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Amorphous and Crystalline Solids

The state of matter in which the constituent particles are closely packed and occupy fixed positions is called the solid state. They can, however, vibrate about their fixed positions.Solids are characterized by the following properties:

Fixed shape and volume
Strong intermolecular forces
Least intermolecular distances
Incompressible and rigid

Solids can be broadly classified into two types:

Crystalline Solids
Amorphous Solids

Crystalline Solids

The solids having highly ordered arrangements of their particles (atoms, ions, and molecules) in microscopic structures are called crystalline solids. A crystalline solid usually consists of a large number of small crystals, each with a definite characteristic geometrical shape.The crystals have a long range order which means that there is a regular pattern of arrangement of particles which repeats itself periodically over the entire crystal.

Since crystalline solids have ordered arrangement of particles they are regarded as true solids. Examples of crystalline solids are:

They possess a sharp melting point, that is, they melt at a fixed temperature and become a liquid.

If they are cooled, original structure appears again.
Crystalline solids are anisotropic in nature. This means measurement of properties such as electrical conductivity, refractive index, thermal expansion, electrical resistance, etc, gives different values along different directions.

Amorphous Solids

The solids in which the particles are not arranged in any specific order are called amorphous solids. These solids do not possess definite geometrical shape and have irregular patterns, that is why amorphous solids are said to possess short range order of arrangement.
For example; glass, wax, rubber
Amorphous solids melt over a range of temperature and can be moulded and blown into various shapes

These solids are isotropic in nature means they show same value of properties such as thermal expansion, electrical conductivity, electrical resistance,etc, in all the directions. Amorphous solids are called pseudo-solids or super-cooled liquids due to their tendency to flow. Quartz glass is the most important example of an amorphous solid.

Difference Between Crystalline and Amorphous Solids

Column 1	Column 2	Column 3
Property	Crystalline Solids	Amorphous Solids
Shape	Definite geometrical shape	Irregular Shape
Melting Point	Melt at sharp and fix temperature	Gradually softens over a range of temperature
Heat of Fusion	Definite heat of fusion	No definite heat of fusion
Cleavage Property	Flat edges when cut	Irregular edges when cut
Anisotropy Nature	Anisotropic in nature , True Solid	Isotropic in nature, Pseudo-solids
Order of Arrangement	Long Range Order	Short Range Order

Classification of Crystalline Solids

Crystalline solids are classified on the basis of nature of bonds that hold the constituent particles together into four different types. They are

1. Molecular Solids
2. Ionic Solids
3. Covalent Solids
4. Metallic Solids

1. Molecular Solids: The constituent particles of molecular solids are atoms or molecules. They are of three types

Non-polar solids:

- Soft
- Insulator of electricity
- Very low melting point
- Intermolecular forces- Dispersion or London Forces
- Examples are $A r, C C l_{4}, H_{2}, C O_{2}$

Polar solids:

Soft
Insulator of electricity
Low melting point
Intermolecular forces- Dipole-dipole interaction
Examples are $H C l, S O_{2}$

Hydrogen-bonded solids:

- Hard
- Insulator of electricity
- Low melting point
- Intermolecular forces- Hydrogen bonding
- Examples are $H_{2} O$

1. Ionic Solids: The constituent particles of ionic solids are ions. These are formed by the arrangement of positive and negative ions in a three dimensional network.

- They possess strong electrostatic forces.
- They are hard, brittle and have high melting and boiling points.
- High heat of fusion and poor conductor of heat and electricity.
- In molten state, they conduct electricity.
- Examples are NaCl, KCl, LiF, AgI, etc.

1. Covalent Solids: One or more types of atoms are bonded together by covalent bond in a three dimensional network. Covalent bonds are strong and directional in nature, therefore atoms are held very strongly in their positions.

- These solids are very hard and brittle.
- They have high melting points.
- They are poor conductors of heat and electricity.

Graphite belongs to this class of crystals, but it is soft and is a conductor of electricity. Its exceptional properties are due to its structure.

All carbon atoms are arranged in different layers and each atom is covalently bonded to three of its neighbouring atoms in the same layer, but the fourth valence electron of each atom is present between different layers and is free to move. These free electrons make graphite a good conductor of electricity.

Metallic Solids: Metals are orderly collection of positive ions surrounded by a sea of free electrons.

