This presentation discusses the structure of materials from the atomic to macro scale. It describes the crystal structures of metals including body centered cubic, face centered cubic, and hexagonal close packed. The key points covered include the definition of a unit cell, space lattice, coordination numbers, and packing factors for different crystal structures. Common metals exhibiting body centered cubic, face centered cubic, and hexagonal close packed crystal structures are given as examples.

1. A
Presentation
on
Topic : Structure of Materials
Sub Topic : Crystal Structure, Structure of-
Solids, Space lattice, Unit Cell &
Packing factor
By
M.Kiran Kumar M.Tech
CL/Mechanical Dept.
Government Polytechnic, Kataram
MKK_18M-304C_SM_Engg_Mat 1

2. MKK_18M-304C_SM_Engg_Mat
1. Structure of Materials - Introduction
2. Structure of Solids
3.Space Lattice
4. Unit Cell
5. Crystal Structures
6. Primitive & Non-Primitive Cells
7. Packing factor
2
Topics to be covered in this Presentation
2

3. MKK_18M-304C_SM_Engg_Mat 3
• The structure of metals greatly influences their behavior
and properties
•A knowledge of structure guides us in controlling and
predicting behavior of metal in various manufacturing
processes.
All elements can exists as either solids, liquids, or gases
3

4. MKK_18M-304C_SM_Engg_Mat 4
Structure of a solid material
In the order of decreasing magnification, the structure of a
solid material can be expressed as follows:
(i) Atomic structure
(ii) Crystal structure
(iii) Micro structure
(iv) Macro structure

5. MKK_18M-304C_SM_Engg_Mat 5
Atomic structure
- It resembles a miniature solar system
- It may considered as a tiny sphere
- Atom consists of nucleus and the Electrons
- Nucleus is situated at the centre and carrying net positive
charge
- Electron revolve around the nucleus in definite orbits

6. MKK_18M-304C_SM_Engg_Mat 6
Fig 1

7. MKK_18M-304C_SM_Engg_Mat 7
Grouping of Atoms
 Metallic properties depend, not only on the nature of
atoms, but also on the manner in which atom have been
assembled
 Depending upon their grouping materials
classified into 3 categories
- Molecules structure
- Crystal structure
- Amorphous structure

8. MKK_18M-304C_SM_Engg_Mat 8
Molecules structure
• In forms when a limited no. of atoms come together and
get strongly bonded to one another
• Resulting groups are called molecules
Ex: H2o, Co2, CCl4, O2, N2 etc
• With in these molecules, the atoms are held together by
strong attractive forces that usually have covalent or ionic
bonds

9. MKK_18M-304C_SM_Engg_Mat 9
Crystal Structure
 Atomic arrangements which have a repetitive pattern in
all the three dimension of space called Crystal structure
or crystals
 Fundamental unit of the arrangement repeats itself at
intervals in three dimension
 Most of the metals are crystalline
Ex Iron, copper aluminium, zinc etc

10. MKK_18M-304C_SM_Engg_Mat 10
Amorphous Structure
 When atoms do not have long range repetitive pattern of
arrangement are called amorphous structure
 Pattern breaks at different places
 Common examples of this group are glasses and
polymers

11. MKK_18M-304C_SM_Engg_Mat 11
Structure of Metals Vs Polymers
 Metals, ceramics are arregates of atoms which can be
regarded as arrays of hard and spherical atoms in three
directions of space
 Polymers form long flexible chain in which molecules are
twisted up and inter- twined with each other

12. MKK_18M-304C_SM_Engg_Mat 12
Micro Structure
 The appearance of structure of a material under a
microscope is called Micro structure
 Micro structure of a material consists of phase structure
and grain structure
 Phase structure expresses various phases present
 Grain structure shape and size of grains (crystals) which
form material
 Typical examples of grains structure are columnar,
dendritic and equiaxed grain

13. MKK_18M-304C_SM_Engg_Mat 13
Macro Structure
 The appearance of the structure of materials with naked
eye is called Macro structure

