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Chemistry: Solid State

Topics are arranged as per SYLLABI published by Maharashtra State Board of Secondary and Higher Secondary Education.

There are three physical states of matter namely solid, liquid and gas. They differ in intermolecular or interatomic or interionic forces which are strongest in the solid state. By raising the temperature of solids to their melting point, solids are converted into liquids. While heating liquids to their boiling points, the liquids can be converted into vapour or gaseous state. By cooling the gases to very low temperature and subjecting to high pressure they can be transformed into liquid which on further cooling can be transformed into solid state. The equilibrium existing between three states of matter may be represented as:

Presence or absence of orderly arrangement of the constituent particles of the solid distinguish the solids into two types: Crystalline & Amorphous:

Crystalline Solids Amorphous Solids
Definition Homogeneous solid in which the constituent particles like atoms, ions or molecules are arranged in a definite repeating pattern throughout the solid is called crystalline solid. A substance which appears like solid but does not have perfectly ordered crystalline structure and no regular arrangement of constituent particles in structure is called amorphous solids.
Ex: NaCl, KNO3 Glass, Rubber, Plastic
Melting Point Sharp Melting Point. Do NOT have sharp melting point.
When cut They split into pieces with newly generated plain & smooth surfaces. They split into pieces with irregular and rough surfaces.
Measure Physical Properties The ability of crystalline solids to change their physical properties when measured in different direction is called Anisotropy. The ability of amorphous solids to exhibit identical physical properties even though measured in different direction is called isotropy.
Shape Definite Geometrical Shape. Irregular Shape.
Referred as True Solid Pseudo Solids or Super cooled Liquids
Fusion Definite heat of fusion Do NOT have definite heat of fusion
When two or more crystalline substances have the same crystalline structure, they are said to be isomorphous. Ex: K2SO4 and K2SeO4

Molecular solids have very low binding energy (less than 40 Kg/mol normally held together by weak van der Waal’s forces) and Melting points (less than 273 K). (Ex: dry ice, solid Ar, etc).
In the crystalline molecular solids, the constituents particles are molecules of the same compound. According to the types of molecules involved and the nature of intermolecular forces in the crystal, they are further classified into three types:

Polar Molecular Solids Non-Polar Molecular Solids Hydrogen bonded molecular Solids
Since polar molecules have two separated opposite charges, they are called dipoles and they possess permanent dipole moment. Attracted by strong dipole-dipole forces. Atoms or non-polar molecules are held by weak dispersion forces or London forces. Molecules are held by Hydrogen bonds in which H atom of one molecule is bonded to electronegative atom (like F, N or O) of another molecule.
Melting points are higher than non-polar molecular solids but lower than ionic and metallic solid. Very Low melting point. Very Low melting points and generally at room temperature they exist in the liquid or gaseous state.

Ice has hexagonal three dimensional crystal structure formed due to hydrogen bonding. In H2O, two hydrogen atoms are covalently bonded to oxygen atom. The structures of liquid water and solid ice are almost identical.
Each O-H bond is polar hence H2O is a polar molecule.
H2O molecules are linked to each other involving dipole-dipole interaction and hydrogen bonding. In ice, H2O molecules are linked forming a tetrahedral arrangement. In this arrangement, two covalently bonded H atoms and two H atoms bonded by hydrogen bonds are at four corners of the tetrahedron.

Ionic Covalent (Network) Metallic
Crystalline Solids Crystalline Solids Shiny Crystal Lattice forming a "sea of electrons"
High melting points and non volatile (wide temperature range for liquid phase). High melting points. Are solids at room temperature (except for mercury); melting points vary.
Many dissolve in water, but not in organic solvents. Hard, but brittle (are solids at room temperature) Insoluble in all common solvents. Are insoluble in water or other solvents.
Do not conduct in solid phase. Conduct electricity in the liquid phase and in solution. Poor electrical conductors (Except Graphite). Conduct electricity in the solid and liquid phase, but not in the gaseous phase.
Ex: NaCl Ex: Carbon, Diamond Ex: Gold
Binding Energy 400-4000 KJ / mol Binding Energy 150-500 KJ / mol Binding Energy 70-1000 KJ / mol

A crystal is a solid composed of molecules, atoms or ions arranged in an orderly repetitive array having a three dimensional pattern with a characteristic shape and geometry. Unit Cell is the smallest repeating structural unit of a crystalline solid (or crystal lattice) which is repeated in different directions produces the crystalline solid (lattice).

