UNIT-V

UNIT-V

CRYSTAL PHYSICS

Solids are broadly classified into two categories namely crystalline and amorphous solids. Crystalline solids are further classified into single crystal or an aggregate of many crystals called polycrystalline. Crystalline solids or crystals are those in which the atoms or molecules are arranged in a regular fashion in 3-dimension. A crystal has different periodic arrangements in all the three directions. So the physical properties of the crystal vary with direction and therefore they are called anisotropic substances. Amorphous substances do not possess any regular shape or structure. They also have no directional properties and so they are called isotropic substances. 5.2Fundamental Definitions

Space lattice and lattice points

Regular and periodic arrangement of 3-dimensional patterns of atoms or molecules in space is called crystal structure. Within crystal structure, the positions of atoms or molecules are located by points known as Lattice points. An infinite array of lattice points in three dimensions such that every point has identical surroundings or environmental conditions as that of the other point can be called as space lattice.

Basis and crystal structure

When every lattice point is replaced by an atom or a group of atoms, then we get a regular periodic arrangement of atoms.

A crystal structure is formed by associating identically a building unit with each and every lattice points. This building unit is called as Basis. Thus a basis consists of an atom or groups of atoms.

Hence,

Lattice point + Basis = Crystal structure

Unit Cell

The atoms in a crystal are arranged in a periodic array. It is possible to isolate a group of atoms or molecules or ions which represents all the characteristics of the crystal.

Unit cell is the smallest geometric figure or a minimum volume cell which contains minimum number of atoms of crystailine solid which when repeated in three dimensional directions produces the entire crystal. Primitive CellThe unit cell formed by the primitives a, b, and c is called primitive cell. A primitive cell will have only one lattice point. All the primitives are unit cells but it is not necessary that the unit cell should be a primitive cell. 5.3Lattice ParameterFig. 5.2 shows a unit cell in 3-dimension. An unit cell in 3-dimension is known as parallelopipped. The lines drawn parallel to the lines of intersection of any three faces of the unit cell which do not lie in the same plane are called crystallographic axes. The translational vectors a, b and c lie along the crystallographic axes. The intercepts a, band c gives the dimension of an unit cell and are known as primitives or lattice constants. Let a be the angle between b and c, ( the angle between c and a, and ( the angle between a and b, These angles a, ( and ( are known as interfacial angles. The lattice constants a, band c and interfacial angles a, ( and ( together are called lattice parameters of the crystal. 5.4Bravais LatticeBravais showed that there are only fourteen possible different ways of arranging identical points in a 3-dimentional space so that in all ways they have identical surroundings. When an atom is placed at each lattice point, the lattice is called a Bravais lattice. They belong to seven crystal systems.

Thus, Bravais lattice are nothing but the fourteen different ways of rearrangement of lattice points of all the seven crystal systems. Table 5.1: Seven Crystal Systems Crystal System(Unit vector)Angles

Cubica = b = c( = ( = ( = 90(

Tetragonala = b ( c( = ( = ( = 90(

Orthorhombica ( b ( c( = ( = ( = 90(

Monoclinica ( b ( c( = ( = 90( ( (

Triclinica ( b ( c( ( ( ( ( ( 90(

Trigonal or Rhombohedral a = b = c( = ( = ( ( 90(

Hexagonal a = b ( c( = ( = 90( ( = 120(

Table 5.2 Seven crystal systems with Bravais lattices

S.NoCrystal SystemBravais latticePrimitives & Interfacial anglesExamples

1.CubicSimple cubic (SC) Body centered cubic (BCC)

Face-centered

cubic (FCC)a = b = c

( = ( = ( = 90(NaCl, CaF2,

Fe, Au, Cu

2.TetragonalSimple cubic (SC) Body-centered

cubic (BCC)a = b ( c

( = ( = ( = 90(TiO2, SnO2,

NiSO4

3.OrthorhombicSimple cubic (SC) Body centered cubic (BCC)

Face-centered

cubic (FCC)

