1. Properties of engineering materials

2. materials Metals (ferrous and non ferrous) Ceramics Polymers
Composites
Advanced (biomaterials, semi conductors)

3. Properties Optical Electrical Thermal Mechanical Magnetic
Deteriorative

4. The Structure of Crystalline Solids
- Crystalline : atoms/ crystals
Non crystalline or amorphous
Solidification?

5. Packing of crystals: Non dense =random Dense = regular

6. Unit cell and lattice parameters
Unit cell : small repeated entities
It is the basic structural unit or building block of the crystal structure
Its geometry is defined in terms of 6 lattice parameters:
3 edges length (a, b, c)
3 interaxial angles

7. Unit cell parameters

9. Metallic crystals 3 crystal structures: Face-Centered Cubic FCC
Body-Centered Cubic BCC
Hexagonal close-packed HCP
Characterization of Crystal structure:
Number of atoms per unit cell
Coordination number (Number of nearest neighbor or touching atoms)
Atomic Packing Factor (APF) : what fraction of the cube is occupied by the atoms

10. The Body-Centered Cubic Crystal Structure
Coordination no. = ?
Number of atoms per unit cell = ? ?
what fraction of the cube is occupied by the atoms or Atomic packing factor

11. The Body-Centered Cubic Crystal Structure

12. APF = 0.68 solve ? Relation between r and a

13. Solution

14. The Face-Centered Cubic Crystal Structure
Coordination no. = ?
Number of atoms per unit cell = ? ?
what fraction of the cube is occupied by the atoms or Atomic packing factor

15. The Face-Centered Cubic Crystal Structure

16. APF = 0.74 solve ? Relation between r and a

17. Solution

18. The Hexagonal Close-Packed Crystal Structure

19. HCP
The coordination number and APF for HCP crystal structure are same as for FCC: 12 and 0.74, respectively.
HCP metal includes: cadmium, magnesium, titanium, and zinc.

20. Examples

21. Polymorphism

22. THEORETICAL DENSITY

23. Crystallographic Points, Directions, and Planes

24. POINT COORDINATES
Point position specified in terms of its coordinates as fractional multiples of the unit cell edge lengths
( i.e., in terms of a b and c)
0,0,0 Z Y X
1,1,1

25. Solve point coordinates (2,3,5,9)

26. solution

27. Crystallographic directions
1- A vector of convenient length is positioned such that it passes through the origin of the coordinate system. Any vector may be translated throughout the crystal lattice without alteration, if parallelism is maintained. 2. The length of the vector projection on each of the three axes is determined; these are measured in terms of the unit cell dimensions a, b, and c. 3. These three numbers are multiplied or divided by a common factor to reduce them to the smallest integer. 4. The three indices, not separated by commas, are enclosed as [uvw]. The u, v, and w integers correspond to the reduced projections along x, y, and z axes, respectively.

28. Example

29. Solution

30. Z Y X
[0 1 0]
[1 0 1]

31. Planes ( miller indices)
1- If the plane passes through the selected origin, either another parallel plane
must be constructed within the unit cell by an appropriate translation, or a
new origin must be established at the corner of another unit cell.
2. At this point the crystallographic plane either intersects or parallels each of
the three axes; the length of the planar intercept for each axis is determined
in terms of the lattice parameters a, b, and c.
3. The reciprocals of these numbers are taken. A plane that parallels an axis
may be considered to have an infinite intercept, and, therefore, a zero index.
4. If necessary, these three numbers are changed to the set of smallest integers
by multiplication or division by a common factor.
5. Finally, the integer indices, not separated by commas, are enclosed within
parentheses, thus: (hkl).

32. example

33. Solution

34. Example : solve Z Y X

35. solve z x y a b c z x y a b c

36. Crystallographic Planesz x y a b c
example
a b c
Intercepts 
Reciprocals
1/ / /
Reduction
Miller Indices (110)
example
a b c z x y a b c
Intercepts
1/  
Reciprocals
1/½ 1/ 1/
Reduction
Miller Indices (100)

37. Crystallographic Planesz x y a b c
example
a b c
Intercepts
1/ /4
Reciprocals
1/½ 1/ /¾ /3
Reduction
Miller Indices (634)

38. FCC Stacking Sequence
repeated every third plane

39. (HCP)
repeated every second plane

40. Polycrystals
• Most engineering materials are polycrystals.
1 mm

41. The various stages in solidification of polycrystalline
materials.
Polycrystalline crystalline solids composed of many crystals or grains.
Various stages in solidification:
Small crystallite nuclei
Growth of the crystallites; of obstruction of some grains that are adjacent to one another is also shown.
c. Upon completion of solidification, grains that are adjacent to one another is also shown.
d. Grain structure as it would
appear under the microscope.

42. Anisotropy
Physical properties (e.g., Elastic modulus, index of refraction) of single crystals of some substances depend on crystallographic direction in which measurements are taken (i.e., anisotropy).
It results from variation of atomic or ionic spacing with crystallographic direction.
Isotropic materials: Substances in which measured properties are independent of the direction of measurement.

44. X – ray diffraction

45. X ray diffraction

47. BCC crystal structure, h+ k+ l must be even
Case study: explain why?
Group of four . Dead line: 30/12/ 2015
BCC crystal structure, h+ k+ l must be even
FCC, h, k, and l must all be either odd or even

49. Linear and Planar Densities
Atomic linear density:
LD = number of atoms centered on direction vector / length of direction vector
Planar density: Fraction of total crystallographic plane area that is occupied by atoms (represented as circles).
PD = number of atoms centered on a plane / area of plane
Linear and planar densities are important for deformation

50. Indices?

51. notes for cubic crystals
Planes having the same indices, irrespective of the order and sign are equivalent. For example, both (123) and (312) belong to the family ( 123)