UNIT-1 THE SOLID STATE

T.JAYANTHI

PGT CHEMISTRY

JNV VELERU ,KRISHNA DIST

PART -1 OUTLINE

• Characteristics of solids

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• Classification of solids

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• Classification of crystalline solids

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Characteristics of Solids

• Solids have definite shape and volume, rigidity incompressibility and high density .
• In solids the constituent particles are very closely packed and occupy fixed positions.
• Constituent particles oscillate about their mean position

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CLASSIFICATION OF SOLIDS

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Types:-

1.Crystalline solid. 2.Amorphous solid.

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Amorphous(Glass)

800px-Quartz,_Tibet from wikipedia.jpg ,

Crystalline(Quartz)

220px-Oldf_Fashioned_Glass from wikipedia

AMORPHOUS SOLIDS

• The constituent particles have no regular arrangement and have short range order.
• No sharp melting point and melt over a range of temperature.
• Isotropic :- Physical properties are same in all directions.
• Considered as pseudo solids or super cooled liquids.
• Irregular cleavage.
• Amorphous solids on heating become crystalline at some temperature.

Ex: Glass objects of ancient civilization appear milky . (Why……….)

• Amorphous solids have fluidity property.

Ex: Glass windows in old buildings appear thick at bottom . (Why……….)

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amormphous powder from wikipedia.jpg

��CRYSTALLINE SOLIDS��

• The constituent particles are orderly arranged .
• Have long range order and sharp melting points.
• Anisotropic :- some of the physical properties like refractive index are different in different directions.
• These are considered as true solids.
• They undergo a clean cleavage.
• Crystalline solids have definite heat of fusion.

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e.g. Diamond, Graphite, metals like Fe, Co, Cu etc., Ionic compounds like NaCl, ZnS, KCl etc.

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704px-Quartz_Brésil from wikimedia.jpg

• TYPES
• OF CRYSTALLINE SOLIDS
• MOLECULAR SOLIDS

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• IONIC SOLIDS

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• METALLIC SOLIDS

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• COVALENT SOLIDS

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TYPES OF CRYSTALLINE SOLIDS�1.MOLECULAR CRYSTALLINE SOLIDS

Iodine-unit-cell-3D-vdW from wikimedia

Iodine

• Constituent particles are polar or non –polar molecules or H-bonded molecules.

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• Force of attraction is dispersion force or dipole- dipole interaction or hydrogen bonding.

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• Low melting and boiling point.
• Insulators

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• EX: Iodine

TYPES OF CRYSTALLINE SOLIDS� 2.IONIC SOLIDS�

• Constituent particles are ions.

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• Force of attraction is ionic bond .

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• High melting and boiling points.

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• Electrical insulators in the solid state but conductors in aqueous solution and molten state .

e.g: NaCl, LiF, MgO, ZnS, CaF₂ etc.

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TYPES OF CRYSTALLINE SOLIDS�3.METALLIC SOLIDS

• Constituent particles are +vely charged metal ions and free electrons.

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• Force of attraction is metallic bond.

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• High electrical and thermal conductivity.

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• Malleable and ductile.

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• High melting and boiling point.

e.g.: Fe, Cu, Ag, Mg etc

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Iron_from.jpg from wikimedia

Iron

TYPES OF CRYSTALLINE SOLIDS�4. COVALENT AND NETWORK SOLIDS

• Constituent particles are neutral atoms.

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• Force of attraction is covalent bond .

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• High melting point

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• Insulators

e.g.: Diamond, quartz, SiC, AlN,

• Conductor :- Graphite

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Graphite-233436.jpg from wikipedia

Graphite

SUMMARY

• Characteristics of solids
• Classification of solids:-Crystalline and amorphous
• Classification of crystalline solids :- Molecular , Ionic, Metallic and Covalent solids .

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QUESTIONS

• 1. Write a feature that will distinguish a metallic solid from an ionic solid. 

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• 2. Write a distinguish feature of covalent solid. 

