solid states notes
FRIENDSWAY LEARNING CLASSES
CHAPTER:- SOLID STATE
SOLID- Solids are defined as substances that retain their shape, even when they are not confined. Substances usually assume the solid state of being at lower temperatures than they do when they are liquids, gases or plasmas.
CLASSIFICATION ON THE BASIS OF ARRANGEMENT OF CONSTITUENT PARTICLES
1. Crystalline Solids:-
A solid is said to be crystalline if its various constituent particles [ions, atoms, molecules] are arranges in a definite geometric pattern in the three dimensional space so that there is short as well as long range order of constituent particles.Example:- Sodium, Calcium, Stones, Gems, Wood etc.
2. Amorphous Solid:-
If there is no regular arrangement of constituent particles or there is only the short range order of its constituent particles then the solid is called amorphous solid.Example:- Rubber, Glass, Pitch, Silica etc.
3. Isotropy:-
In the amorphous solids there is no regular arrangement of particles thus the properties like electrical conductivity, thermal expansion are identical in all the direction. This property is called isotropy.
Amorphous solid are isotropic in nature.
4. Anisotropy:-
Due to regular arrangement of constituent particles, the different particles are fall in different ways of a crystalline solid. The values of properties like electrical conductivity and thermal expansion not remains same in all the direction this is called anisotropy.
And crystalline solids are anisotropic in nature
AMORPHOUS IS VERY USEFUL IN OUR DAILY TO DAILY LIFE SUCH AS:-
The glasses [Amorphous] are used in construction house ware, laboratory ware etc.
A large no. of amorphous plastics is being used in forming no. of articles.
Amorphous silica has found to be the best material for converting sunlight into electricity
AMORPHOUS VS CRYSTALLINE SOLID:-
Amorphous and crystalline solids differ in the properties such as cleavage property, melting point, shape, anisotropy etc.
Amorphous structure of a glassy solid (left) and lattice structure of a crystalline solid (right).
Amorphous solids
1. There is only a short range order in amorphous solids
2. Amorphous solids do not have a sharp melting point; they are softened in a range of temperature.
3. Amorphous solids undergo irregular or conchoidal breakage
4. Amorphous solids are isotrophic-the properties will be independent of the direction in which they are measured.
5. Less rigid.
Examples of Amorphous solids: Fibre glass, Cellophane, Teflon, Polyurethane, Napthalene, Polyvinyl chloride
Crystalline solids
1. There is a long range order in crystals.
2. Melt at a sharp temperature.
3. Crystalline solids can be cleaved along definite planes.
4. Crystalline solids, in general are anisotrophic (It means that, their properties such as electrical conductivity, refractive index, thermal expansion etc. will be different directions).
5. More rigid.
Examples of Crystalline solids: Copper, Potassium nitrate, Benzoic acid
CLASSIFICATION OF CRYSTALLINE SOLIDS:-
Based upon nature of constituent particles and binding forces present in them:-
1. Ionic Solids:-
*In these solids constituent particles are positive and negative ions. (cation or anions). They are held together by strong columbic electrostatic forces of attraction examples are NaCl, CaCl2, MgCl2, BaCl2 etc.
Characteristics of ionic solids:-
*They have high melting and boiling points
They are soluble in polar solvents but are insoluble in non polar solvents.
Due to strong electrostatic forces of attraction they are closely packed hence hard but they are brittle.
2. Molecular Solids:-
In these solids the constituent particles are molecules on the nature of molecules they can further subdivided into following three types:-
1. Non polar molecular solids:-
The crystalline solids in which constituent particles are atoms of noble gases [helium, neon] or non polar molecules like [H2, Cl2, I2]
Their characters are:-
*They are soft due to weak intermolecular forces.
*They are non conductors of electricity. They have low melting and boiling points.
2. Polar molecular solids:-
The crystalline solids in which constituent particles are polar molecules like HCl, SO2 etc. the intermolecular forces of attraction are dipole – dipole forces of attraction.
Thus their characters are:-
*They are soft; they are non conductors of electricity.
*Their melting and boiling points are high then non polar solids. They exists gases or liquid at room temperature.
3. Hydrogen bonded – molecular solids:-
*In these solids the constituent particles are which contain hydrogen atom linked to high electronegative atoms as N, O, F
Their characters are:-
*They exists as volatile liquids or gases at room temperature.
*They are non conductor of electricity.
*Their melting and boiling points are high.
3. Covalent or network solids:-
In these crystalline solids the constituent particles are non metal atoms linked to adjacent atom by covalent bond throughout the crystal. They forms a network of covalent bonds and exists as giant molecules. Example: Diamond
Their main characteristics are:-
*As covalent bond is strong and directional in nature, these solid are very hard and brittle.
*They have extremely high melting points and decompose before melting.
*They are insult of and do not conduct electricity one exception is graphite which is covalent solid but is soft and also a good conductor of electricity.
4. Metallic solids:-
In natural the constituent particles are positively charged metal ions – and free electrons.
*They are formed of metal atoms which lose their valance electrons to left behind positively charged ions.
*These metal atoms are surrounded by the sea of electrons each metal atom contributes one or more electrons to this sea of electrons.
*The electrons are simultaneously attracted by the +ve ions and holds these +ve ions ether
Metallic bond:-
The force that holds the metal ion together in the crystal is called metallic bond.
Properties of metallic solids:-
*They possess high electrical and thermal conductivity.
*They possess lusture and colour in some case due to presence of sea of free electrons.
