1. Imperfections in Solids
Chapter 4
Imperfections in Solids

2. Imperfections in Solids
Why Study Imperfections in Solids?
The properties are profoundly influenced by the presence of imperfections.
Pure metals + Impurities Alloys
Sterling Silver (92.5% Silver, 7.5% Copper) is much harder and stronger than pure silver

3. Introduction Perfect order in solids does not exist.
All solids contain large number of various defects (imperfections).
Many material properties are profoundly sensitive to deviations from crystalline perfection.

4. Introduction (Cont.) Crystalline defect: A lattice irregularity
Defects are classified according to geometry or dimensionality of the defect: (1) Point defect (associated with one or two atomic position), (2) Linear (one dimensional), (3) Interfacial defects or boundaries (Two dimensional), (4) Bulk or volume (three dimensional).

5. TYPES OF IMPERFECTIONS
• Vacancy atoms
• Interstitial atoms
• impurities
Point defects
Line defects
Area defects
• Dislocations
• Grain Boundaries

6. (1) Point Defects 1. Vacancy vacant lattice sites in a structure.
All crystalline solids contain vacancy, presence of vacancies increases the entropy (randomness) of the crystal (preferable).
Impossible to create a material without vacancies.

7. Vacancies and Self-Interstitials

8. Distortion of Atomic Planes Due to Point Defects

9. Equilibrium Number of Vacancies
Equilibrium number of vacancies Nv:
Where: N is the number of atomic sites, Qv is the activation energy for vacancy formation, K is Boltzmann’s constant, and T is absolute temperature.
For most metals, Nv/N is of the order of 10-4 (just below the melting temperature).

10. Cont…..
Find the equil. # of vacancies in 1m of Cu at 1000C. Given: K= 8.62x 10-5 ev/atom.K Avog. Number: 6.023X1023 atoms/mol

11. Estimating Vacancy Concentration3
Find the equil. # of vacancies in 1m of Cu at 1000C.
• Given:
• Answer:

12. 2. Self-interstitial "extra" atoms positioned between atomic sites.
It introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated.
THUS: Its formation is not highly probable, it exists in small concentrations (lower than vacancies).

13. 3. Impurities
Pure metal is not possible. Impurity (foreign) atoms will always be present.

14. Impurities (Cont.)
Addition of impurity atoms to a metal results in formation of solid solution AND/OR new second phase (Depending on: Kind of impurity, Impurity concentration, Temperature of the alloy).
Solvent: Element or compound that is present in the greatest amount (host atoms).
Solute: Element or compound present in minor concentrations.

15. Impurities (Cont.)
Solid solution: It forms when solute atoms are added to host material.
Features of solid solutions:
Crystal structure is maintained.
No new structure is formed.
Homogenous composition (impurity atoms are randomly and uniformly dispersed within the solid).

16. Impurities (Cont.) Types of impurity point defects:
(1) Substitutional (Impurity atoms substitute or replace for the host atoms).
(2) Interstitial
Features of solute and solvent atoms that determine degree to which solute dissolves in solvent: Atomic factor size, Crystal structure, Electronegativity, Valences.

17. Substitutional & Interstitial Impurity Atoms

18. Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects) OR
Substitutional alloy
(e.g., Cu in Ni)
Interstitial alloy
(e.g., C in Fe)
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
--different composition
--often different structure.

19. Impurities in Solids (Contd.) SPECIFICATION OF COMPOSITION
Two most common ways to specify the composition or concentration are Weight or mass percent: weight of a particular element relative to the total alloy weight.
Weight %: C1 = {m1 / (m1+ m2)} x 100
where m1 and m2 represent the weight or mass of elements.
Atom percent: number of moles of an element in relation to the total moles of the elements in the alloy.
Atom %: C1' = {nm1 / (nm1 + nm2)} x 100
where No. of moles (nm) = {(mass in grams) / Atomic weight )

20. SPECIFICATION OF COMPOSITION (Contd.)
COMPOSITION CONVERSIONS
Weight% to Atom% C1

21. SPECIFICATION OF COMPOSITION (Contd.)
Weight% to Kg/m3 (mass of one component per unit volume of material)

22. SPECIFICATION OF COMPOSITION (Contd.)
Density and Atomic Weight of Binary Alloy

23. (2) Dislocations-Linear Defects
Dislocation: Linear (1-D) around which some of the atoms are misaligned.
Types
Edge
Screw
Mixed
Most dislocations are of mixed type.

24. MISCELLANEOUS IMPERFECTIONS Dislocations __ Linear Defects
Dislocation is a linear or one dimensional defect around which some of the atoms are misaligned.
Edge dislocation: An extra portion of a plane of atoms, or half plane, the edge of which terminates within the crystal. Dislocation line: For the edge dislocation in Figure, it is perpendicular to the plane of the paper.

25. Screw Dislocation: May be thought of as being formed by a shear stress that is applied to produce the distortion as shown
The upper front region of the crystal is shifted one atomic distance to the right relation to the bottom portion.
Atomic distortion is also linear and along a dislocation line, Line AB.
Derived name from the spiral or helical path or ramp traced around the dislocation line.
Symbol in Figure

26. All three dislocations are represented in Figure
Most dislocations found in crystalline materials are probably neither pure edge nor pure screw, but mixed.
All three dislocations are represented in Figure
The lattice distortion that is produced away from the two faces is mixed, having varying degrees of screw and edge character.

27. Dislocations (Cont.)
Dislocations can be observed using electron microscope.
All crystalline materials contain dislocations introduced during: Solidification, plastic deformation, and as a consequence of thermal stresses resulting from rapid cooling.

28. TEM Of dislocations (dark lines) in titanium alloy

29. Lattice Distortion Around Dislocations
Some localized lattice distortion within the region around the dislocation line. Some atoms are squeezed together (compression) and others are pulled apart (tension).
Magnitude of distortion decreases with distance away from the dislocation line. At positions far removed, crystal lattice is virtually perfect.

30. Dislocations (Cont.)
Burgers vector: Determines magnitude and direction of lattice distortion associated with the dislocation.
For metallic materials, Burgers vector points in a closed-packed crystallographic direction and is of magnitude equal to interatomic spacing.
Nature of dislocation (edge, screw, or mixed) defined by: Relative orientations of dislocation line and Burgers vector (perpendicular for edge, parallel for screw).