They are good conductors of heat and electricity
Malleable
Ductile
Possess metallic characteristics

Crystal lattice and Unit Cell

Crystal Lattice

The three dimensional arrangement of structural units(atoms, molecules or ions) in a crystal is called crystal lattice or space lattice. In crystal lattice, the structural units are closely packed in a particular pattern in all directions in space.
Some characteristics of crystal lattice are as follows:

Each point in the crystal lattice is called lattice point or lattice site.
Each point in a crystal lattice represents one constituent particle(atom, molecule or ion).
The lattice points are connected by straight lines to bring out the geometry of the lattice.
The total crystal lattice is a three-dimensional structure formed by repetition of a small three dimensional group of lattice points called the unit cell.

Unit Cell

Unit cell can be defined as the smallest three dimensional group of lattice points. When repeated in three dimensions in space, it gives the whole crystal lattice. In other words, we can say that the unit cell is the building block of crystal lattice.
A unit cell is characterised by following parameters:

The lengths along the three edges a, b and c.
The angles between the pair of edges (b,c), (c,a), and (a,b) are $α, β, γ$ respectively.

Classification of unit cell:

Primitive Unit Cell: The unit cell in which constituent particles are present only on the corners is called the primitive unit cell.
The French scientist Auguste Bravais in 1850 observed that only 7 types of unit cells or primitive unit cells exists. Based on this, he categorised crystal lattice into seven crystal system. These are also called Bravais lattice. Each system is categorised based on edge lengths of a,b,and c and magnitude of angles

α, β, γ

Seven Primitive Unit Cells and their Possible Variations as Centred Unit Cells

Body-centred Unit Cell: The unit cell has constituent particles(atom, ion or molecule) at the corners and at the centre.

Face-centred Unit Cell: The unit cell has constituent particles at all corners of the crystal lattice and at the centre of each face.

End-centred Unit Cell: The unit cell with constituent particles at all the corners of the crystal lattice and at centre of any two opposite faces.

Number of Atoms in a Unit Cell

Crystal lattice is made up of many unit cells and every lattice point is occupied by one constituent particle.
Primitive Cubic Unit Cell: It has 8 atoms atoms on its corners and each corner is shared with 8 adjacent units.

Therefore, total number of atoms in one unit cell is given by:

8 (\frac{1}{8 ^{t h}}) = 1 a t o m

.
Body Centred Cubic Unit Cell: It has atoms at the corner and one atom at the centre. The number of atoms in each unit cell can be calculated as shown below:

Face Centred Cubic Unit Cell: This unit cell contains atoms at all the corners and at the centre of all the faces of the cube. The number of atoms per unit cell can be calculated as:

Close Packed Structures

The constituent particles in solids are closely packed, leaving minimum vacant space. These constituent particles are hard spheres. Let's see packing in one, two and three dimensions

Close Packing in 1-Dimension:

Each sphere is in contact with two of its neighbours.
The number of nearest neighbours of a particle is called its coordination number.
The coordination number is 2.

Close Packing in 2-Dimension:

We can form a closed packed structure in two ways:
(i) Square close packing:

The spheres of the second row are exactly above those of the first row.
The spheres possess vertical as well as horizontal alignment and it forms squares, hence, called square closed packing in two dimension.
The coordination number is 4.
It is of AAA... type pattern.

(ii) Hexagonal close packing:

The second row is placed above first row in such a way that its spheres fit in the depressions of the first row.
This type of packing forms hexagons and is known as hexagonal closed packing.
It is of ABA type.

Close Packing in 3-Dimension:

Crystal lattice has a three dimensional structure. This structure is obtained by placing two dimensional structures one over the other. This is of two types:
(i) 3-Dimensional close packing from 2-dimensional square close-packed layers:

The second layer is placed over the first layer such that the spheres of the upper layer are exactly above those of the first layer.
If arrangement of spheres in one layer is of A type then all the layers have same arrangement and is of AAA...type arrangement.

(ii) 3-Dimensional close packing from 2-dimensional hexagonal close-packed layer:
Three dimensional close packed structure can be generated by placing layers one over the other
(a) Placing second layer over the first layer:
The spheres of the second layer are placed in the depressions of the first layer.

Since all the triangular voids are not covered by the spheres of second layer. This leads to the different arrangements.
Wherever a sphere of second layer is above the first layer, tetrahedral voids are formed.

