Notes for Class 12 Chemistry Chapter 1 Solid State in pdf

Notes for Class 12 Chemistry Chapter 1 Solid State in pdf

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Notes
Chapter 1 The Solid State

Solids are the substances which have definite volume and definite shape. Their constituent particles are held together by strong intermolecular forces and occupy at their fixed position so that solids are rigid and incompressible. In solids thermal energy is low but intermolecular forces are strong. 

Solids can be classified into two categories on the basis of geometrical pattern of their constituent particles :

1.) Crystalline solids

2.) Amorphous solids

1.)  Crystalline solids

  • Constituent particles are arranged in definite geometrical pattern in 3d space.
  • They are said to have Long range order because a regular and periodically repeating pattern is observed over the entire crystal.
  • They have sharp melting point.
  • They show anisotropy (that means different physical properties in different directions).
  • When crystalline solids are cut by tools like knife, the two smooth and soft surfaces are produced.

Example:-  All Elements (like Fe, Ag, Au etc.), all Ionic solids (like NaCl etc.), Quartz, graphite, diamond etc.

This image describe the basic structural difference between crystalline and amorphous solids. Particles arranged in definite pattern and particles are not arrange in definite pattern.

2.)  Amorphous solids

  • Constituent particles are not arranged in definite geometrical pattern in 3d space.
  • They are said to have short range order.
  • They don’t have sharp melting point. They first soft and then melt over range of temperature.
  • They show isotropy (that means same physical properties in all directions).
  • When amorphous solids are cut by tools like knife, the two rough and irregular surfaces are produced.

Example:-  plastics, rubber, glass, Quartz glass, amorphous silicone etc.

Amorphous Solids are sometimes called pseudo solids or super cooled liquids because Like liquids, amorphous solids have a tendency to flow, though very slowly.

Some glass objects are found to become milky in appearance on annealing because of some crystallisation having taken place.

Classification of Crystalline Solids:

Solids can be classified into 4 categories on the basis of nature of constituent particles and type of intermolecular forces.

  • Molecular solids
    • Polar molecular solids 
    • Non-polar molecular solids
    • Hydrogen bonded molecular solids
  • Ionic solids
  • Metallic solids
  • Covalent or Network solids.
    • Two-dimensional covalent solids
    • Three-dimensional covalent solids

Molecular solids: Constituent particles are molecules. Molecular solids are bad conductor of electricity. They are soft and generally gaseous or liquids at room temperature. They have low enthalpy of vaporisation. Molecular solids further classified into 3 categories on the basis of intermolecular forces:

  • Polar Molecular solids :  Molecules are held together by dipole -dipole force. Example solid HCl, solid SO2 etc.
  • Non-polar Molecular solids :  Molecules are held together by london-dispersion forces. Example solid H2, solid Cl2, solid Br2, I2, solid , solid He, Ne, etc.
  • Hydrogen bonded Molecular solids :  Molecules are held together by polar Hydrogen bonds. They are formed between Hydrogen and strong electronegative elements such as F, O, N.  Example :  water (ice), HF, HNO3 etc.

Ionic Solids :  Constituent particles are positively and negatively charged ions (called cation and anion respectively). They are held together by strong electrostatic or coulombic forces or ionic bonds. They are very hard and brittle. They have very high melting and boiling point. Their ions are not free to move in solid state so they are insulators of electricity but in molten or aqueous solution their ions free to move so become good conductor of electricity. They are non-volatile compounds. Examples : all salts like NaCl, KCl, K2SO4 etc.

Metallic Solids :  Constituent particles are positively charged ions (called  kernals) which are immersed in sea of mobile electrons. When electric field is applied these electrons free to move through positive kernals and conduct electricity. They have property of malleable and ductile that means can be beaten into sheets and drawn into wires. Examples :  Fe, Ag, Au, Pt, W, Cu, Ni, Al, Zn etc

Covalent solids :  Constituent particles are atoms which held together by strong covalent bonds. They have very high melting and boiling point and may even decompose before melting. They show property of Polymorphism (Allotropy). Example :  Carbon, Silicon carbide, Aluminium nitride etc.