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• 3.Why graphite is good conductor of electricity although it is a network (covalent solid)?

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•  4. What type of interactions hold the molecules together in a polar molecular solid?

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PART-2 OUTLINE

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• Crystal lattice and lattice points
• Unit cell
• Bravais lattices
• Lattice points in unit cell

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���CRYSTAL LATTICE AND LATTICE POINT��

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• The regular arrangement of the constituent particles (atoms ,ions or molecules )of a crystal in three dimensional space is called crystal lattice or space lattice.

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• Each point in a crystal lattice is called lattice point or lattice site.

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UNIT CELL

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• Unit cell is the smallest portion of the crystal lattice which , when repeated in different directions generates the entire lattice .
• Unit cell is characterized by 6 parameters.

(i) Edges (a, b ,c)

(ii)Angle between the edges .

�CLASSIFICATION OF UNIT CELLS

Types :-

• Primitive or simple Unit cells
• Centered unit cells

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PRIMITIVE UNIT CELLS:

When constituent particles are present only at the corners of a unit cell, it is called primitive unit cell.

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Classification of Unit cells

CENTERED UNIT CELLS:

Constituent particles are present at and other other centred positions.

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(i) BODY CENTERED UNIT CELL:

Constituent particles at each corners and one at the centre of the body.

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(ii) FACE CENTERED UNIT CELLS:

Constituent particles at each corners and other at the centre of the faces.

(iii) END CENTERED UNIT CELL:

Constituent particles at each corners and other at the centre of the alternate faces.

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BRAVAIS LATTICES

On the basis of six parameters of unit cell , The total number of possible unit cells (primitive and centred) in 3-dimensional lattice is 14.which are called Bravais Lattices. 

BRAVAIS LATTICES

BRAVAIS LATTICES

BRAVAIS LATTICES

NUMBER OF ATOMS IN UNIT CELL

• Primitive or simple cubic unit cell :-

Total no. of atoms for unit cell

= 8 x 1/8 = 1 atom

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• Body centred unit cell :-

Total no. of atoms for unit cell

= 8 x 1/8 + 1= 2 atoms

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NO. OF ATOMS IN A UNIT CELL

• Face centred unit cell :-

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Total no. of atoms for unit cell

= 8 x 1/8 + 6x1/2 = 4 atoms

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VISUALIZATION OF UNIT CELL

Courtesy – Next Education

SUMMARY

• Crystal lattice and lattice point
• Unit cell :- Primitive and Centred(bcc, fcc , ecc)
• Bravais lattice:- 14 types(7 Primitive and 7 Centred )
• No. of atoms of unit cell :- For scc-1atom,

bcc-2 atoms and fcc-4 atoms.

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QUESTIONS

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• 1. What is the significance of lattice point?

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• 2. Explain how much portion of an atom located at (i) corner an (ii) body centre of a cubic unit cell is part of its neighbouring unit cell.

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PART -3 OUTLINE

• Review of previous session

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• Closed packing in solids

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• Voids in solids

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REVIEW OF PREVIOUS SESSION

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• Characteristics of solids
• Classification of solids:-Crystalline and amorphous
• Classification of crystalline solids :- Molecular , Ionic, Metallic and Covalent solids .
• Crystal lattice and lattice points
• Unit cell :- Primitive and Centred(bcc, fcc , ecc)
• Bravais lattices:- 14 types(7 Primitive and 7 Centred )
• No. of atoms of unit cell :- For scc-1atom,

bcc-2 atoms and fcc-4 atoms.

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CLOSE PACKING IN SOLIDS

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• The constituent particles in solids are

close packed leaving minimum vacant space .

• The packing pattern follows in one

dimension , two dimension and three

dimension .

• The no. of spheres neighbor to one sphere is called its co-ordination no.

��CLOSE PACKING IN SOLIDS�CLOSE PACKING IN ONE DIMENSION �

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• In one dimensional close packing arrangement , each sphere is in contact with two of its neighbours .

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• Coordination number is 2 .

