In this article, we are going to discuss Solid State class 12 Notes of chemistry.
Solid: A substance that possesses rigidity and has definite shape and size.
Cause of existence of some sort substances as solids:
Intermolecular Forces: These are the forces existing among the constituent particles of the substance which keeps them close together.
Thermal energy: The energy possessed by the constituent particles as it tends to make them move fast. At low temperature, the thermal energy is low and intermolecular forces are strong. The constituent particles thus oscillate about their mean position and the substance exists as solid.
Characteristics of solid:
The constituent particles are closely packed. They occupy fixed positions and can only oscillate about their mean positions. They also have high density, definite shape, and volume and possesses rigidity. The intermolecular distances are very small. They are also incompressible.
Classification on the basis of the arrangement of constituent particles
Crystalline solid: A crystalline solid has its various constituent particles arranged in a definite geometric pattern in the three-dimensional space. There is a short range as well as a long-range order of the constituent particles. Example NaCl,Quartz,etc.
Amorphous solid: When the arrangement of constituent particles is not regular or there is only a short-range order of its constituent particles, then it is an amorphous solid. Example: silica, rubber, glass, etc.
Isotropy: There is no regular arrangement of particles in the amorphous solids. The properties like electrical conductivity, thermal expansion are identical in all directions. This property is called isotropy. Solids that are isotropic in nature are the Amorphous solids
Anisotropy: Due to regular arrangement of constituent particles, the particles become arranged differently in different directions in a crystalline solid and hence the values of physical properties like electrical conductivity and thermal expansion does not remain the same in all the direction and is said to be anisotropic in nature.
A regular three dimensional (3-D) arrangement of points in space is called a space lattice or crystal lattice or simply lattice.
- Each point in a lattice is known as lattice points or lattice site.
- Each lattice points represents one constituent particles which may be an atom, molecule, ion.
- The Lattice points when joined by straight lines gives the geometry of the lattice.
Bravais Lattices: There are only 14 possible three dimensional (3-D) lattices, they are called Bravais Lattices.
A unit cell is a set of lattice points so chosen that the entire lattice can be built up by moving the unit cell along its edges.
A unit cell is characterized by:
- Its dimensions along the edges which may or may not be mutually perpendicular.
- Angles between the edges.
Unit cells are divided into two categories- primitive unit cell and centred unit cells.
Primitive unit cell:
A unit cell is a primitive unit cell when the constituent particles are present only at the corner positions of a unit cell.
Centred unit cell:
A unit cell is a centred unit cell when it contains one or more constituent particles at positions other than corners in addition to those present at the corners.
Types of Centred unit cells:
Face centred unit cell: It constitutes that one constituent particle is present at each face besides the ones at the corners.
Body centred unit cell: It constitutes that one constituent particle is present at the body centre beside the one at the corners.
End centred unit cell: It constitutes that one constituent particle is present each on any two opposite faces besides the one at the corners.
There are 7 types of primitive unit cells:
Calculation of the number of particles one unit cell of a cubic crystal system:
Calculation of contribution of atom present at different lattice sites.
A corner atom is shared by 8 unit cells so its contribution is 1 * 1/8 =1/8.
An atom on the face is shared between two unit cells so its contribution is 1*1/2=1/ 2.
A centre atom of a unit cell is not shared by any other unit cell so the contribution of it is 1.
An atom at the edge is shared by 4 unit cell so contribution of it is 1* 1/ 4 =1/4.
Calculation of the number of atoms per unit cells:
Simple (primitive) unit cell: It has only 8 atoms present at the corners and each has a contribution of 1/8.So 8 * 1/8 = 1 atom.
In body centred unit cell (BCC): It has 8 atoms at the corners = 1 /8 *8 = 1 atom.
1 atom at the centre =1 * 1 = 1
So, the total no. of atoms =2 atoms.
In face centred unit cell (FCC):
Contribution by atom at the corners = 1/8 * 8 = 1
Contribution of atoms at the faces = 1/2 *6 = 3
So, the total number of theatoms = 1 + 3 = 4 atoms.
Close packing in the Crystals:
For the better understanding of 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 a way such that they occupy maximum available space and leaves minimum empty space is called close packing.
Close packing in:-
(i) One dimension: Each sphere touches two of its neighbours, so it has a coordination number 2.
(ii) two dimensions: A two-dimensional close-packed structure is formed. This stacking can be done in two ways.
AAA type:- The sphere in the 2nd row may be placed in such a way, that they are touching each sphere of 1st row exactly above the spheres of the 1st row. The coordination number is 4 and is called square close packing in two dimensions.