Unit Cell and Crystal Lattice

Crystal lattice is a regular arrangement of the constituent particles (atom, ions, or molecules) of a crystalline solid in three-dimensional space.

unit cell and crystal lattice. Unit cell is a cubic structure which when repeated over and over give rise a complete crystal lattice. Both crystal lattice and unit cell can be represented as:

Unit Cell is the smallest repeating unit in space lattice which when repeated over and over, again produces the complete crystal lattice.

Types of Unit Cell. These are simple or primitive unit cell, Body centered unit cell, Face centered unit cell and End centered unit cell.
Parameters of Unit Cell

Total parameters = 6

Parameters of Length = 3  (a, b, c)

Parameters of Angle =  3  (α, β, γ )

Parameters of unit cell represent its length and angles. Lengths of unit cell are along x, y and z axis.
Seven Crystal System

Based on various six parameters of length and angle, a simple unit cell is of seven types. These are called Seven Crystal System: Cubic, Tetragonal, Orthorhombic, Monoclinic, Hexagonal, Rhombohedral, Triclinic.

Seven Crystal System are the seven cubic system formed on the basis of six parameters of length and angle. These system are; Cubic, Tetragonal, Orthorhombic, Monoclinic, Hexagonal, Rhombohedral and Triclinic.
Number of Atoms in a Unit Cell 

The contribution of each atom to the unit cell is:

At cube corner =  1/8
At cube face =   1/2             
Within body = Full sphere 
At cube edge = 1/4
At hexagonal corner =  1/6

contribution of atom to the unit cell

Simple or Primitive Cubic Unit Cell:

Part of atom present at the one corner = 1/8 

[ Total number of corners = 8 ]

Total Number of Atoms present in unit cell = 1/8 × 8 = 1 atom

number of atoms in simple unit cell. Each atom on corner is shared by 8 unit cells.

Body Centered Cubic Unit Cell:

Atoms present at corners = 1/8 × 8 = 1 Atom

Atom present in center of unit cell = 1 Atom 

Total Number of Atoms present in unit cell = 1 + 1 = 2 atoms

Face Centered Unit Cell:

Atoms present at corners = 1/8 × 8 = 1 Atom

Part of atom present at face centre =  1/2   

[ Number of faces = 6 ]

Atoms present at face centre = 1/2 × 6 = 3 Atoms

Total Number of Atoms present in unit cell = 3 + 1 =  4 atoms

Relationship between Edge Length (a), Distance between two nearest atoms (d) and Radius of atom (r)
relationship between a d and r for simple unit cell
Face centered unit cell (relationship between a d and r)
body centered unit cell (relationship between a d and r)
relationship between a d and r
Packing Efficiency

It is the percentage of space occupied by the spheres in the unit cell. It can be calculated by the given formula:

Packing Efficiency =\(\frac{Volume~occupied~by~spheres~in~unit~cell~\times 100}{Total~volume~of~unit~cell}\)

Packing Efficiency for Simple Unit Cell is 52.4% or \(\frac{\pi \times 100}{6}\)

Packing Efficiency for Body Centered Unit Cell is 68% or \(~\frac{\pi \sqrt{3}\times 100}{8}\)

Packing Efficiency for Face Centered Unit Cell is 74% or \(\frac{\pi \times 100}{3\sqrt{2}}\)

Packing Efficiency for HCP Unit Cell is 74% or \(\frac{\pi \times 100}{3\sqrt{2}}\)

Cubic Close Packed Structures
Cubic Close Packing in One Dimension

There is only one way of arranging spheres in which the spheres are placed in a horizontal row touching with each other. In this arrangement each sphere is in contact with two of its neighbors, so that the coordination number is 2.

cubic close packing in one dimension
Cubic Close Packing in Two Dimensions

Two-dimensional close packed structure can be generated by placing the rows of closed packed spheres. The rows can be combined in the following two ways:

Square close packing in two-dimensions

The spheres in second row are exactly above those of the first row. The second row is exactly same as the first one. Each sphere is in contact with four other spheres. Thus, the coordination number of each sphere is 4.

