Chemistry

Solid State-III

Session Objectives

• Radius Ratio

• Structure of Ionic Crystals

• Imperfections in Solids

• Electrical Properties

• Magnetic Properties

• Dielectric Properties

Coordination no. increases with

rcationranion

Coord #

< .155 .155-.225 .225-.414 .414-.732 .732-1.0

ZnS (zincblende)

NaCl (sodium chloride)

CsCl (cesium chloride)

2 3 4 6 8

rcationranion

Where do these numbers come from?

Zinc blende structure

Rock salt structure

Cesium chloride structure

Coordination number and ionic radii

e.g. 3-coordinate

WhenCA

A

rr

r

cos

With = 30o

Rewrite as 1cos

1

A

C

r

r

155.0A

C

r

r

Minimum ratio for 3-coordinate

Cation-anion stable configuration

Illustrative example

Bromide ions form cubic close packed structure. Radius of Br– is 195 pm. What would be the minimum radius of cation which fits in the tetrahedral void?

r0.225

r

Solution:

For a tetrahedral void

or r+ = 0.225 × 195 = 80.735 pm

Ionic Crystals

Contain both cations and anions in the lattice. Simple ionic crystals are of two types

(i) AB (where the two ions are in 1 : 1 ratio) Examples NaCl, CsCl etc.

(ii) AB2 (where the ratio of ions is 1 : 2) Examples CaF2 etc.

Structure of NaCl (Rock salt Structure)

Cation (Na+) radius =0.98 Å

Anion (Cl-) =1.81 Å

Radius Ratio=0.541

Cl– ions form fcc .

Na+ ions occupy edge centre and body centre.

Four NaCl formula units per unit cell.

Coordination number Na+:Cl- = 6:6

ar r

2

1 1

Cl 8 6 48 2

1

Na 12 1 44

                                             

                                              

Structure of cesium chloride(CsCl)

c a3a

r r4

Cs in simple cubic structure with Cl- in center (or vice versa).

Cl– = 0.83Cs+ size (0.73r in center is ideal).

It has bcc arrangement and coordination number is 8.

Rare structure, need big cation (Cs, Tl only cations known with this structure).

Zinc blende (ZnS)

• Cation (Zn+2) radius =0.83 Å.

• Anion (S2-) radius=1.82 Å.

• Radius ratio=0.456.

• S2– form a face centered cubic arrangement.

• Zn2+ occupy alternate tetrahedral holes.

• Coordination number, Zn2+ : S2- = 4:4.

c a3 a

r r4

Structure of CaF2 (Fluorite structure)

Ca2+ ions form ccp or fcc arrangement.

Two tetrahedral holes are there for each Ca2+.

F– ions occupy all the tetrahedral holes.

Coordination number of Ca2+ is 8 and that of F– is 4.

4 CaF2 formula units per unit cell.

c a3 a

r r4

Structure of Na2O (anti-fluorite structure)

• Oxide ions forms ccp arrangement.

• Na+ occupy all tetrahedral holes.

• Coordination number of Na+ is 4and that of oxide ion is 8.

c a3 a

r r4

This structure is just the reversed form of fluorite struture

Illustrative exampleThe edge length of the unit cell of KCl (NaCl like structure, fcc) is 6.28A°. Assuming anion cation contact along the cell edge, calculate the radius of the potassium ion.

0For KCl, a 6.28 A

For Rock salt structure, when anion cation

contact is there along the cell edge,

r0.731 (1)

r

ar r (2)

2

Solution:

Solution

Dividing (2) with r

r a 11

r 2 r

16.281 1.368

2 r

03.14r 1.326 A

2.368

Defects

If an atom is missing from a latticesite there is a vacancy;

self-interstitial

A foreign atom occupying a latticesite — substitutional impurity.Whereas one place off a site is an interstitial impurity.

An atom out of place

Departure in the orderly pattern

Point defects

Impurity defects

Stoichiometric defects:

A + B - A + A +

B - B - A + B -

A + B - A + B - A +

• Decreases density of the material. • Schottky defects are found in NaCl, KCl, KBr etc.

• Equal number of cations and anions are missing from lattice sites. Electrical neutrality is maintained.

Schottky defect

Frenkel defect

• The ratio between Cations and Anions remains same.

• An ion missing from the lattice occupies any interstitial void.

• Electrical neutrality and stoichiometry remains same.

