The Solid State

The Solid State:-

In solid state the particles are closely packed.

These are held together by strong intermolecular force of attraction.

These are held at fixed position and can only oscillate about their mean position.

These are incompressible and rigid and have short intermolecular distances.

They have definite mass, volume and shape.

On the basis of the arrangement of their constituent particles solid are classified as:-

i. Crystalline solid:-

The solid in which the constituent particles i.e (atom, ion or molecule) are arranged in definite geometrical pattern in 3D are called crystalline solid.

For ex:- Quartz, Diamonds, salt etc.

It has long range order because its constituent particles are arranged over a large distance in a crystals in orderd manner.

They are anisotropic in nature i.e some of physical properties like refractive index and electrical conductivity are different in different direction.

Crystalline solids have a sharp melting point.

It gives a clean cleavage or cut when cut with a sharp edged knife and considered as true solid.

ii. Amorphous solid:-

The solid in which the constituent particles are arranged in irregular pattern are called amorphous solid.

For ex:- Glass, Rubber, Plastics etc.

It has short range order because the regular arrangement of constituent particle is observed over as short distance.

They are isotropic in nature i.e some of its physical properties like refractive index and electrical conductivity are identical in all direction.

Amorphous solids do not have sharp melting point.

An amorphous solid gives an irregular cut when cut with a sharp edged knife.

These are considered as pseudo solid or supercool liquid because they have a tendency to flow like liquids.

On the basis of nature of intermolecular forces solid are classified as:-

1. Molecular solids:-

The solid in which the constituent particles of the lattice points are molecules are considered as molecular solid.

Note:- The intermolecular forces holding the molecules together in crystal lattice are the weak van der Waals forces.

These are further divided into three categories:

i. Non polar molecular solids:-

They are composed of either atoms or molecules.

The molecules in such substances are formed by non polar covalent bonds.

In these solids, the atoms or molecules are held together by weak dispersion forces or London forces.

They are soft and non conductors of electricity.

They have low melting and boiling point.

 At room temperature and pressure they usually exist in liquid or gaseous state.

For ex:- Methane, Chlorine, Hydrogen, Oxygen.

ii. Polar Molecular Solids:-

They are composed of polar molecules.

The molecules in such substances are formed by polar covalent bonds.

In these solids, the molecules are held together by strong dipole dipole interaction.

These solids are soft and non conductor of electricity.

Their melting point are higher than those of non polar molecular solids.

Under room temperature and pressure usually exist in liquid or gaseous state.

For ex:- Ethanol, Ammonia etc.

iii. Hydrogen bonded molecular solids:-

The molecules of such solid contain polar covalent bonds between the molecules having hydrogen atoms and molecules having (F, O or N) atoms.

In these solids the molecules are held together by strong hydrogen bonding.

They are non conductor of electricity.

Under room temperature and pressure they are exist as volatile liquids or soft solids.

For Ex:- H2O (Ice).

2. Ionic solids:-

In the solids, the constituent particles are composed of ions (cations and anions).

These ions are held together by the strong electrostatic forces of attraction.

These solids are hard and brittle in nature.

They have high melting and boiling points.

They are electrically insulator in solid state.

But they are good conductor of electricity in the molten state and in the solution because their ions become free to move about in molten state.

For Ex:- NaCl, MgO, NH4Cl etc.

3. Metallic solids:-

These solids consists of positively charged metals ions (kernels).

The ions are held together by metallic bond.

The metallic bond arises due to the presence of mobile electrons.

Metallic solids are hard but malleable and ductile.

Metal possesses high melting points and high densities.

They are good conductor of electricity in solid as well as molten state.

Metals have high electrical and thermal conductivity due to the availability of free and mobile electrons.

They are lecturers in nature.

For Ex:- Copper, Gold, Zinc etc.

4. Covalent or network solids:-

In these solids, the lattice points are occupied by atoms which are linked together by network of covalent bonds to form a giant molecule.

Diamond is an example of this type of solid in which the carbon atoms are linked together by covalent bonds to give a 3D structure.