At other places, triangular voids in the second layer are above the triangular voids in the first layer, and the triangular shapes of these do not overlap.
Such voids are surrounded by six spheres and are called octahedral voids
These voids depend upon the closed packed structures: Let the number of close packed spheres be N, then: The number of octahedral voids generated = N , The number of tetrahedral voids generated = 2N

(b) Placing third layer over the second layer: There are two possible ways of placing third layer over the second layer.
(i) Covering tetrahedral void:

Spheres of 3rd layer are aligned with the first
The pattern is often written as ABABABA..
Hexagonal closed packing(hcp)

(ii) Covering Octahedral Voids:

Spheres of third layer are not aligned with either first or second layer
This type of pattern is called ABCABCAB..
This type of structures are called cubic closed packed structure(ccp) or face-centred cubic closed packing(fcc)

In these types of packing, about 74% of the space in the crystal is filled. The coordination number is 12 in both the cases, as each sphere is in touch with 12 other spheres.

Packing Efficiency and Calculations involving unit cell dimensions

Packing Efficiency

Packing efficiency is the percentage of total space filled by the particles. It is given by the following formula:

So, if N particles are present in a unit cell

If we consider particle as hard sphere in solids, then

Let, radius of particle be r
Let, length of unit cell be a
Then, packing efficiency is given by:

We have to just find out the value of a and N and by substituting in the above equation we can get the packing efficiency.

Packing efficiency in simple cubic unit cell:

Step 1: Radius of sphere
Edge length =

a

Radius =

r

From the figure it is clear that $a = 2 r$
Step 2: Number of particles
Simple cubic unit cell contains only one particle.
So, N=1
Step 3: Packing Efficiency
By plugging in the values of a and N we can get the packing efficiency:

The packing efficiency in simple cubic unit cell is 52.3%.

Packing efficiency in body centred cubic unit cell:

Step 1: Radius of sphere
In bcc, particles are at the corners and in addition one particle is present at the centre of the cube. This means diagonal of the cell passes through the centre of two corner particles and body centred particle.
For triangle FED,

F D^{2} = F E^{2} + E D^{2} = a^{2} + a^{2} = 2 a^{2}

(s i n c e F E = E D = a) . . . . . . . . . . . . . . . . . e q u a t i o n (1)

For triangle AFD,

A F^{2} = A D^{2} + F D^{2} . . . . . . . . . . . . . e q u a t i o n (2)

Substituting values of

F D^{2}

into equation (2), we get

A F^{2} = a^{2} + 2 a^{2} = 3 a^{2}

(A D = a) . . . . . . . . . . . . e q u a t i o n (3)

From the figure

A F = 4 r

. . . . . . . . . . . . . . equation (4)
Substituting value of

A F

in equation (4), we get:

3 a^{2} = 4 r

Step 2: Number of particles
Body centred cubic unit cell contains two particles.
Hence, N=2
Step 3: Packing Efficiency
By plugging in the values of a and N we get the packing efficiency of the unit cell:

The packing efficiency in simple cubic unit cell is 68%.

Packing efficiency in hcp and ccp:

Step 1: Radius of sphere
In hcp, the corner particles touch the particle on the face of ABCD

A C^{2} = A B^{2} + B C^{2} = a^{2} + a^{2} = 2 a^{2}

(A B = B C = a)

A C^{2} = 2 a^{2}

A C = 2 a . . . . . . . . . . . . . . . . e q u a t i o n (4)

From figure,

A C = 4 r . . . . . . . . . . . . . e q u a t i o n (5)

Substituting value of AC in equation (5)

2 a = 4 r

a = \frac{a}{2 2}

Step 2: Number of particles
We know each unit cell in ccp structure, has effectively 4 particles.
N=4
Step 3: Packing efficiency
By putting the values of a and N, we get the packing efficiency

The packing efficiency of hcp and ccp is 74%.

Calculations involving unit cell dimensions

From unit cell dimensions, volume and mass can be calculated

In case of Cubic crystal

Volume of unit cell =

a^{3}

Mass of unit cell =

z \times m

z = Number of atoms in unit cell
m = Mass of each atom

Mass of an atom present in the unit cell, $m = \frac{M}{N _{A}}$

Therefore,

D e n s i t y o f u n i t c e l l = \frac{M a s s o f u n i t c e l l}{V o l u m e o f u n i t c e l l}

D e n s i t y o f u n i t c e l l = \frac{z . m}{a ^{3}}

d = \frac{z . M}{a ^{3} . N _{A}}

Density of the unit cell is same as density of the substance.