Base centered cubica ( b ( c

( = ( = ( = 90(BaSO4,

MgSO4,

KNO3

4.MonoclinicSimple cubic (SC) Face-centered

cubic (FCC)a ( b ( c

( = ( = 90( ( (CaSO42H2O,

FeSO4,

Na2SO4

5.TriclinicSimple cubic (SC)a ( b ( c

( ( ( ( ( ( 90(CuSO4,

K2Cr2O7

6.Trigonal (Rhombohedral)Simple cubic (SC)a = b = c

( = ( = ( ( 90(Bi, Sb, As

7.HexagonalSimple cubic (SC)a = b ( c

( = ( = 90(

( = 120(Quartz, Zn,

Mg, SiO2

5.5Miller indices and lattice planesA crystal consists of atoms, ions or molecules. Any face of a crystal consists of layer of atoms or ions or molecules. The aggregate of a set of parallel equidistant planes passing through at least one lattice point or a number of lattice points are called lattice planes. The lattice plane can be choosen in many ways for a given crystal as in Fig. 5.4. It is very important to designate the lattice planes. Miller developed a method to designate the planes and is known as Miller indices. These indices are based on the intercepts of a plane with the three crystal axes i.e., the three edges of the unit cell.

Miller indices are the three smallest possible integers, which have the same ratio as the reciprocals of intercepts of the plane concerned on the three axes. Thus Miller indices describe the angular position of planes with respect to the crystallographic axes but not their actual distances from the origin. The miller indices for a particular crystal plane can be determined as follows1. Determine the intercepts of the plane or face in terms of whole numbers which are multiples or submultiples of the intercepts a, b and c. 2. Take reciprocals of these numbers. 3. Reduce the reciprocals to their smallest possible values by multiplying throughout by the least possible common factor. 4. Enclose these three integral numbers in brackets without commas in between.

Let us consider a plane with intercepts 2,3,4 along the 3 axes as an example. The reciprocals are Reducing to the possible smallest value by multiplying with the least commont multiple (12) we get 6,4,3. So the Miller indices are (643). The miller indices for the prominent crystal planes are shown in Fig. 5.6. In general the Miller indices are indicated as (h k l), This means that a set of parallel planes (h k l), cuts the x-axis into h parts, y-axis into k parts and z-axis into l parts. Characteristics of Miller indicesThe characteristic features of the Miller indices are as follows

1. All equally spaced parallel planes have the same Miller indices.

2.A plane parallel to one of the co-ordinate axes has an intercept of infinity and the Miller indices of that plane is zero. 3.If the Miller indices of two planes have the same ratio (like 422 or 211), then the planes are parallel to each other. 4.If a normal is drawn to a plane (h k l), the direction of the normal is (h k l)

5.The indices should be enclosed within the paranthesis without the commas in between the number. 6.If the plane cuts the negative side of the axes, the intercept is a negative number and the miller indices is negative. 7.The negative miller indices is denoted by (h k l).

5.6Inter-Planar distance in a cubic crystalThe distance d between successive members of a series of parallel planes is known as interplanar distance. Let us consider the plane ABC as shown in Fig. 5.6 Let (h k l) be the Miller indices of plane. Let ON = d be the normal from the orgin to the plane. ON makes an angle a,( and ( with the x, y and z axes respectively.

The intercepts on the x, y, z axes are given by

The direction cosines of the normal are

By the property of direction cosines we have

Let ABC be another plane parallel to ABC at a distance OM from the origin. Its intercepts are

The distance between two adjacent planes

i.e., Interplanar spacing

5.7Relation between lattice constant and densityLet us consider a cubical crystal of lattice constant a. Let n be the number of atoms per unit cell and ( the density of the material. If N is the Avagadro's number and A the atomic weight of the material then,

A

Mass of each molecule = N/ A

Mass of 'n' molecules = n N/ AMass of unit cell ( =

Volume of unit cell 5.8Characteristics of Crystal StructuresIt is always essential to know how atoms occupy the unit cells. The fundamental parameters which determine the characteristics of crystal structures are described below.

1.Number of atoms/unit cell

The total number of atoms present in an unit cell is known as number of atoms/unit cell or effective number.

2.Nearest neighbour distance

The distance between the centres of two nearest neighbouring atoms is called nearest neighbour distance. If r is the radius of the atom then the nearest neighbour distance is 2r.

3.Atomic radius

Atomic radius is defined as half the distance between the nearest neighbouring atoms in a crystal.

4.Co-ordination number

Co-ordination number is defined as the number of equidistant nearest neighbours that an atom has in a given structure. 5.Atomic packing factor or packing density. The ratio of volume occupied by atoms in an unit cell to the total volume of the unit cell is called atomic packing factor. This is also called as packing fraction or packing factor.

