Crystalline imperfections of materials
In reality, crystals are never perfect, and they contain various types of imperfections and defects that affect many of their physical and mechanical properties, which in turn affect many important engineering properties of materials such as the cold formability of alloys, the electronic conductivity of semiconductors, the rate of migration of atoms in alloys (Diffusion), and the corrosion of metals.
Crystalline Imperfections
Types of imperfections in crystals
- Zero-dimensional or point defects.
- One-dimensional or line defects (dislocations).
- Two-dimensional or Planar defects.
- Three-dimensional volume defects.
Point defects
- Vacancy.
- interstitial.
- substitutional.
Vacancy defect
- It is the simplest point defect.
- Vacancies are equilibrium defects in metals, and their energy of formation is about 1 eV.
- In metals, the equilibrium concentration of vacancies rarely exceeds about 1 in 10,000 atoms.
- There is an tension strain between the surrounding atoms.
- Vacancies may be produced during solidification as a result of local disturbances during the growth of crystals.
- They may be created by atomic rearrangements in an existing crystal due to atomic mobility.
- Additional vacancies in metals can be introduced by plastic deformation, rapid cooling from higher temperatures to lower ones.
- The number of vacancies increase during heating the metal (increase the temperature) so it is noticed that the metal size increase during heating although, the number of atoms is constant.
- Nonequilibrium vacancies have a tendency to cluster, causing divacancies or tri-vacancies to form.
- Vacancies can move by exchanging positions with their neighbors. This process is important in the migration or diffusion of atoms in the solid state.
Interstitial defect
It is the presence of foreign atoms or particles occupy the spaces between the regular lattice sites which called interstitial site. These foreign particles are referred to as "interstitials."
Interstitial defects can affect the properties of a material, such as its electrical conductivity, mechanical strength, and thermal properties.
- Self-interstitial.
- Interstitial impurity.
- The self-interstitial is very difficult to occur naturally, because the atom is very larger than the interstitial site between the atoms which from the same metal, but it can be introduce into a structure by irradiation.
- The self-interstitial cause structural distortion.
- In this kind there is a compression strain between the surrounding atoms.
- There are conditions for this type to occur put by Hume-Rothery.
- Hume-Rothery refers to atoms of the metal as a solvent, and the interstitial atoms as a solute, all system is an interstitial solid solution.
Hume-Rothery rules for interstitial impurities
- Solute atoms should have a smaller radius than 59% of the radius of solvent atoms.
- The solute and solvent should have similar electronegativity.
- Two elements should have the same valence. The greater the difference in valence between solute and solvent atoms, the lower the solubility.
Substitutional defect
Hume-Rothery rules for substitutional impurities
- The atomic radius of the solute and solvent atoms must differ by no more than 15%.
- The crystal structures of solute and solvent must be similar.
- Complete solubility occurs when the solvent and solute have the same valency. A metal is more likely to dissolve a metal of higher valency, than vice versa.
- The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals tend to form intermetallic compounds instead of solid solutions.
Line defect (Dislocations)
- Dislocations are created during the solidification of crystalline solids.
- They are also formed by the permanent or plastic deformation of crystalline solids.
- Vacancy condensation.
- Atomic mismatch in solid solutions.
- Dislocations tend to strengthen the material.
Types of Dislocations
- Edge Dislocations.
- Screw Dislocations.
- Mixed Dislocations.( combination between screw and edge).
Edge Dislocation
Edge dislocation is created in a crystal by the existence of an extra half plane of atoms, just above the symbol ⊥. The inverted “tee,” ⊥, indicates a positive edge dislocation, whereas the upright “tee,” ⊤, indicates a negative edge dislocation. This extra half plane appears when the other half of the same plane is lost, after the half plane has been lost, the atoms around the dislocation come closer.
The displacement distance of the atoms around the dislocation is called the slip or Burgers vector b and is perpendicular to the edge-dislocation line.
Note that :
- The defect or the dislocation is the missing half plane not the existing half plane.
- Dislocations are nonequilibrium defects, and they store energy in the distorted region of the crystal lattice around the dislocation.
- The edge dislocation has a region of compressive strain at the extra half plane and a region of tensile strain below the extra half plane of atoms.
Screw Dislocation
The screw dislocation can be formed in a perfect crystal by applying upward and downward shear stresses to regions of a perfect crystal that have been separated by a cutting plane.
These shear stresses introduce a region of distorted crystal lattice in the form of a spiral ramp of distorted atoms or screw dislocation.
- Most dislocations in crystals are of the mixed type, having edge and screw components.
- A region of shear strain is created around the screw dislocation in which energy is stored.
- The slip or Burgers vector of the screw dislocation is parallel to the dislocation line.
Planar Defects
Planar defects occurs on the external surfaces. The external surfaces are considered defects because the atoms on the surface are bonded to other atoms only on one side. Therefore, the surface atoms have a lower number of neighbors. As a result, these atoms have a higher state of energy when compared to the atoms positioned inside the crystal with an optimal number of neighbors. The higher energy associated with the atoms on the surface of a material makes the surface susceptible to erosion and reaction with elements in the environment. This point further illustrates the importance of defects in the behavior of materials.
- Grain boundaries.
- Twins or twin boundaries
- Low-angle boundaries.
- High-angle boundaries.
- Twists.
- Stacking faults.
Grain boundaries
Grain boundaries are surface imperfections in polycrystalline materials that separate
grains (crystals) of different orientations.
The grain boundary itself is a narrow region between two grains of about two to five atomic diameters in width and is a region of atomic mismatch between adjacent grains.
The shape of the grain boundaries is determined by the restrictions imposed by the growth of neighboring grains.
- Grain boundaries also have some atoms in strained positions that raise the energy of the grain-boundary region.
- The higher energy of the grain boundaries and their more open structure make them a more favorable region for the nucleation and growth of precipitates.
- At ordinary temperatures, grain boundaries also restrict plastic flow by making it difficult for the movement of dislocations in the grain boundary region.
- In metals, grain boundaries are created during solidification when crystals formed from different nuclei grow simultaneously and meet each other.
Twins or twin boundaries
- Twin boundaries form when a material is permanently or plastically deformed (deformation twin).
- They can also appear during the recrystallization process in which atoms reposition themselves in a deformed crystal (annealing twin), but this happens only in some FCC alloys.
- Twin boundaries form in pairs.
- Similar to dislocations, twin boundaries tend to strengthen a material.
Low-angle boundaries
- small-angle tilt boundary.
- small-angle twist boundary.
When an array of edge dislocations are oriented in a crystal in a manner that seems
to misorient or tilt two regions of a crystal, a two-dimensional defect called a small-angle tilt boundary is formed.
A similar phenomenon can occur when a network of screw dislocations create a small-angle twist boundary.
The misorientation angle θ for a small-angle boundary is generally less than 10 degrees.
As the density of dislocations in small-angle boundaries (tilt or twist) increases, the misorientation angle θ becomes larger.
If θ exceeds 20 degrees, the boundary is no longer characterized as a small-angle boundary but is considered a general grain boundary.
Similar to dislocations and twins, small-angle boundaries are regions of high energy due to local lattice distortions and tend to strengthen a metal.
Volume Defect
Volume or three-dimensional defects form when a cluster of point defects join to form
a three-dimensional void or a pore. Conversely, a cluster of impurity atoms may join
to form a three-dimensional precipitate. The size of a volume defect may range from
a few nanometers to centimeters or sometimes larger.
Such defects have a tremendous effect or influence on the behavior and performance of the material. Finally, the concept of a three-dimensional or volume defect may be extended to an amorphous region within a polycrystalline material.
