Solid State Chemistry Ipe

Solid state

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SOLID STATE Characteristic properties of solid state 1) Solids have definite mass, volume and shape. 2) They are incompressible and rigid. 3) Their constituent particles (atoms or ions or molecules) are arranged very closely and the attractions between them are strong. 4) Their constituent particles have fixed positions and can only oscillate about their mean positions. Translatory and rotatory motions are restricted.

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Crystalline and amorphous solids Solids can be classified into crystalline and amorphous on the basis of the nature of order present in the arrangement of their constituent particles. Crystalline solids Crystalline solids have definite characteristic geometrical shape. They have long range order which means that there is a regular pattern of arrangement of particles which is repeated over the entire crystal. They possess definite and characteristic melting points and heats of fusion. They show anisotropic nature. Anisotropic substances exhibit different values for some physical properties like refractive index, electrical resistance etc., in different directions. E.g.., Sodium chloride, crystalline quartz etc., Amorphous solids Amorphous solids have irregular shape. They possess only short range orders i.e., the regular pattern of arrangement is repeated over short distance only. They do not possess definite and characteristic melting points and heats of fusion. They show isotropic nature as they exhibit same values for some physical properties in different directions. These are actually considered as super cooled liquids or pseudo solids. E.g.., Glass, rubber, amorphous quartz, plastics (organic polymers) etc., Distinction between Crystalline and Amorphous Solids Crystalline solids Amorphous solids Definite characteristic geometrical shape Irregular shape Melt at a sharp and characteristic Gradually soften over a range of temperature temperature Cleavage When cut with a sharp edged tool, they split When cut with a sharp edged tool, they cut property into two pieces and the newly generated into two pieces with irregular surfaces. surfaces are plain and smooth Heat of fusion They have a definite and characteristic They do not have definite heat of fusion heat of fusion Anisotropy Anistropic in nature Isotropic in nature Nature True solids Pseudo solids or super cooled liquids Order Long range order Only short range order Property Shape Melting point

Classification of solids based on nature of attractions Crystalline solids are classified based on nature of attractions between constituent particles in them into four categories viz.,1) molecular, 2) ionic, 3) metallic and 4) covalent solids 1) Molecular solids : Molecules (or rarely noble gas atoms ) are the constituent particles. They are attracted by weak van der wall's forces of attractions or by hydrogen bonds. Based on the nature of these intermolecular forces, molecular solids are again subdivided into i) van der wall's crystals : In these solids, the intermolecular forces of attraction are very weak van der wall's forces (Like London dispersion forces or dipole-dipole attractions). These solids have very low melting points and relatively soft. E.g., Solid H2, N2, CO2, SO2 etc.,

Solid state

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ii) Hydrogen bonded Crystals : In these solids, the constituent molecules are attracted by hydrogen bonds. These are usually hard. E.g., Ice (Solid H2O), solid HF, solid NH3 etc., Usually the melting points of molecular solids are below room temperature. They are bad conductors of electricity. 2) Ionic Solids : Ions are the constituent particles. The cations and anions are arranged regularly in three dimensions and strongly held together by electrostatic attractions. These solids are rigid with high melting points. But they are brittle and non elastic. As the ions are not free to move, ionic solids are electrical insulators in solid state. E.g., NaCl, KCl etc.,

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3) Metallic Solids : Metallic crystals constitute orderly arranged metal atom in a sea of free electrons. These electrons held the metal atoms together. Metals are rigid and possess high melting points due to strong metallic bonds. Due to the presence of free electrons, they are good electrical and thermal conductors. They are also lustrous, opaque, malleable and ductile. E.g., Cu, Al, Fe etc.,

Type of solid (1) Molecular solids (i) van der wall's solids (ii) Hydrogen bonded (2) Ionic solids

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4) Covalent Crystals : The entire crystal is considered as a giant molecule. It is a three dimensional network of atoms bonded covalently. These solids are very hard with extremely high melting points. They do not conduct electricity (except graphite). E.g., diamond, graphite, SiC, SiO2 etc., The differences between above types of solids is summarized below

Constituent particles

Molecules

Ions

(3) Metallic solids Positive ions in a sea of delocalised electrons Atoms (4) Covalent or network solids

Attractive Forces

Examples

Physical Nature

Electrical Conductivity

Soft

Insulator

Hard

Insulator

Melting point

van der wall's forces Hydrogen bonding

Ar, CCl4, H2, I2, CO H2O (ice)

Very low Low

Coulombic or electrostatic

NaCl, MgO, Hard but ZnS, CaF brittle

Insulators High in solid state but conductors in molten state.