Square close packing in two dimension

Hexagonal close packing in two-dimensions

The spheres are packed in such a way that the spheres in the second row are placed in the depressions between the spheres of the first row. Each sphere is in contact with six spheres. Thus, the coordination number of each sphere is 6.

hexagonal close packing in two dimension
Hexagonal close packing in Three Dimensions

(i)   3 D close packing from 2 D square close packed layer

Starting from the square close packed layer, the second layer and all further layers will be built up such that they are horizontally as well as vertically aligned with each other. This type of packing is also called simple cubic packing. 52.4 % of the available space is occupied by the spheres. Coordination number of each sphere is 6.

Simple cubic packing in 3d

(ii)   3 D close packing from 2 D hexagonal close packed layer

Let us mark the spheres in first layer as ‘A’. In the first layer there are some empty spaces called voids or holes. These are triangular in shape. These triangular voids are of two types marked as ‘a’ and ‘b’. All voids are equivalent.

Let us place the spheres on voids marked ‘b’ to make second layer which may labelled as B layer. Obviously, the voids marked ‘a’ remain unoccupied while building the second layer. A new void marked ‘c’ is formed in the second layer.

cubic close packed structures

A simple triangular voids like ‘b’ and ‘c’ in a crystal is surrounded by four spheres and is called tetrahedral void. A double triangular void with apices in opposite direction (like ‘a’) is surrounded by six spheres and is called octahedral void.

octahedral and tetrahedral voids

Now the third layer can be built up by placing spheres above tetrahedral voids marked ‘c’ or octahedral voids marked ‘a’.

Covering tetrahedral voids

When third layer is placed over the second layer in such a way that the sphere covers the tetrahedral or ‘c’ voids. Third layer become exactly identical to the first layer. This type of packing is called hexagonal close packing (hcp). Coordination number of each sphere is 12.

three dimensional hexagonal close packing by covering tetrahedral voids Notes for Class 12 Chemistry Chapter 1 Solid State in pdf

Covering octahedral voids

When third layer is placed over the second layer in such a way that the sphere covers the octahedral or ‘a’ void. Third layer become differ to the first layer ‘A’ and second layer ‘B’. Let us call it as layer ‘C’. This type of packing is called cubic close packing (ccp) or face-centred cubic packing (fcc). Coordination number of each sphere is 12.

3d packing by covering octahedral void
Keep in Mind

Let the number of closed packed spheres be N, then:

The number of tetrahedral voids generated = 2N

The number of octahedral voids generated = N

Total number of tetrahedral and octahedral voids = 3N

Location of voids in a crystal

Octahedral voids: 

One octahedral void is present at the body center of the cube and 12 octahedral voids are present on the centers of the 12 edges of the cube. Therefore, the effective number of octahedral voids in the ccp structure = 1 + 1/4 × 12  =  1 + 3 = 4.

location of octahedral void in crystal

Tetrahedral voids:

The tetrahedral voids are found to be present on the body diagonals, two on each body diagonal at one-fourth of the distance from each end. Each sphere at the corner touches three spheres present on the face-centers of the three joining faces, each give rise to one tetrahedral void.

location of tetrahedral void in crystal
Formula of a compound and number of voids filled

Ionic solids, the bigger ions (usually anions) form the close packed structure and the smaller ions (usually cation) occupy the voids (may be tetrahedral or octahedral).

Formula of compound and number of voids filled
Size of Tetrahedral and Octahedral voids

Size of octahedral void [Relationship between Radius of octahedral void (r) and Radius of sphere (R)]

r  = 0.414 R

Size of Tetrahedral void [Relationship between Radius of Tetrahedral void (r) and Radius of sphere (R)]

r  = 0.225 R

Radius Ratio

In case of ionic solids, the ratio of radius of the cation to radius of the anion is called radius ratio.

