Solid State PDF

1 Solid State · Solid: A form of matter which possesses rigidity, do not flow and hence they have a definite shape and a definite volume is called solid. · Classification of solids: On the basis of the nature of order present in the arragement of th...

1 Solid State · Solid: A form of matter which possesses rigidity, do not flow and hence they have a definite shape and a definite volume is called solid. · Classification of solids: On the basis of the nature of order present in the arragement of their constituent particles (atoms, ions or molecules), solids are classified as crystalline and amorphous. A. Crystalline solids: A crystalline solid is a homogeneous solid in which the constituent particles (atoms, ions or molecules) are arranged in a definite repeating pattern. They are further classified as: a. Isomorphous form (iso-same, renorphous-form): Two or more substances having the same crystal structure are said to tbe isomorphous. e.g. i. NaF and MgO (atoms in the ratio 1 : 1) ii. Cr2O3 and Fe2P3 (atoms in the ratios 2 : 3) b. Polymorphous /Allotropic form (Poly-many, morphous-form): A single substance that crystallises in two or more forms under different conditions is called polymorphous. e.g. i. Carbon has two polymorphous forms i.e. Graphite and diamond. ii. Sulphur has two polymorphous form i.e. Rhombic and Monoclinic sulphur. B. Amorphous solid/Pseudo solids! Super cooled solids: The substances that appear like solids but do not have well developed perfectly ordered crystalline structure are called amorphous (no form) solids. e.g. Jar, glass, plastic, rubber, butter, starch, cellulose, proteins etc. · Distinguish between crystalline solids and amorphous solids: S.N. Property Crystalline Solids Amorphous Solids l. Geometry They have definite geometry. They have no definite geometry. 2. Shape They have regular shape. They have irregular shape. 3. Melting point They have sharp melting point. They do not sharp melting point. 4. Solid They are true solids. They are pseudo solid/super cooled liquids. 5. Arrangement of They have long range order. They have short range order. particles 6. Cleavage property When cut, they undergo When cut, they undergo irregular clean cleavage. surface of two pieces. 7. Directional nature They are anisotropic They are isotropic. of properties i.e. have different physical i.e. have same physical properties in all properties in all directions. directions. 8. Heat of fusion Heat of fusion values are Heat of fusion values are not definite. definite. 9. Examples Cu, Ag, ZnS, NaCl, KNO3 etc. Glass, Rubber, Plastics etc. (1) · Glass: Glass is an optically transparent material produced by fusing together silicon oxide with sodium oxide, boron oxide and a trace amount of transition metal oxide is added to impart colour to the glass. Types of glass Composition Pyrex glass 60 to 80% SiO2 + 10 to 25% B2O3 some amount of of A12O3. Soda lime glass 75% SiO2 + 15% Na2O + 10% CaO. Red glass Trace amount of gold and copper. Yellow glass UO 2. Blue glass It contain CoO or CuO. Green glass It contain Fe2O., or CuO. Classification of Crystalline solid: Crystalline solid are classified into four main types depending on nature of bonds: 1. Molecular solids 2. Ionic solids 3. Metallic solids an 4. Covalent solids Sr. Types of Constituent Nature of Examples Physical Electrical Melting Other No solid particles binding nature conductivity point characte- ristics 1. Molecular Molecules Weak forces Low density solids And volatile, i) non polar Atoms of London Ar,H212S Soft Insulator Very low noble gas dispersion Soli CO2 low enthalpies or non-polar forces (dry ice) of fusion molecules CH 3 and ii) Polar Polar Dipole-dipole HCl,SO2 Soft Insulator Low vaporization. molecules attractions iii) Hydrogen Molecules Hydrogen H2O(ice), Generally Insulator Low bounded containing bonding NH 3 soft or H linked to some are F, O or N hard 2. Ionic solids Positive Coulombic aCl, LiF, Hard Insulators High Soluble in (W.Kossel) and or MgO,ZnS, but brittle in solid polar solvents, negative electrostatic CaF 2 state but insoluble in ions forces of conductors nonpolar attraction in molten solvents. High state or enthalpies of aqueous fusion and solution vapourisation. 