PHYSICS-15-10- 11th (PQRS) SOLUTION

https://docs.google.com/document/d/1h7aogrKt5SgHPwUEzeNX0IM7Dhd7Du22/edit?usp=sharing&ouid=109474854956598892099&rtpof=true&sd=true amorphous and crystalline solids (elementary idea); Bragg’s Law and its applications; Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids; Electrical, magnetic and dielectric properties. CLASSIFICATION OF CRYSTALLINE SOLID Ionic Solids : The structural unit of these crystals are ions. The forces holding the ions together are electrostatic in nature. These forces are non- directional. Examples : All the electrovalent compounds, NaCl, KCl, BaSO4, K2 SO4 etc. Covalent Solids : The structural unit in these crystals are atoms of the same or different kind. These units are joined together by covalent bond extending throughout the crystal. These crystals have no molecules. It is also known as atomic crystals. These crystals are most incompressible and hard. Examples : Diamond, graphite, silicon carbide, silver iodide. Molecular Solids : In molecular crystals, the structural units are the molecules. The forces holding molecules together in these crystals are Van der Waal’s forces, dipole-dipole attraction and hydrogen bonding. Examples : CO2, naphthalene, iodine, argon, xenon, phosphorous, sulphur, nitrogen, hydrogen etc. Metallic Solids : Lorentz advanced a theory about the bonding in metallic solids. According to this theory, a metallic solid is considered as a collection of positive metal kernels, embedded in a sea of electrons. The presence of electrons between the positive metal ions serves to produce electrostatic force of attraction to hold these ions in metallic crystal. It is a very special type of bonding whose actual mechanism is not clear till date. Examples : Be, Mg, Co, Zn, Cd, Cu, Ag, Au, Pb, Al etc. THIS CHAPTER INCLUDES Classification of crystalline solid Elements of Symmetry Types of cubic unit cell Crystal system Packing in metallic crystal Struc ture of simple ionic compounds Imperfections in solids Properties of solids ELEMENTS OF SYMMETRY The total no. of planes, axes and centre of symmetries possessed by a crystal is termed as its elements of symmetry. A cubical crystal possesses a total of 23 elements of symmetry. Planes of symmetry = 3 + 6 = 9 Axis of symmetry = 3 + 4 + 6 = 13 Centre of symmetry = 1 Total number of symmetry elements = 23 TYPES OF CUBIC UNIT CELL Type of unit cell Number of atoms Total number of atoms per unit cubic cell at corners within body on faces 1. Simple cube 1 8 × 8 = 1 0 0 1 2. Body centred cube (BCC) 1 8 × 8 = 1 1 0 2 3. Face centred cube (FCC) 1 8 × 8 = 1 0 1 2 × 6 = 3 4 CRYSTAL SYSTEM On basis of geometrical consideration, main seven crystal system are present also known as seven primitive unit cells, which differ three-dimensionally in axial edge length (a, b and c) and axial angles (α, β, γ). Crystal System Axial distance or Edge lengths Axial angles Example Cubic a = b = c α = β = γ = 90° KCl, ZnS Rhombohedral a = b = c α = β = γ ≠ 90° HgS Tetragonal a = b ≠ c α = β = γ = 90° SnO2, TiO2 Orthorhombic a ≠ b ≠ c α = β = γ = 90° CaCO3 Monoclinic a ≠ b ≠ c α = γ = 90°, β ≠ 90° PbCrO2 Hexagonal a = b ≠ c α = β = 90°, γ = 120° ZnO Triclinic a ≠ b ≠ c α ≠ β ≠ γ = 90° K2Cr2O7 PACKING IN METALLIC CRYSTALS Two dimensional packing Square close packing (scp) Hexagonal close packing (hcp) scp hcp 3D packing is given by hcp which gives two types of void present in the crystal Tetrahedral void Octahedral void Tetrahedral void Octahedral void Radius of octahedral void (RO). i.e. RO = 0.414 Ratom Radius of tetrahedral void (Rt) i.e. Rt = 0.225 Ratom hcp 1st layer 2nd layer Relationship between the nearest neighbour distance(d) and the edge length (a) of a unit cell of a cubic crystal Simple Body-centred Face-centred d = a d = 3 a = 0.866 a 2 d = 2 a = 0.707 a 2 Relationship between atomic radius, r (which is = edge length (a) of the unit cell of a cubic crystal d for crystals of pure elements) and the 2 Packing fraction for Cubic Crystal System where Z = number of atoms per unit cell Volume of cube = a3 Volume of sphere = 4 πr 3 3 Thus P.F for SC, FCC and BCC respectively are 54%, 74% and 68%. Density of crystal Density = i.e., mass of unit cell volume of unit cell where Z = number of atoms per unit cells. M = Molar mass NA = Avogadro’s number a = Edge length (in cm) Radius ratio r+/r– Geometry Co-ordination number Example 0.155 – 0.225 Triangular planar 3 B2O3 0.255 – 0.414 Tetrahedral 4 ZnS 0.414 – 0.732 Octahedral 6 NaCl 0.732 – 1 Cubic 8 CsCl STRUCTURE OF SIMPLE IONIC COMPOUNDS AB type : Consisting positively and negatively charged ions in the ratio 1 : 1 These compound can have any one of the following structures Rock salt (NaCl) type structure Characteristics It