They show high melting and boiling points.

They are extremely hard and brittle.

They are insulators and do not conduct electricity.

Graphite is soft and act as good conductor of electricity.

It is because of delocalisation of electron in its structure.

These arise because each atom is only bonded to three other carbon atom leaves one electron to become delocalised.

However in diamond all four outer electrons on each carbon atom are used in covalent bonding so there are no delocalisation of electrons.

Graphite is used as lubricant due to its slippery nature.

Crystal lattices and Unit cells:-

The regular arrangement of atoms, ions and molecules constituting the crystal in the 3-D space with in the crystal is called crystal or space lattice.

There are only 14 possible 3D lattices.

These are called Bravais Lattices.

The characteristics of a crystal lattice:-

a. Each point in a lattice is called lattice  

    site or lattice point.

b. Each point in a crystal lattice 

    represents one constituent particle 

    which may be an atom, ion or molecule.

    

c. Lattice points are joined by straight 

    lines to bring all the geometry of the 

    lattice.

Unit cells:-

The smallest portion of a crystal lattice, which when repeated over and over again in different directions produces the complete crystal lattice, is called the unit cell.

The characteristics of unit cell:-

(a) A unit cell has three edges a, b and c.

      These edges may or may not be 

      mutually perpendicular.

 

(b) A unit cell has three angles α, β and γ 

      between the respective edges.

      The angle between the edges b and c 

      is (α) a and c is (β) and that of 

      between a and b is (γ).

Thus, a unit cell is characterized by six parameters (a, b, c, α, β and γ).

Unit cells can be divided into four types:

1. Simple or primitive unit cell:-

When constituent particles are present only at the corner of the unit cell, called primitive unit cell.

2. Body centred unit cell:-

If the constituent particles are present at the centre and at the corner of the unit cell, called body centred unit cell.

3. Face centred unit cell:-

If the constituent particles are present or located at the centre of each faces in addition to the corners, called face centred unit cell.

4. End centred unit cell:-

If the constituent particles are located or arranged at the centre of end faces or at the centre of any two opposite faces in addition to the corner, called end centred unit cell.

Note:- There are seven types of primitive unit cells.

Number of atoms in a unit cell:-

Following points should be kept in mind.

a. A corner atom contributes 1/8 of each unit cell.

b. A face atom contributes 1/2 of each unit cell.

c. An edge atom contributes 1/4 of each unit cell.

d. An atom inside the cube contributes fully to that unit cell.

Number of atoms in primitive cubic unit cell:-

Contribution of 1 corner atom= 1/8

Contribution of 8 corner atoms=8×1/8= 1

Hence, the total number of atoms in a primitive unit cell is 2.

Number of atoms in body-centered cubic unit cell:-

Contribution of 8 corner atoms=8×1/8= 1

Contribution of 1 central atom= 1

Thus, the total number of atoms in a unit cell of BCC is= 1+1= 2

Number of atoms in face-centered cubic unit cell:-

Contribution of 8 corner atoms=8×1/8= 1

Contribution of 6 face atoms= 1/2×6= 3

Thus, the total number of atoms in a unit cell of FCC is= 1+3= 4

Closed packed structure:-

In solids the constituent particles are closely packed by leaving minimum vacant space.

Let us considered the constituent particles as a spheres of equal size.

(a) Close packing in one dimension:-

In one dimension close packing, spheres are arranged in a row such that adjacent atoms are in contact with each other or with two of its neighbours.

Coordination number:-

 

Coordination number is defined as the no. of the nearest neighbour particles. 

 

In case of one dimension close packing, coordination number is equal to two.

(b) Close packing in two dimensions:

In two-dimensional close packing, row of closed packed spheres are stacked (placed) one above the other to obtain a two-dimensional pattern. 

This can be done in two ways:

(i) Square close packing (AAA type):

The second row can be placed exactly below the first row in a close packing. 

Thus, if we call the first row as “A” type row, the second row being arranged exactly the same as the first one, is also of “A” type.

