Download Enthalpy - Career Launcher

Chemistry
Solid State-III
Session Objectives
•
Radius Ratio
•
Structure of Ionic Crystals
•
Imperfections in Solids
•
Electrical Properties
•
Magnetic Properties
•
Dielectric Properties
Coordination number and ionic radii
Coordination no. increases with
Zinc blende
structure
Rock salt
structure
Cesium
chloride
structure
Where do these numbers come from?
Cation-anion stable configuration
e.g. 3-coordinate
rA
When cos  
rA  rC
rC
1

1
Rewrite as
rA cos 
With  =
Minimum ratio for 3-coordinate
30o
rC
 0.155
rA
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?
Solution:
r
 0.225
r
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
Cl  8 
Anion (Cl-) =1.81 Å
Radius Ratio=0.541
1
1
6  4
8
2
Na  12 
1
1  4
4
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
r  r 
a
2
Structure of cesium chloride(CsCl)
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).
rc  ra 
3a
4
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.
rc  ra 
3a
4
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.
rc  ra 
3a
4
Structure of Na2O (anti-fluorite structure)
•
Oxide ions forms ccp arrangement.
•
Na+ occupy all tetrahedral holes.
•
Coordination number of Na+ is 4
and that of oxide ion is 8.
rc  ra 
3a
4
This structure is just the reversed form of fluorite struture
Illustrative example
The 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.
Solution:
0
For KCl, a  6.2 8 A
For Rock salt structure, when anion  cation
contact is there along the cell edge,
r
 0.731    (1)
r
r  r 
a
   (2)
2
Solution
Dividing (2) with r
1
r a 1
 
r 2 r
1  1.368 
6.28 1

2
r
0
3.14
 r 
 1.326 A
2.368
Defects
Departure in the orderly pattern
Point defects
If an atom is missing from a lattice
site there is a vacancy;
Impurity defects
An atom out of place
self-interstitial
A foreign atom occupying a lattice
site — substitutional impurity.
Whereas one place off a site is an
interstitial impurity.
Stoichiometric defects:
Schottky defect
•
Equal number of cations and anions are missing from lattice
sites.
Electrical neutrality is maintained.
+
A
B
-
B-
A+
•
•
B-
+
A
A
+
B-
A
+
B-
A+
B-
A+
Decreases density of the material.
Schottky defects are found in NaCl, KCl, KBr etc.
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.
•
•
Schottky
Frenkel
Non stoichiometric defects
•
•
The ratio of anions and cations become
different from the chemical formula.
It happens due to some imperfection.
F – Centres
•
•
•
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.
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
Diamagnetic substances
•
Weakly repelled by the external magnetic field.
•
Have no unpaired electron
•
Examples are NaCl, C2H6, TiO2 etc.
Paramagnetic substances
• Attracted by the external magnetic field.
• Have unpaired electron
• Examples are O2, Cu2+, Fe3+, CuO 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
Magnetic properties of substances
Ferrimagnetic substances
•
Presence of unequal parallel and anti-parallel
moments.
•
Expected to posses large magnetism but have small
net dipole moment.
•
Example is Fe3O4.
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.
2.
3.
4.
Conductor
Insulator
Semiconductor
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 in
silicon.
Superconductivity
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.
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.
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.
Solution:
Fullerene(C60) is the isotope of carbon which exhibits
super conductivity.
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 are
permanently 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 the
crystals does not possess net dipole moment are said to have
anti-Ferro electricity.
Example: Lead zirconate(PbZrO3)
Thank you