AND
METALLURGICAL APPLICATIONS

2. Atoms
Crystals (Unit Cells)
Grains
Final Metal

3. Important
properties of
the unit cells
are
R
Radius of the Atom
Cell Dimensions
Side a in cubic cells, side
of base a and height c in
HCP in terms of R.
N
Number of atoms per unit
cell. For an atom that is
shared with m adjacent unit
cells, we only count a
fraction of the atom, 1/m.
CN
The coordination number,
which is the number of
closest neighbors to which
an atom is bonded.
APF
The atomic packing factor,
which is the fraction of the
volume of the cell actually
occupied by the hard
spheres. APF = Sum of
atomic volumes/Volume of
cell.

4. Crystalline solid Amorphous solid

7. FACE CENTERED CUBIC STRUCTURE
(FCC)
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
Coordination # = 12
Atoms touch each other along face diagonals.
example: Al, Cu, Au, Pb, Ni, Pt, Ag
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
In FCC atoms located at each of the corners and the
centers of all the cube faces. This is called the face-
centered cubic (FCC) crystal structure.

8. ATOMIC PACKING FACTOR: FCC
Unit cell contains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
a
2 a
APF =
4
3
p ( 2 a/4 )3
4
atoms
unit cell atom
volume
a 3
unit cell
volume
• APF for a face-centered cubic structure = 0.74

9. • Coordination # = 8
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.
BODY CENTERED CUBIC STRUCTURE
• Atoms touch each other along cube diagonals.
example: Cr, W, Fe (), Tantalum, Molybdenum
2 atoms/unit cell: 1 center + 8 corners x 1/8
In BCC atoms located at all eight corners and a single atom at
the cube center. This is called a body-centered cubic (BCC)
crystal structure.

10. ATOMIC PACKING FACTOR: BCC
Unit cell c ontains:
1 + 8 x 1/8
= 2 atoms/unit cell
• APF for a body-centered cubic structure = p3/8 =
0.68
a
R

11. Hexagonal Close-Packed Structure (HCP)
• ABAB... Stacking Sequence
• 3D Projection
• 2D Projection
c
a
A sites
B sites
A sites Bottom layer
Middle layer
Top layer
• Coordination # = 12
• APF = 0.74
• c/a = 1.633
6 atoms/unit cell ex: Cd, Mg, Ti, Zn

12. Type of
Crystal
Body
Centered
Cubic(BCC)
Face
Centered
Cubic (FCC)
Hexagonal
Close Packed
(HCP)
Properties
Atomic
Packing
Fraction
0.68 0.74 0.68
Coordination
Number
12 8 12
Close Packing
Direction
Body Diagonal Face Diagonal Hexagonal
Side
Examples Fe, Cr, Cu, Au, Ag, Zn,

13. Close packed crystals
…ABCABCABC… packing
[Face Centered Cubic (FCC)]
…ABABAB… packing
[Hexagonal Close Packing (HCP)]
A plane
B plane
C plane
A plane

16. ATOMIC ARRANGEMENT IN CRYSTALS

18.  Single Crystals
An object composed of randomly
oriented crystals, formed by
rapid solidification
A single crystal is formed by the growth of a crystal
nucleus without secondary nucleation or impingement on
other crystals.
 Polycrystals
--If grains are textured, anisotropic.
--Properties vary with direction: anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron:
--Properties may/may not vary with
direction.
ISOTROPIC MATERIALS
ANISOTROPIC MATERIALS MICROSTRUCTURE
--If grains are randomly oriented: isotropic.
(Epoly iron = 210 GPa)

19. Cooling Nucleation
Grain
Formation

21. Nucleation is the process of forming a nucleus. It is the initial process in
crystallization. Nucleation is the extremely localized budding of a distinct
thermodynamic phase. It is the process in which ions, atoms, or molecules
arrange themselves in a pattern characteristic of a crystalline solid, forming a
site in which additional particles deposit as the crystal grows.
A good example is the famous Diet Coke and Mentos eruption. Nucleation
normally occurs at nucleation sites on surfaces contacting the liquid or vapor.

23. Grain formation is the process by which the nuclides having the same orientation merge
together to form larger grains. It is the final stage in the process of solidification. If
the grain formation is made to take place in a controlled temperature gradient system,
it gives rise to a Single Crystal Metal structure which has uniform properties in all
directions and has a very few number of crystal imperfections. Such metals are used in
Aeronautical, Hydropower and Military Applications which require precise strength,
hardness and other factors.