*They are highly malleable and ductile.
*They are closely packed. They exhibit high melting points and high density
Crystal lattice:-
a. Such a regular arrangement of the constituent particles [atoms, ions or molecules] of a lattice.
b. The constituent particles of crystalline solids are arranged in definite fashion in three dimensional space.
Characteristic of crystal lattice:-
a. Each point in the crystal lattice represents a constituent particle which may be atom, molecule, ion.
b. Each points in the lattice is called lattice point or lattice site.
c. The points are joined by lines just to represent the geometry of the lattice.
Unit cell:-
The smallest three dimensional portion of a complete space lattice which when repeated over and over again in different directions produce the complete space lattice is called the unit cell.
Parameters of a unit cell:-
a. Its dimensions (length) along the three edges may or may not be perpendicular
b. Angles between the edges, angle alpha(a) between b and c, β between a and c, γ between a and b. Thus a unit cell is chaterised six parameters.
Based upon difference in the parameters there are basically seven types of unit cell are:-
Primitive unit cell:-
The unit cell in which the constituent particles are present only at the corners are called “simple unit cells” or “primitive unit cells”.
Face centred:-
When particles are present not only at the corners, but also at the centre of each face of unit cell, it is called face centred unit cell.
End centred:-
When in addition to the particles at the corner, there are also the particles at the centre of any of two opposite faces it is called end centred unit cell.
Body centred:-
When in addition to the particles present at the corner one particle is also present at the centre of unit cell it is called body centred unit cell.
Bravais Lattices:-
The fourteen lattices corresponding to seven crystal systems are known as the bravais lattices.
We generally represents the unit cells by three dimensional arrangement of spheres.
Coordination Number:-
The coordination number of any constituent particle in a given unit cell is the no. of particles touching that particle.
CALCULATION OF NUMBER OF PARTICLES PER UNIT CELL OF A CUBIC CRYSTAL SYSTEM:-
1. Calculation of contribution of atom present at different lattice sites.
An atom at the corner is shared by eight unit cells so its contribution is = 1x(1/8)=1/8
An atom on the face is shared between two unit cells so its contribution is =1x(1/2)=1/2
An atom present at centre of unit cell is not shared by any unit cell so it contribution is = 1
An atom present at the edge is shared by four unit cells so its contribution is =1x(1/4)=1/4
2. Calculation of number of atoms per unit cell:-
Simple [primitive] unit cell:- It has only Eight atom present at corner each have contribution 1/8 so 8 x 1/8 = 1 atom.
In body centred unit cell (BCC):- 1. 8 atom on corner = 1/8 x 8 = 1 atom
1 atom at the centre = 1 x 1 = 1
So total no. of atoms = 1 + 1 = 2 atoms.
3. In face centred unit cell [FCC]:-
Contribution by atoms at corner = 1/8 x 8 = 1
Contribution by atoms at faces = 1/3 x 6 = 3
So total atoms = 3 + 1 = 4 atoms.
CLOSE PACKING IN THE CRYSTALS:-
In order to understand the close packing of the constituent particles in a crystal, it is assumed that these particles are hard spheres of identical size.
Close packing:- The packing of spheres in such away such that they occupy maximum available space and left minimum empty space it is called close packing.
Close packing in one dimension:– In one dimension the spheres can be arranged in a row touching each other called packing in one dimension each sphere touch two of its neighbors so its coordination no. is 6
Close – packing in two dimensions:- When the rows are stacked over each other a two dimensional close packed structure [called crystal plane] is formed. This stacking can be done in two ways.
AAA type:-The sphere in second row may be placed in the way such that they are touching each sphere of first row and exactly above sphere of first row in this type coordination no. is 4
ABA type:- The sphere in second row may be placed in depression of first row. This produces a different raw from 1st type in this coordination no. is 6.
Close packing in three dimensions:- Three dimensional close packing from two dimensional (AAA) square close packed structure:-
Starting from square close packed layer:- The second layer and all further layers are build up such that they are horizontally as well as vertically aligned on each other. Thus their lattice is of AAA type. It unit cell is primitive unit cell.
Three dimensional close packing from two dimensional hexagonal close packed layer:-
Let in hexagonal close packing the sphere are marked as A and voids between spheres are marked as a, b alternatively.
When the second layer is placed in such a way that its spheres. Find place in a voids of first layer the b void left in occupied since in this arrangement no sphere can be placed in them.
Now come to have the two types of voids c and d.
Tetrahedral void:- A simple triangular void like c in crystal is surrounded by four spheres and is called a tetrahedral void.
Octahedral void:- Void like (d) is surrounded by six spheres and is called an octahedral void.
The voids or holes in the crystals are also called interstices.Now when a third layer placed over second layer in such a way that sphere cover the tetrahedral (c) void a three dimensional close packing of ABAB patter or hexagonal close packing is obtained.
Example:-Molybdenum, Magnesium have hcp [hexagonal close packing structure].
When third layer is placed over the second layer in such a way that spheres covers the octahedral or (d) voids a three dimensional pattern of ABCABC or Cubic Close Packing (CCP) is formed. It is similar to FCC (Face Centred Packing).
Iron, Nickel, Copper exists in CCP structures.
Coordination Number:-
The number of closest (or nearest) neighbors of any constituent particles in the crystal lattice is called the coordination number
Packing efficiency:-
The percentage of the total space filled by the particles in the three dimensional close packing is known as the packing efficiency.
Packing fraction:-
The total fraction of the space filled in three dimensional close. Packing is called the packing fraction.