Radius Ratio = \(\frac{radius~of~cation}{radius~of~anion}\)

Since, cations have a tendency to get surrounded by the maximum number of the anion. Therefore, larger the cation radii, the greater will be its coordination number.

The relationship between radius ratio, the coordination number and structure arrangement is called radius ratio rule.

radius ratio
Calculations Involving Density of Unit Cell

Consider a Cubic unit cell :

  • The length of the edge of the cell = ‘a’ cm
  • Volume of unit cell = (‘a’ cm)3 = a3 cm3

Density of unit cell = \(\frac{Mass~of~unit~cell}{Volume~of~unit~cell}\) = \(\frac{Mass~of~unit~cell}{a^{3}}\)

Mass of unit cell = Number of atoms in unit cell (Z) × Mass of one atom (m) = Z × m

  • Mass of one atom (m) = \(\frac{Atomic~Mass~(M)}{Avogadro~number~(N_{A})}\)

Mass of unit cell = \(\frac{Number~of~atom~in~unit~cell~\times ~Atomic~mass}{Avogadro~number}\) = \(\frac{Z~\times ~M}{N_{A}}\)

Density of unit cell = \(\frac{Number~of~atom~in~unit~cell~\times ~Atomic~mass}{Volume~of~unit~cell~\times ~Avogadro~number}\) =\(\frac{Z~\times ~M}{a^{3}~\times ~N_{A}}~~gram/cm^{3}\)

Imperfections or Defects in Solids

An ionic crystal which has the same unit cell constituting the same lattice points throughout the whole of crystal is known as ideal crystal. However, such ideal crystals exist only at absolute zero (0 K) temperature.

Any deviation from perfectly ordered arrangement of constituent particles in crystal is called imperfection or defect.

Ideal crystal and Non-ideal crystal or Imperfection in solids

There are commonly two types of imperfections:

  • Electronic imperfections
  • Atomic imperfections or point defects.

Electronic Imperfection

The perfectly ionic or covalent crystals at 0 K have electrons present in the fully occupied lowest energy states. But at higher temperature (above 0 K), some of the electron may occupy higher energy states, depending upon the temperature, then the defect arises is called electronic imperfections.

Electronic Imperfection

Atomic Imperfection

When the deviations or irregularities exist from the ideal arrangement around an atom in a crystalline substance, the defect is called point defect or atomic defect

However, when the deviation from the ideal arrangement exists in the entire row of lattice points, the defect is called line defect or dislocation.

point defect and line defect

The point defects or atomic defects in ionic crystals may be classified as:

  1. Defects in stoichiometric crystals.
  2. Defects in non-stoichiometric crystals.
  3. Impurity defects.

DEFECTS IN STOICHIOMETRIC CRYSTALS

Stoichiometric compounds are those in which the numbers of positive and negative ions are exactly in the ratios indicated by their chemical formulae.

In these compounds two types of defects are generally observed. These are:  

  • Schottky defect
  • Frenkel defect

Schottky defect

In an ionic crystal, if equal number of cations and anions are missing from their lattice sites by leaving behind cation vacancy and anion vacancy so that the electrical neutrality is maintained, it is called Schottky defect. In this defect, the density of the crystal markedly lowered. 

Schottky defect

Frenkel defect

In an ionic crystal, when an ion is missing from its normal position and occupies an interstitial site between lattice points is called Frenkel defect or interstitial defect

Frenkel defect

DEFECTS IN NON-STOICHIOMETRIC CRYSTALS

Non-stoichiometric compounds are those in which the numbers of positive and negative ions are different in the ratios as indicated by their chemical formulae but crystal remains neutral.

Non-stoichiometric behavior is most commonly found in transition metal compounds.

Defects in non stoichiometric crystals

IMPURITY DEFECT

These defects in ionic crystals arise due to the presence of some impurity ions at the lattice sites or at the vacant interstitial sites.