Imperfection in Solids
Crystals possess perfect arrangement only at 0 K. Any deviation from perfectly ordered arrangement in a crystal is known as imperfection in a solid or defects in crystals.
Defects can be broadly classified into two:

Point Defect
Line Defect

Point Defect

The deviations from perfect arrangement around a point or an atom in a crystalline substance is called point defect.

Stoichiometric Defects: The point defects that do not disturb the stoichiometry of the crystal are called stoichiometric defect. They are also referred to as intrinsic or thermodynamic defects.
Basically these are of two types:
(i) Vacancy Defect: When some of the lattice points are vacant, the crystal is said to have vacancy defect. As a result, the density of the substance decreases. This defect can also develop when a substance is heated.

(ii) Interstitial Defect: When some atoms or molecules occupy an interstitial site, the crystal is said to possess interstitial defect. This defect increases density of the substance.

Non-ionic solids show vacancy and interstitial defect. But ionic solids show Frenkel and schottky defect as they have to maintain electrical neutrality.
(iii) Frenkel Defect: This defect arises when cation leaves its lattice site and occupies interstitial site. It creates a vacancy defect at its original site and an interstitial defect at its new location. Frenkel defect is also called dislocation defect. It does not change the density of substance.
(iv) Schottky Defect: This defect arises when some of the lattice points in a crystal are unoccupied. It decreases the density of the substance.

Impurity Defects: This defect arises when foreign atoms are present at the lattice point in place of host atoms. These are of two types

Interstitial Impurity: A point defect that results when an impurity atom occupies an octahedral hole or a tetrahedral hole in the lattice between atoms. It is usually a smaller atom that can fit into the octahedral or tetrahedral holes in the metal lattice.
Substitutional impurity: It is a point defect that results when an impurity atom occupies a normal lattice site. It is a different atom of about the same size that simply replaces one of the atoms that compose the host lattice. Example; solid solutions of metal alloys.

Non-stoichiometric Defects: When the stoichiometry of the crystal gets disturbed, then it is called non-stoichiometric defect. These are of two types:

(i) Metal Excess Defect:

Metal excess defect due to anionic vacancies: It arises when an anion is missing from its lattice site, creating a hole and the hole is occupied by an electron to maintain electrical neutrality of the crystal. The electrons trapped in anion vacancies are called F-centres.
Presence of extra cation at interstitial positions: This defect arises when an extra positive ion or cation is present in an interstitial site.

(ii) Metal Deficiency Defect: This defect arises when a positive ion is missing from its normal lattice site and the charge is balanced by a nearby metal ion having higher positive charge.

Line Defect

Line defects are the deviations from perfect arrangement in entire rows of lattice points. These irregularities are called crystal defects or lattice defects.

Electrical and Magnetic Properties
Properties of solids are related to their structure and compositions.

Electrical Properties:

Solids exhibit a large range of electrical conductivities. Solids can be classified on the basis of conductivity:

Conductors: The solids with conductivities between

1 0^{4}

1 0^{7}

o h m^{- 1} m^{- 1}

are called conductors.
Insulators: Insulators have very low conductivity in the range of

1 0^{- 20}

1 0^{- 10}

o h m^{- 1} m^{- 1}

.
Semiconductors: The solids with conductivities in the intermediate range from

1 0^{- 6}

1 0^{4}

o h m^{- 1} m^{- 1}

.
Band:
The atomic orbitals of metal atoms form molecular orbitals which are so close in energy to each other as to form a band.
Band theory has two types of bands:

Conduction band: It is formed by the interaction of the outermost energy levels of closely spaced atoms in solids. Electrons in conduction band are mobile and delocalized over the entire solid.

Valence band: Valence band has lower conductivity than conduction band. Electrons in valence band are tightly bound to nuclei and hence are not free.

The energy difference between the conduction band and valence band is known as band gap.