Metallic bonding

Fe, Cu,Ag, Mg,

Covalent bonding

SiO2 (quartz), SiC, C (diamond), AlN, C(graphite)

Hard but malleable and ductile Hard

Conductors in solid state as well as in molten stste Insulators

Soft

Conductor (exception)

Fairly high

Very high

Solid state

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Metalling bonding The bonding in metals can be explained by using following theories. 1) Electron sea model (Drude-Lorentz theory) According to this theory i) A metal lattice comprises of rigid spheres of metal ions in a sea of free electrons. ii) Metal atoms contribute their valence electrons to the sea of free electrons. iii) These electrons move freely through the interstices. iv) The attraction between metal ions and free electrons is called metallic bond. v) This theory could explain the electrical and thermal conductivity of metal. But it fails in explaining the lattice energies quantitatively.

-

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+ -

+

+

-

-

+ -

+

+

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+

+

-

+

-

+ -

-

+ -

+

-

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+ -

+

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+

-

- Free electron

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+ Metal ion

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2) Valence bond theory This theory was proposed by Linus Pauling. According to this theory, metallic bond is considered as a highly delocalized covalent bond between metal atoms. Metal can exhibit several resonance structures due to the delocalization of one electron and electron pair covalent bonds. These resonance structures confer stability to the metallic crystal. Various resonance forms in sodium metal are shown below. +

-

Na Na

Na Na

Na Na

Na Na

Na Na

Na Na

Na Na +

-

Na Na

+

Na Na -

Na Na

-

Na Na +

etc.,

Na Na

This theory could not explain metallic lustre, heat conduction by metals and retention of metallic properties in molten and solution state of metals. Crystal lattice and unit cell Crystal lattice: The regular three dimensional arrangement of lattice points in space is called crystal lattice. The points at which the constituent particles (atoms or ions or molecules) of crystal are found are called lattice points. Unit cell : The smallest part of the crystal lattice which generates entire crystal when repeated in three dimensions is known as unit cell. Crystal parameters The three edges of unit cell are denoted by a,b and c and the angles between these edges are denoted by  ,  and 

   between b & c    between a & c    between a & b

Solid state

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z-axis

c 



a



b

y-axis

x-axis

Note: a,b,c, α,β and γ are called crystal parameters.

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Types of unit cells 1) Primitive or simple unit cell: The constituent particles are only present at the corners of the unit cell.

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2) Body centered unit cell: It contains particles at all the eight corner as well as at the centre of the unit cell.

3) Face centered unit cell: In this unit cell, all the eight corners and six faces are occupied by the constituent particles in the unit cell.

4) End centre unit cell: In this unit cell, one constituent particle is present at the centre of any two opposite faces besides those present at the corners.

Crystal systems and Bravais lattices: Based on crystal parameters, crystal systems are divided into seven types by considering only primitive arrangements. But there are 14 crystal lattices possible with all types of unit cell arrangements which are called Bravais lattices. The requirement of this classification is that the geometric shape of the crystal

Solid state

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Crystal System 1. Cubic

2. Tetragonal

3. Orthorthombic

4. Rhombohedral (OR) Trigonal 5.Hexagonal

6. Monoclinic

7. Triclinic

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lattice must be same as that of the solid crystal itself. The seven crystal systems and Bravais lattices are summarized below.