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CLOSE PACKING IN TWO DIMENSION

Square close packing in 2D(AAA….type ) :-

• Second row is placed adjacent to the first row and so on .
• Co-ordination no. is 4 .

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Hexagonal close packing in 2D(ABAB….type) :-

• second row is placed in the depressions of spheres adjacent to first row .
• Co-ordination no. is 6 .

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PLACING OF SECOND LAYER ON FIRST LAYER

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• When the second layer of spheres is placed in the depressions in first layer , two types of voids get formed.

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• Tetrahedral voids

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• Octahedral voids

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VOIDS IN SOLIDS

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• The vacant space surrounded by the spheres in the solids are called voids.

Types:-

1. Tetrahedral voids :-

Holes surrounded by 4 spheres.

2. Octahedral voids :-

Holes surrounded by 6 spheres.

NUMBER OF VOIDS IN SOLIDS

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• Let the no. of close packed spheres = N

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• Then the no. of octahedral voids = N

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• Then the no. of tetrahedral voids = 2N

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Visualisation(voids in solid)

Courtesy:- university of north carolina

CLOSE PACKING IN THREE DIMENSION(AAA…TYPE)

3D close packing from 2D square close packed layers :-

• Spheres of the second layer are placed just above the first layer and so on

as AAA…..type .

• The lattice generated in simple cubic lattice .
• Unit cell is primitive .
• e.g. polonium

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CLOSE PACKING IN THREE DIMENSION

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3D close packing from 2D hexagonal close packed layers :-

• Spheres of the second layer are placed in the depression of first layer .
• The third layer covers the tetrahedral voids and forms ABAB…. Pattern and forms hcp .
• Coordination no. is 12 .

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CLOSE PACKING IN THREE DIMENSION

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3D close packing from 2D hexagonal close packed layers :-

• Spheres of the second layer are placed in the depression of first layer .
• The third layer covers the octahedral voids and forms ABCABC…. Pattern and forms ccp .
• Coordination no. is 12 .

Visualisation(close packing in solids)

Courtesy- Shiksha House

SUMMARY

• Close packing pattern in one , two and three dimension in solids.

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• Tetrahedral and octahedral void .The number of tetrahedral voids are double the number of spheres in the solid.

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QUESTIONS

1. Distinguish between

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a)hexagonal close packing and cubic close packing.

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b) Tetrahedral void and octahedral void

PART -4 OUTLINE

• Packing efficiency

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• Calculation of packing efficiency in simple cube ,bcc and fcc

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RELATION BETWEEN EDGE LENGTH(a) AND RADIUS(r) OF ATOM

scc

fcc

bcc

PACKING EFFICIENCY

The fraction of the total volume of the crystal occupied by the constituent particles is called packing efficiency .

PACKING EFFICIENCY

Packing efficiency of simple cubic unit cell :-

a =2r

Volume of cubic unit cell = a³

PACKING EFFICIENCY

= volume occupied by four spheresx 100%

total volume of the unit cell = 1 x (4/3)πr³ x 100%

(2r)³

= π x 100 = 52.36% = 52.4%

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PACKING EFFICIENCY

Packing efficiency of face centred cubic unit cell :-

In ∆ABC AC²=BC²+AB²

b²=a²+a²

b= √2 a

If r is the radius of the sphere

b= 4r= √2 a

a=4r/√2

PACKING EFFICIENCY = volume occupied by four spheresx 100%

total volume of the unit cell

= 4 x (4/3)πr³ %

(2 √2r)³

= (16/3)πr³ %

(16 √2r)³

= 74%

PACKING EFFICIENCY

Packing efficiency of body centred cubic unit cell :-

In ∆ EDF

b²=a²+a²

b= √2 a

Now in ∆ AFD

c²= a²+ b²

= a²+ 2 a²= 3a²

c= √3 a

c = 4r

4r= √3 a

r = √3/4 a ,a = (4/√3) r

PACKING EFFICIENCY = volume occupied by four spheres x 100%

total volume of the unit cell

= 2 x (4/3)πr³ x100%

( (4/√3) r )³

= (8/3)πr³ x100% = 68%

64/3√3) r ³

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COMPARISON OF PACKING EFFICIENCIES

Summary

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• Packing efficiency :- scc - 52.4% , fcc – 74% , bcc – 68 % .