has fcc or ccp arrangement in which Cl– ions occupy the corners and face centres of a cube while Na+ occupy body centres and edge centres (Octahedral voids). This structure has 6 : 6 coordination number. A unit cell of NaCl consist of 4Na+ ion and 4Cl– ions. 1 i.e., Number of Cl– ions 8 × 8 + 1 × 2 6 = 4 Number of Na+ ions 1 4 × 12 +1= 4 Examples : Alkali metals halides (except Cs), Halides of Ag (except AgI). Caesium chloride (CsCl) type structure Characteristics It has bcc arrangement This structure has 8 : 8 coordination number The unit cell of CsCl consists of one Cs+ ion at body centre and eight Cl– ion at each corner i.e. one CsCl formula unit per unit cell. Example : CsBr, Csl, CsCN, TlCl, TlBr, TlI, TICN, Zinc blende (ZnS) type structure Characteristics It has ccp arrangement in which S2– ions are present at the corners as well as at the centre of each face of the cube. Zn+2 ion are present at alternate tetrahedral void [50% of tetrahedral void]. This structure has 4 : 4 coordination number. Example : CuCl, CuBr, CuI, AgI, and BeS AB2 type - Consisting positively and negatively charged ions in the ratio of 1 : 2 Calcium fluorite (CaF2) type structure Characteristics It has ccp arrangement in which Ca2+ ions are present at the corners and the centre of each face of the cube. The F– ions occupy all the tetrahedral holes. This structure has 8 : 4 coordination number. Example : BaI2, BaCl2, SrF2, SrCl2, CdF2 Spinel Structure : (MgAl2O4) O–2 ions are present at FCC. Mg+2 ions occupy 1/8th of tetrahedral void. Al+3 ions occupy 1/2 of the octahedral void. Thus formula ratio is 1 : 2 : 4 for Mg+2 : Al+3 : O–2. Other examples, ZnAl2O4, MgIn2O4. Inverse Spinel Structure : (Fe3O4) O–2 ions are present at FCC. Fe+3 ions occupy 1/8th of tetrahedral void. Remaining Fe+3 and Fe+2 are equally distributed in 1/2 of the octahedral voids. Thus formula ratio is 1 : 2 : 4 for Fe+2 : Fe+3 : O2–. Other examples, Mn3O4, Pb3O4. Effect of temperature and pressure on crystal structure Increase of temperature decreases the coordination number while increase of pressure increases the coordination number. NaCl structure ⎯⎯Pr⎯es⎯s u⎯r⎯e →CsCl structure (6 : 6 ) ←⎯⎯⎯⎯⎯ Temp ( 8 : 8) IMPERFECTION IN SOLIDS The imperfection i.e., irregularities in crystal is known as crystal defects. Defects are of two types Stoichiometric Defect Non-stoichiometric Defect Stoichiometric Defect : In these defects stoichiometric ratio of constituent ions is not disturbed. Schottky Defect : When equal number of cation and anion are missing from its normal site Schottky defect is created. This defect causes decrease in density of crystal. e.g., In NaCl, there are approximately 106 Schottky pair per cm3 at room temperature. [In 1 cm3 there are about 1022 ions and therefore there is one Schottky defect per 1016 ions. Frenkel Defect : Found mostly in ionic solids. The ion leaves its position in the lattice and occupies an interstitial void. This defect does not affect density of crystal. This is majorly shown by crystals having less C.N. (e.g., ZnS). e.g., Silver halide shows Frenkel defect. Non Stoichiometric Defect : In these defects stoicheometric ratio of constituent ions is changed. Metal excess defect : Extra cations occupying voids. Neutrality is maintained by additional electrons occupying nearby sites. It is possible by some anion vacancies; also charge is balanced by electrons occupying these vacancies (F–centres). These electrons are responsible for imparting colour (Farbe = colour). Crystals with either type of metal excess defect possess free electrons and if they migrate they conduct electric current. But the amount of current conducted is very small and so these material resulting from interstitial cation are called n–type semiconductors. Further free electrons may be excited to higher energy levels causing colour. ZnO is yellow when hot and white when cold. Metal deficiency : defect occurs when the metal shows variable valency. It is due to missing of a cation and the presence of the cation having higher charge (e.g +2 instead of +1) in adjacent site. FeO, FeS etc. PROPERTIES OF SOLIDS Electrical properties : Solids with electrical conductivity are classified as conductors, semiconductors, insulators. Magnetic properties : Solids show magnetic properties due to magnetic moment (orbital and spin) of electron. Ferromagnetic Antiferrom agnetic Ferrimagnetic : ↑ ↑ ↑ ↑⎫ : ↑ ↓ ↑ ↓⎪ allignment of magnetic moment. : ↑ ↑ ↓ ↑⎪ Dielectric properties : Crystal with net dipole moment exhibit piezoelectricity when these crystals are deformed by mechanical stress. Where electricity is produced due to displacement of ion. This piezoelectric crystals when heated produce small electric potential i.e. pyroelectricity. ❑ ❑ ❑