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2. Chapter Learning Objectives
Describe the various point defects in crystalline materials (vacancy, substitutional/interstitial).
Explain concept & geometry of edge & screw dislocation and their strengthening effects.
Identify the likely slip system for a given crystal structure.
Explain the role of grain boundaries and grain size in strengthening polycrystalline materials.
Explain the process of work hardening and its effects on the strength of crystalline materials.
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3. Chapter Outline Sections 4-1 Point Defects 4-2 Other Point Defects
4-3 Dislocations
4-4 Significance of Dislocations
4-5 Schmid’s Law
4-6 Influence of Crystal Structure
4-7 Surface Defects
4-8 Importance of Defects
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4. 4-1 Point Defects
Point defects are localized disruptions in otherwise perfect atomic/ionic arrangements in a crystal structure.
Effects of these disruptions are often felt over the surrounding region.
Often, these defects are caused by the introduction of other atoms/ions into the crystal structure.
Impurities are introduced due to processing conditions (O2 in Si crystals).
Dopants are deliberately introduced to affect properties (Carbon in iron to make steel).
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5. 4-1 Point Defects
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6. 4-1 Point Defects
A vacancy (found in all crystalline materials) is when an atom/ion is missing from its normal site in the crystal structure.
Vacancies increase entropy, and thus thermodynamic stability of crystalline materials.
The vacancy concentration in a material follows an Arrhenius type behavior:
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7. 4-1 Point Defects
An interstitial defect is formed when an extra atom/ion is inserted into the crystal structure at a normally unoccupied position.
Although smaller than atoms at lattice points, interstitial atoms introduce a localized stress in their vicinity.
This stress often strengthens the material. For instance, interstitial carbon atoms in an iron lattice strengthen the iron.
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8. 4-1 Point Defects
A substitutional defect is introduced when one lattice atom/ion is replaced by a different atom/ion.
Substitutional atoms often have different sizes than the regular lattice atoms, disturbing their surroundings.
Substitutional atoms often increase the strength of metallic materials.
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9. 4-2 Other Point Defects
An interstitialcy is created when an atom identical to lattice atoms occupies an interstitial site.
A Frenkel defect is a vacancy-interstitial pair formed when a lattice atom jumps to an interstitial site, leaving behind a vacancy.
A Schottky defect is unique to ionic materials. To preserve electrical neutrality in ionic materials, for any vacancies, a stoichiometric number of cations & anions must be removed from the lattice.
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10. 4-2 Other Point Defects
In ionic solids, when point defects are introduced, the following rules must apply:
A charge balance must be maintained
A mass balance must be maintained
Number of crystallographic sites must be conserved
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11. We use Kröger-Vink notation to write defect chemistry equations.
4-2 Other Point Defects
We use Kröger-Vink notation to write defect chemistry equations.
The main letter describes vacancy/name of element
The superscript indicates effective charge on defect
(·) indicates +1 charge, (‘) indicates -1 charge
x indicates no net charge
Free electrons/holes are indicated by e/h
Subscripts denote location of the defect
Sometimes multiple Kroger-Vink reactions can explain a defect, so experimental verification and energy considerations are required to find the correct one.
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12. Dislocations are line imperfections in an otherwise perfect crystal.
They are present in all materials, including ceramics and polymers.
They are especially useful in explaining deformation & strengthening in metallic materials.
The 3 kinds of dislocations are the screw, edge and mixed dislocations.
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13. 4-3 Dislocations Screw dislocation
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14. 4-3 Dislocations Edge dislocation
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15. 4-3 Dislocations Mixed dislocation
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16. 4-3 Dislocations
The concept of stress, or force per area, is important to understanding the motion of dislocations. The 2 types of stress are:
Normal: force is applied perpendicular to area of interest
Shear: force acts parallel to area of interest
A plane that contains both the dislocation line and the Burgers vector is known as a slip plane.
If a sufficiently large force is applied parallel to the Burgers vector (the slip direction), dislocations can move in a crystal via the slip process.