ABA-type:- The sphere in the 2nd row may be placed in the depression of 1st row. This produces a different row from 1st type. Here the coordination number is 6 and this packing is called hexagonal close packing in two dimensions.
Close packing in three dimensions:
Three-dimensional close packing can be obtained from two dimensional (AAA) square close-packed structures.
Two types of packing are possible:
The spheres of the 3rd layer are aligned with the spheres of 1st layer and are represented as ABABABABAB…. packing and is known as hexagonal close packing ( hcp). Example:- beryllium, cadmium, magnesium, zinc, etc.
The spheres of the 3rd layer are not aligned with the spheres of the 1st layer while the spheres of the 4th layer are aligned with the spheres of the 1st. This type is represented as ABCABCABC…. packing and is known as cubic close packing (ccp) or face centred cubic (fcc). Example:- Gold, Nickel, Platinum, Silver, iron, copper, etc.
It is the number of nearest neighbours of a sphere in a lattice.
The coordination number of hcp structure is 12 (3 above, 6 in a plane and 3 below). CCP structures have a coordination number 12 ( 4 above, 4 in a plane and 4 below)
It is impossible to pack identical spheres with a coordination number greater than 12. Close packing of structures is associated with lowering of energy. Crystals with directional Bonds have lower coordination number than crystals with non-directional bonds.
Voids or holes are created during the packing of atoms in crystals. They are the empty spaces in close-packed structure. Voids are of two types-
Octahedral voids: These are formed when holes of upper and lower layers fall over each other. Tetrahedral voids: These are formed when a sphere of 1 layer falls above the holes of the second layer.
The no. of these two types of voids depends upon the no. of the closed packed spheres. Let us consider the number of close packed spheres to be N, then
The no. of octahedral voids thus generated = N
The no. of tetrahedral voids thus generated = 2N
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 occupied in the three-dimensional close packing.
simple cube , a=2r =d packing efficiency =52.4%
face centred cube , a= 2√2 =√2d packing efficiency = 74%
body centred cube , a 4r/√3 = 2d/√3 packing efficiency= 68%
Where a= equal edge length of the unit cell; d= diameter of the sphere present in the unit cell; r= radius of the sphere present in the unit cell.
Density of a unit cell:
Where a= edge length of the unit cell; m= mass of each atom; z= number of atoms in a unit cell; M= molar mass; NA= Avogadro’s number.
Defect on Imperfection:
The defects in the Crystal arise when crystallization take place at the fast or moderate rate and thus the constituent particles do not get sufficient time to arrange in perfect order.
There are mainly two types of defects:-
Point defect:- The deviation or irregularities that exist from ideal arrangement around a point or an atom in a crystalline substance.
Line defect:- The deviation from the ideal arrangement that exists in the entire row of lattice points.
Types of Point defect: Stoichiometric defects, Non-stoichiometric defects, and Impurity defects
Stoichiometric defect:- The Stoichiometry of the solid is not disturbed by these defects .i.e., the constituents in a particular solid are present in the same ratio as predicted by their formulae. They are also called as intrinsic or thermodynamic defects. These defects are of the following types-
Vacancy defect:- When some of the lattice sites are vacant in a crystalline substance. Hence the density of the substance decreases.
Interstitial defect:- When some extra constituent particles are present in the interstitial site of a crystal. Hence the density of the crystal increases.
These above types of defects are shown only by non- ionic solids.
Ionic solids show the following defects:-
Schottky defect: An ionic crystal of the type A+B– containing an equal number of cations and anions if found missing from the lattice site so as to maintain the electrical neutrality, then it is called the Schottky defect.
Conditions favouring Schottky defect are:-
High coordination number In which cations and anions have almost identical sizes and Compound exhibiting Schottky defect are NaCl, KCl, CsCl, KBr, AgBr, etc.
Frenkel defect: When an ion is missing from its lattice site and occupies the interstitial site to maintain the electrical neutrality and stoichiometry of the compound. This type of defect is also called as dislocation defect.
Conditions favouring Frenkel defect are:-
Low coordination number In which the anions are bigger in size as compared to the cations and Compounds exhibiting Frenkel defect are AgI, AgCl, ZnS, AgBr, etc.
Non-stoichiometric defects: When the ratio of the cations and anions becomes different from that of the ideal chemical formula due to the defects in the Crystal. They are two types-
Metal excess defect: A Negative Ion may be found missing from its lattice site, thus leaving a hole which is then occupied by an electron thereby maintaining the electrical neutrality. The imparting colour to the crystals is due to the F-centres.