Transfer of electrons from valence band to conduction band depends upon the size of band gap.
When gap is small, electrons from higher energy levels in valence band can be promoted to conduction band by absorption of energy.
When the gap is too large to promote electrons from valence band to vacant conduction band by thermal energy, it is called the forbidden gap

Electrical properties of metals, insulators and semiconductors can be explained with band theory.
Conduction in Metals:
The number of electrons in conduction band is large, therefore, metals are good conductors of electricity. If the band is partially filled or it overlaps with a higher energy unoccupied conduction band, then electrons can flow easily under an applied electric field and the metal shows conductivity
Metals conduct electricity in solid as well as molten state.
Conduction in Insulators:
If the gap between filled valence band and the conduction band is large, electrons cannot jump to it, such a substance is called an insulator.
Conduction in Semiconductors:
The gap between the valence band and conduction band is small, some electrons may jump to conduction band and show some conductivity. Semiconductors conduct small amount of electricity when electric potential is applied. Electrical conductivity of semiconductors can be increased by increase in temperature - this allows more electrons to jump into the conduction band.

The pure form of semiconductors are known as intrinsic semiconductors. The electrical conductivity of intrinsic semiconductors is very low, so it can be increased by adding a suitable amount of impurity. Examples of intrinsic semiconductors are silicon and germanium.

The process of adding impurity is known as doping.
Doped semiconductors are known as extrinsic semiconductors.
Doping can be done by adding electron rich impurities or electron deficient impurities.
Tetravalent atoms like silicon and germanium are doped with two types of impurities as shown in the image.

Electron-rich impurities:

Silicon and germanium are doped with electron rich impurities to increase their electrical conductivity.
Silicon and germanium have four valence electrons each as they are from group 14 of the periodic table.
Whereas As and P are from group 15 of the periodic table and they have 5 valence electrons.
When silicon is doped with phosphorous or arsenic, four electrons out of five make covalent bonds with four neighbouring silicon atoms leaving one electron free; which increases the electrical conductivity of silicon.
Since the electrical conductivity of silicon or germanium is increased because of negatively charged particle (electron), hence silicon doped with electron-rich impurity is called n-type semiconductor.

Electron-deficit impurities:

Electrical conductivity of silicon or germanium can also be increased by doping them with electron deficient impurities.
B, Al, Ga have only 3 valence electrons as they belong to 13th group of the periodic table.
The three valence electrons present in B, Al, Ga make covalent bonds with silicon atoms, leaving a hole.
The place where one electron is missing is called electron hole or electron vacancy.
When the silicon or germanium is placed under electrical field, electron from neighbouring atom fills the electron hole, but in doing so another electron hole is created at the place of movement of electron.
Semiconductor formed by the doping with electron deficient impurities; are called p-type semiconductors.

Applications of n-type and p-type semiconductors

Combination of n-type and p-type semiconductors are used to make different electrical components. For example diode.
Diode is used as a rectifier.
Photodiodes are also used in solar cells to produce electricity.
Transistors are also made up of n-type and p-type semiconductors.
npn and pnp transistors are used to detect and boost radio or audio signals

Magnetic Properties:

Each and every substance has some magnetic properties. Depending upon their behaviour towards magnetic fields, substances can be divided into following categories:

Paramagnetic Substances: The substances which are weakly attracted by magnetic fields are called paramagnetic. Examples of paramagnetic substances are $O_{2}$ , $C u^{2 +}$ , $F e^{3 +}$ , etc.

Diamagnetic Substances: They have completely filled orbitals so no magnetic moment. They are magnetised in the opposite direction of magnetic field, hence get repelled. Some examples of diamagnetism are $H_{2} O$ , $N a C l$ , and $C_{6} H_{6}$ .

Ferromagnetic Substances: The substances which are strongly attracted by magnetic fields and show permanent magnetism even in the absence of magnetic field are called ferromagnetic substances.

Antiferromagnetic Substances: The substances which possess zero magnetic moment inspite of the presence of unpaired electrons are called antiferromagnetic substances. Example is Nickle oxide.

Ferrimagnetic Substances: Ferrimagnetism is observed when the magnetic moments of the domains in the substance are aligned in parallel and anti-parallel directions in unequal numbers. Examples are magnesium and zinc.

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best notes on solid state class 12

Crystalline Solids

Amorphous Solids

Difference Between Crystalline and Amorphous Solids

Classification of Crystalline Solids

Crystal Lattice