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17. 4-3 Dislocations
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18. 4-3 Dislocations
In the process of slip, bonds are broken and reformed one row at a time, which is energetically favorable.
The combination of a slip plane and a slip direction forms a slip system.
During slip, a dislocation moves from one set of surroundings to an identical set of surroundings. The Peierls-Nabarro stress is required to move a dislocation between 2 equilibrium positions
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19. 4-3 Dislocations
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20. 4-3 Dislocations
Dislocations move in a slip system which requires the least expenditure of energy. Factors determining most likely active slip systems are:
Slip direction should have high density/small repeat distance.
Slip planes should have a high planar density.
Dislocations do not easily move in materials with covalent/directional bonds
Materials with ionic bonding are also resistant to slip because dislocation movement disrupts charge balance between cations & anions.
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21. 4-3 Dislocations
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22. 4-3 Dislocations
Example 4-7. Planar density of (112) plane in BCC iron is 9.94 x 1018 atoms/m2. Calculate (a) planar density of (110) plane and (b) interplanar spacings for both (112) & (110) planes. On which plane would slip occur?
Lattice parameter of BCC iron is nm. For the (110) plane, ¼ of the 4 corner atoms plus 1 center atom lie within an area of
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23. The interplanar spacings are
4-3 Dislocations
The interplanar spacings are
Planar density is higher and interplanar spacing larger for (110) plane, so (110) plane is the preferred slip plane.
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24. 4-4 Significance of Dislocations
Plastic deformation is the irreversible change in shape when the force/stress causing the change is removed.
Applying stress causes dislocation movement, and cumulative slip of numerous dislocations causes plastic deformation.
However, there are also other mechanisms that cause permanent deformation.
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25. 4-4 Significance of Dislocations
Slip is important in understanding mechanical behavior of metals.
Slip explains why the strength of metals is times lower than predicted from the metallic bond.
Slip provides ductility in metals which enables plastic deformation.
Mechanical properties of metals/alloys can be controlled by interfering with dislocation movement e.g. by adding point defects which prevent slip.
Dislocations can also influence electronic & optical properties of materials.
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26. 4-5 Schmid’s Law
We can understand differences in behaviors of metals with different crystal structures by looking at the force required to initiate the slip process.
In order for a dislocation to move, a shear force/stress acting in the slip direction must be produced by the applied force.
Schmid’s law gives the resolved shear stress in the slip direction , where
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27. 4-5 Schmid’s Law
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28. 4-5 Schmid’s Law
The critical resolved shear stress is the stress required for slip to occur.
Thus, slip occurs when the applied stress equals the critical resolved shear stress
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29. Therefore the rod should be oriented at 45° and 65.3°
4-5 Schmid’s Law
Example 4-9. We want to produce a single crystal rod of aluminum with a CRSS of 1020 kPa. The rod should be oriented so that, upon an axial applied stress of 3447 kPa, the rod deforms by slip in 45° direction to the rod axis. Design the rod.
From Schmid’s Law,
Since
Therefore the rod should be oriented at 45° and 65.3°
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30. 4-6 Influence of Crystal Structure
Schmid’s Law can be used to compare properties of metals having FCC, BCC, and HCP structures.
This discussion is limited to nearly perfect crystals. Engineering materials are rarely perfect crystals, and tend to be polycrystalline.
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31. 4-6 Influence of Crystal Structure
A high CRSS implies a material has high strength. FCC structures have many close-packed planes, and hence low CRSS.
BCC structures have no close-packed planes, high CRSS, and are therefore much stronger than FCC materials.
For HCP materials,
If c/a < 1.633, strength is comparable to BCC.
If c/a > 1.633, strength is similar to FCC systems.
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32. 4-6 Influence of Crystal Structure
The number of slip systems is correlated with the ductility of metals.
HCP systems have few slip systems, hence low ductilities, although there are exceptions.
FCC structures have 12 slip systems, hence they have high ductilities.
BCC structures can have up to 48 slip systems, hence they are very ductile.