3. Metallic Positive ions Metallic All metals Hard Conductor Fairly Malleable solids In a sea bonds and alloys in solid high and ductile (Drude and of mobile state as and possess Lorentz) electrons. well as luster, high molten enthalpies state of fusion. 4. Covalent Atoms Covalent Dimond. Hard Bad High Moderate solids bonds SiO2 Soft Good enthalpies of (G.N. Lewis) Graphite fusion. (2)  Allotropic modification of carbon: i. Diamond ii. Graphite iii. Fullerene 1. Diamond: Occurence : It occurs in nature. It can also be prepared artificially. Structure: i. In dimond, carbon is sp3 -hybridised. ii. Each carbon is tetrahedrally linked to four neighbouring carbon atoms through four strong C-C, sp 3 - sp3,  -bonds. iii. This network extends in three dimensions to form bin naint network of covalent solid. Properties: i. Purity: Diamond is the purest form of carbon. ii. Bond length: C-C bond length in diamond are 1.54 A (154 pm). iii. Hardness: It is the hardest substance known with high density and melting point. iv. Conductivity: Diamond is a bad conductor of electricity. Since all the electrons are firmly held in C-C, -bonds. v. Transparency: It is a transparent. Because of its high refractive index (2·5) diamond can reflect light. Uses: i. Diamond is used for cutting glass, making borers for rod drilling and for making abrasives. ii. When diamond is cut and polished, brilliant light is refracted from its surface. That is why diamond is used for making precious gems and jewellery. Graphite: Occurence : It occurs in nature and can also be manufactured artificially by heating coke to 3273-3300 K in an electric furnace. Structure: i. In graphite, carbon is sp2-hybridized. ii. Each carbon is thus linked to three other carbon atoms forming hexagonal rings. iii. The remaining half filled unhydrized 2pz orbital is for 1t bonding so that layers of C atoms are formed. iv. Graphite has a two dimensional sheet like (layered) structure consisting of a number of benzene rings fused together. v. The various sheets or layers are held together by weak vander Waal’s forces of attraction. vi. The distance between any two successive layers is 3.40 A (340 pm). (3)  Properties: i. Purity: Graphite is also the purest form of carbon. ii. Bond length: The C-C bond length in graphite are 1.415 A (141.5 pm) iii. Softness: Graphite is a soft and a good lubricating agent because in graphite any two successive layers are held together by weak forces of attraction, one layer can slip over the other. iv. Conductivity: Graphite is a good conductor of heat and electricity because in graphite onlr three electrons of each carbon are used in making hexagonal rings and fourth valence electron of each carbon is free to move. v. Opaqueness: Graphite is a black substance and possesses a metallic lustre. · Uses: i. In making electrodes. ii. Cores lead pencils. iii. Moderator in atomic reaction. 3. Fullerenes: Discovery: Third crystalline allotrope of carbon called fullerenes was discovered collectively by three scientists namely K.E. Smalley and R.F, Curl and H.W. Kroto. For this discovery, these scientists shared the 1996 Nobel prize in chemistry. · Composition: C2n where (n > 30). · Preparation: By evaporation of graphite using a powerful laser. · Structure: i. All the carbon atoms are equivalent and they undergo sp2 hybridization. Each carbon atom forms three -bonds with other three carbon atoms. The remaining electron of each carbon is delocalized in molecular orbitals which, in turn, give aromatic character to the molecule, ii. C60 allotrope is most stable among all the fullerenes. It looks like a soccer ball and is sometimes called as bucky ball. It contains 12 five membered rings and 20 six membered rings. iii. Six-membered rings are fused both to other six-membered rings and five-membered rings, but the five- membered rings are connected only to six membered rings. iv. C70 fullerene, resembles a rugby ball. It consists of 12 five membered