Packing factor = v/ VWhere v is the volume of atoms in unit cell V is the total volume of the unit cell.

5.9Simple Cubic (SC) structure A crystal structure is said to be simple when the atoms are present only at the corners of the unit cell as in Fig. 5.7

No. of atoms per unit cellA unit cell is not an isolated entity. The adjacent cells share each lattice point. In simple cubic structure each corner atom is shared by 8 adjacent unit cells. Only 1/8th part of an atom is contributed to each lattice point. Number of atoms in the unit cell = 1/8 x 8 = latom Co-Ordination number

Co-ordination number of an atom in a crystal is the number of nearest neighbouring atom. Let us consider one corner atom. This atom is surrounded by 4 equally spaced neighbouring atoms in the same plane, one vertically above and one exactly below this atom. The co-ordination number = 4 + 1 + 1 + = 6

Atomic radius

Let us consider the atoms are sphere. The unit cell has atoms only at the corner of the cube. Each corner atom touch each other along the edges of the cube. If r is the atomic radius and a the side of the cube, then from Fig 5.8 b we can write 2r = a

r = a/2

Atomic packing factor

Atomic packing factor is the ratio of volume of atoms in the unit cell to the total volume of unit cell.

APF = Volume of all atoms in unit cell Volume of unit cell

Number of atoms present in unit cell x Volume of one atom

Volume of unit cell

Number of atoms in unit cell = 1

volume of one atom =

volume of unit cell = a3

Where r is radius of each atom a is side of the cube

Atomic packing factor = (/6 = 0.5236 = 52%

52% of the space in the unit cell is occupied by atoms. Thus this structure is a loosely packed one. 5.10Body centered Cubic (BCC) structure The body centered cubic structure has one atom at the centre of the cube apart from the eight corner atoms as shown in Fig. 5.9

Number of atoms per unit cellIn this crystal structure each corner atom is shared by 8 adjoining unit cells. Hence 1/8th part of an atom is present in every corner of the cube.

The share of each corner atom in a unit cell = 1/8 x 8 = 1 atom. The body centered atom which is at the centre of the unit cell is not shared by any other unit cell. Hence the central atom fully contributes to this unit cell. .'. Total number of atoms in a unit cell = 1 + 1 = 2 atoms (one corner atom and the other is the body centered atom).

Co-ordination number

Consider the body centered atom in this cube. This atom is surrounded by the corner atoms and is situated at equidistant from all the corner atoms. This atom almost touches all the corner atoms. So the nearest neighbour for a body centered atom is the 8 corner atoms.

Hence the co-ordination number = 8

Atomic radius

The unit cell has 8 atoms at the corners of the cube and 1 atom at the centre of the cube. Here the corner atoms do not touch each other, but each corner atom touches the central atom. Two atoms are in a straight line along the diagonal inside body and the centre atom is along the body diagonal. So in calculating the distance between the atoms, the central atom should be taken into consideration. If 'r' is the atomic radius and 'a' is the side of the cube then from the Fig. 5.10 In (ABC,

AC2 =AB2 + BC2 = a2 + a2 AC2=2a2

In (( ADC,

AD2 =AC2 + CD2 = 2a2 + a2 AD2=3a2

AD= (3a APF = Volume of all atoms in the unit cell (v) Volume of unit cell (V)

APF = Number of atoms present in a unit cell x Volume of one atom Volume of unit cell (V)

Number of atoms present in unit cell = 2

Volume of one atom=

Where r is the radius is the of the atom.

Volume of unit cell a3Substituting the value of 'r' from equation (2) we get Atomic packing factor = Thus packing fraction is about 68%. Hence this structure is not a closely packed one. This means that only 68% of the space of the unit cell is occupied by atoms and the remaining 32% is unoccupied. 5.11Face Centered Cubic (FCC) Structure (Number of atoms per unit cell)In FCC structure there are 8 atoms present in 8 corners of the cube and one atom on each of the face centers of the cube as in Fig. 5.12. In this crystal structure each corner atom is shared by 8 adjoining unit cell. Hence 1/8th part of an atom is present in every corner of the cube. Along with this each face centered atom is shared by 2 adjoining unit cells.

The share of corner atom in a unit cell =

Number of face centered atoms = 6 atoms.