A cross-slip occurs when a dislocation moving along one slip systems starts moving in a different slip system when it encounters an obstacle. Cross-slip is possible in FCC & BCC metals, and in HCP metals which have been heated or alloyed.
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33. 4-7 Surface Defects
Surface defects are boundaries/planes which separate a material into regions, which may have same crystal structure but different orientations.
The material’s exterior surface represents surfaces where the crystal abruptly ends. The surface atoms have incomplete bonding, and the surface may be rough and very reactive.
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34. The Hall-Petch equation relates the grain size to yield strength
4-7 Surface Defects
Grain boundaries are narrow zones where the atoms are not properly spaced.
We can increase a material’s strength by reducing grain size/increasing grain boundaries. This way, dislocations can only travel a short distance before stopping.
The Hall-Petch equation relates the grain size to yield strength
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35. 4-7 Surface Defects
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36. One way of specifying the grain size is the ASTM grain size number n
4-7 Surface Defects
One way of specifying the grain size is the ASTM grain size number n
A small angle grain boundary is an array of dislocations that produces a small misorientation between adjacent crystals.
Stacking faults occur in FCC metals, and represent an error in the stacking of close-packed planes.
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37. 4-7 Surface Defects
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38. 4-7 Surface Defects
A twin boundary is a plane across which there is a mirror image misorientation of the crystal structure.
Electronic & magnetic materials contain small regions called domains, where the material’s magnetization/polarization is the same. Domain boundaries can also be considered defects.
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39. 4-7 Surface Defects
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40. 4-8 Importance of Defects
Defects play an important role in controlling the mechanical properties of materials (generally metals) by interfering with slip and strengthening the material.
Defects have less of an effect on the properties of ceramics, which are dictated more by porosity, and on polymers, which are amorphous.
Strain hardening is the process of strengthening a material by deforming it, which increases dislocation density.
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41. 4-8 Importance of Defects
The effects of strain hardening can be reversed by heat treatment/annealing, which decreases dislocation density and increases material ductility.
Solid-solution strengthening takes place when atoms/ions of a guest material are incorporated into the crystal structure. The interstitial/ substitutional atoms are considered as defects.
Grain-size strengthening occurs by increasing the number of grains, or reducing the grain size.
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42. 4-8 Importance of Defects
Point defects can also have a dramatic effect on the optical, magnetic & electrical properties of materials.
In semiconductors, dopants are critical to achieving desired performance; however , defects like dislocations negatively affect properties.
Addition of small amounts of foreign atoms/ions in materials can also be used to produce dramatic color changes in the original material e.g. colored glasses.
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43. Summary
There are 3 types of imperfections/defects in crystalline materials:
Point defects
Line defects or dislocations
Surface defects
The number of vacancies depends on the material’s temperature. Interstitial & substitutional atoms are often deliberately introduced and are typically unaffected by temperature changes.
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44. Summary
Dislocations are line defects that move and cause a metallic material to deform when a force is applied.
The critical resolved shear stress is the stress required to move a dislocation.
The dislocation moves in a slip system, composed of a slip plane & a slip direction.
The slip-direction is typically a close-packed direction. The slip plane is also typically close-packed or nearly close-packed.
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45. Summary
In metallic crystals, the number & type of slip systems influences the metal’s properties.
In FCC metals, critical resolved shear stress is low, leading to an optimum number of slip planes which causes FCC metals to be ductile.
BCC metals have no close-packed planes and have high critical resolved shear stress, which causes BCC metals to be strong.
HCP metals have a limited number of slip systems, which tends to make them brittle.
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46. Summary
Point defects introduce compressive or tensile strain fields which disturb atomic arrangements in the surroundings.
Hence the material is strengthened because dislocations cannot easily slip near point defects.
Surface defects include grain boundaries. Producing a very small grain size increases the grain boundary area.
Because dislocations cannot easily pass through grain boundaries, the material is strengthened (Hall-Petch equation).
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47. Summary
The number & type of defects control the ease of dislocation movement, therefore directly influencing the material’s mechanical properties.
Defects in materials have a significant effect on their electrical, optical & magnetic properties.
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