4.0 CRYSTALLINE STRUCTURE
4.1 INTRODUCTION
If we examine a few metallic solid materials with which we daily come across, we shall find that most of them do not have any characteristic difference in their out ward appearance. These solids can be classified in two types, namely crystalline solids, and non-crystalline solids.
CRYSTALLINE SOLIDS
Crystalline solids are those in which the atoms or molecules are arranged in a very regular and orderly manner in the three dimensional pattern. Metals and alloys are the examples of crystalline solids. It may be either in the form of single structure or as ploy crystalline structure.
AMORPHOUS SOLIDS
Amorphous solids are those in which the atoms or molecules are arranged in an irregular pattern. These are non-crystalline in nature. Some of the examples an wood, glass, plastics, etc.
Crystal
The term crystal of a material may be defined as a small body having a regular polyhedral form, bounded by smooth surfaces, which are acquired under the action of its intermolecular force. The crystals are also called as grains, the boundary separating the two adjacent grains is called grain boundary, by research it has been observed that the crystals are symmetric in nature, which helps us in the classification of crystals and describing their behavior.
Crystal structure
A crystal structure is a regular array of atoms arranged one over the other. Many have crystal structure that are best described as a close packed or closest packed since the atoms packed together so that a minimum of free space or unoccupied volume is present with in the structure.
If the atoms are represented by spheres, such as Ping-Pong balls, these layers of these spheres can be built which corresponds to a close packed layer of atoms. The below fig. Shows the crystal structure. (4.1)
4.2 SPACE LATTICE
Space lattice
A space lattice is an infinite, three-dimensional pattern of atoms in space. The regularity with which atoms are packed in solids arises from geometrical conditions, which are imposed by directional bonding and close packing. Crystal structure observed in solids are described in terms of an idealized geometric concept called space lattice and may be rationalized in terms of the way CO-ordination polyhedral pack together to minimize the energy of solids.
Unit cell.
We have already discussed that atoms are arranged in a crystal system in a particular fashion, the general arrangement of particles into small parts is called as unit cells. The above fig 4.2. Shows the three-dimensional view of unit cell. It is formed by intercepts a, b and c, along their axis respectively. The three angles (alpha, beta, gamma) are called inter facial angles.
Primitive cell.
The term primitive cell may be defined as a unit cell, which possesses lattice point at its corners only; a simple cubic cell is an example of a primitive cell. The unit cells which contain more than one lattice point are called one lattice point are called non-primitive cells.
Types of crystal lattice:
There are 32 classes of crystals systems based on the geometrical consideration. But it is common practice to divide all the crystal systems in to seven groups or basic groups, these seven basic crystals are distinguished from one another by the angles between the three axis and the intercepts of the faces along them. These seven basic crystal systems are
- Cubic.
- Tetragonal.
- Orthorhombic.
- Rombhohedral.
- Hexagonal.
- Monoclinic.
- Triclinic.
Table shows 14 basic Bravies lattices with their characteristics.
Metallic structure:
It has been found that most of the common metals possess cubic or hexagonal structure. The type of metallic structure is
Cubic structure.
Body centered cubic structure (BCC).
Face centered cubic structure (FCC).
Hexagonal close packed structure (HCP)
BODY CENTERED CUBIC STRUCTURE:
In BCC structure there is one atom at each corner of the cube and one atom at the center of the cube. For any corner atom of the unit cell, the nearest atoms are the atoms, which are at the centers of unit cell. As eight units cells having eight body-centered atom, hence CO ordinate number surrounding such corner atom is 8. Similarly by considering the center atom of each unit cell, we can say that the coordination number is 8, because the eight equidistant neighbor atoms surround every center atom. Hence coordination number for BCC structure is 8. The nearest distance between two atoms is √3a/2.