1. Calculation of packing efficiency in cubic unit cell (simple cubic):-
In simple cubic unit cell we have the particles present only at the corners thus
Suppose the edge length of the unit cell = a and radius of sphere = r
As sphere are touching each other evidently
=> a = 2r
No. of spheres per unit cell = 1/8 x 8 =1
Volume of sphere = 4/3pr3
Volume of cube = a3 = (2r)3 = 8r3
Packing efficiency [Fractio] =
So packing efficiency of simple cubic unit cell is = 52.4%
2. Packing efficiency of face centred cubic structure [cubic close packing]:-
As the sphere on the face centre is touching the spheres at the corners evidently AC = 4r
But from right angled triangle ABC
Or packing efficiency = 0.74 x 100 = 74%
Thus the packing efficiency of hcp and ccp structures are 74%.
3. Calculation of packing efficiency of body contred cubic structure:-
As the sphere at the body centre touches the spheres at the corner body diagonal AD = 4r
Further face diagonal
Or packing efficiency = 0.68 x 100 = 68%
Thus the packing efficiency in BCC structure is 68%.
LOCATION OF VOIDS IN THE CRYSTAL:-
In a closed packed structure [ccp or hcp] if there are n spheres (atoms or ions) in the packing then
No. of octahedral voids = n
No. of tetrahedral voids = 2n
Example:
In cubic close packing (ccp)
No. of atoms = 4
So No. of octahedral voids = 4
No. of tetrahedral voids = 8
a. Octahedral Voids:-
One octahedral void is present at the body centre of cube and 12 octahedral voids are present on the centres of the 12 edges of the cube. But void on each edge is shared by 4 unit cells so its contribution is = 1/4
b. Tetrahedral Voids:-
There are & tetrahedral voids are present in the ccp structure at different location thus:-
In ccp total no. of voids per unit cell = 8 + 4 = 12
In hcp total no. of voids per unit cell = 12 +6 = 18
CALCULATION OF DENSITY OF CUBIC CRYSTAL FROM ITS EDGE:-
By knowing edge of a cubic crystal from x – ray differ action method and knowing type of crystal possessed by it. The density of crystal can be calculated.
For cubic crystal of ionic compound:-
Suppose the edge of unit cell = a pm
No. of atoms (ions) present per unit cell Z
Atomic [molecular] mass = M
Volume of unit cell = (a pm)3
Mass of the unit cell = No. of atoms in unit cell x Mass
of each atom = Z x m
Defect or Imperfection:-
Any departure from perfectly ordered arrangement of the constituent particles in the crystal called imperfection or defect.
The defects in the crystal are arises when crystallization takes place at the fast or moderate rates because the constituent particles does not get sufficient time to arrange in perfect order.
There are mainly two types of defects:-
Point defect:-When the deviation or irregularities exists from ideal arrangement around a point or an atom in a crystalline substance the defect is called the point defect.
Line defect:- When the deviation from the ideal arrangement exists in the entire row of lattice points the defect is called as line defect.
Types of the point defects:-
1. Stoichiometric defects
2. Non stoichiometric defects
3. Impurity defects
Stoichiometric defect:-
If imperfection in the crystal are such that the ratio between cation and onions remains same. Stoichiometry of substance do not disturbed defect is called stoichiometric defect these defects are of the following types.
1. Vacancy defect:-
When is in a crystalline substance, some of the lattice sites are vacant the crystal is said to have vacancy defect it results in decrease of density of substance.
2. Interstitial defect:-
When some extra constituent particles are present in the interstitial site the crystal is said to be have interstitial defect.
This defect increases density of the crystal
These above types of defects are shown only by non – ionic solids.
3. Schottky defect:-
If in an ionic crystal of the type A+B- equal number of cations and anions are missing from the lattice site. So that electrical neutrality is remained is called schottky defect.
Compounds exhibiting schottky defect are NaCl, KCl
Which compounds have small difference in size of cation and anions show defect.
Frenkel defect:- If an ion is missing, from its lattice site and is occupies the interstitial site, electrical neutrality as well as Stoichiometry of the compound are maintained this type of defect is called frenkel defect. It is also called dislocation defect.
Example:-
(AgCl, AgBr, AgI, ZnS) shows this defect which have a large difference in size of cations and anions.
Main points of difference between schottky and frankel defect
Non stoichiometric defects:-
If a result of the imperfactions in the crystal the ratio, of the cations and anions becomes difference from that indicated by ideal chemical formula. The defects are called non-stoichiometric defects.
They are of two types:-
i. Metal excess defects:-
A negative ion may be missing from its lattice site, leaving a hole which is occupied by an electron, there by maintain the electrical neutrality.
The interstitial sites containing the electron thus trapped in the anion vacancies are called the F – centers. They are responsible for imparting colour to the crystals.
Example:- When NaCl is heated in an atmosphere of Na vapours. The excess of Na atoms deposition the surface of NaCl crystal Cl- ions then diffuse to the surface where the combine with Na+ ions which becomes due to losing electrons.
These electrons loses by Na atom are diffuse back into the crystal and occupy the vacant site created by Cl- ions and imparts Yellow colour to NaCl crystal
ii. By presence of extra cation in interstitial sites:-
• Metal excess may also be caused by an extra cation occupying the interstial site.