Share of face centered atom = 1/2 x 6 = 3 atoms. Total number of atoms in a unit cell

Co-ordination numberIn FCC structure the nearest neighbours of any corner atom are the face centered atoms of the surrounding unit cells. Any corner atom has four such atoms in its own plane, four in the plane above it and four in the plane below it.

Hence the coordination number = 4 + 4 + 4 = 12. Atomic radius

The unit cell has 8 atoms at the corner of the cube and one atom at the face centre of the cube. Here the corner atoms do not touch each other. But each corner atom touches every nearby face centered atom. If 'r' is the atomic radis and 'a' is the side of unit cell then from the Fig. 5.12

APF = Volume of all atoms in the unit cell (v) Volume of unit cell (V)

APF = Number of atoms present in a unit cell x Volume of one atom Volume of unit cell (V)

Number of atoms per unit cell = 4

Volume of one atom =where r is the radius of the atom

Volume of unit cell = a3

Substituting the value of 'a' from equation (1) we get

Atomic packing factor =

Thus the packing fraction is about 74%. This means that 74% of the unit cell is occupied with atoms, When compared with simple cubic and body centered cubic, structures, face centered has highest packing factor. 5.12 Hexagonal closed packed (HCP) structure Fig.5.13 represents a unit cell of HCP structure. In this structure there are three layers of atoms in a unit cell. The bottom layer has six corner atom and one face centered atom. Similarly the top layer has six corner atom. There is a middle layer containing three atoms at the centre of the body at a distance c/2 from the bottom layer. Number of atoms per unit cell

Consider the bottom layer. It consists of six corner atoms and one face centered atom. Each corner atom contributes 1/6th of it in one unit cell and face centered atom contributes 1/2 of its part in the unit cell. Similarly in the upper layer there are 6 corner atoms and one central atom whose contributions are the same as that of the bottom layer.

Total number of corner atoms in the upper and bottom layer =12 1

Share of each corner atom = 12 x 1/ 6 = 2

Total number of central atoms = 2 Contribution of each central atom = 2 x = 1In the middle layer there are 3 atoms which are not shared by any unit cell. Hence the contribution is full. Total number of atoms m one unit cell = 12 x 1/6 + 2 x 2 x 1/2 + 3 = 6 atoms.

Co-Ordination numberConsider the face centered atom in the bottom layer. It is surrounded by she corner atoms. Above the face centered atom there is a layer containing 3 atoms. Similarly below the face centered atom there is a layer containing 3 atoms. So the number of atoms surrounding a particular atom is 6 + 3 + 3 = 12.

Hence the coordination number = 12.

This is true if the co-ordination number is calculated considering any other atom in the structure. Atomic radiusIn this structure the atoms touch each other along the edges of hexagon and the face centered atom touches all the corner atoms. If 'r' is the radius of atom and 'a' is the side of the hexagon then we can writeAtomic Packing factor

For calculating packing factor first we have to calculate the (C/a) ratio, where c is the height of the unit cell and a is the constant or the edge of the unit cell.

Calculation of (c/a) ratioLet c be the height of the unit cell and a be the distance between two neighbouring atoms. Consider the ( ABO in the bottom layer. Here A, B, O represents the atoms in the bottom layer, at a distance c/2 the next layer of atoms lies at C.

From Fig 5.15 (b)

In ( ABA1 5.13Other important Structure 5.13.1 Diamond cubic structure Diamond cubic structure is exhibited by germanium, silicon and carbon crystals. This structure is a combination of two interpenetrating FCC sub-latticles as shown in Fig. 5.16 One sub-lattice X has its origin at (000) and the other sub-lattice Y has its origin at a point one quarter apart along the body diagonal ie., at Number of atoms per unit cellThe unit cell consists of eight corner atoms, six face centered atoms and four atoms located inside the unit cell. The eight corner atoms are shared by eight adjacent unit cells and six face centered atoms are shared by two unit cells .

total number of atoms in a unit cell = 1/8 x 8 + 1/2 x 6 + 4 = 8 Co-ordination numberConsider an atom along the body diagonal. This is tetragonaly bonded with four atoms. These atoms are the nearest neighbours and so the co-ordination number is 4. Atomic radiusConsider a corner atom and an atom along the body diagonal. The diagonal atoms lies at a distance one fourth of the body diagonal length.

