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Solids have definite volumes and definite shapes. The particles in solidsare held together by strong forces and the solid state is the most orderedstate. In terms of kinetic molecular model, solids have regular order ofconstituent particles (atoms, ions or molecules). These particles are heldtogether by fairly strong forces and therefore, they are present at fixedpositions.

����� IMPORTANT TERMS, FORMULAE AND FACTS

CLASSIFICATION OF SOLIDSSolids can be classified into two classes:1. Crystalline solidsThe substances whose constituents are arranged in a definite orderly

arrangement are called crystalline solids. For example, elements like copper,silver, iron, sulphur, phosphorus, iodine, sodium chloride, zinc sulphide,quartz, etc., are crystalline solids.

The crystalline substances• have definite regular geometry• have sharp melting points• have physical properties (electrical conductivity, thermal

conductivity, refractive index, mechanical strength etc.) differentin different directions i.e. crystalline substances are anisotropic.

• can be cleaved along definite planes.2. Amorphous substancesThe substances whose constituents are not arranged in an orderly

arrangement are called amorphous substances.

e.g. glass, rubber, quartz glass, plastics, etc.

• Crystalline substancesexhibit anisotropy i.e. theyhave dif ferent physicalproperties in dif ferentdirections.

• Amorphous substancesexhibit isotropy i.e. they havesimilar properties in alldirections.Amorphous substances arealso called PSEUDO SOLIDS.

16/1

16 THE SOLID STATE

16/2 MODERN’S abc OF OBJECTIVE CHEMISTRY (NEET)

The amorphous solids• do not have regular arrangement of constituents• do not have sharp melting points• have physical properties (electrical conductivity, thermal

conductivity, refractive index, mechanical strength, etc.) same inall directions i.e. amorphous substances are isotropic.

• cannot be cleaved along definite planes.

It may be noted that some amorphous solids have some orderlyarrangement but it is not extended to more than a few Angstrom units.Thus, amorphous solids are said to have short range order. On the otherhand, crystalline substances are said to have long range order.

TYPES OF CRYSTALLINE SOLIDSThe crystalline solids may be classified into (i) molecular, (ii) ionic,

(iii) covalent and (iv) metallic crystals. Their important characteristics aresummed up in the following table:

Table 1 : Important characteristics of crystals

Types of Crystals

Characteristics Molecular Ionic Covalent Metallic

Constituent Small Positive and Atoms Positive ions in aparticles molecules negative ions sea of electronsBinding Van der Waals Strong electro- Covalent Metallic bondsforces forces static forces bond forces (electric attraction

between +ve ionsand electrons).

Properties Soft, low melting Hard and brittle, Very hard, Soft to hard,point, volatile high m.p., poor high m.p., poor moderate togood insulators, conductors of heat conductors of high m.p., goodlow heats of fusion and electricity, very heat and electri- conductors, metallic

high heats of fusion city, high heats lustre, ductile andof fusion malleable, moderate

heats of fusionExamples Solids CO2, H2,I2, Salts like NaCl, Diamond, SiC, Common metals

ice, SO2, CCl4 KNO3, LiF, BaSO4 quartz, SiO2 (Cu, Na, Fe) andsome alloys

UNIT CELL AND SPACE LATTICESpace LatticeThe arrangement of points showing how constituent particles (atoms,

ions or molecules) of a crystal are arranged at different positions in a threedimensional space is called space lattice.

Unit CellThe smallest repeating unit in space lattice which when repeated over

and over again gives the crystal of the given substance is called unit cell.The unit cell is characterized by the distances a, b and c along the

three edges of the unit cell and the angles α, β and γ between the pair ofedges.

TYPES OF UNIT CELLS AND CRYSTAL SYSTEMSIn all, there are seven types of basic or primitive unit cells or crystal

systems. These are given in Table 2.Fig. 1. Three dimensional lattice

Space Lattice and Unit Cell

THE SOLID STATE 16/3Table 2 : Seven types of basic crystal systems

System Axial distance Axial angles Examples

Cubic a = b = c α = β = γ = 90° NaCl, KCl, zinc blende, Cu, AgTetragonal a = b ≠ c α = β = γ = 90° White tin, SnO2, TiO2Orthorhombic a ≠ b ≠ c α = β = γ = 90° Rhombic sulphur, KNO3, PbCO3Monoclinic a ≠ b ≠ c α = γ = 90°, Monoclinic sulphur,

β ≠ 90° CaSO4 . 2H2ORhombohedral a = b = c α = β = γ ≠ 90° Calcite, quartz, As, Sbor TrigonalTriclinic a ≠ b ≠ c α ≠ β ≠ γ = 90° K2Cr2O7 . H3BO3Hexagonal a = b ≠ c α = β = 90°, Graphite, ZnO, CdS

γ = 120°

In addition to above seven primitive unit cells, there are non-primitiveunit cells having points at other positions also. For example, a cubic systemmay be simple (or primitive), body centred cubic and face centred cubic as :

THREE CUBIC SYSTEMSThere are three common types of cubic systems:1. Simple or primitive having points at all the corners of the unit cell.2. Body centred cubic having points at all the corners as well as at the

centre of the cube.3. Face centred cubic having points at all the corners as well as at the

centre of each face.