Crystal Lattice Unit Cell
It is a regular arrangement of constituent particles of a crystalline solid in three dimensional space. It is the smallest repeating structural unit, which when repeated in space in all dimensions, generates a crystal lattice.
It is made up of a large number of unit cells. It is one fundamental unit of crystal lattice which possesses all the properties of the crystal.
Crystal lattice is defined in terms of properties of unit cell. Unit cell describes the fundamental properties of the crystal lattice.
Crystal lattice on further splitting may form numerous unit cells. Unit cell can’t be further subdivided without changing the crystalline properties.
Crystal lattice can be prepared, handled and studied experimentally. Unit cell is a hypothetical object which is the smallest possible imaginary part of the crystal lattice and cannot be handled and studied individually.
It is macroscopic system. It is a microscopic molecular size system.

Consider a cubic unit cell of edge length a. Then the volume of the unit cell = a3. Consider M is the atomic mass of the constituting element or metal and NA is the Avogadro Number, then the mass of one atom will be Solid State
If z is the number of atoms present in the unit cell, then the Mass of unit cell = mass of z atoms = z X Solid State
Density of unit cell = Mass of Unit CellVolume of Unit Cell = d = Solid State

The packing of spheres of equal size takes place as follows :
One Dimensional Packing: When the spheres are placed in horizontal row, touching each other, an edge of the crystal is formed.
Two Dimensional Packing: It is of two types

  • A)Square close packing (scp): The particles, when placed in the adjacent rows, show a horizontal as well as vertical alignment and from squares.
  • B) Hexagonal close packing (hcp) : The particles in every next row are placed in the depression between the particles of the first row. The particles in the third row will be vertically aligned with those in the first row.

Three Dimensional Packing: It is of two types
  • A)Hexagonal Closed Packing (HCP): The first layer as layer A and second layer as layer B, the arrangement is called AB AB… pattern or hexagonal closed packing (hcp).
  • B) Cubic Close Packing (CCP) : When the third layer is placed over the second layer in such a way that spheres cover the octahedral voids, a layer different layers A and B is produced. Let us call it as layer C. This pattern or cubic close packing (ccp). It is similar to face centred cube (fcc) packing.

Hexagonal Close Packing Cubic Close Packing
In this three dimensional building of unit cell, spheres of three layer are placed on triangular shaped tetrahedral voids of the second layer. In this three dimensional building of unit cell, the crests of spheres of third layer are placed in the positions of tetrahedral voids having apices upwards.
The spheres of third layer lie directly above the spheres of first layer. The spheres of third layer do not lie above the spheres of first layer.
First and third layers are identical. First and third layers are different.
First and fourth layers are different. First and Fourth layers are identical.
The arrangement of packing is ABAB type. The arrangement of packing is ABCABC type.

A vacant space or a space not occupied by the constituent particles in the unit cell is called a void space. Even in the closest packing of constituents particles like atoms, ions or molecules in the crystalline structure, certain empty space is left vacant. This vacant space left in between the closest packed arrangement of constituent particles is called interstitial void or interstitial site.
In a single layer of packing of spheres the voids of the square close packing are called "square voids" because void is present between four touching spheres whose centres lie at the corners of square. Similarly the voids of the hexagonal close packing are called "Triangular voids" because void is present between three touching spheres whose centres lie at the corners of a triangle.

Tetrahedral Void Octahedral Void
Voids Per Sphere Two voids per sphere in the crystal lattice. If the number of closed packed spheres is N then the number of tetrahedral voids is 2N. One void per sphere in the crystal lattice. If the number of closed packed spheres is N then the number of octahedral voids is also N.
Coordination Number FOUR SIX
Radius of void If R is the radius of the constituent atom, then the radius of the tetrahedral void is 0.225 R. If R is the radius of constituent atom, then the radius of the octahedral void is 0.414 R.