14. MKK_18M-304C_SM_Engg_Mat 14
Crystalline Solids
 Two types of crystalline structure
i. Single crystalline
ii. polycrystalline
14

15. MKK_18M-304C_SM_Engg_Mat 15
Crystalline solids
 In a single crystalline the atomic pattern is continuous
 Eg .Silicon and Quartz
 In a poly crystalline, several crystals are bonded together
 Most of engineering materials are polycrystalline solids
15

16. MKK_18M-304C_SM_Engg_Mat 16
Anisotropy And Isotropy
 The un equality of properties in various crystallographic
directions is called anisotropy
 Displaying the same properties in any direction or a plane
is called isotropy
16

17. MKK_18M-304C_SM_Engg_Mat 17
Space Lattice
 Lattice is the regular geometrical arrangement of
atoms in crystal space
 The imaginary lines that connect lattice points in a
configuration is called space lattice
17
Fig.2
• Space lattice is a three dimensional network of
imaginary lines connecting the atoms.

18. MKK_18M-304C_SM_Engg_Mat 18
Unit Cell
 The smallest unit having the full symmetry of the crystal is
called the unit cell
 A unit cell is specified by three intercepts a, b, &c
 Crystallographic axis X, Y and Z
 Interfacial angles α, β and
 These specifications are called lattice parameters of unit
cell
18


19. MKK_18M-304C_SM_Engg_Mat 19
Unit Cell
b
c
19
Fig.3
Z
Y
X
a



b
c

20. MKK_18M-304C_SM_Engg_Mat 20
Parameters of Unit Cell
 Shape and size of the unit cell is given by six lattice
parameters a, b, c, α, β, and γ
 Depending upon the relation between these parameters,
the unit cell can be divided into seven groups, know as
crystal system
 The simple crystal system is cubic system
where a=b=c and α=β=γ=900

21. MKK_18M-304C_SM_Engg_Mat 21
Lattice Parameters of a Unit Cell
Z
Y
X
a


 b
c
Fig 1

22. MKK_18M-304C_SM_Engg_Mat 22
Crystal system
 There are seven different types of crystal systems
 Depending upon the basic arrangement of atoms within a
unit cell, crystal systems are sub-divided into 14 types

23. MKK_18M-304C_SM_Engg_Mat 23
Basic Arrangements for Atoms in a Unit Cell
 There are 4 different basic arrangements for atoms within
a cell
1. Simple arrangements with lattice points
only at cell corners
2. End centered arrangements with lattice points
centered on the opposite faces or ends of the crystal
3. Face centered arrangements with lattice points
centered on all faces of the crystal
4. Body centered arrangements with lattice points at
the centre of volume of the unit cell

24. MKK_18M-304C_SM_Engg_Mat 24
Basic Arrangements for Atoms in a Unit Cell

25. MKK_18M-304C_SM_Engg_Mat 25
Fig 2

26. MKK_18M-304C_SM_Engg_Mat 26
Fig 3

27. MKK_18M-304C_SM_Engg_Mat 27
Fig 4

28. MKK_18M-304C_SM_Engg_Mat 28
Fig 5

29. MKK_18M-304C_SM_Engg_Mat 29
Fig 6

30. MKK_18M-304C_SM_Engg_Mat 30
Bravais lattices
30
Fig.7

31. MKK_18M-304C_SM_Engg_Mat 31
Typical Crystal Structure of Common Metals
S.No
1.
2.
3.
Crystal structure
Body centered
cubic BCC
Face centered
cubic
Close packed
Hexagonal
Typical metals
Cr, α-Fe, Mo, W
Al, Cu, Au, Ag, Pb,γ-
Fe
Co, Cd, Zn, Mg

32. MKK_18M-304C_SM_Engg_Mat 32
No. of Atoms Per Unit Cell
 Total no. of atoms per unit cell is given by following equation
Ni = No of atoms per unit cell
Nf = No. of atoms on faces
Nc = no. of atoms on corners
8
2
c
f N
N
Ni
N 