❑ It may be noted that there is another type of non-primitive unit cellknown as end centred unit cell. This has points at all the corners andat the centres of two end faces.All systems do not have end centred unit cells. Only orthorhombicand monoclinic systems have end centred unit cells.

BRAVAIS LATTICESIf all types of space lattices are counted, there are fourteen in all and

these are known as Bravais lattices. These are shown in Fig. 2.

CLOSE PACKING OF PARTICLESThere are two common types of close packing of particles in a crystalline

substance :Hexagonal close packing. This type of packing is referred to as

ABABA....... arrangement.Cubic close packing. This type of packing is referred to as ABCABCA.......

arrangement.In both types of packing 74% of the available space is occupied by spheres.

INTERSTITIAL SITESTwo important interstitial sites are:(i) Tetrahedral site. When a sphere in the second layer is placed above

three spheres which are touching one another, a tetrahedral site is formed.(ii) Octahedral site. This type of site is formed at the centre of six spheres

and is produced by two sets of equilateral triangles which point in oppositedirections.

COORDINATION NUMBER AND RADIUS RATIOCoordination numberThe number of nearest neighbours with which a given sphere is in contact

is called the coordination number. The coordination number in hcp andccp arrangement is 12.

Contribution of atoms in aunit cell

Atoms at corners = 18

Atoms at edges = 14

Atoms in the face = 12

Atoms in the body = 1

No. of atoms in different unitcells

Simple cubic = 1Body centred cubic = 2Face centred = 4(fcc or ccp)hcp = 6

• There are two tetrahedralsites for each sphere.

• There is one octahedral sitefor each sphere.

16/4 MODERN’S abc OF OBJECTIVE CHEMISTRY (NEET)

Radius ratioThe ratio of the radius of the cation to the radius of the anion is called radius ratio. This is very important

in determining the structure of ionic solids. The limiting radius ratios in different crystals and their coordinationnumbers are given in Table 3.

Cubic

a = b = cα = β = γ = 90°

Tetragonal

a = b ≠ cα = β = γ = 90°

Primitive Body-centred Face-centred

Primitive Body-centred

Primitive Body-centred Face-centred End-centred

ab

c

Orthorhombic

a ≠ b ≠ cα = β = γ = 90°

Primitive End-centred

Primitive

Primitive Primitive

Monoclinic

a ≠ b ≠ cα = γ = 90°β ≠ 90°

Hexagonal

a = b ≠ cα = β = 90°γ = 120°

Rhombohedral

a = b = cα = β = γ ≠ 90°

Triclinic

a ≠ b ≠ cα ≠ β ≠ γ ≠ 90°

Fig. 2. Fourteen Bravais Lattices

• There are seven types ofcrystal systems.

• There are 14 space lattices,called Bravais lattices.

THE SOLID STATE 16/5

Relationship between nearest neighbour distance (d) and radiusof atom (r) (for crystals of pure elements) and edge of unit cells (a)

For simple cubicd = a r = a/2

For face centred cubic

d =a

�

r = a

� �

For body centred cubic

d =�

�

a r = �

�

a

DENSITY OF A CRYSTALDensity of a crystal can be calculated by knowing the edge length of the

unit cell.

Density =Na3

Z Mg cm3,

where a = length of the edge of unit cell in cmZ = number of atoms per unit cellM = atomic mass of element or formula mass of the compoundN = Avogadro number

STRUCTURES OF SIMPLE SUBSTANCESIn simple ionic solids ccp or hcp types of arrangement are generally

present. The large ions (anions) adopt these arrangements and the smallerions (cations) occupy interstitial sites. The summary of some commoncrystals is given below:

• If ‘a’ is in pm, thenEdge length = a pm

= a × 10–12 m= a × 10–10

cmand a3 = a3 × 10–30 cm3

• Z is the number of atomsper unit cell or formulaunits per unit cell.e.g. for fcc, Z = 4

for bcc, Z = 2 for simple cubic, Z = 1

Some Common types of structures of ionic compounds

Compound Description Coordination number Other Examples

NaCl ccp arrangement of Cl–, Na+ Na+ = 6 Li, Na, Kin all the octahedral sites Cl– = 6 halides, AgCl,

AgBr, MgO, CaOZnS ccp arrangement of S2–, Zn2+ Zn2+ = 4 BeS, CuCl,(Zinc blende) in alternative tetrahedral sites S2– = 4 CuBr, CuICsCl Simple cubic arrangement of Cs+ = 8 CsBr, CsI

Cl–, Cs+ in cubic sites Cl– = 8CaF2 ccp arrangement of Ca2+, F– Ca2+ = 8 SrF2, BaF2(Fluorite structure) occupy all tetrahedral sites F – = 4Na2O ccp arrangement of O2–, Na+ Na+ = 4 Li2O, K2S(Antifluorite structure) occupy all tetrahedral sites O2– = 8

Table 3

Radius ratio Possible coordination Structural Examples(r+/r–) number arrangement

0.225 – 0.414 4 Tetrahedral ZnS0.414 – 0.732 6 Octahedral NaCl0.732 – 1.0 8 Cubic CsCl1 12 Close packing Metals

Packing Efficiency. It is thepercentage of total space filledby the particles.

Structure Packingefficiency

1. Hexagonal closedpacked (hcp) 74%

2. Cubic close packed(ccp) or face centredcubic (fcc) 74%

3. Body centredcubic (bcc) 68%

4. Simple cubic 52.4%

16/6 MODERN’S abc OF OBJECTIVE CHEMISTRY (NEET)

POINT DEFECTS IN CRYSTALSIdeal crystals with perfect arrangement of constituents are found only

at 0 K. Above this temperature, all crystalline solids have some defects inthe arrangement of its unit cells. An ideal crystal of A+B– type may berepresented as shown in Fig. 3.

Defects in the crystals may give rise to(A) Stoichiometric and(B) Non-stoichiometric structures.(A) Stoichiometric structuresThe compound A+B– is stoichiometric if it contains equal number of

atoms A+ and B– as suggested by the chemical formula of the compound.There are two types of defects in stoichiometric structures :

(i) Schottky Defect. This defect consists of vacancies at cation sitesand equal number of vacancies at anion sites. It is predominant in compoundswith high coordination number and where the ions are of similar size.

(i) Schottky defect (ii) Frenkel defect

Fig. 4 Schottky and Frenkel defects in crystals

(ii) Frenkel Defect. This defect consists of vacancies at cation sites inwhich the cation move to another position in between two layers calledinterstitial sites. This defect is most predominant in compounds which havelow coordination number and ions of different sizes.

(B) Non-stoichiometric compounds.The compounds in which the ratio of the number of atoms of A+ to the

number of atoms of B– does not correspond to a simple whole number assuggested by the formula are called non-stoichiometric compounds.

The non-stoichiometric defects are of two types :1. Metal excess defects. In these defects, positive ions are in excess

and arise due to :(i) Anion vacancies. Vacancies at anion sites and their electrons remain

trapped. The electrons trapped in anion vacancies are called F-centres.

Fig. 5. Metal excess defects due to anion vacancy

Fig. 3. Ideal crystal A+ B–

The electrons trapped in anionvacancies are called F-centresbecause they impart colour tocrystals. For example.• excess of Na in NaCl imparts

yellow colour,• excess of K in KCl imparts

violet (lilac) colour,• excess of Li in LiCl makes it

appear pink.

Electronremainstrappedin anionvacancy

THE SOLID STATE 16/7

2+

(ii) Cation occupying interstitial sites. Excess cations are present ininterstitial sites and equal number of electrons trapped in neighbouringinterstitial sites.

Fig. 6. Metal excess defects due to extra cation

2. Metal deficient defects. This arises due to(i) Cation vacancies. Vacancies at cation sites and the extra negative

charge is balanced by extra charge (higher oxidation state) of equalnumber of some cations.

Cationvacancy

Metalacquiring

higher charge

Fig. 7. Metal deficient defect due to cation vacancy

(ii) Anion occupying interstitial sites. Excess anions are present ininterstitial sites and the corresponding increase in negative charge isbalanced by oxidation of equal number of cations to higher oxidationstates.