24. Cooling processes are very important in determining
the properties of the metal that is obtained. If the
cooling takes place in a slow manner, the grain size is
generally bigger. This can also play a vital role in heat
treatment of metals and alloys for industrial
applications.
COARSE /BIGGER GRAIN SIZE

25. If the cooling takes place instantaneously (FAST), like in the
process of quenching, the grain size is generally finer. This
can also play a vital role in heat treatment of metals and
alloys for industrial applications.
FINER GRAIN SIZE

26. RAPID /FAST COOLING
More hardness
More tensile strength
More grain boundary
More grain area/volume
Less machineabilty due
fine/more grains
SLOW COOLING
Less hardness
Less tensile strength
Less grain boundary
Less grain area/volume
More machineabilty due to
coarse /less grains
COARSE /BIGGER GRAIN SIZE FINER GRAIN SIZE

27.  Miller indices - A shorthand notation to describe certain
crystallographic directions and planes in a material.
Denoted by [ ], <>, ( ) brackets. A negative number is
represented by a bar over the number.
Points, Directions and Planes in the
Unit Cell

28. • Coordinates of selected points in the unit cell.
• The number refers to the distance from the origin in terms
of lattice parameters.
Point Coordinates

29. Point Coordinates
Point coordinates for unit cell
center are
a/2, b/2, c/2 ½ ½ ½
Point coordinates for unit cell
corner are 111
Translation: integer multiple of
lattice constants 
identical position in another
unit cell
z
x
y
a b
c
000
111
y
z

2c



b
b

30. Determine the Miller indices of directions A, B, and C.
Miller Indices, Directions
(c) 2003 Brooks/Cole Publishing /
Thomson Learning™

31. SOLUTION
Direction A
1. Two points are 1, 0, 0, and 0, 0, 0
2. 1, 0, 0, -0, 0, 0 = 1, 0, 0
3. No fractions to clear or integers to reduce
4. [100]
Direction B
1. Two points are 1, 1, 1 and 0, 0, 0
2. 1, 1, 1, -0, 0, 0 = 1, 1, 1
3. No fractions to clear or integers to reduce
4. [111]
Direction C
1. Two points are 0, 0, 1 and 1/2, 1, 0
2. 0, 0, 1 -1/2, 1, 0 = -1/2, -1, 1
3. 2(-1/2, -1, 1) = -1, -2, 2
2]
2
1
[
.
4

32. Crystallographic Directions
1. Vector repositioned (if necessary) to pass
through origin.
2. Read off projections in terms of
unit cell dimensions a, b, and c
3. Adjust to smallest integer values
4. Enclose in square brackets, no commas
[uvw]
ex: 1, 0, ½ => 2, 0, 1 => [201]
-1, 1, 1
z
x
Algorithm
where overbar represents a
negative index
[111]
=>
y

33.  For some crystal structures, several nonparallel directions with
different indices are crystallographically equivalent; this means that
atom spacing along each direction is the same.
Families of Directions <uvw>

34.  If the plane passes thru origin, either:
 Construct another plane, or
 Create a new origin
 Then, for each axis, decide whether plane intersects or parallels the axis.
 Algorithm for Miller indices
1. Read off intercepts of plane with axes
in terms of a, b, c
2. Take reciprocals of intercepts
3. Reduce to smallest integer values
4. Enclose in parentheses, no commas.
Crystallographic Planes

35. Crystallographic Planes
• Crystallographic planes are specified by 3 Miller
Indices (h k l). All parallel planes have same Miller
indices.

36. Crystallographic Planes z
x
y
a b
c
4. Miller Indices (110)
Example a b c
z
x
y
a b
c
4. Miller Indices (200)
1. Intercepts 1 1 
2. Reciprocals 1/1 1/1 1/
1 1 0
3. Reduction 1 1 0
1. Intercepts 1/2  
2. Reciprocals 1/½ 1/ 1/
2 0 0
3. Reduction 2 0 0
Example a b c

37. Crystallographic Planes
z
x
y
a b
c



4. Miller Indices (634)
Example
1. Intercepts 1/2 1 3/4
a b c
2. Reciprocals 1/½ 1/1 1/¾
2 1 4/3
3. Reduction 6 3 4

38. Family of Planes
 Planes that are crystallographically equivalent have the same atomic
packing.
 Also, in cubic systems only, planes having the same indices, regardless of
order and sign, are equivalent.
 Ex: {111}
= (111), (111), (111), (111), (111), (111), (111), (111)
(001)
(010), (100), (010),
(001),
Ex: {100} = (100),

39. FCC Unit Cell with (110) plane

40. BCC Unit Cell with (110) plane

41. SUMMARY
Crystallographic points, directions and planes are
specified in terms of indexing schemes.
Materials can be single crystals or polycrystalline.
Material properties generally vary with single
crystal orientation (anisotropic), but are
generally non-directional (isotropic) in
polycrystals with randomly oriented grains.
Some materials can have more than one crystal
structure. This is referred to as polymorphism (or
allotropy).

43. Tungsten Carbide (WC)

44. Cementite

45. Martensite

46. Aluminium Oxide