• Density is not affected.

• This defect are found in AgCl, AgBr etc.

Frenkel

Schottky

Non stoichiometric defects

• The ratio of anions and cations become different from the chemical formula.

• It happens due to some imperfection.

• Free electrons trapped in the site of anion vcancies.

• Electrons are responsible for colour of the solid.

• Due to this KCl crystal exhibits violet colour.

F – Centres

Illustrative Example

Calculate the concentration of cation vacancies if KCl is doped with 10-3 mole of CaCl2.

Solution:

One Ca2+ replaces two K+ units

10-3 moles of Ca2+ will replace 2 × 10-3 moles of K+.

Hence cationic vacancies = 10-3 mole percent

Magnetic properties of substances

Paramagnetic substances • Attracted by the external magnetic field. • Have unpaired electron

• Examples are O2, Cu2+, Fe3+, CuO etc.

Diamagnetic substances

• Weakly repelled by the external magnetic field.

• Have no unpaired electron

• Examples are NaCl, C2H6, TiO2 etc.

Magnetic properties of substances

Ferromagnetic substances • Show permanent magnetism.• Once magnetized such substances retain their magnetic

property.• Transform to paramagnetic state at high temperature.• Examples are Fe, Co, Ni. Anti-ferromagnetic substances• Have unpaired electrons.• Presence of equal numbers of magnetic moments aligned in

opposite directions and have zero net magnetic moment. • Transform to paramagnetic state at high temperature.

• Examples are MnO, MnO2, FeO + Fe2O3

Ferrimagnetic substances

• Presence of unequal parallel and anti-parallel moments.

• Expected to posses large magnetism but have small net dipole moment.

• Example is Fe3O4.

Magnetic properties of substances

Illustrative example

What happens when Fe3O4 is heated to 850 K temperature?

Solution:

Ferrimagnetic Fe3O4 on heating to 850 K becomes paramagnetic because on heating there will be greater alignment of spins in one direction.

Electric behaviour of substances

On the basis of electric behaviour, we can divide them in following types

1. Conductor2. Insulator3. Semiconductor4. Super conductor

Semiconductors

• Electrical conductivity is between that of a conductor and an insulator.

• Conductivity can be modulated by adding impurities such as boron or phosphorus.

• Example is silicon.

p-type semiconductors • Obtained when a group 14

element is doped with group 13 element.

• Holes responsible for conduction.

• Example: aluminum doped in silicon.

n-type semiconductors

• Obtained when group 14 elements doped with group 15 elements.

• Electron is responsible for electrical conduction.

• Example: Arsenic doped insilicon.

Superconductivity

Type I superconductors – expel all magnetic fields below a critical temperature, Tc (Meisner effect).

Type II superconductors – below a critical temperature exclude all magnetic fields completely. Between this temperature and a second critical temperature, they allow partial penetration by the magnetic field.

Conduct electricity without resistance below a certain temperature. Once set in motion, electrical current will flow forever in a closed loop.

Mercury(Hg) behave like superconductor below 4 K.

Theory of Superconducting

•Cooper pair theory

–Bardeen, Cooper, and Schrieffer

–Electrons travel through the material in pairs.

–The formation and propagation of these pairs is assisted by small vibrations in the lattice.

Illustrative Example

Name the allotrope of Carbon which exhibits superconductivity.

Fullerene(C60) is the isotope of carbon which exhibits super conductivity.

Solution:

Dielectric properties : Piezoelectricity

Ability to generate voltage in response to applied mechanical stress.

• The piezoelectric effect is reversible.• When subjected to an externally applied voltage,

change in shape occurs.

Examples:Quartz, titanates of barium and lead, lead zirconate(PbZrO3),SiO2, LiNbO3, LiTaO3, and ZnO

Pyroelectricity: When piezoelectric crystals are heated, they produce small electric current.

Dielectric Properties

Ferroelectricity In some of the piezoelectric crystals,the dipoles arepermanently polarised even in the absence of electric field.On applying electric field the direction of polarization is changed.Example: Barium titanate(BaTiO3), sodium potassium tartarate

(Rochelle salt), KH2PO4.

Antiferroelectricity In some crystals ,the dipoles point up and down so that thecrystals does not possess net dipole moment are said to haveanti-Ferro electricity.Example: Lead zirconate(PbZrO3)

Thank you