For example when ZnO is heated it loses oxygen and turns yellow due to following ZnO → Zn+2 + (1/2)O2 + 2e-
The excess interstitial sites and the electrons in neighbouring interstitial sites
Metal deficiency defect:- This defect occurs when the metal shows the variable valancy. Due to metal deficiency the compounds obtained are non stoichiometric. For example it is difficult to prepare ferrous oxide with ideal composition because ferum exists as both Fe+2 and Fe+3 ions thus we obtain Fe0.95O or FexO with x = 0.93 to 0.96
Impurity defects:-
Defect or Imperfection:-
Any departure from perfectly ordered arrangement of the constituent particles in the crystal called imperfection or defect.
The defects in the crystal are arises when crystallization takes place at the fast or moderate rates because the constituent particles does not get sufficient time to arrange in perfect order.
There are mainly two types of defects:-
Point defect:-When the deviation or irregularities exists from ideal arrangement around a point or an atom in a crystalline substance the defect is called the point defect.
Line defect:- When the deviation from the ideal arrangement exists in the entire row of lattice points the defect is called as line defect.
Types of the point defects:-
1. Stoichiometric defects
2. Non stoichiometric defects
3. Impurity defects
Stoichiometric defect:-
If imperfection in the crystal are such that the ratio between cation and onions remains same. Stoichiometry of substance do not disturbed defect is called stoichiometric defect these defects are of the following types.
1. Vacancy defect:-
When is in a crystalline substance, some of the lattice sites are vacant the crystal is said to have vacancy defect it results in decrease of density of substance.
2. Interstitial defect:-
When some extra constituent particles are present in the interstitial site the crystal is said to be have interstitial defect.
This defect increases density of the crystal
These above types of defects are shown only by non – ionic solids.
3. Schottky defect:-
If in an ionic crystal of the type A+B- equal number of cations and anions are missing from the lattice site. So that electrical neutrality is remained is called schottky defect.
Compounds exhibiting schottky defect are NaCl, KCl
Which compounds have small difference in size of cation and anions show defect.
Frenkel defect:- If an ion is missing, from its lattice site and is occupies the interstitial site, electrical neutrality as well as Stoichiometry of the compound are maintained this type of defect is called frenkel defect. It is also called dislocation defect.
Example:-
(AgCl, AgBr, AgI, ZnS) shows this defect which have a large difference in size of cations and anions.
Main points of difference between schottky and frankel defect
Non stoichiometric defects:-
If a result of the imperfactions in the crystal the ratio, of the cations and anions becomes difference from that indicated by ideal chemical formula. The defects are called non-stoichiometric defects.
They are of two types:-
i. Metal excess defects:-
A negative ion may be missing from its lattice site, leaving a hole which is occupied by an electron, there by maintain the electrical neutrality.
The interstitial sites containing the electron thus trapped in the anion vacancies are called the F – centers. They are responsible for imparting colour to the crystals.
Example:- When NaCl is heated in an atmosphere of Na vapours. The excess of Na atoms deposition the surface of NaCl crystal Cl- ions then diffuse to the surface where the combine with Na+ ions which becomes due to losing electrons.
These electrons loses by Na atom are diffuse back into the crystal and occupy the vacant site created by Cl- ions and imparts Yellow colour to NaCl crystal
ii. By presence of extra cation in interstitial sites:-
• Metal excess may also be caused by an extra cation occupying the interstial site. For example when ZnO is heated it loses oxygen and turns yellow due to following ZnO → Zn+2 + (1/2)O2 + 2e-
The excess interstitial sites and the electrons in neighbouring interstitial sites.
Metal deficiency defect:- This defect occurs when the metal shows the variable valancy. Due to metal deficiency the compounds obtained are non stoichiometric. For example it is difficult to prepare ferrous oxide with ideal composition because ferum exists as both Fe+2 and Fe+3 ions thus we obtain Fe0.95O or FexO with x = 0.93 to 0.96
Impurity defects:-
These defects are arises when foreign atoms are present at the lattice site in place of the host atom. Or it is present at the vacant interstitial site example n – type semi conductor, p – type semi conductor.
The process of adding impurities to the crystalline is called as doping.
In case of ionic solids the impurities are introduced by adding impurity of ions. If the impurity ions are in different valnce state from that of host ions. Vacancies are created if mole ten NaCl containing a little impurity of SrCl2 and is allowed to cool. The vacancies of Na+ ions are created and thses are occupied by sr+2 ions.
Introducing Impurity in covalent solids:-
i. Doping with electron rich impurities (formation of n – type semi conductor):-
Group in elements like silicon or germanium has 4 electrons in valance Shell. Thus it form four covalent bonds with neighbouring atoms. When it is doped by group 15 element like P or As, the silicon or germanium atom at some lattice sites are substituted by P or As.
Now doped atom have 5 valence electrons after forming four covalent bonds. The fifth free electron is gets delocalized. This increases conductivity of silicon.
As conductivity is increases due to electrons thus the germanium crystal doped with e- rich impurity are called n – type semi conductors.
ii. Doping with electron deficit impurities:- (P – type semi conductor)
If group 14 element like silicon are doped with 3 valance electron containing 13 group elements like Al or Ga.
Due to three valance electron all atom forms 3 valance bond with 3 silicon atoms. Thus a hole is get created at the site of fourth electron is missing. This is called electron hole or electron vacancy.
If an electron jump from neighbouring site to fill this hole a another hole is generated at that site and it continues.
Thus if electric field is applied the electrons move towards +vely charged plate and electron holes move towards negative charged plate as they carry +ve charge. Thus a semiconductor with increased conducting is formed and called P – type semiconductor.