Metal deficiency defect: When the metal shows the variable valence, then this defects can occur. The compound thus obtained are non-stoichiometric due to metal deficiency.
Impurity defect: The impurity ions are in different valance state from that of host ions. Vacancies are created when molten NaCl containing a little impurity of SrCl2 is allowed to cool. The vacancies of Na+ ions are created and are occupied by Sr2+ ions.
Electrical properties of solids:
Conductors: The solids which have the conductivities in the range 104 to 107 ohm-1m-1 are called the conductors. Metals are the best conductor of electricity.
Insulators: The solids which have extremely low conductivities ranging between 10-20 to 10-10 ohm-1m-1 are called insulators. Example: wood, plastic, rubber, etc.
Semiconductors: The solids which have conductivities in between those of conductors and insulators ranging from 10-6 to 10-4 ohm-1m-1 are called the semiconductors. Example: Silicon, Germanium.
On applying an electric current on the molecular orbitals, electrons can move in vacant levels. Thus electric current flows.
Thus the band formed by lower energy valence orbitals is called valence band. It generally contains electrons and band formed by the higher energy orbitals is the conduction band.
Explanation of behaviour of conductors, insulators and semiconductors on the basis of Band theory:-
In case of metals (conductors):- In conductors, the valence band is partially filled with electrons which overlap with higher energy conduction band. Thus metals have high conductivity.
Insulators: In case of insulators, the gap between the conduction band and valence band is very large and thus an electron cannot jump from Valence band to the conduction band and hence cannot exhibit conductivity.
Semiconductors: The gap between valence band and conduction band is very small and some electrons may jump from Valence band to the conduction band and can show immoderate conductivity.
Effect of temperature on conductivity:
The electrical conductivity of metal decreases with increasing the temperature or heating. The electrical conductivity of semiconductors increases on heating since more electrons can jump from Valence band to the conduction band.
Doping: The process of adding impurities to increase the conductivity of semiconductors is called doping.
Conduction of electricity in semiconductors:
Doping with electron-rich impurities (formation of N-type semiconductor):
Group 14 elements like Silicon or Germanium has 4 electrons in the valence shell. Thus it forms 4 covalent bonds with neighbouring atoms. When it is doped by group 15 elements like Phosphorus or arsenic, the Silicon or Germanium atom at lattice sites is substituted by Phosphorus or arsenic. Now the dopped atom has 5 Valence Electrons. After forming four covalent bonds, the fifth electron get delocalised. This increases the conductivity of silicon or Germanium. As conductivity increases due to the negatively charged electron, thus the Germanium or silicon crystal doped with an electron-rich impurity are called n-type semiconductor.
Doping with electron-deficient impurities (P-type semiconductor):
Here silicon is doped with group 13 elements like aluminium or Boron having 3 Valence Electrons. Due to 3 Valence Electrons, they found 3 valence bond with 3 Silicon atoms. Thus a hole is created at the site of the fourth missing electron. Ifan electric field is applied the electrons move towards the positively charged plate and electron holes move towards negative charged played as they carry a positive charge. Thus a semiconductor with increased conductivity is formed and is called P-type semiconductor.
Magnetic properties of solid:
Due to difference in magnetism, magnetic substances are divided into the following categories:-
Diamagnetic substances:– These are the substances which are weakly repelled by the external magnetic fields are called diamagnetic substances. It is shown by fully filled orbitals of a substance. Example C6H6, H2O, NaCl.
Paramagnetic substances:– These are the substances which are attracted by the external magnetic fields are called paramagnetic substances. Paramagnetism is shown by substances whose atoms and ions have unpaired electrons. Example: O2 ,Cu 2+ ,Fe3+.
Ferromagnetic substances:- They show permanent magnetic moment even in the absence of magnetic field. . Example: Nickel, Iron, Cobalt, etc.
Antiferromagnetic substances:- These are the substances which have a domain structure similar to the ferromagnetic substances but the domains are oppositely oriented thereby canceling their magnetic moments are called antiferromagnetic substances. Example: MnO.
Ferrimagnetic substances:- These are the substances which have a domain aligned in parallel and antiparallel direction in an unequal amount resulting in the permanent magnetic character are called paramagnetic substances. Example: Fe3O4.
Radius ratio: It is defined as the ratio of the radius of cation to that of the anion in an ionic crystalline solid.
Radius ratio = radius of cation (r+) / radius of anion (r–).
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