33. MKK_18M-304C_SM_Engg_Mat 33
Primitive Vs Non Primitive cells
 Unit cells containing only one atom per unit cell are called
Primitive cells
 Unit cells containing more than one atom per unit cell are
called non Primitive cells

34. MKK_18M-304C_SM_Engg_Mat 34
Body Centered Cubic Structure
 In BCC structure the atoms are located at the corners
and one atom at the centre of cube
 Each corner atom is shared by 8- Unit cells
 The effective number of atoms in BCC structure are two
Eg :-Vanadium , molybdenum, tungsten etc…
34

35. MKK_18M-304C_SM_Engg_Mat 35
35
Body Centered Cubic Structure
Fig.8

36. MKK_18M-304C_SM_Engg_Mat 36
BCC Unit Cell
FIG.9

37. MKK_18M-304C_SM_Engg_Mat 37
Fig 10

38. MKK_18M-304C_SM_Engg_Mat 38
Fig 11

39. MKK_18M-304C_SM_Engg_Mat 39
Effective No Of Atoms In BCC Unit Cell
 Central atom = 1
 Corner atoms = 8x1/8 =1
(shared by 8 adjacent cells)
 Total effective no of atoms =1+1= 2

40. MKK_18M-304C_SM_Engg_Mat 40
• In FCC cubic structure, there is one atom at each
corner of cube and one atom at the centre of each
face of the cube.
 The effective number of atoms in FCC structure are
four
Eg :- copper , silver , gold ,
aluminum and γ – iron etc….
 Metals with FCC structure possess
good ductility
40
Face Centered Cubic structure

41. MKK_18M-304C_SM_Engg_Mat 41
Fig 12

42. MKK_18M-304C_SM_Engg_Mat 42
Fig 13

43. MKK_18M-304C_SM_Engg_Mat 43
Face Centered Cubic Structure
43
Fig.14

44. MKK_18M-304C_SM_Engg_Mat 44
FCC Unit Cell
FIG.15

45. MKK_18M-304C_SM_Engg_Mat 45
 Corner atoms = 8x1/8=1
(shared by 8 adjacent cells)
 Face atoms =6x1/2=3
(shared by 6 faces)
Therefore total effective no. of atoms =1+3=4
Effective no. of atoms in FCC unit cell

46. MKK_18M-304C_SM_Engg_Mat 46
HCP Structure (CPH Structure)
 The HCP structure is in the shape of a right hexagonal
Prism
 The effective number of atoms in HCP structure are-6.
 E.g.: Zinc, Cadmium, Beryllium, Zirconium etc…are
examples of HCP structure.
 Packing of three body centered rhombohedral constitute
the shape of hexagonal
46

47. MKK_18M-304C_SM_Engg_Mat 47
Fig 16

48. MKK_18M-304C_SM_Engg_Mat 48
Close Packed Hexagonal Structure
48
Fig.17

49. MKK_18M-304C_SM_Engg_Mat 49
Coordination Numbers for Different Crystal
Structures
 The no- of nearest surrounding neighbours of any atom is
called the Coordination Numbers
 More closely packed atoms in the lattice will have higher
Coordination Numbers
S.No Crystal structure Coordination numbers
1. BCC 8
2. FCC 12
3. HCP 12

50. MKK_18M-304C_SM_Engg_Mat 50
Packing Factor
 It is the ratio between the total volume of atoms in the
cell and the cell volume is called packing factor.
 It is useful in computing the density of material
 Packing factor =
50
atoms
cells
V
V

51. MKK_18M-304C_SM_Engg_Mat 51
APF =
For simple cube
 3
3
2
3
4
1
r
r
X
APF








52
.
0

Where r = atomic radius
No. of atoms per unit cell x Volume of one atom
Volume of unit cell
Packing Factor

52. MKK_18M-304C_SM_Engg_Mat 52
 Packing factor for BCC structure is 0.68
 Packing factor for FCC structure is 0.74
 Packing factor for HCP structure is 0.74
M403.14 52
Packing Factor

53. Thank you
MKK_18M-304C_SM_Engg_Mat 53