THEORETICAL DENSITY, r

 

CLOSE PACKED CRYSTALS

IONIC CRYSTALS

COORDINATION NO 3

 

IONIC CRYSTALS

SIMPLE IONIC COMPOUNDS

Two Views of CsCl Unit Cell

Either arrangement leads to formula of 1 Cs+ and 1 Cl- per unit cell

NaCl CONSTRUCTION

THE SODIUM CHLORIDE LATTICE

Many common salts have FCC arrangements of anions with cations in OCTAHEDRAL HOLES — e.g., salts such as NaCl

•   FCC lattice of anions ---->  4 A-/unit cell

•   C+ in octahedral holes ---> 1 C+ at center

                  + [12 edges • 1/4 C+ per edge]

                  =  4 C+  per unit cell

Formula Na4Cl4 = NaCl

NETWORK SOLIDS

BRAGG’S LAW

• Incoming X-rays diffract from crystal planes Braggs law Þ nl = 2dsin(q)

FUN FACTS ABOUT BRAG’ LAW

Sir William Lawrence Bragg was an Australian-born British physicist who discovered (1912) Bragg's law of X-ray diffraction. He was joint winner (with his father, William Henry Bragg) of the Nobel Prize in Physics in 1915 Bragg was knighted in 1941.

As of 2018, he is the youngest ever Nobel laureate in physics, having received the award at the age of 25 years.[4

Bragg was the director of the Cavendish Laboratory, Cambridge, when the discovery of the structure of DNA was reported by James D. Watson and Francis Crick in February 1953.

Stoichiometric defects are point defects that do not disturb or change the Stoichiometry (Stoichiometric composition or formula) of the crystalline substance. They are also called intrinsic or thermodynamic defects.

    1. Vacancy defects or Schottky Defect

 Vacancy defects or Schottky Defect

        • Some of the lattice sites of the crystal are vacant.
        • This defect decreases the density of the crystal.
        • This defect can be developed by heating the substance. Due to irradiation or sputtering effect. Due to presence of residual tensile stress within the solid.
        • Vacancy defect for ionic crystals is called Schottky defect. Here equal no of cations and anions are missing so the stoichiometry of salt does not change

Interstitial defects

Interstitial defects: -

        • Some constituent particles occupy the interstitial sites of the crystal.
        • This defect increases the density of the crystal
        • In case of ionic solids equal no of cations and anions are added

Frenkel Defect: -  

(i) The ion (smaller ion, usually cation) is dislocated (moved) from its normal lattice site to an interstitial site. So it is also called dislocation defect It creates vacancy defect at its normal lattice site and interstitial defect at its new location Condition:

(ii) The difference between the size of the ions (cation and anion) should be larger. Examples: ZnS ,AgCl, AgBr, and AgI due to small size of Zn2+ and Ag+ ions

(iii)  It does not change the density of the crystal

Non Stoichiometric defects are point defects that disturb the Stoichiometry of the crystalline substance

 Metal deficiency defect Due to cation vacancies. Eg. In FeO crystal, some Fe2+ cations are missing and extra negative charge is balanced by acquiring extra positive charge by adjacent Fe2+ ion to become Fe3+ ion

METAL EXCESS OR F-CENTRE

(i) Due to anionic vacancies or F- Centres: The anionic vacancies occupied by unpaired electrons. F-centres impart colour to the crystals (Eg. NaCl to Yellow, KCl to violet) due to excitation of these electrons by absorbing energy from the visible light falling on the crystals

(ii) Due to presence of extra cations interstitial sites, Eg. ZnO

IMPURITY DEFECTS

Impurity defects – Ex- Solid solution of NaCl containing SrCl2 impurity. Solid solution of AgCl and CdCl2

Doping: The process of adding an appropriate amount of suitable impurity to increase the conductivity of semiconductors

Solids can also be classified into three types based on their electrical conductivities:

  • a. Conductors-The solids with conductivities ranging between 104 to 107 ohm–1m–1 are called conductors.
  • b. Insulators - These are the solids with very low conductivities ranging between 10–20 to 10–10 ohm–1m–1.
  • c. Semi- conductors. These are the solids with conductivities in the intermediate range from 10–6-104 ohm–1

ELECTRICAL CONDUCTION

TYPES OF SEMICONDUCTORS:

  • a. Intrinsic: These are those semiconductors in which the forbidden gap is small. Only some electrons may jump to conduction band and show some conductivity. They have very low electrical conductivity. Example: Silicon, germanium
  • b. Extrinsic: When an appropriate impurity is added (doping) to an intrinsic semiconductor. Their electrical conductivity is high.

Types of extrinsic semi conductors:

 MAGNETIC PROPERTIES

  • Piezoelectricity:- When polar crystal is subjected to mechanical stress, electricity is produced.  E.g. BaTiO3, Rochelle salt
  • Pyroelectricity:- When polar crystal is subjected to heat stress, electricity is produced.  E.g. PbZrO3

IMPORTANT FORMULAE

  1. Elements of symmetry in simple cubic crystals
    1. Plane of symmetry     = 3 + 6 =9
    2. Axis of symmetry     = 3 + 4 + 6 =13
    3. Center of symmetry = 1
    4. Total elements of symmetry = 9 + 13 + 1= 23
  2.  Density of lattice matter=  n is number of atoms per unit cell and ‘a’ is the unit cell edge length
  3. Braggs law:  2dsinq = nl
  4. Atoms per unit cell(n) = Nc + NF/2 + NE/4+ NV/8
  5. No. of tetrahedral voids = 2 x n
  6. No of octahedral voids = n