In a unit cell, atom’s coordination number is the number of atoms it is touching.

  • The hexagonal closest packed (hcp) has a coordination number of 12 and contains 6 atoms per unit cell.
  • The face-centered cubic (fcc) has a coordination number of 12 and contains 4 atoms per unit cell.
  • The body-centered cubic (bcc) has a coordination number of 8 and contains 2 atoms per unit cell.
  • The simple cubic has a coordination number of 6 and contains 1 atom per unit cell.
Unit Cell Coordination Number Atoms Per unit Cell % Space
Simple Unit Cell 6 1 52 %
Body Centered Cubic 8 2 68 %
Face Centered Cubic 12 4 74.04 %
Hexagonal Closed Packed 12 6 74.04 %

It is the deviation from ideal arrangement of constituent atom. Point defects are two types (a) Vacancy defect (b) Interstitial defect.
Point defects in the ionic crystal may be classified as:

  • Stoichiometric defect (Ratio of cation and anion is same).
  • Non Stoichiometric defect (disturb the ratio).
  • Impurity defects (due to presence of some other ions at the lattice sites).

Sr. No. Defect Nature of Defect
1 Schottky Atom or ion missing from the lattice point and thus giving a vacancy. Density of the crystal is lowered.
2 Interstitial Atom or ion in a vacant void, also called hole (or interstitial site).
3 Frenkel This is hybrid type of defect produced from the combination of (1) and (2). Atom or ion at the lattice point displaced to an interstitial site creating a vacancy.
4 F-centre Electron trapped in an anionic vacancy. If the concentration of F-centre is high, colourless crystals (like KCl, LiCl,NaCl) develop some colour.
5 Dislocation Line defects are called dislocations.
6 Non-stoichiometric It is in cases where the compounds contain the combining elements in a ratio different from that required by their stoichiometric formulae.
These imperfection / defect are found as Schottky and Frenkel defects.
Schottky Defect Frenkel Defect
It is due to equal number of cations and anions missing from the lattices slites. It is due to the missing of ions (usually cations) from the lattices sites and they occupy the interstitial sites.
This result in the decrease in density of crystal. It has no effect on the density of crystal.
This type of defect is found in highly ionic compounds with high coordination number eg: NaCl CsCl, AgBr. This type of defect is found in crystals, where the difference in the size of cations and anions is very large. Eg AgCl, AgBr, ZnS etc.

Materials are classified based on their electrical properties as conductors, semiconductors and insulators. New to this group are super conductors. Charge that flows comprised of electrons, ions, charged holes, and their combinations. Material’s electric resistance is NOT an intrinsic-property i.e. it depends on object geometry.
Electrical Properties: Solids are classified into following classes depending on the extent of conduction nature:

Conductivity
Metals Solid State
Insulators Solid State
Semiconductors 10-5 to 106Solid State
Conductivity of the solids may be due to the movement of electrons, holes or ions. Due to presence of vacancies and other defects, solids show slight conductivity which increases with temperature. Metals show electronic conductivity. The conductivity of semiconductors and insulator is mainly governed by impurities and defects. Metal oxides and sulphides have metallic to insulator behaviour at different temperatures.
Conductivity
Insulator-like Insulator-to-metal Metal Like
FeO, Fe2O3 Ti2O3 TiO
V2O5 VO2 VO