CHAPTER:- SOLID STATE
SOLID- Solids are defined as substances that retain their shape, even when they are not confined. Substances usually assume the solid state of being at lower temperatures than they do when they are liquids, gases or plasmas.
CLASSIFICATION ON THE BASIS OF ARRANGEMENT OF CONSTITUENT PARTICLES
1. Crystalline Solids:-
A solid is said to be crystalline if its various constituent particles [ions, atoms, molecules] are arranges in a definite geometric pattern in the three dimensional space so that there is short as well as long range order of constituent particles.Example:- Sodium, Calcium, Stones, Gems, Wood etc.
2. Amorphous Solid:-
If there is no regular arrangement of constituent particles or there is only the short range order of its constituent particles then the solid is called amorphous solid.Example:- Rubber, Glass, Pitch, Silica etc.
3. Isotropy:-
In the amorphous solids there is no regular arrangement of particles thus the properties like electrical conductivity, thermal expansion are identical in all the direction. This property is called isotropy.
Amorphous solid are isotropic in nature.
4. Anisotropy:-
Due to regular arrangement of constituent particles, the different particles are fall in different ways of a crystalline solid. The values of properties like electrical conductivity and thermal expansion not remains same in all the direction this is called anisotropy.
And crystalline solids are anisotropic in nature
AMORPHOUS IS VERY USEFUL IN OUR DAILY TO DAILY LIFE SUCH AS:-
The glasses [Amorphous] are used in construction house ware, laboratory ware etc.
A large no. of amorphous plastics is being used in forming no. of articles.
Amorphous silica has found to be the best material for converting sunlight into electricity
AMORPHOUS VS CRYSTALLINE SOLID:-
Amorphous and crystalline solids differ in the properties such as cleavage property, melting point, shape, anisotropy etc.
Amorphous structure of a glassy solid (left) and lattice structure of a crystalline solid (right).
Amorphous solids
1. There is only a short range order in amorphous solids
2. Amorphous solids do not have a sharp melting point; they are softened in a range of temperature.
3. Amorphous solids undergo irregular or conchoidal breakage
4. Amorphous solids are isotrophic-the properties will be independent of the direction in which they are measured.
5. Less rigid.
Examples of Amorphous solids: Fibre glass, Cellophane, Teflon, Polyurethane, Napthalene, Polyvinyl chloride
Crystalline solids
1. There is a long range order in crystals.
2. Melt at a sharp temperature.
3. Crystalline solids can be cleaved along definite planes.
4. Crystalline solids, in general are anisotrophic (It means that, their properties such as electrical conductivity, refractive index, thermal expansion etc. will be different directions).
5. More rigid.
Examples of Crystalline solids: Copper, Potassium nitrate, Benzoic acid
CLASSIFICATION OF CRYSTALLINE SOLIDS:-
Based upon nature of constituent particles and binding forces present in them:-
1. Ionic Solids:-
*In these solids constituent particles are positive and negative ions. (cation or anions). They are held together by strong columbic electrostatic forces of attraction examples are NaCl, CaCl2, MgCl2, BaCl2 etc.
Characteristics of ionic solids:-
*They have high melting and boiling points
They are soluble in polar solvents but are insoluble in non polar solvents.
Due to strong electrostatic forces of attraction they are closely packed hence hard but they are brittle.
2. Molecular Solids:-
In these solids the constituent particles are molecules on the nature of molecules they can further subdivided into following three types:-
1. Non polar molecular solids:-
The crystalline solids in which constituent particles are atoms of noble gases [helium, neon] or non polar molecules like [H2, Cl2, I2]
Their characters are:-
*They are soft due to weak intermolecular forces.
*They are non conductors of electricity. They have low melting and boiling points.
2. Polar molecular solids:-
The crystalline solids in which constituent particles are polar molecules like HCl, SO2 etc. the intermolecular forces of attraction are dipole – dipole forces of attraction.
Thus their characters are:-
*They are soft; they are non conductors of electricity.
*Their melting and boiling points are high then non polar solids. They exists gases or liquid at room temperature.
3. Hydrogen bonded – molecular solids:-
*In these solids the constituent particles are which contain hydrogen atom linked to high electronegative atoms as N, O, F
Their characters are:-
*They exists as volatile liquids or gases at room temperature.
*They are non conductor of electricity.
*Their melting and boiling points are high.
3. Covalent or network solids:-
In these crystalline solids the constituent particles are non metal atoms linked to adjacent atom by covalent bond throughout the crystal. They forms a network of covalent bonds and exists as giant molecules. Example: Diamond
Their main characteristics are:-
*As covalent bond is strong and directional in nature, these solid are very hard and brittle.
*They have extremely high melting points and decompose before melting.
*They are insult of and do not conduct electricity one exception is graphite which is covalent solid but is soft and also a good conductor of electricity.
4. Metallic solids:-
In natural the constituent particles are positively charged metal ions – and free electrons.
*They are formed of metal atoms which lose their valance electrons to left behind positively charged ions.
*These metal atoms are surrounded by the sea of electrons each metal atom contributes one or more electrons to this sea of electrons.
*The electrons are simultaneously attracted by the +ve ions and holds these +ve ions ether
Metallic bond:-
The force that holds the metal ion together in the crystal is called metallic bond.
Properties of metallic solids:-
*They possess high electrical and thermal conductivity.
*They possess lusture and colour in some case due to presence of sea of free electrons.
*They are highly malleable and ductile.