Fig. 8. Metal deficient defect due to extra anion

IMPURITY DEFECTSThese defects in ionic crystals arise due to the presence of some impurity

ions at the lattice sites (in place of host ions) or at the vacant interstitialsites. For example, if molten NaCl containing a little amount of SrCl2 isallowed to crystallize, some of the sites of Na+ ions are occupied by Sr2+

ions. For each Sr2+ ion introduced, two Na+ ions are removed to maintainelectrical neutrality. One of these lattice site is occupied by Sr2+ ion andthe other remains vacant. Therefore, these vacancies result in increasedelectrical conductivity of the solid. Similar defect and behaviour is observedwhen CdCl2 is added to AgCl.

Because of metallic lustre ofsome minerals of iron pyrites,they shine like gold and havebeen nick named as fool’s gold.

The common example of this typeof defect is zinc oxide. It is whitein colour at room temperature.On heating, it loses oxygenreversibly at high temperatureand turns yellow in colour.

The crystals with metal excessdefect are n-type semiconductors.

Metal deficient defect is found inferrous oxide, ferrous sulphide,nickel oxide, etc. These crystalsacquire metallic lustre.

Crystals with metal deficientdefects are p-type semiconductors.

16/8 MODERN’S abc OF OBJECTIVE CHEMISTRY (NEET)

Introduction of a cation vacancy in NaCl by substitution of Na+ bySr2+.

ELECTRICAL PROPERTIES OF SOLIDSSolids exhibit an interesting range of variation of electrical conductivities

extending from 10–20 to 107 ohm–1 m–1.On the basis of electrical conductivity, solids can be classified into

three types:(i) Conductors. The solids which allow the passage of electric current

are called conductors. They have conductivities in the range 104 to 107

ohm–1 m–1. For example, metals have conductivities of the order of 107

ohm–1 m–1 and hence are the best conductors of electricity. Conductorsare of two types:

(a) Metallic conductors are those which allow the electricity to passthrough them without undergoing any chemical change. For example, copper,silver etc. Metals conduct electricity in solid as well as in molten state. Inmetallic conductors, the conductance is due to the movement of electrons.

(b) Electrolytic conductors are those which allow the electricity topass through them by undergoing chemical change. The conduction inionic solids is due to the migration of ions or other charged particlesunder the applied field.

(ii) Insulators. The solids which do not allow the passage of electriccurrent through them are called insulators. They have very very lowconductivities ranging between 10–20 to 10–10 ohm–1 m–1. For example,wood, sulphur, phosphorus, rubber etc.

(iii) Semi-conductors. The solids whose conductivity lies betweenthose of typical metallic conductors and insulators are called semi-conductors. The semi-conductors have conductivity in the range of 10–6 to104 ohm–1 m–1. The conductivity of semi-conductors is due to the presenceof impurities and defects.

Conduction of electricity in metals Metals conduct electricity in the solid as well as in molten state. The

conductivity of metals depends upon the number of valence electronsavailable per atom. The atomic orbitals of metal atoms form molecularorbitals which are close in energy to each other and form a band. If thisband is partially filled or it overlaps with a high energy vacant band(called conduction band), then electrons flow easily under an appliedelectric field and the metal shows conductivity. If the gap between filledvalence band and the next higher unoccupied band (conduction band) islarge, electrons cannot jump to it and such substance has very smallconductivity and it behaves as an insulator.

Fig. 10.The gap between valence band and conduction band is small in case of

semiconductors. Therefore, some electrons may jump to conduction bandand show some conductivity. The electrical conductivity of semiconductors

Fig. 9. Impurity defect.

Range of conductivity● Conductors : 104 to 107

ohm–1m–1

● Semiconductors : 10–6 to 104

ohm–1m–1

● Insulators : 10–20 to 10–

10 ohm–1m–1

With increase in temperatureelectrical conductivity of● metals decreases● semiconductors increases.

THE SOLID STATE 16/9increases with rise in temperature because more electrons can jump toconduction band. Silicon and germanium show this type of behaviour andare called intrinsic semiconductors.

The conductivity of these intrinsic semiconductors is very low to be ofpractical use. Their conductivity can be increased by introducing anappropriate amount of suitable impurity. This process is called doping.The conductivity of Si or Ge increases drastically by doping it either withelectron rich impurities or with electron deficit (or acceptor) impurities.

For example, when Ge is doped with some electron rich atoms such asP or As containing five valence electrons, these will randomly replace Geatoms. Four of the electrons in P or As will form four covalent bonds withsurrounding Ge atoms and the fifth electron will remain free. The extraelectron will be able to conduct and this type of conduction is calledn-type conduction. On the other hand, when Ge is doped with electrondeficit atoms such as Ga or In containing three valence electrons, theatoms of Ga or In will replace Ge atoms. Each In or Ga atom will use itsthree electrons for forming three covalent bonds with the neighbouring Geatoms and the place for fourth bond will remain missing and is calledelectron vacancy or hole. Such holes can move through the crystal likea positive charge giving rise to conductivity. This type of conduction iscalled p-type conduction.