FACE CENTERED CUBIC STRUCTURE:
In this type of structure, the unit cell contains one atom at the center of each face in addition to the atoms at the corners as shown in the figure. In this it is noted that this type of structure dose not contain any atom at the center of atom and is obvious that each nit cell shares 14 atoms. The coordination number for this case is 12 and the nearest distance between the two atoms is a/√ 2
HEXAGONAL CLOSE PACKED STRUCTURE:
In this type of structure, the unit cell contains one atom at each corner on the hexagonal prism, one atom each at the center of the hexagonal faces and three more atoms within the body of the cell as shown in the figure. It is obvious that each unit cell shares 14 atoms and contains three atoms within it. It has a coordination number of 12 and nearest distance between two atoms is a/√2.
CRYSTALLOGRAPHIC PLANES AND DIRECTIONS
Introduction:
The layers of atoms or planes along which the atoms are arranged are known as atomic or crystallographic plane. As one becomes more and more interested in the study of the crystals, the need for the symbols to describe the orientation in space is of importance. Crystallographic planes and directions become evident. The Miller system of designating indices for crystallographic planes and directions is universally accepted for the purpose.
MILLER INDICES:
The orientation of a plane, in every crystal system, is described in terms of coordinates through which they pass along x-x axis, y-y axis and zz axis. This orientation of faces of a crystal and plane and direction of atom within that crystal is called “MILLER INDICES”.
Identification of the miller Indices:
Millers suggested that it is more useful to describe the orientation of a plane by the reciprocals of its numerical parameters rather than by its linear parameters. These reciprocals when approximately converted into whole numbers, it is known as Miller indices.
Procedure for finding Miller Indices:
In order to find out the Miller indices of an atom, one comer of the unit cell is assumed to be the origin of the coordinates then
-Find the intercepts on the three axis in multiples or fractions of unit distances on each axis from the origin.
-Take the reciprocals of these numbers.
-Change these reciprocals to the smallest integers having the same ratio, i.e., by multiplying each reciprocals with L.C.M
-Enclose the values in parenthesis.
Example To Find out Miller Indices
A plane in fig that has intercepts x=1, y=1 and z=1 has reciprocal intercepts 1/1,1/1,1/1
And the Miller Indices are (111).
A plane in fig has intercepts x=1/3,y=2/3, z=1 has reciprocal intercepts 3,3/2,1.Reduce these reciprocals to the smallest integers, that are 6,3,2. Then Miller Indices are (632) (Written without commas and enclosed within round brackets). Miller indices are always whole numbers, and are never fractions. The directions ox, oy and oz are all regarded as positive, but directions measured on the other side of the origin are regarded as negative. If the parameters are negative the corresponding index is written with the negative sign above it as shown in fig 4.6 g indicated as (100) and as (110) respectively.
CRYSTAL DIRECRIONS:
A direction in general may be represented in terms of three axes with reference to the origin and a lattice point represents the direction of lattice point.
Procedure for finding crystal direction of Miller indices:
The following are the procedure adopted for finding the Miller indices direction. Draw a straight line OD passing through the origin O and parallel to the crystal direction RS. whose Miller Indices are required to be determined as shown in fig.
Now draw any point P on the line OD, and draw perpendiculars PL, PM.PN on x-x axis, y-y axis z-z axis respectively.
Find the intercepts of OL, OM, ON in terms of axial units.
Reduce these intercepts in the smallest integers. Dividing the values of three intercepts does this. Enclose the smallest integers in square brackets.
4.3 Crystal Imperfections:-
A crystal is a solid composed of atoms, ions or molecules arranged in a pattern, which is respective in three-dimensional structure. In an Ideal crystal, the atomic arrangement is perfectly regular and continuous throughout. But, real crystal as in cast or welded objects is never perfect. Lattice distortion and various imperfections, irregularities or defects are generally present in them.
CRYSTAL DEFECTS OR IMPERFECTIONS:-
It has been observed that the crystals are rarely found to be perfect. The atoms do not have their full quota of electrons in the lowest energy level. But the atoms vibrate due to thermal effect and the electrons also change their position. There are many other types of defects found in the structure of the crystals. It will be interesting to know that the type and magnitude of any defect, in the structure of the metal crystals, plays an important role at the time of its selection as well as actual use.