Magnetic Properties of Solid :
S. No. Properties Description Alignment of magnetic dipoles Examples Applications
1 Diamagnetic Feebly repelled by the magnetic fields. Non-metallic element (excerpt O2, S) inert gases and species with paired electors are diamagnetic. All Paired Electrons Solid State NaCl Insulator
2 Paramagnetic Attracted by the magnetic field due to the presence of permanent magnetic dipoles. In magnetic field, these tend to orient themselves parallel to the direction of the field and thus product magnetism in the substance. At least one unpaired electron Solid State VO, TiO Electronic appliances
3 Ferromagnetic Permanent magnetism even in the absence of magnetic field. Above a temperature called Curie temperature there is no ferromagnetism. Dipoles are aligned in the same direction Solid State Fe, Ni, Co CrO2 is used in audio and video tapes
4 Antiferromagnetic This arises when net dipole alignment is zero due to equal and opposite alignment. Solid State FeO, NiO
5 Ferrimagnetic This arises when there is net dipole moment Solid State Ferrites
Dielectric properties of Solids:
Property Description Alignment of electric dipoles Applications
Piezoelectricity When polar crystal is subjected to as mechanical stress electricity is produced and vice versa. It acts as a mechanical-electric transducer.
  • Piezoelectric Crystals with permanent dipoles are said to have ferroelectricity.
  • Piezoelectric crystals with zero dipole are said to have antiferroelectricity.
In some Piezoelectric crystals, the dipoles are permanently polarised even in absence of electric field. However on applying electric field, the direction of polarisation changes; this is ferroelectricity. Record-Players
Pyroelectricity Small electric current is produced due to heating of some of polar crystal - a case of pyroelectricity. M

For each individual atom there are discrete energy levels that may be occupied by electrons.
As atoms come within close proximity, electrons are acted upon by the electrons and nuclei of adjacent atoms. This causes each distinct atomic state to split into a series of closely spaced electron states in the solid, to form what is termed an electron energy band.

n-type semiconductors : Group 14 elements when doped with group 15 elements are called n-type semiconductors.
p-type semiconductors: Group 14 elements when doped with group 13 elements are called p-type semiconductors.

Conductor Semiconductor Insulator
A substance which conducts heat and electricity to a greater extent is called conductor. A substance which has poor electrical conductance at low temperature but higher conductance at higher temperature is called semiconductor. A substance which cannot conduct heat and electricity under any conditions is called insulator.
Conduction band and valence bands overlap or are very closely spaced. Conduction bands and valence bands are spaced closely. Conduction bands and valence bands are far apart.
There is no energy difference or very less energy difference between valence bands and conduction bands. The energy difference between conduction bands valence bands is small. Energy difference between conduction bands and valence bands is very large.
There are free electrons in the conduction bands. The electrons can be easily excited from valence bands to conduction bands by heating. There are no free electrons in the conduction band and electrons cannot be excited from valence bands to conduction bands due to large energy difference.
Conductance decreases with the increase in temperature. Conductance increases with the increase in temperature. No effect of temperature on conducting properties.
Conduction properties cannot be improved by adding third substance. By doping, conducting properties improve. No effect of addition of any substance.
Ex: Metals Ex: Si Ex: Wood