From Fig 5.16 (c)

From equation (1) and (2)

Atomic packing factor

APF= Volume of all atoms in the unit cell (v)

Volume of unit cell (V)

No. of atoms present in unit cell = 8

Volume of one atom =

Volume of unit cell = a3Atomic packing factor

Thus packing fraction is about 34%. So this is a loosely packed structure.

5.13.2 Zinc Blende or Sphalerite Cubic Structure This structure is similar to diamond cubic structure with the exception that the two sublattices are occupied by two different elements. This structure is possessed by semiconductors like InSb, GaAs, CuCl and ZnS. Fig. 5.1 shows the zinc sulphide (ZnS) structure which is the result of Zn atoms on one FC lattice and S atoms on other FCC lattice 5.13.3 Sodium Chloride StructureSodium chloride crystal is an ionic crystal. The sodium ions and chlorine ions are situated side by side in the sodium chloride lattice. This structure consists of two FCC sublattices. One sublattice has its origin at (0, 0 ,0) with chlorine ions and the other sublattice has its origin midway along a cube edge at with sodium ions as in Fig. 5.18 .

Each ion in the sodium chloride lattice has six nearest neighbour ions at a distance a/2 leading to co-ordination number as 6. Each unit cell in sodium chloride structure has four sodium ions and four chlorine ions. Hence each unit cell has four NaCI molecules. 5.13.4 Graphite Structure

The graphite structure is shown in Fig. 5.19. Here the carbon atoms are arranged in layer or sheet structure. Carbon atom, ca form four covalent bonds with other carbon atoms. Graphite is formed when only three covalent bonds are formed with the other carbon atoms. The fourth electron which is left forms metallic bond which holds the sheets together. The spacing between the sheets is about 3.4 and spacing between the carbon atoms in each layer is 1.42 . The sheets are held together in a crystal by van der waals bonds.

5.14Polymorphism and Allotropy

In a solid if the change in temperature or pressure is not accompanied by melting or vaporization, the internal arrangement of atoms of the solid changes.

The ability of a material to have more than one structure is called polymorphism. If the change in structure is reversible, then the polymorphic change is known as allotropy. This means that an element can have more than one structure and in all structures the physical properties change whereas the chemical properties remains unaltered. Cobalt at ordinary temperature has HCP structure and when heated above 477 C, its structure changes to FCC. Similarly iron at room temperature has BCC structure and is known as a-Iron. When heated above 910 C its structure changes to FCC and is called as, iron. On further heating to above 1400 C, it changes to BCC structure and is known as 6-Iron. At 1539 C it melts. All these changes are reversible on cooling.

Carbon also exists in allotropic forms. Diamond and graphite are the two allotropic forms. Diamond structure is a combination of two interpenetrating FCC sublattices. The atoms are united by covalent bonds and so it acts as a good electrical insulator. Also it is a very hard material. In the graphite structure carbon atoms of each hexagonal layer are united by covalent bonds by loosing one valence electron. The layers are easily separable as there is no strong bonding between the layers. This makes graphite to act as a good electrical conductor. 5.15Crystal defects

A perfect crystal is considered to be constructed by the infinite regular repetition of identical structural units or building blocks. In actual crystals imperfects or defects are always present. The effects of defects are important in knowing the properties of crystals. Properties such as mechanical strength, ductility, dielectric strength, conduction, magnetic hysteresis etc., are greatly affected by the defects.

The structural imperfections can be classified based on their geometry as follows Point defects

Line defects

Surface defects

Volume defects

5.15.1 Point defectsPoint defects are lattice errors occurring at isolated lattice points. They are point-like regions in the crystals and so referred as zero-dimensional defects. The most common point defects are Vacancy

Interstitial

Substitutional impurities

Interstitial impurities

Schottky defect Frenkel defects Electronic defectsThe first four types of defects occur in elemental crystals, whereas the last two defects occur in ionic crystals. Vacancy

Vacancy refers to the missing of an atom from its site as in Fig. 5.20 (a). This defect may rise either from imperfect crystal packing or from thermal vibrations of atoms at high temperatures. To create a vacancy the thermal energy required is of the order of 1 eV per vacancy. Interstitial In a close-packed arrangement of atoms if the atomic packing factor is low, an extra atom may be lodged within the crystal structure as in Fig. 5.20 (b). This is known as interstitials. This may also be created by thermal agitations. Substitutional Impurities A substitutional impurity is created when a foreign atom substitutes for or replaces a parent atom in the lattice Fig. 5.20 (c). In brass, zinc is a substitutional atom in the copper lattice. Interstitial ImpuritiesA foreign atom or ion occupying the void between regularly occupied sites in crystals creates interstitial impurities (Fig. 5. 20(d)). The foreign atom gets well fitted if its size is relatively small compared to the parent atom.