The three types of defects are 1.Point defects 2.Line defects 3.Surface defects
POINT DEFECT: - The defects, which take place due to imperfect packing of atoms during crystallization, are known as Point Defects. The point defects are also caused due to vibrations of atoms at high temperatures. Different types of point defects are
Vacancies: - Whenever one or more atoms are missing from a normally occupied position the defect caused is known as vacancy. It may be noted that there may be single vacancy (if one) atom is missing), di-vacancies (If two atoms missing), Tri-vacancies (If three atoms are missing) and so on.
Interstitial defects: - Whenever an extra atom occupies interstitial position i.e. voids in the crystal system, the defect caused is known as interstitial defect. It may be noted that the atom, which occupies the interstitial position, is generally smaller than the parent atom.
Frenkle defect: -When ever a missing atom (responsible for vacancy) occupies interstitial positions (responsible for interstitial defect) the defect caused is known as Frankel defect It may be noted that a Frankel defect is a combination of vacancy and interstitial defects. This type of defects is more commanin ionic crystal, because the positive ions, being smaller in size, get lodged easily in the interstitial position.
Substitution defect: - When ever a foreign atom (i.e. other than the parent atoms) occupies a position, which was initially meant for the parent atom or in other words replaces the patent atom the defect caused is known as Substitution defect. It may be noted that in this type of defect the atom, which replaces the parent atom, may be of the same size or slightly smaller or larger as that of the parent atom.
Schottky drfect: -Whenever a pair of positive and negative ion is missing from a crystal the defect caused is known as schottky defect .It may be noted that in this type of defect, the crystal is electrically neutral.
Phonon: -Whenever a group of atoms is displaced from its ideal location, the defect caused is known as Phonon. It may be noted that such a defect caused by thermal vibration. It happens as the atoms interact with one another, they tend to vibrate in synchronism in the same way as waves on the ocean surface. It will be interesting to know that this defect effects electrical and magenetic properties.
LINE DEFECTS: - The defect which takes place due to dislocation or distortion of atoms along a line in some direction, ate called as Line defects. The line defects also takes place when a central portion of a crystal lattice slips without effecting the outer portion.
Edge dislocation: - Whenever a half plane of atom is inserted between the planes of atoms in a perfect crystal, it is called Edge dislocation Figure shows a cross- section of a crystal where dots represents atoms arranged in an orderly manner (Draw fig from 340) Figure (b) shows the displacement of atoms when an extra half plane is inserted from the top .It may be noted from this figure, that top & bottom of the crystal above and below the line x-y appears perfect if the extra of plane is inserted form top the defect so produced is represented by ┴ =Z and if the extra half plane is inserted form the bottom the defect so produced is represented >=T
Screw dislocation: -whenever the atom are displaced in two separate planes perpendicular to each other the defect so produced is know as screw dislocation. Figure shows the displacement of atoms in the region ABC in the screw dislocations the arrangement of atoms appear like in the screw or a helical surface.
Surface defects: - Defects which take place on the surface of the material are known as surface defects it my be noted that the surface defects takes place either due to imperfect packing of atoms during crystallizations or defective orientation of surface the following are the important types of surface defects.
Grain boundary: - Whenever grains of different orientation separate the general pattern ot atom and exhibits a boundary as in the figure the defect caused is know as grain boundary and this generally takes place during the solidifications of liquids metal.
Twin boundary: - When the boundaries in which the arrangement on one side of the boundary is somewhat mirror of the arrangement of the atoms of the other side as in figure This defect know as twin boundary.
Stacking fault: - whenever the stacking of atoms is not in proper sequence thought the crystal the fault cased is known as stacking fault. Figure shows the proper sequence of atomic planes. If we read form bottom to top is A-B-C-A-B-C-A-B-C. Now figure show the sequence of atomic Planes as A-B-C-B-A-B-A-B-C. The region in which the stacking fault occurs (A-B-A-B) form a thin region of hexagonal close packing in a ‘FCC crystal.
Stacking Fault
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