Similarly, we may place more rows to obtained "AAA" type of arrangement.

This type of packing is referred as “AAA” type.

In such an arrangement each sphere is in contact with four other spheres.

Hence, it has a coordination number equal to four.

If the centres of the four immediate neighbouring spheres are joined, a square is formed.

Hence, this type of packing in crystalline solids is known as square close packing in two dimensions.

(ii) Hexagonal close packing (ABAB type) :-

The second row can be placed below the first row in a staggered manner such that its spheres fit in the depressions of first row.

Thus, if we call the first row as “A” type row, the second row being arranged differently can be named as “B” type. Again the third row appears as “A” type.

 This type of packing is referred as “ABAB” type.

 

In such an arrangement each sphere is in contact with six other spheres.

Hence, it has a coordination number equal to six.

We observe that if the centres of the six immediate neighbouring spheres are joined, a hexagon is formed.

This type of packing in solids is known as hexagonal close packing in two dimensions.

Note:- It has lesser free space and hence higher packing efficiency in comparison to square close packing.

In ABAB type close-packing we find triangular empty spaces called voids.

These are of two types:

Apex of triangle pointing upwards

Apex of triangle pointing downwards.

(c) Close packing in three dimensions:-

Three dimensional close packed structure can be obtained by stacking (placing) two dimensional layers one above the other.

This can be done by two ways:-

(i) Three-dimensional close packing from two-dimensional square close packed layers:-

Formation of three dimensional closed packing can be done by placing the second layer over the first layer such that the shperes of the upper layer are exactly about those of first layer.

Similarly, we may place more layers one above the other.

If the arrangement of sphetes in the first layer is called 'A' type, all the layers have the same arrangement.

Thus this lattice has 'AAA....' type pattern.

The lattice thus generated is the simple cubic lattice and its unit cell is the primitive cubic unit cell.

(ii) Three-dimensional close packing from two-dimensional hexagonal close packed layers:-

This close packed structure can be generated by placing there one over the other.

 

(a) Placing second layer over the first layer:-

Suppose we take two dimensional hexagonal close packed layer 'A' and place it over the second layer 'B' such that the spheres of the second layer are placed in the depression of first layer.

Since the squares of the two layers are aligned differently.

We observe that a tetrahedral void (T) is formed when a sphere of second layer is above the void (empty space) of the first layer.

These voids are called tetrahedral voids because a tetrahedron is formed when the centres of these four spheres are joined.

Adding further we notice octahedral voids (O) at the layer are placed right above triangular void of the first one in such a way that triangular space does not overlap.

Search voids are surrounded by six spheres and are called octahedral voids.

The number of these two types of voids depend upon the number of closed packed spheres

If there are 'N' closed spheres, then

Number of octahedral voids= N

Number of tetrahedral voids= 2N.

(b) Placing third layer over the second layer:-

There are two possible ways of placing the third layer over the second layer:-

(i) Covering tetrahedral voids:-

In this kind of three dimensional packing the spheres of the third layer are aligned right above the spheres of the first layers.

If we name first layer as 'A' and second layer is 'B' then the pattern will be 'ABAB....'.

The structure formed is called hexagonal close packed structure (hcp).

This kind of arrangement of atoms is found in many metals like magnesium (Mg) and zinc (Zn).

(ii) Covering octahedral voids:-

In this kind of packing the spheres of the third layer are not placed with either of the second or first layer.

The third layer 'C' may be placed above the second layer in a manner such that its spheres cover the octahedral voids.

Only when fourth layer is placed, its spheres are aligned with those of the first layer.

This pattern of layers will be 'ABCABC....'.

The structure formed is called cubic close packed (ccp) or face centred cubic (fcc).

For example metals like iron (Fe), Copper (Cu) and silver (Ag) crystallize in the structure.

The coordination number in both cases will be 12 as each spheres in the structure is in direct contact with 12 other spheres.

The packing is highly efficient and around 74% of the crystal is completely occupied.

Note:- All real structures are 3D structures.