Crystal imperfections

             

In crystal, the atom or ions are arranged in a regular and periodic manner in three dimensions. Generally, the natural crystals are not always perfect and there are some deviations from their regular arrangement. In a natural crystal, there are some missing atoms or lattice imperfection.

                Any deviation in a natural crystal from the regular and the periodic arrangement of atoms is known as crystal imperfection.

                Crystal defects or imperfections are classified into three categories, namely: (i) Point Defect, (ii) Line Defect, (iii) Surface and grain Boundary Defect and (iv) Volume Defect.

(i) Point Defects or Imperfections. [Zero Dimensional]: This is irregular arrangement due to distortion.

                In some cases, when missing atoms, displaced atoms or extra atoms are involved, there may be point defects. These defects are completely local in effect. Eg. A vacant lattice site. Point imperfections are always present in crystals and their presence results in a decrease in the free energy.

                The number of defects at equilibrium concentration at a certain temperature can be computed as

                n = N e^-Ed/Kt, Where, n = No. of imperfections, N = No. of atomic sites per mole, K = Boltzmann’s Constant, Ed = the free energy required to form the defect, T = Absolute Temperature.

(a) Vacancies: A vacancy is the simplest point defect in a crystal which arises when temperature rises from 0 K. This refers to a missing atom or vacant atom site. Such defects may arise either from imperfect packing during the original crystallization or form thermal vibrations of the atoms at high temperature.

Vacancy may be single or two or more of them may condense into a divacancy or trivacancy.

(b) Interstitialcies: In a close packed arrangement of atoms, if the atomic packing factor is low, an extra atom may be logged within the crystal structure. This is known as interstials.

(c) Substitutional Impurities: In this, a foreign atom or ion occupies a regular site in a crystal lattice.

(d) Interstitial Impurities: Here a foreign atom or ion occupies a place into the void between regularly occupied sites in crystals. The foreign atom can be fitted well if its size is relatively small compared to the crystal atom.

(e) Schottky Defect: This is closely related to vacancies and is obtained when an atom or ion is removed from a normal lattice site and replaced by an ion on the surface of the crystal. Both vacancies and schottky defects facilitate atomic diffusion. In closely packed structure (Eg. FCC & HCP) vacancies and schottky defects occur more. For ionic crystal numbers of ion pair production is,

                n = N e^-Et/2Kt, Where, n = No. of imperfections, N = No. of lattice site, K = Boltzmann’s Constant, Et = energy required to create a pair of ion vacancy inside crystal lattice, T = Absolute Temperature.

(f) Frankel Defect: This is closely related to interstices. An ion displaced from the lattice site into an interstitial site is called a frankel defect. Closed packed structures have fewer interstalices and frankel defects, because additional energy is required to force the atom into a new position Eg. BCC.

(g) Electronic Defect: Electronic defect are the result of errors in charge distribution in solids. These defects are free to move in the crystal under the influence of an electronic field.

(ii) Line Defects or Imperfections [One Dimensional]: It is a line defect in which a line of atoms is not in proper position. Consider a crystal in which an extra line of atoms terminates in the middle of the crystal. This type of imperfection along a line of the crystal is known as line imperfection.

(a) Edge Dislocation: The line imperfection is known as edge dislocation and is represented by the symbol ┴. Due to the dislocation, the atom moves through some atomic distance inside the crystal. The magnitude of the atom dislocation is known as burger vector (b), which is measure of dislocation.

                A line drawn through the dislocation region is called as the dislocation line. The atoms lying above the dislocation line are compressed, whereas the atom that are lying below the dislocation line exhibit tension. Thus, a stress field is acting around the dislocation region.

(b) Screw Dislocation: The upper portion (In fig.) of the crystal is sheared through a distance of one atomic distance.

 The line, separating the dislocated portion and undislocated portion is known as the dislocation line A. A circular arrow is the symbolic representation of screw dislocation.

                In some crystal, the edge and screw dislocations may occur simultaneously. Such as called mixed dislocation.

(iii) Surface Defects or Imperfection [Two Dimensional]: surface imperfections of a structural nature arise from a change in the stacking of atomic planes on or across a boundary. The change may be one of the orientation or of the stacking sequence of the planes.

                In geometric concept surface imperfections are two dimensional. There are two types: External and Internal.

(a) External Surface Imperfection: Imperfection is represented by a boundary. Boundary is the external boundary.

(b) Internal Surface Boundary: Internal Surface imperfections are manifested by such defects as grain boundaries, tilt boundaries, twin boundaries and stacking faults.

b(i) Grain Boundaries: Usually all crystal lattice are polycrystalline containing a large number of crystallites or grains. When the three dimensional lattice periodicity is terminated abruptly at the surface, boundaries of adjacent grains incline towards one another with a wide angle grain boundary area is inversely proportional to the grain.

b(ii) Tilt Boundaries: They consists of a series of edge dislocations lying one above other. The angle of inclination is small and given by    θ = a/h.

b(iii) Twin Boundaries: They are formed when two sets of screw dislocations intersect each other. The angle of inclination is very small, given by α = a/h.

b(iv) Twist Boundaries: The crystal is distorted along a plan. The mirror image of one undistorted portion locks like the other one. This type of defect is known as twin boundary.

                Twin Boundary is produced during the growth of a crystal. Twin boundary can also be produced during recrystallization (mechanical working) or as a result of annealing after plastic deformation. Therefore, the twin boundaries are classified into two types namely mechanical twins and annealing twins.

b(v) Stacking Faults: The cubic close packed structure is formed whenever a crystal is built by a stacking sequence of ABCABCABC….. and so on. A stacking fault occurs if the sequence goes wrong, example as in the series ABCABCBCABC…. Here a layer A is missing or an extra layer A has been inserted as in series ABCABCABACABC…. . In some crystals, the stacking faults extend through the entire crystal and in some crystals they occupy only a part of the plane.

A ____________          A_____________         A _____________ A

B -------------------         B --------------------       B --------------------- B

C ………………          C ………………..        C…………….…….C

B -------------------         A_____________         A _________          A  

C ……………….         B --------------------        B -----------              B

A ____________          C ………………..        A ______

B -------------------                                              C…………              C

C ………………                                                B --------------          B

                                                                           A ______________ A

(iv)Volume Defect: Volume defects occur due to the inclusions of foreign particles, voids and non – crystalline region of at least a few angstroms. The crack that arises due to a small electrostatic dissimilarity between the stacking sequences in metals is also called volume imperfection.