3 (P, I, F)

Axes or edge length parameters a=b=c

2 (P, I )

a=b  c

     = 900

White tin, SnO2, TiO2, CaSO4

4 (P, I, F, C)

a  b  c

     = 900

Rhombic sulphur, KNO3, BaSO4

1 (P)

a=b  c

      900

1 (P)

a=b=c

   = 900 ;  = 1200

Calcite (CaCO3), HgS (cinnabar) Graphite, ZnO, CdS,

2 (P, C)

a  b  c

 =  = 900 ;   900

1 ( P)

a  b  c

      900

Bravais Lattices

Angles

Examples

     = 900

NaCl, Zinc blende, Cu

Monoclinic sulphur, Na2SO4.10H2O CuSO4

Solid state

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simple (P)

1. Cubic

a  b  c       90 o

Face Centred (F)

a a

abc

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a

2. Tetragonal

Body Centred (I)

c

      90 o

a

abc

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a

      90 o

b

4. Rhombohedral or Trigonal

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a

c

abc

      90o

a

a

5. Hexagonal



a

abc

c

    90o ;   120o 120o

6. Monoclinic

abc

c

    90o ;   90o

7. Triclinic

abc       90o

a

a

 a

b



c

  a

b

End Centred (C)

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Packing in metallic solids Metal atoms in metallic crystal can be packed closely in four different arrangements as described below. 1) Simple cubic arrangement Simple cubic arrangement of metallic crystal is obtained when two dimensional square close packed layers are arranged over each other such that the spheres in the second layer are present exactly over the spheres of first layer. The coordination number of each sphere in this arrangement is six. The packing fraction is only 52%. E.g., Polonium

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2) Body centered cubic (BCC) arrangement In this arrangement, the two dimensional square close packed layers are arranged such that the spheres in every next layer are arranged over the voids of the first layer. The coordination number is eight and packing fraction is 68% in this arrangement. E.g., Na, K, Rb, Cs, ba, Cr, Mo, W etc.,

3) Hexagonal close packed (HCP) arrangement In this arrangement, the closest packed layers are arranged in ABAB pattern. There are two types of closest packed layers in which the spheres in every second layer (B) are present over the voids of one type in first layer (A). The coordination number is twelve and packing fraction is 74%. E.g., Be, Mg, Cd, Co, Zn, Ti, Tl etc.,

4) Cubic close packed arrangement (CCP) or Face centered cubic (FCC) arrangement In this arrangement, the closest packed layers are arranged in ABCABC pattern. The spheres in the second layer (B) are arranged over one type of voids in the first layer (A). Whereas the spheres in

Solid state

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The coordination number is twelve and packing fraction is 74%. E.g., Al, Cu, Au, Pt, Pb, Pd, Ni, Ca etc., Packing fraction It indicates how much of space is occupied by constituent spheres in a crystal lattice. Packing fraction =

volume of all the spheres volume of the crystal

Coordination number : The number of closest atoms surrounding an atom in a metallic crystal is known as coordination number of that crystal.

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In simple cubic unit cell: z = 8 x 1/8 = 1

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Number of atoms (z) present in a unit cell The atoms at the corners of a unit cell contribute only 1/8th part of them to the unit cell. The atoms at the centre of a face of unit cell contribute only 1/2 part of them. The atoms on the edges of unit cell contribute 1/4th part of them.

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In Body centered unit cell: z = (8 x 1/8 ) + (1) = 2

In Face centered unit cell: z = (8 x 1/8 ) + ( 6 x 1/2) = 1+3 = 4

Density (  ) of the crystal It is possible to calculate the density of crystal from the dimensions of unit cell and mass of atoms in it. density  ρ  =

mass of atoms in unit cell Zm  3 volume of unit cell a

where Z = no. of atoms in a unit cell

Solid state

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m = mass of one atom =

Molar mass  M  Avogadro number  N A 

a = edge length ρ=

Z.M N A .a 3

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Types of voids Trigonal void :The empty space between adjacent three spheres in a layer of closely packed crystals is called trigonal void .

trigonal void

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If the number of atoms in closely packed crystals ( hcp or ccp) is 'X' then the number of trigonal voids in them is '8X'. Tetrahedral void : The three dimensional empty space formed in between closely spaced three spheres in a layer and another sphere in the next layer is called tetrahedral void.

