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 When Rewrite as With a = 30o Minimum ratio for 3-coordinate

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: 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

                                                                                            

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).

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.

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.

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. 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:

Solution

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. 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. Frenkel Schottky

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. Conductor 2. Insulator 3. Semiconductor 4. 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. n-type semiconductors Obtained when group 14 elements doped with group 15 elements. Electron is responsible for electrical conduction. Example: Arsenic doped in 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.

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)

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