Example:  If molten NaCl containing a little amount of SrCl2 is allowed to crystallize, some of the sites of Na+ ions are occupied by Sr+2 ions. For each Sr+2 ion introduced, two Na+ ions are removed to maintain electrical neutrality.

Impurity defect
Electrical Properties of Solids

Solids exhibit electrical conductivities which varies from as low as 10-20 ohm-1 m-1 to 107 ohm-1 m-1.

Conductors insulators and semiconductors (Electrical properties of solids)

MECHANISM OF ELECTRICAL CONDUCTION (Valence Band Theory)

Lower energy band is filled with electrons called valence band while the empty higher energy band is called conduction band. The space between valence band and conduction band represents energies forbidden to electrons called energy gap or forbidden zone.

Mechanism of Electrical Conduction (Valence Band Theory)

EXTRINSIC SEMI-CONDUCTION

The conductivity of the intrinsic semiconductors is too low. Their conductivity is increased by adding an appropriate amount of suitable impurity. This process is called doping.

The impurities are of two types:

  • Electron rich impurities (or donor)
  • Electron deficit impurities (or acceptor)

Electron rich impurities (or donor):

Silicon and Germanium belong to group 14 and have 4 electrons in their valence shell. When their crystal is doped with impurities having more than 4 electrons in valence shell such as Group 15 elements (P, As, Sb), a minute proportion of Si or Ge atoms are randomly replaced by dopant.  The dopant uses 4 of its electrons in covalent bond formation similar to Si or Ge and 5th electron remains free. This extra electron becomes delocalised and contributes towards electrical conductivity.  This type of conduction is known as n-type semi-conduction.

n type semiconductor (doping with electron rich impurities)

Electron deficit impurities (or acceptor):

When Silicon and Germanium crystals are doped with impurities belong to Group 13 elements (like Al, Ga or In), having 3 electrons in valence shell form three bonds in the lattice and unable to form 4 bonds to complete the network structure.  As a result, some sites are normally occupied by electrons will left empty and give rise to electron deficiencies called positive hole. The migration of positive hole continues and current is carried throughout the crystal. This type of conduction is called p-type semi-conduction.

p type semiconductor (doping with electron deficient impurities)
Magnetic Properties of Solids 

The magnetic properties of materials are due to magnetic moment associated with individual electron. Each electron in atom has magnetic moment which originates from two sources:

  • Orbital motion of electron around the nucleus.
  • Spin of electron around its own axis.

Based on the behavior in external magnetic field, the substances are divided into five different categories:

  • Diamagnetic Substances
  • Paramagnetic substances
  • Ferromagnetic substances
  • Anti-ferromagnetic Substances
  • Ferrimagnetic Substances

Diamagnetic Substances

Substances which are weakly repelled by the external magnetic field are called diamagnetic substances and phenomenon is called diamagnetism. Diamagnetism arises when all the electrons are paired which cancels their magnetic moments.

Paramagnetic Substances

Substances which are weakly attracted by the external magnetic field and lose their magnetism in the absence of external magnetic field are called paramagnetic substances and the phenomenon is called paramagnetism. This property is shown by those substances whose atom, ions or molecules contain unpaired electrons.

Ferromagnetic Substances

Substances which are strongly attracted by the external magnetic field and show permanent magnetism even in the absence of external magnetic field are called ferromagnetic substances and the phenomenon is called ferromagnetism.

Anti-ferromagnetic Substances 

A substance which is expected to possess paramagnetism or ferromagnetism on the basis of unpaired electrons but possesses zero magnetic moment is called anti-ferromagnetic substance. This is because all domains are aligned in equal number in opposite directions and the net magnetic moment is zero.    

Ferrimagnetic Substances 

Substances which are expected to possess large magnetism on the basis of the magnetic moments of domains but actually have small net magnetic moment are called ferrimagnetic substances. This is because domains are aligned in parallel and anti-parallel directions in unequal numbers resulting in magnetic moment. 

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