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• packing efficiency is maximum in fcc unit cell.

Questions

1.Calculate the packing efficiency in case of a metal crystal for body centred cubic .

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2.What is the packing efficiency of a simple cube?

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3.Which unit cell has maximum packing efficiency and what is the packing efficiency percentage?

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PART 5 OUTLINE

• REVIEW OF PREVIOUS SESSION

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• IMPERFECTIONS IN SOLIDS

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• TYPES OF POINT DEFECTS

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REVIEW OF PREVIOUS SESSION

• Close packing pattern in one , two and three dimension in solids.

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• Tetrahedral and octahedral void .

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• Packing efficiency :- scc - 52.4% , fcc – 74% , bcc – 68 % .

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IMPERFECTION IN SOLIDS

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Any deviation from perfectly ordered arrangement of constituent particles In crystal lattice is called imperfection in solids .

Ideal crystal

After imperfection

Types of imperfections

There are 2 types of imperfections known in crystal lattice.

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• Point defect :- Arises due to disorder in the regular arrangement of constituent particles around a point .

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• Line defect :- Arises due to disorder in the regular arrangement of constituent particles in entire row .

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TYPES OF IMPERFECTIONS

1. Impurity defect

Types of point defect :- 2.Stoichiometric defect

3.Non- stoichiometric defect

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IMPURITY DEFECT

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• Arises when foreign atoms are present at the lattice site in place of host atoms generates impurity defect.

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• When a little amount of SrCl₂ is added to NaCl, then at some lattice sites Na⁺ ions are substituted by Sr ²⁺ maintaining electrical neutrality .

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• The cationic vacancies produced are equal to number of Sr ²⁺ ions added .

SrCl₂ added to NaCl

VACANCY AND INTERSTITIAL DEFECT

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• These are seen in non ionic compounds.

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• Vacancy defect :- Arises when some of the lattice points are left vacant during the crystal formation .

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• Interstitial defect :- Arises when some of the constituent particles accommodate in the interstitial sites other than the lattice points.

SCHOTTKY DEFECT

• It is seen in ionic compounds.
• Equal no of cations and anions are missing from their lattice sites generates schottky defect.

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• The vacancy defect(schottky) of ionic solids decreases the density of solid

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• Shown by the crystals with high coordination no. and similar size of cation and anion .
• e.g.NaCl, KCl, NaBr, AgBr

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FRANKEL DEFECT

• It is seen in ionic compounds.
• In ionic solids in which the smaller ion i.e. cation is dislocated from its normal site to an interstitial site generates Frenkel defect.

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• In the interstitial defect (Frankel) of ionic solid ,density remains same .

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• Shown by the crystals with low coordination no. and large difference in the size of cation and anion .

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• e.g. ZnS, AgCl, AgBr, AgI.

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METAL EXCESS DEFECT

By anion vacancies :-

It is seen in alkali halides.

• An anion may be missing from the lattice sites, and the hole is occupied by an electron that maintains electrical neutrality is known as

F-centre. ( Farbenzenter)

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• The crystals become coloured due to excitation of these unpaired electrons when they absorb energy from visible light falling on the crystals .

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• Excess of Li-makes LiCl crystals pink , K -makes KCl crystals violet and Na –makes NaCl crystals yellow .

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METAL EXCESS DEFECT

By extra cations :-

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• Arises due to the presence .of extra cations in the interstitial sites .

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• Electrical neutrality is maintained by an electron present in neighbouring interstitial sites.

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• ZnO is white in colour at room temp. When ZnO is heated, it loses oxygen and turns yellow.