  • The state of matter whose M.P is above room temp is solid state.
  • Solids have definite shape and volume, having high density and constituent particles are held strongly.
  • Crystalline solids have regular arrangement of constituent particles throughout, melting point is sharp, Anisotropic (Some Physical Properties Like Refractive Index, Electrical Conductance may vary in different directions) in nature and give clear cut cleavage.
  • Amorphous solids have no regular arrangement, no sharp M.P, isotropic (Some Physical Properties Like Refractive Index, Electrical Conductance may not vary in different directions) in nature they do not exhibit cleavage property.
  • Amorphous silica is used in photovoltaic cells.
  • Space lattice is a regular 3D arrangement of constituent particles in the crystalline solid.
  • Smallest repeating unit in a space lattice is called unit cell.
  • There are 4 types of unit cells, 7 crystal systems and 14 bravais lattices.
  • Types of unit cell No. of atoms per unit cell:
    Simple cubic unit cell 8 X 1/8 =1
    FCC (Face centered cubic) 8 X 1/8 +6 X 1/2 = 4
    BCC (Body centered cubic) 8 X 1/8 + 1 X 1=2
  • Hexagonal close packing and cubic close packing have equal efficiency i.e 74% and coordination no. is 12.
  • Coordination no.: The no. of nearest neighbor points surrounding a particular (May point is called coordination no (point may be atom, ions & molecules).
  • Packing Efficiency = (Volume occupied by total spheres / volume of unit cell ) X 100
  • For simple cubic unit cell the packing efficiency = 52.4 %
  • The packing efficiency in bcc =62 %
  • The packing efficiency in fcc =74 %
  • Unoccupied spaces in solids are called interstitial voids or interstitial sites.
  • Two important interstitial voids are (I). Tetrahedral void and (II). Octahedral void.
  • Radius ratio is the ratio of radius of void to the radius of sphere. For tetrahedral void radius ratio =0.225 For octahedral void radius ratio=0.414
  • No. of tetrahedral void=2 X N (N=No. of closed packed particles)
  • No. of octahedral void=N
  • Formula of compound depends upon arrangement of constituent particles in unit cell.
  • The relationship between edge length and radius of atom and interatomic or interionic distance for different types of unit cell is as given below
    Simple cubic unit cell Solid State
    FCC Solid State
    BCC Solid State
  • Interatomic distance=2r
  • Interionic distance=Rc+Ra (Rc=Radius of cation, Ra=Radius of anion)
  • Imperfection is the irregularity in the arrangement of constituent particles.
  • Point defect or Atomic defect - It is the deviation from ideal arrangement of constituent atom. Point defects are two types (a) Vacancy defect (b) Interstitial defect
  • Vacancy defect lowers the density.
  • Interstitial defect increases the density of crystal.
  • Point defects in the ionic crystal may be classified as:
    a.Stoichiometric defect (Ratio of cation and anion is same).
    b.Non Stoichiometric defect (disturb the ratio).
    c.Impurity defects (due to presence of some other ions at the lattice sites)
  • Schottky defect arises due to missing of equal no. of cations and anions from lattice sites in the crystalline solid and it lowers the density of crystal e.g. NaCl.
  • Frenkel defect is the combination of vacancy and interstitial defects. Cations leave their actual lattice sites and occupy the interstitial space in the solid. In this defect density remains same e.g. AgCl.
  • AgBr is the compound which shows both Schottky Defect and Frenkel Defect.
  • Non stoichiometric defect
    a. Metal excess defect due to anion vacancy.
    b. Metal excess due to presence of extra cation.
    c. Metal deficiency due to absence of cation.
  • F-Center - In metal excess defect, trapping of electrons in the anion vacancies which act as color center. Ex. NaCl gives yellow color in excess of Na+ ions.
  • Out of crystal systems (in the scope of our study) Triclinic is the most unsymmetric system.
  • AgBr has both Schottky and Frenkel Defects.
  • Atoms in a solid vibrate like a simple harmonic oscillator. They have different modes of vibrations. When transition takes place from a higher vibrational state to lower vibrational state, a quantum of thermal energy is emitted. This quantum of thermal energy is called phonon in analogy to photon for light energy. Absorptions of phonons by a crystal can produce atomic displacement leading to imperfections.
  • F-centres are the sites where anions are missing and instead electrons are present. They are responsible for colour (F = Farbe = Colour)
  • Laws of Crystallography:
    • Law of Constancy of Interfacial Angles (Steno’s Law) : The angles between the corresponding faces of a crystal are always the same irrespective of the size and external shape of the crystal.
    • Law of Symmetry : Crystals of a particular substance possess the same elements of symmetry. Ex: Cubic crystals always posses 23 different elements of symmetry (9 planes, 13 axes, 1 centre of symmetry)
    • Law of Rational Indices (Hauy’s Law): Intercepts made by any face of a crystal on suitable crystallographic axes are equal to or some simple whole number multiples of the intercepts made by the unit plane.
  • There are three types of elements of Symmetry:
    • Plane of Symmetry (Imaginary plane passing through the crystal which divide the crystal into two halves such that one is the mirror image of the other).
    • Axis of Symmetry (Imaginary line passing through the crystal such that when the crystal is rotated about this line, exactly similar appearance occurs more than once in one revolution. Ex; triad : three fold)
    • Centre of Symmetry (Imaginary point within the crystal such that line passing through this point intersect the opposite faces of the crystal at equal distance).
  • Born-Haber Cycle is used to calculate the lattice energy of an ionic compound through cyclic process.