Fig. 11. Arsenic doped germanium Fig. 12. Indium doped germaniumsemiconductor semiconductor

MAGNETIC PROPERTIESSubstances can be divided into the following types depending upon

their response to the magnetic fields :1. Diamagnetic substances. The substances which are weakly repelled

by the magnetic fields are known as diamagnetic substances. For example,NaCl, benzene, TiO2, V2O5, etc.

2. Paramagnetic substances. The substances which have permanentmagnetic dipoles and are attracted by magnetic field are known asparamagnetic substances. These consist of atoms, ions or moleculeshaving unpaired electrons. The common examples are O2, Cu2+, Fe3+,TiO, Ti2O3, VO, CuO, etc. They lose their magnetism in the absence ofmagnetic field.

3. Ferromagnetic substances. These substances are attracted by themagnetic field and show permanent magnetism even when the magneticfield is removed. Once such a material is magnetised, it remainspermanently magnetised. Iron is the most common example. Otherexamples are cobalt, nickel, CrO2, etc.

In this case, the magnetic moments are aligned in the same direction.4. Antiferromagnetic substances. In these substances, the alignment

of the magnetic moments is in a compensatory way so as to give zero netmagnetic moment. For example, MnO, MnO2, FeO, Fe2O3, NiO, Cr2O3.

5. Ferrimagnetic substances. These are the substances in which themagnetic moments are aligned in parallel and anti-parallel directions in

Fig. 13. Alignment of magneticmoments in (a) ferromagnet (b) anti-

ferromagnet (c) ferrimagnet

16/10 MODERN’S abc OF OBJECTIVE CHEMISTRY (NEET)

unequal numbers giving a net magnetic moment. For example, Fe3O4,ferrites of the formula M2+, Fe2O4, where M = Mg, Cu, Zn, etc.

X–RAY DIFFRACTION STUDIESX-ray studies have helped to know the arrangement of atoms, ions

or molecules in crystals. The phenomenon of X-rays by the crystals wasstudied by W.L. Bragg and W.H. Bragg. By analysing the diffractionpatterns, Bragg deduced a simple relationship between the distancebetween the layers, the wavelength of X-rays used and the angle ofdiffraction. This relation is known as Bragg equation and is given as:

nλ = 2d sin θ,where 2 θ = angle made by a diffracted X-rays beam with the

direction of incident beam.λ = wavelength of X–rays usedd = distance between the planes of the constituent par-

ticles in the crystal.n = positive integer (1, 2, 3......, etc.) which stands for

serial order of diffracted beams.Using Bragg's law, we can calculate the distance between rows of

constituent particles in a crystal. These distances are characteristic of acrystal and depend upon the size and geometry or arrangement of theseparticles.

STRUCTURES OF METALSThe crystal structures adopted by some metallic elements at 25°C and

1 bar pressure are :

Crystal Structure Elements

hcp Be, Cd, Co, Mg, Ca, Ti, Znfcc Ag, Al, Au, Ca, Cu, Ni, Pb, Ptbcc Ba, Cr, Fe, Ir, alkali metalsPrimitive cubic Po

� Example 1. Which of the following statement is not true about crystallinesolids ?(a) Polar molecular solids have higher enthalpies of vaporisation than

those of non-polar molecular solids.(b) Graphite, though covalent solid, is a good conductor of electricity.(c) Ionic solids are conductors in molten state.(d) Non-polar molecular solids have London forces between the

constituents and have higher melting points than polar molecularsolids.

Strategy/Solution : It is a conceptual question and we are to select the wrongstatement. Choices (a), (b) and (c) are true but choice (d) is not true. The non polarmolecular solids have London forces or dispersion forces between their molecules.These are weak forces and therefore, the solids have low melting points. On theother hand, polar solids have strong dipole-dipole forces between their moleculesand have melting points higher than those in non-polar solids.

Correct Answer: (d)� Example 2. A spinel mineral has the formula MgAl2O4. In this O2– ions

are present in ccp arrangement, Mg2+ ions occupy the tetrahedral voidswhile Al3+ ions occupy the octahedral voids. The percentage of tetrahedral

MOD ABC Of Objective Chemistry ForNEET Part-2

Publisher : MBD GroupPublishers

ISBN : 9789351846772Author : Dr. S. P. Jauhar,Dr. Sheenu Jauhar

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