*They are closely packed. They exhibit high melting points and high density
Crystal lattice:-
a. Such a regular arrangement of the constituent particles [atoms, ions or molecules] of a lattice.
b. The constituent particles of crystalline solids are arranged in definite fashion in three dimensional space.
Characteristic of crystal lattice:-
a. Each point in the crystal lattice represents a constituent particle which may be atom, molecule, ion.
b. Each points in the lattice is called lattice point or lattice site.
c. The points are joined by lines just to represent the geometry of the lattice.
Unit cell:-
The smallest three dimensional portion of a complete space lattice which when repeated over and over again in different directions produce the complete space lattice is called the unit cell.
Parameters of a unit cell:-
a. Its dimensions (length) along the three edges may or may not be perpendicular
b. Angles between the edges, angle alpha(a) between b and c, β between a and c, γ between a and b. Thus a unit cell is chaterised six parameters.
Based upon difference in the parameters there are basically seven types of unit cell are:-
Primitive unit cell:-
The unit cell in which the constituent particles are present only at the corners are called “simple unit cells” or “primitive unit cells”.
Face centred:-
When particles are present not only at the corners, but also at the centre of each face of unit cell, it is called face centred unit cell.
End centred:-
When in addition to the particles at the corner, there are also the particles at the centre of any of two opposite faces it is called end centred unit cell.
Body centred:-
When in addition to the particles present at the corner one particle is also present at the centre of unit cell it is called body centred unit cell.
Bravais Lattices:-
The fourteen lattices corresponding to seven crystal systems are known as the bravais lattices.
We generally represents the unit cells by three dimensional arrangement of spheres.
Coordination Number:-
The coordination number of any constituent particle in a given unit cell is the no. of particles touching that particle.
CALCULATION OF NUMBER OF PARTICLES PER UNIT CELL OF A CUBIC CRYSTAL SYSTEM:-
1. Calculation of contribution of atom present at different lattice sites.
An atom at the corner is shared by eight unit cells so its contribution is = 1x(1/8)=1/8
An atom on the face is shared between two unit cells so its contribution is =1x(1/2)=1/2
An atom present at centre of unit cell is not shared by any unit cell so it contribution is = 1
An atom present at the edge is shared by four unit cells so its contribution is =1x(1/4)=1/4
2. Calculation of number of atoms per unit cell:-
Simple [primitive] unit cell:- It has only Eight atom present at corner each have contribution 1/8 so 8 x 1/8 = 1 atom.
In body centred unit cell (BCC):- 1. 8 atom on corner = 1/8 x 8 = 1 atom
1 atom at the centre = 1 x 1 = 1
So total no. of atoms = 1 + 1 = 2 atoms.
3. In face centred unit cell [FCC]:-
Contribution by atoms at corner = 1/8 x 8 = 1
Contribution by atoms at faces = 1/3 x 6 = 3
So total atoms = 3 + 1 = 4 atoms.
CLOSE PACKING IN THE CRYSTALS:-
In order to understand the close packing of the constituent particles in a crystal, it is assumed that these particles are hard spheres of identical size.
Close packing:- The packing of spheres in such away such that they occupy maximum available space and left minimum empty space it is called close packing.
Close packing in one dimension:– In one dimension the spheres can be arranged in a row touching each other called packing in one dimension each sphere touch two of its neighbors so its coordination no. is 6
Close – packing in two dimensions:- When the rows are stacked over each other a two dimensional close packed structure [called crystal plane] is formed. This stacking can be done in two ways.
AAA type:-The sphere in second row may be placed in the way such that they are touching each sphere of first row and exactly above sphere of first row in this type coordination no. is 4
ABA type:- The sphere in second row may be placed in depression of first row. This produces a different raw from 1st type in this coordination no. is 6.
Close packing in three dimensions:- Three dimensional close packing from two dimensional (AAA) square close packed structure:-
Starting from square close packed layer:- The second layer and all further layers are build up such that they are horizontally as well as vertically aligned on each other. Thus their lattice is of AAA type. It unit cell is primitive unit cell.
Three dimensional close packing from two dimensional hexagonal close packed layer:-
Let in hexagonal close packing the sphere are marked as A and voids between spheres are marked as a, b alternatively.
When the second layer is placed in such a way that its spheres. Find place in a voids of first layer the b void left in occupied since in this arrangement no sphere can be placed in them.
Now come to have the two types of voids c and d.
Tetrahedral void:- A simple triangular void like c in crystal is surrounded by four spheres and is called a tetrahedral void.
Octahedral void:- Void like (d) is surrounded by six spheres and is called an octahedral void.
The voids or holes in the crystals are also called interstices.Now when a third layer placed over second layer in such a way that sphere cover the tetrahedral (c) void a three dimensional close packing of ABAB patter or hexagonal close packing is obtained.
Example:-Molybdenum, Magnesium have hcp [hexagonal close packing structure].
When third layer is placed over the second layer in such a way that spheres covers the octahedral or (d) voids a three dimensional pattern of ABCABC or Cubic Close Packing (CCP) is formed. It is similar to FCC (Face Centred Packing).
Iron, Nickel, Copper exists in CCP structures.
Coordination Number:-
The number of closest (or nearest) neighbors of any constituent particles in the crystal lattice is called the coordination number
Packing efficiency:-
The percentage of the total space filled by the particles in the three dimensional close packing is known as the packing efficiency.
Packing fraction:-
The total fraction of the space filled in three dimensional close. Packing is called the packing fraction.