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ZnO Zn ²⁺ + 1/2 O₂ + 2 e^-

e-

A⁺

white yellow

SUMMARY

• IMPERFECTIONS IN SOLIDS :
• Line and point defects
• TYPES OF POINT DEFECTS –
• Vacancy defect, interstitial defect,Schottky defect,Frenkel defect
• Impurity defect, stoichiometric defect, non scoichiometric defect

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INTEXT QUESTIONS

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•  What type of stoichiometric defect is shown by AgCl? 

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• What are F-centres?

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• Which crystal defect lowers the density of solid?  

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• Which point defect in its crystal unit increases the density of a solid?

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• Why ZnO becomes yellow on heating ?

PART-6 OUTLINE

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• Electrical properties of solids

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• Magnetic properties of solids

ELECTRICAL PROPERTIES OF SOLIDS

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Solid are classified as conductor, semi-conductor and insulator on the basis of the magnitude of electrical conductivity

CONDUCTORS : The solids with conductance ranging between 10⁴ to 10⁷ ohm^-1 m^-1 are called conductors .Metals have conductivities in the order 10⁷ ohm^-1 m^-1 are good conductors.

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INSULATORS : These are the solids with very low conductivities ranging between 10^-20 to 10^-10 ohm^-1m^-1

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SEMICONDUCTORS: These are the solids with conductivities in the intermediate range from 10^-6 to 10⁴ ohm^-1m^-1

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VALENCE BAND THEORY

The conductivity of solids depend upon a number of

valence electron available for atom which can jump from valance band to conduction band .

SEMICONDUCTORS

INTRINSIC SEMICONDUCTOR :-

Elements like Si and Ge

• Show too low electrical conductivity which increases with temperature .

e.g. Si and Ge.

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• Conductivity can also be increased by adding appropriate amount of suitable impurity , process is called doping .

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• Impurity is of two types :-

Electron rich impurity and

Electron deficit impurity.

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Silicon_(14_Si) from wikimedia

Polycrystalline-germanium from wikimedia

SEMICONDUCTORS

EXTRINSIC SEMICONDUCTOR :-

• A doped intrinsic semiconductor is called extrinsic semiconductor .

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• Types :-

1. n-type semiconductor (Doped with electron rich impurities )

2. p-type semi conductor (Doped with electron deficient impurities)

Visualization of n- type semiconductor

Courtesy- Physics4students

Visualization of p- type semiconductor

Courtesy – Physics4students

12-16 and 13-15 group compounds

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• 12-16 Compounds: A semiconductor formed by combination of group-12 and group-16 elements is called 12-16 group compounds.

e.g: ZnS, CdS, HgTe, CdSe etc .

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• 13-15 compound: A semiconductor formed by the combination of group-13 and group-15 elements is called 13-15 group compound.

e.g. AlP, Insb, GaAs etc.

MAGNETIC PROPERTIES OF SOLIDS

The magnetic properties of different solids are due to orbital motion and spinning motion of the electrons which are studied in term of magnetic moments .

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TYPES OF MAGNETIC SUBSTANCES

• Paramagnetic substance
• Diamagnetic substance
• Ferromagnetic substance
• Anti ferromagnetic substance
• Ferrimagnetic substance

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Magnetic properties of solids

• Paramagnetic substance: -
• Weakly attracted by external magnetic field.
• Due to presence of one on more unpaired electrons.

e.g.: O₂, Cu ²⁺, Cr ^{3+ etc.}

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• Diamagnetic substance :-
• Weakly repelled by external magnetic field .
• Due to absence of unpaired electrons.

e.g. H₂O, NaCl, C₆H₆ etc.

Magnetic properties of solids

• Ferromagnetic substance: -
• Strongly attracted by external magnetic field and show permanent magnetism.
• As the metal ions of ferromagnetic substance are grouped into small regions called domains

e.g. Fe, Ni, Co, Gd, CrO₂ etc

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Magnetic properties of solids

• Anti ferromagnetic substance :-
• Zero magnetic moment .
• Domain are arranged in opposite direction in equal no..

e.g MnO.