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tetrahedral void

There are two types of tetrahedral holes in closely packed crystals ( hcp or ccp) . The total number of tetrahedral holes containing 'X' atoms in hcp or ccp crystal is equal to '2X'. Octahedral void : The empty space between three spheres of one layer and three spheres of next layer is called octahedral void.

octahedral void

In hcp and ccp arrangements, the number of octahedral voids is equal to number of atoms in the crystal. Radius ratio in ionic compounds In ionic compounds, the crystal lattice is considered to be formed by bigger ions (usually anions) and the small sized ions (usually cations) occupy the vacancies formed by bigger ions. The geometry around each ion and coordination number of ion are decided by the limiting radius ratio. limiting radius ratio =

radius of small ion rsmall r   radius of large ion rbig r

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Radius ratio ( rs m a ll / r l a rg e )

Geometric shape of the crystal formed

Upto 0.15 0.15 to 0.22 0.22 to 0.41 0.41 to 0.73 0.41 to 0.73 >0.73

Linear Trigonal planar Tetrahedral Square pyramidal Octahedral Cubic

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Coordinatio n number of the ion 2 3 4 4 6 8

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Defects in crystals The irregularities in the arrangement of constituent particles in crystals lead to several types ofdefects in crystals. Defects in crystals affect density, heat capacity, entropy, mechanical strength, electrical conductivity, catalytic activity etc., . Thermodynamically all the crystal have the tendency to become defective because defects increase the entropy of crystals. Defects in crystals are broadly divided into i) Point defects: which occur around a lattice point in a crystal. ii) Line or extended defects: which are present in one or more dimensions. Defects can also be classified into i) Intrinsic : which are present in pure crystals. ii) Extrinsic : which occur due to impurities in crystals

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Point defects: These are of three types : i) Stoichiometric : Stoichiometry is maintained in the defected crystal. ii) Non stoichiometric : Stoichiometry of the defected crystal is not maintained. iii) Impurity defects : These defects otherwise known as extrinsic defects occur due to presence of impurities in crystals. Stoichiometric defects 1. Schottky defect The point defect which arises due to missing of ions at the lattice points of ionic crystal is called schottky defect. In order to maintain electrical neutrality, the number of missing cations and anions must be equal. Schottky defects are shown by ionic compounds in which cation and an ion sizes are equal. They show high coordination numbers ( 6 or 8). Eg :- NaCl, KCl, CsCl etc., The density of crystal decreases with increase in number of schottky defects. It is a thermodynamic defect i.e., the number of defects increases with temperature.

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Frenkel defect It is a point defect formed due to shifting of an atom or ion from its normal lattice point to an interstitial site. It is also called dislocation defect. This defect is shown by ionic compounds in which there is a large difference in size of ions. E.g., AgCl, Ag Br, AgI, ZnS etc., In above compounds cations (Ag+, Zn2+ etc.,) are smaller in size when compared to anions ( like halides). Frenkel defect does not change the density of the crystal.

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Bragg's equation: Consider a crystal surface with planes of lattice points as shown below. Let the inter planar distance between them is 'd'. Now consider two X-rays , of wavelength '  ' ,which are incident on the surface of the crystal and undergoing constructive interference.

1st plane

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1s 2n t ra y d ra y



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d

2nd plane 3rd plane

E

F

A



D   C B

The first ray is reflected at point 'A' on the surface of 1st plane, where as the 2nd ray is reflected at point 'B' on the surface of 2nd plane, both at an angle of  . This is called angle of reflection. Both the rays travel the same distance till the wavefront 'AD'. The second ray travels an extra distance of DB+BC and then interfere with first ray constructively. If the two waves are to be in phase, the path difference between the two rays must be an integral multiple of wavelength of X-ray '  '. i.e., n  DB  BC (where n= an integer and known as order of diffraction) and AB = d = inter planar distance Now or 

DB = BC = d sin DB+BC = 2d sin  n  2d Sin

Above equation is known as Bragg's equation. Electrical properties: Based on electrical conductivity, solids are broadly divided into three types. (i) Conductors: The solids with conductivities ranging between 104 to 107 ohm–1m–1 are called conductors. Metals have conductivities in the order of 107 ohm–1m–1 and are good conductors.