1. Calculation of packing efficiency in cubic unit cell (simple cubic):-
In simple cubic unit cell we have the particles present only at the corners thus
Suppose the edge length of the unit cell = a and radius of sphere = r
As sphere are touching each other evidently
=> a = 2r
No. of spheres per unit cell = 1/8 x 8 =1
Volume of sphere = 4/3pr3
Volume of cube = a3 = (2r)3 = 8r3
Packing efficiency [Fractio] =
So packing efficiency of simple cubic unit cell is = 52.4%
2. Packing efficiency of face centred cubic structure [cubic close packing]:-
As the sphere on the face centre is touching the spheres at the corners evidently AC = 4r
But from right angled triangle ABC
Or packing efficiency = 0.74 x 100 = 74%
Thus the packing efficiency of hcp and ccp structures are 74%.
3. Calculation of packing efficiency of body contred cubic structure:-
As the sphere at the body centre touches the spheres at the corner body diagonal AD = 4r
Further face diagonal
Or packing efficiency = 0.68 x 100 = 68%
Thus the packing efficiency in BCC structure is 68%.
LOCATION OF VOIDS IN THE CRYSTAL:-
In a closed packed structure [ccp or hcp] if there are n spheres (atoms or ions) in the packing then
No. of octahedral voids = n
No. of tetrahedral voids = 2n
Example:
In cubic close packing (ccp)
No. of atoms = 4
So No. of octahedral voids = 4
No. of tetrahedral voids = 8
a. Octahedral Voids:-
One octahedral void is present at the body centre of cube and 12 octahedral voids are present on the centres of the 12 edges of the cube. But void on each edge is shared by 4 unit cells so its contribution is = 1/4
b. Tetrahedral Voids:-
There are & tetrahedral voids are present in the ccp structure at different location thus:-
In ccp total no. of voids per unit cell = 8 + 4 = 12
In hcp total no. of voids per unit cell = 12 +6 = 18
CALCULATION OF DENSITY OF CUBIC CRYSTAL FROM ITS EDGE:-
By knowing edge of a cubic crystal from x – ray differ action method and knowing type of crystal possessed by it. The density of crystal can be calculated.
For cubic crystal of ionic compound:-
Suppose the edge of unit cell = a pm
No. of atoms (ions) present per unit cell Z
Atomic [molecular] mass = M
Volume of unit cell = (a pm)3
Mass of the unit cell = No. of atoms in unit cell x Mass
of each atom = Z x m
Defect or Imperfection:-
Any departure from perfectly ordered arrangement of the constituent particles in the crystal called imperfection or defect.
The defects in the crystal are arises when crystallization takes place at the fast or moderate rates because the constituent particles does not get sufficient time to arrange in perfect order.
There are mainly two types of defects:-
Point defect:-When the deviation or irregularities exists from ideal arrangement around a point or an atom in a crystalline substance the defect is called the point defect.
Line defect:- When the deviation from the ideal arrangement exists in the entire row of lattice points the defect is called as line defect.
Types of the point defects:-
1. Stoichiometric defects
2. Non stoichiometric defects
3. Impurity defects
Stoichiometric defect:-
If imperfection in the crystal are such that the ratio between cation and onions remains same. Stoichiometry of substance do not disturbed defect is called stoichiometric defect these defects are of the following types.
1. Vacancy defect:-
When is in a crystalline substance, some of the lattice sites are vacant the crystal is said to have vacancy defect it results in decrease of density of substance.
2. Interstitial defect:-
When some extra constituent particles are present in the interstitial site the crystal is said to be have interstitial defect.
This defect increases density of the crystal
These above types of defects are shown only by non – ionic solids.
3. Schottky defect:-
If in an ionic crystal of the type A+B- equal number of cations and anions are missing from the lattice site. So that electrical neutrality is remained is called schottky defect.
Compounds exhibiting schottky defect are NaCl, KCl
Which compounds have small difference in size of cation and anions show defect.
Frenkel defect:- If an ion is missing, from its lattice site and is occupies the interstitial site, electrical neutrality as well as Stoichiometry of the compound are maintained this type of defect is called frenkel defect. It is also called dislocation defect.
Example:-
(AgCl, AgBr, AgI, ZnS) shows this defect which have a large difference in size of cations and anions.
Main points of difference between schottky and frankel defect
Non stoichiometric defects:-
If a result of the imperfactions in the crystal the ratio, of the cations and anions becomes difference from that indicated by ideal chemical formula. The defects are called non-stoichiometric defects.
They are of two types:-
i. Metal excess defects:-
A negative ion may be missing from its lattice site, leaving a hole which is occupied by an electron, there by maintain the electrical neutrality.
The interstitial sites containing the electron thus trapped in the anion vacancies are called the F – centers. They are responsible for imparting colour to the crystals.
Example:- When NaCl is heated in an atmosphere of Na vapours. The excess of Na atoms deposition the surface of NaCl crystal Cl- ions then diffuse to the surface where the combine with Na+ ions which becomes due to losing electrons.
These electrons loses by Na atom are diffuse back into the crystal and occupy the vacant site created by Cl- ions and imparts Yellow colour to NaCl crystal
ii. By presence of extra cation in interstitial sites:-
• Metal excess may also be caused by an extra cation occupying the interstial site.