Schottky defectIn an ionic crystal, if there is a vacancy in a positive-ion site and charge neutrality is achieved by creating a vacancy in a neighbouring negative-ion stie, such a pair of vacant sites is called schottky defect (Fig. 5.20 (e)). Frenkel defect

In ionic crystals, an ion displaced form the lattice into an interstitial site is called a frenkel defect. As captions are generally smaller ions, it is possible for them to get displaced into the void space present in the lattice. A frenkel imperfection does not change the overall electrical neutrality of the crystal.

Electronic defects

Electronic defects are nothing but the errors in charge distribution in solids. These defects are produced when the composition of an ionic crystal does not correspond to the exact stoichiometric formula. 5.15.2 Line defectsIn a crystal, if a plane of atoms just partway, the defect formed by the edge of such a plane is in the form line and is called line defect. This is also known as a dislocation. In geometrical sense, these defects are one-dimensional defects. Line defects are formed in the process of crystallization. The two types as dislocation are 1. Edge dislocation and

2. Screw dislocation

Edge dislocationThe atoms are expected to be arranged in a regular fashion in an ideal crystal. However if any of this regular arrangement is not extended to the full length of the crystal and ends in between within the crystal as in Fig. 5.22, then it is known as edge dislocation. The discontinuity of the atom leads to a distortion of the crystal shape around the edge. Edge dislocation is said to be positive when the incomplete plane starts from the top of the crystal and is denoted as T. The edge dislocation is said to be negative when the incomplete plane starts from bottom of the crystal and is denoted as T. The magnitude and direction of the displacement are determined by a vector called the Burgers vector which is perpendicular to the dislocation line. To draw the Burger circuit, start from p move right through x atomic steps move down through y atomic steps, move left by X atomic steps and then move up through the same point P. This closed path around the dislocation line is called Burger circuit.

In a perfect crystal we come to the same point P when the above operations are done. However in imperfect crystal, when the above operations are done, we end up at Q and not at P as in Fig 5.23. The distance QP(b) represents the magnitude and direction of the Buger vector. The Burger vector and dislocation are perpendicular to each other. Screw dislocationWhen the dislocation tends the atom to get displaced in two separate planes perpendicular to each other, it is called as screw dislocation. In this case the lattice planes of the crystal spiral the dislocation line and so are called screw dislocation (Fig 5.23).

In screw sislocation the burger vector and the dislocation are parallel to each other. The force required to initiate screw dislocation is greater than that is required to initiate edge dislocation. 5.15.3 Surface defects

In a crystal, the defects that take place on the surface of the material are known as surface defects or plane defects. In geometrical sense, these imperfections are two dimensional and their thickness is of few atomic diameters. Surface defects are classified as 1. Grain boundary 2. Twin boundary and 3. Stacking fault

Grain Boundary

These are defects which separate crystals of different orientations in a polycrystalline aggregate. During recrytallization of polycrystalline crystals, the new crystals get randomly oriented with respect to each other. As the crystals grow they impinge on the adjacent regions. The atoms held in between these crystals are pulled by each crystal in its own direction. Thus depending on the force the atoms occupy their equilibrium position. The boundary region between the two crystals is distorted and this region is called grain boundary. When the misorientation between the crystals is of order 10, they are called low angle boundaries. If the misorientation is greater than 10 we call it high angle boundries.

Twin boundary

If the atomic arrangements on one side of the boundary is the mirror reflection of arrangements on the other side of the boundary, then such a boundary is known as twin boundary as in Fig. 5.25 The region between pair of boundries is called twinned region. Stacking faults

These are imperfection arised due to the dissimilarity in the stacking sequences of atomic planes in crystals. This occur in the closed pack FCC and HCP structures. For example for an ideal stacking like

ABCABCABC we get ABCA BCBC ABC

Plane A is missing giving rise to stacking faults. 5.15.4 Volume defects

During the crystal growth process, the presence of a void or vacancy due to the missing cluster of atoms is referred as volume defects. The volume defects such as cracks may arise when there is electrostatic dissimilarity between the stacking sequence of closed packed planes in metals.