Magnetic properties of solids

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• Ferrimagnetic substance : -
• Attracted by external magnetic field .
• Domains are aligned unequally in opposite

direction .

e.g. Fe3O4, MgFe₂O₄ (ferrite) etc

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SUMMARY

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PROPERTIES OF SOLIDS

• ELECTRICAL PROPERTIES point defect and line defect
• Impurity , Stoichiometric , Non- stoichiometric defect .
• – Band theory , Electrical conduction , n- and p- type semiconductor
• MAGNETIC PROPERTIES OF SOLID
• – Para magnetism , Diamagnetism , Ferromagnetism , Anti ferromagnetism , Ferrimagnetism .

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QUESTIONS

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• How may the conductivity of an intrinsic semiconductor be increased?
• What type of semi-conductor is obtained when silicon is doped with arsenic? 
• What is meant by ‘forbidden zone’ in reference to the band theory of solid?
• What type of semi-conductor is obtained when silicon is doped with Indium?

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PART -7 NUMERICALS

NUMERICALS IN SOLID STATE

• Determination of the formula of the compound
• Calculations involving unit cell dimensions.
• Calculation of fraction of metal ion in a non stoichiometric metal oxides.

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DETERMINATION OF THE FORMULA OF THE COMPOUND

• A cubic solid is made of two elements X and Y. Atoms Y are at the corners of the cube and X at the body centre. What is the formula of the compound?

  Ans :-

Number of X atom per unit cell = 1

Number of Y atom per unit cell = 1/8 x 8 = 1

Formula of compound = XY

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DETERMINATION OF THE FORMULA OF THE COMPOUND

• A cubic solid is made of two elements X and Y. Atoms Y(anions) are at the corners of the cube and X(cations) at present at face-centre of the cubic lattice. What is the formula of the compound?

Ans :-

Number of X atom per unit cell = 1/2 x 6 = 3

Number of Y atom per unit cell = 1/8 x 8 = 1

Formula of compound = X₃Y

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CALCULATION OF THE DENSITY OF THE UNIT CELL

NUMERICALS

• 1.Chromium metal crystallises with a body centred cubic lattice The length of unit cell is found to be 287 pm. Calculate atomic radius, the number of atoms per unit cell and density of chromium. (Atomic mass of Cr = 52. g/ mol Avogadro No. = 6.02 x 10²³)
• 2. Silver forms ccp lattice and X-ray studies of its crystals show that the edge length of its unit cell is 408.6pm.  Calculate the density of silver( Atomic mass = 107.9 u)
• 3. Niobium crystallizes in body centered cubic structure. If density is 8.55 gm/cm³, calculate atomic radius of niobium using its atomic mass 93u .

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Silver crystallises in fcc lattice. If edge length of the cell is 4.07 × 10^–8cm and density is 10.5 g cm^–3, calculate the atomic mass of silver�

Ans:

Given:�Edge length, a = 4.077 × 10⁻⁸ cm�Density, d = 10.5 g cm⁻³�

The given lattice is of fcc type,�Thus the number of atoms per unit cell, z = 4�

We also know that N_A = 6.022 × 10²³ / mol�let M be the atomic mass of silver.�We know, d = zM/a³N_A�

=> M = da³N_a / z

• = 10.5 x 4.077 × 10⁻⁸ x 6.022 × 10²³ ) / 4 = 107.13 g /mol�

CALCULATION OF FRACTION OF METAL ION IN A NON STOICHIOMETRIC METAL OXIDES.�

• Analysis shows that nickel oxide has formula Ni _0.98O _1.00 .What fraction of nickel exists as Ni²⁺ and Ni³⁺ ions?
• Let the number of Ni²⁺ = x

The number of Ni³⁺ =(0.98-x)

sum of positive ions is equal to negative ions

2(x) + 3(0.98-x)= 2(1.00)

2x + 2.94-3x=2.00

X = 0.94 x= Ni²⁺

% of Ni²⁺ =0.94/0.98x 100=96%

% of Ni³⁺ = 100-96= 4%

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