Solid state

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(ii) Insulators : These are the solids with very low conductivities ranging between 10–20 to 10–10 ohm– 1 –1 m . (iii) Semiconductors : These are the solids with conductivities in the intermediate range from 10–6 to 104 ohm–1m–1.

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A conductor may conduct electricity through the movement of electrons or ions. Metals conduct electricity in solid as well as molten state through the movement of electrons. The conductivity of metals can be explained as follows. The atomic orbitals of metal atoms form molecular orbitals which are so close in energy to each other and form a band. There are two types of molecular orbitals possible. The molecular orbitals with low energy are referred to as bonding and with high energy are called anti-bonding orbitals. The band formed by bonding molecular orbitals is generally called valence band and that band formed by anti-bonding orbitals is called conduction band. If the valence band is partially filled or it overlaps with conduction band, then electrons can flow easily under an applied electric field and the metal shows conductivity. The conductivity of metals decreases with increase in temperature due to increase in vibrations of atoms. In case of insulators, the gap between valence and conduction bands is very large and hence the electrons cannot jump from filled valence band to unoccupied conduction band. Hence these substances exhibit poor electrical conductivity. But in case of semiconductors, there is a small gap between valence and conduction bands. Therefore, some number of electrons can jump into conduction band and show some conductivity. The conductivity of semiconductors increases with raise in temperature as more number of electrons can jump to conduction band.

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Energy

conduction band

S

partially filled valence band

valence band

forbidden zone large energy gap

small energy gap

S

S

Insulators

Semiconductors

overlapping bands

conductors (metals)

Semiconductors can be divided into intrinsic and extrinsic types. Intrinsic semi conductors: The pure semiconductors are called intrinsic semiconductors. Their conductivity is too low to be of practical use. Eg., pure silicon, germanium Extrinsic semiconductors: The conductivity of semiconductors, can be greatly enhanced by adding suitable impurity. The semiconductors containing impurity are called extrinsic semiconductors. Doping: The process of addition of impurities (dopant) to enhance the conductivity of semiconductors is called doping. Extrinsic semi conductors are divided into two types based on type of impurity (dopant) added viz., n-type and p-type semi conductors.

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i) n-type semi-conductors: The extrinsic semi conductors which contain electron-rich impurities are called n-type semi conductors. The electrical conductivity is due to movement of electrons. Eg., Silicon or germanium doped with phosphorus or arsenic (15th group elements) Mechanism: Silicon and germanium belong to group 14 of the periodic table and have four valence electrons each. In their crystals each atom forms four covalent bonds with its neighbors . When doped with a group 15 element like P or As, which contains five valence electrons, they occupy some of the lattice sites in silicon or germanium crystal . Four out of five electrons are used in the formation of four covalent bonds with the four neighboring silicon atoms. The fifth electron is extra and becomes delocalized. These delocalized electrons increase the conductivity of doped silicon (or germanium). Here the increase in conductivity is due to the negatively charged electron, hence silicon doped with electron-rich impurity is called n-type semiconductor.

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ii) p-type semiconductors: The extrinsic semi conductors which contain electron-deficit impurities are called p-type semi conductors. The electrical conductivity is due to electron holes. Eg., silicon or germanium doped with boron or aluminium or gallium (13th group elements) Mechanism: Silicon or germanium doped with a 13th group element like B, Al or Ga which contains only three valence electrons. As they can form only three bonds, an electron vacant site called 'electron hole' on the dopant atom is formed. An electron from a neighboring atom can jump into this electron hole by creating a new hole on the neighboring atom. Thus there is a movement of electron holes and electrons in opposite direction. As the conductivity is increased due to formation of positively charged holes, the substances are called p-type semi conductors.