For example when ZnO is heated it loses oxygen and turns yellow due to following ZnO → Zn+2 + (1/2)O2 + 2e-
The excess interstitial sites and the electrons in neighbouring interstitial sites
Metal deficiency defect:- This defect occurs when the metal shows the variable valancy. Due to metal deficiency the compounds obtained are non stoichiometric. For example it is difficult to prepare ferrous oxide with ideal composition because ferum exists as both Fe+2 and Fe+3 ions thus we obtain Fe0.95O or FexO with x = 0.93 to 0.96
Impurity defects:-
Defect or Imperfection:-
Any departure from perfectly ordered arrangement of the constituent particles in the crystal called imperfection or defect.
The defects in the crystal are arises when crystallization takes place at the fast or moderate rates because the constituent particles does not get sufficient time to arrange in perfect order.
There are mainly two types of defects:-
Point defect:-When the deviation or irregularities exists from ideal arrangement around a point or an atom in a crystalline substance the defect is called the point defect.
Line defect:- When the deviation from the ideal arrangement exists in the entire row of lattice points the defect is called as line defect.
Types of the point defects:-
1. Stoichiometric defects
2. Non stoichiometric defects
3. Impurity defects
Stoichiometric defect:-
If imperfection in the crystal are such that the ratio between cation and onions remains same. Stoichiometry of substance do not disturbed defect is called stoichiometric defect these defects are of the following types.
1. Vacancy defect:-
When is in a crystalline substance, some of the lattice sites are vacant the crystal is said to have vacancy defect it results in decrease of density of substance.
2. Interstitial defect:-
When some extra constituent particles are present in the interstitial site the crystal is said to be have interstitial defect.
This defect increases density of the crystal
These above types of defects are shown only by non – ionic solids.
3. Schottky defect:-
If in an ionic crystal of the type A+B- equal number of cations and anions are missing from the lattice site. So that electrical neutrality is remained is called schottky defect.
Compounds exhibiting schottky defect are NaCl, KCl
Which compounds have small difference in size of cation and anions show defect.
Frenkel defect:- If an ion is missing, from its lattice site and is occupies the interstitial site, electrical neutrality as well as Stoichiometry of the compound are maintained this type of defect is called frenkel defect. It is also called dislocation defect.
Example:-
(AgCl, AgBr, AgI, ZnS) shows this defect which have a large difference in size of cations and anions.
Main points of difference between schottky and frankel defect
Non stoichiometric defects:-
If a result of the imperfactions in the crystal the ratio, of the cations and anions becomes difference from that indicated by ideal chemical formula. The defects are called non-stoichiometric defects.
They are of two types:-
i. Metal excess defects:-
A negative ion may be missing from its lattice site, leaving a hole which is occupied by an electron, there by maintain the electrical neutrality.
The interstitial sites containing the electron thus trapped in the anion vacancies are called the F – centers. They are responsible for imparting colour to the crystals.
Example:- When NaCl is heated in an atmosphere of Na vapours. The excess of Na atoms deposition the surface of NaCl crystal Cl- ions then diffuse to the surface where the combine with Na+ ions which becomes due to losing electrons.
These electrons loses by Na atom are diffuse back into the crystal and occupy the vacant site created by Cl- ions and imparts Yellow colour to NaCl crystal
ii. By presence of extra cation in interstitial sites:-
• Metal excess may also be caused by an extra cation occupying the interstial site. For example when ZnO is heated it loses oxygen and turns yellow due to following ZnO → Zn+2 + (1/2)O2 + 2e-
The excess interstitial sites and the electrons in neighbouring interstitial sites.
Metal deficiency defect:- This defect occurs when the metal shows the variable valancy. Due to metal deficiency the compounds obtained are non stoichiometric. For example it is difficult to prepare ferrous oxide with ideal composition because ferum exists as both Fe+2 and Fe+3 ions thus we obtain Fe0.95O or FexO with x = 0.93 to 0.96
Impurity defects:-
These defects are arises when foreign atoms are present at the lattice site in place of the host atom. Or it is present at the vacant interstitial site example n – type semi conductor, p – type semi conductor.
The process of adding impurities to the crystalline is called as doping.
In case of ionic solids the impurities are introduced by adding impurity of ions. If the impurity ions are in different valnce state from that of host ions. Vacancies are created if mole ten NaCl containing a little impurity of SrCl2 and is allowed to cool. The vacancies of Na+ ions are created and thses are occupied by sr+2 ions.
Introducing Impurity in covalent solids:-
i. Doping with electron rich impurities (formation of n – type semi conductor):-
Group in elements like silicon or germanium has 4 electrons in valance Shell. Thus it form four covalent bonds with neighbouring atoms. When it is doped by group 15 element like P or As, the silicon or germanium atom at some lattice sites are substituted by P or As.
Now doped atom have 5 valence electrons after forming four covalent bonds. The fifth free electron is gets delocalized. This increases conductivity of silicon.
As conductivity is increases due to electrons thus the germanium crystal doped with e- rich impurity are called n – type semi conductors.
ii. Doping with electron deficit impurities:- (P – type semi conductor)
If group 14 element like silicon are doped with 3 valance electron containing 13 group elements like Al or Ga.
Due to three valance electron all atom forms 3 valance bond with 3 silicon atoms. Thus a hole is get created at the site of fourth electron is missing. This is called electron hole or electron vacancy.
If an electron jump from neighbouring site to fill this hole a another hole is generated at that site and it continues.
Thus if electric field is applied the electrons move towards +vely charged plate and electron holes move towards negative charged plate as they carry +ve charge. Thus a semiconductor with increased conducting is formed and called P – type semiconductor.
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