Material science

1. Imperfections or defects in Solids

4. 4. Three dimensional or Volume or bulk defects: Cracks, Voids, foreign inclusions

24. Simple cubic lattice  Front view
Imagine them as pack of cards.

31. This seems to planar defect right, as it can be seen as a extra half plane of atoms
are inserted or there is a missing of half plane of atom? But why it is called as
line defect??

32. Hiding the lower part of the crystal, See Now it is not an extra half plane, it is part of
The perfect crystal.

34. So, either missing half plane or extra half plane is not a defect.

35. Defect is concentrated only to the circled region where the extra half plane is suddenly
Ended. So this sudden abrupt ending is creating the problem not the whole plane of atoms.
So defect is only at the bottom edge of the extra half plane of atoms.

36. Draw a line close to the bottom edge and this will represent the defect named it as
Dislocation line.

37. Since this dislocation line is at the bottom edge of the extra half plane it is named as
Edge dislocation line.

39. We may think the effected region as a defect, but if extend it to the 3d, the length of this
Region (cylinder ) is very much higher than the dia. It is like a long thread, that’s why it
Is a linear defect.

46. More general way of defining dislocation

50. Model: We can see extra half plane of atoms

51. The line formed by marker at the edge of half plane of atoms represents the
edge dislocation line. The dislocation line is going parallel to the bottom edge of the
Half plane of atoms. Which way in space the dislocation line is oriented? It is given by
Tangent vector.

52. The plane through the pen represents the slip plane. Which is going inside the crystal.
On the left hand side and above the slip plane, the first plane of atoms are missing, which
Are bonded with the second plane of atoms of below slip plane atoms. The magnitude of this
Slip is inter planar or inter atomic spacing and the direction is horizontal. This magnitude and
Direction of the slip is called Burger vector of dislocation line.

53. These two vectors, tangent vector and burger vector characterize the dislocation line.
Tangent vector in slip plane is represented with a unit tangent vector t, which is parallel or
tangent to the dislocation line.

55. Classification of dislocations

56. Cap represents the burger vector and the black pen represents the dislocation line or tangent
Vector. We can see that burger vector and dislocation line are orthogonal (perpendicular to
Each other.

62. The vertical plane represents the slip plane. And it divides the crystal structure into two halves.
Right side slipping w.r.t to left side but it is confined only to front side of slip plane.

63. The name screw comes from the fact that, if we try to make a circuit on the top face
Of the crystal, starting from a point and going clockwise on the top , we can see that
We will not reach the starting point at the end instead it will end next down plane.
All these planes connected like a single spiral.

65. Front side, we can see the slip in the planes (right hand side and right hand side have a slip
w.r.t to each other.

67. We can see at the back side, there is no slip. Crystal is perfect.

68. 2D Defects:
Interfacial defects are boundaries that have two dimensions and normally separate
regions of the materials that have different crystal structures and/or crystallographic
orientations.
These imperfections include external surfaces, grain boundaries, twin boundaries, stacking
faults, and phase boundaries.
External Surfaces
Obvious boundaries is the external surface, along which the crystal structure terminates.
Surface atoms are not bonded to the maximum number of nearest neighbors, and
are therefore in a higher energy state than the atoms at interior positions.
The bonds of these surface atoms that are not satisfied give rise to a surface
energy, expressed in units of energy per unit area (J/m2 or erg/cm2).

69. Grain Boundaries
The boundary separating two small grains or crystals having different crystallographic
orientations in polycrystalline materials.
Various degrees of crystallographic
misalignment between adjacent grains are
possible.
When this orientation mismatch is slight, on
the order of a few degrees (< 5 °), then the
term small- (or low- ) angle grain boundary is
used, if mismatch is greater the term high
angle grain boundary is used

70. The atoms are bonded less regularly along a grain boundary (e.g., bond angles are longer), and
consequently, there is an interfacial or grain boundary energy similar to the surface energy .
The magnitude of this energy is a function of the degree of misorientation, being larger for high-
angle boundaries.
Grain boundaries are more chemically reactive than the grains themselves as a consequence of
this boundary energy.
Furthermore, impurity atoms often preferentially segregate along these boundaries because of
their higher energy state. (as material always tries to be in lower energy state)
The total interfacial energy is lower in large or coarse-grained materials than in fine-grained
ones, since there is less total boundary area in the former.

71. Twin Boundaries
A twin boundary is a special type of grain boundary across which there is a specific mirror lattice
symmetry; that is, atoms on one side of the boundary are located in mirror-image positions of
the atoms on the other side .
The region of material between these boundaries is appropriately termed a twin.
Twins result from atomic displacements that are produced from applied mechanical shear
forces (mechanical twins), and also during annealing heat treatments following deformation
(annealing twins).

72. Lattice structures are described by stacking of identical planes of atoms one over the other in a
definite manner.
Simple cubic, BCC and FCC are described by stacking of open planes in a manner A A A A …. And
AB AB AB AB… . And ABC ABC ABC ABC…. Respectively.
Stacking faluts result form the stacking of one atomic plane out of sequence on another and the
lattice on either side of the fault is perfect.
The stacking sequence in an ideal FCC crystal is ABC ABC ABC…. . A stacking fault may change the
above sequence to ABC ABC AB ABC ABC….
The stacking fault in this case is due to the missing of C Plane of atoms after the eighth (8th)
plane.
Stacking Faults

73. BULK OR VOLUME DEFECTS
Other defects exist in all solid materials that are much larger than those heretofore
discussed.
These include pores, cracks, foreign inclusions, and other phases. They are normally
introduced during processing and fabrication steps.

74. Liquid metals, with few exceptions, undergo a contraction in volume due to solidification. This
decrease in volume may be as much as 6 percent.
In a properly designed mold, with provision for liquid supply to the portion that solidifies last,
the contraction in volume presents no serious problem.
If, however, the entire exterior of the casting should solidify first, the decrease in volume of the
interior during solidification will result in a large shrinkage cavity at the mid-section.
In the solidification of steel ingots, the shrinkage cavity, called pipe, is usually concentrated in
the top central portion of the ingot. This portion is cut off and discarded before working.
Porosity or blowholes occur whenever gases are trapped in the casting. They are Usually more
numerous and smaller than shrinkage cavities and may be distinguished by their rounded form.
Air may be entrapped in the casting by the sudden rush of metal during pouring. Since gases are
generally more soluble in liquid metal than the solid, dissolved gases may be liberated during
solidification. Gases may also be produced by reaction of the liquid metal with volatile
substances, such as moisture, in the mold .
Porosity may be greatly reduced by proper venting of the mold, and by not unduly compacting
the sand
Hot tears are cracks are due to heavy shrinkage strains set up in the solid
casting just after solidification.