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Applications: 1) Diode is a combination of n-type and p-type semiconductors and is used as a rectifier. 2) Transistors are made by sandwiching a layer of one type of semiconductor between two layers of the other type of semiconductor. 3) npn and pnp type of transistors are used to detect or amplify radio or audio signals. 4) The solar cell is an efficient photodiode used for conversion of light energy into electrical energy. Magnetic properties : Materials can be divided into three different classes viz., diamagnetic, paramagnetic and ferromagnetic substances, depending on their responses to an applied magnetic field. Diamagnetic materials : Diamagnetic materials are weakly repelled by the applied magnetic fields. It is because all the electrons are paired. Eg., NaCl; ZnO2; Benzene. Molecular polarity alignment in Diagmagnetic substance

Paramagnetic materials : There are permanent magnetic dipoles due to the presence of unpaired electrons on atoms, ions or molecules. Eg., O2, NO, Na atoms, Ti2O3, VO2. These materials are attracted into the applied magnetic fields. They lose their magnetism when the applied magnetic fields are removed. Ferromagnetic materials : Ferromagnetic substances show permanent magnetism even after the applied magnetic field is removed. Eg., Fe, CrO2. In these substances there are domains of magnetization, which direct their magnetic moments in the same direction. A spontaneous alignment of magnetic moments in the same direction gives rise to ferromagnetism. Fe, Co, Ni are the only three elements which show ferromagnetism at room temperature.

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Molecular polarity alignment in Ferromagnetic substance

Ferrimagnetism arises when the magnetic moments are aligned in parallel and anti parallel direction in unequally resulting in a net moment. Eg., Fe3O4, Ferrites of the general formula MII (Fe2O4) where M = Mg, Cu, Zn etc., In case of anti ferromagnetism, the magnetic moments of domains are cancel out each other so as to give zero net moment. Eg., MnO

Molecular polar alignment in Anti ferromagnetic substance

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All these magnetically ordered solids transform to the paramagnetic state at elevated temperatures due to the randomization of spins. Eg., V2O3, NiO change from anti-ferrimagnetic phase to paramagnetic phase at 150K and 523K respectively.

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Problems : 1) A Metal crystallizes in fcc lattice. It the edge length of unit cell is 0.56 A0. Calculate the nearest neighbour distance in Al. 2) Na metal crystallizes in body centered cubic lattice the edge length of unit cell is 0.424 nm at 298 K calculate the density of Na metal . 3) An ionic compound contains two elements X and Y. If the atoms of X occupy the corners of unit cell what is the formula of that compound. 4) An X-ray beam of wave length 70.93 pm was scattered by a crystalline solid. The angle ( 2 ) of diffraction for a second order reflection is 14.660. Calculate the distance between parallel planes of atoms from which the scattered beam appears to have been reflected. 5) A crystal when examined by the Bragg's technique using X-rays of wave length 2.29A0 gave an X-ray reflection at an angle of 23020'. Calculate the inter-planar spacing ; With another X-ray source, the reflection was observed at 15026'. What was the wave length of the X-rays of the second source. 6) X-rays of wave length 5460A0 are incident on a grating with 5700 lines per cm. Find the angles of reflection for the 1st and 2nd order diffraction maximum.

TEST YOUR UNDERSTANDING State whether the following statements are true or false. 1) Molecular solids posess high melting points as the attractions between the constituent particles are very strong covalent bonds. 2) The empty space in simple cubic packing is 48%. 3) The unit cell parameters in case of hexagonal crystal system are a  b  c;     900 ,   1200 n 2d 5) The number of atoms belonging to body centered unit cell is equal to two. 6) The coordination number in cubic close packing is 6. 7) The destructive interference occurs when the order of diffraction 'n' is a non integer. 8) K2Cr2O7 belongs to triclinic crystal system. 9) CsCl crystal show Frenkel defect. 10) Stoichiometric compounds are called daltonides, whereas non stoichiometric compounds are called berthollides.

4) Bragg's equation can be written as sin =

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11) The density of crystal with Schottky defects is less than that of perfect crystal. 12) The dopant used in p-type semi conductors belongs to VI A group. 13) Mg(Fe2O4), a ferrite, exhibits ferrimagnetism. 14) If the limiting radius ratio of an ionic compound is 0.71, then the cation will occupy the octahedral void formed by anions. 15) The number of tetrahedral voids found in a crystal of one mole of magnesium metal is equal to N (Avogadro number).