rings and 25 six-membered rings. v. It contains both single and double bonds with carbon-carbon distances of 145.3 and 138.3pm respectively. Applications: i. K3SC60 behaves as superconductor below 18 K. ii. The tubes made from fullerene and graphite are called nanotubcs. iii. These are used aS41igh strength materials, conductors, semiconductors and molecular sensors. (4)  Classify the following solids into different types: Sr. Name of Solid Type of Solid i) Plastic Molecular solid ii) P4 molecule Molecular solid iii) S8molecule Molecular solid iv) Iodine molecule Molecular solid v) Tetra phosphorous decoxide Molecular solid vi) Ammonium phosphate Ionic solid vii) Brass Metallic solid viii) Rubidium Metallic solid ix) Graphite Covalent solid x) Diamond Covalent solid xi) NaCl Ionic solid xii) Silicon Covalent solid Crystallography: The branch of science that deals with the study of structure, geometry and properties of crystal is called crystallography. External features of the crystal: a. Face: The plane surfaces of the crystal are called faces. b. Edge: An adge is formed by the intersection of two adjacent faces. c. Interfacial angles: The angle between the perpendiculars to the two intersecting faces. Crystal lattice or Space lattice: A regular arrangement of the constituent particles (atom, ions or molecules) of a crystal in three dimensional space is called crystal lattice or space lattice. Parameter of unit cell: A. Crystallographic axes: (Axial length) The position of a plans of the crystal in space is shown by the intercepts that it makes on three given lines called crystallographic axes. From fig. there are different types of axes as i. Vertical line is called’ c’ axis. ii. The line running from right to left is called ‘b’ axis. iii. The line running from front to rear is called ‘a’ axis. iv. The point of intersection is called origin ‘0’. B. Crystallographic angles: (Axial angle): i. The angle between ‘b’ and ‘c’ axes is called ‘’. ii. The angle between ‘c’ and ‘a’ axes is called ‘’. iii. The angle between ‘a’ and ‘b’ axes is called ‘’. Bravais lattices: August Bravais(1850) observed that only 7 type of basic or primitive unit cells exist in the crystals. Each system is characterised by the relative lengths of edges i.e. a, band c and the magnitudes of the angle   and . Bravais proved that lattice points can be arranged in maximum fourteen types. The arrangement is called Bravais Lattices. (5)  Sr. Crystal System Latice type Edge Angle Example Maximum No. (No. space latice) length Symmetry l. Cubic (3) Simple/primitive a=b=c  =  = = 90° CsCl Nine planes, & Body centred a=b=c  =  = = 90° Li, Cr, CsCl Thirteen axes, & Face centred a=b=c  =  = = 90° NaCl, Cu, Al, One centre Ca, Ni 2. Tetragonal (2) Primitive a=b  c  =  = = 90° SnO2 Five planes, Body centred a=b  c  =  = = 90° TiO2, CaSO4 & Five axes, 3. Orthorhombic (4) Primitive/Simple a  b  c  =  = = 90° Rhombic sulphur Three planes, Three axes Body centred a  b  c  =  = = 90° KNO 3 Face centred a  b  c  =  = = 90° BaSO4 End centred a  b  c  =  = = 90° MgSO4.7H2O 4. Monoclinic (2) Primi tive/Simple a  b  c == 90°   90° Monoclinic S One plane, End centred a  b  c == 90°   90° Na2SO4 10H2O & One axis 5. Triclinic (1) Primitive a  b  c  =  = = 90° K 2Cr 2O7,H 3BO 3 No plane, & No axis 6. Hexagonal (1) Primitive a=b  c  = = 90°,=120° ZnO, BeO, CaS, Seven planes, SnS, Graphite & Seven axes 7. Rhombohedral (1) Primitive a=b=c  =  = = 90° Calcite, HgS, Seven planes, or trigonal NaNO3, FeeO3 & Seven axes · Three dimenstional space lattice and unit cell : In cubic unit cell there are four types of unit cell as. a. Simple or Primitive cubic unit cell: The unit cell in which constituents particles are present only at its corner. The 8 particles at the 8 corner of the cube, represent atoms or ions. (Total eight points) b. Body centred cubic unit cell: The unit cell in which constituents particles are present at the centre of body in addition to the particles at its corner. The 8 particles at the 8 corner of the cube and one more at the centre, represent atom or ions. (Total 8 + 1 = 9 points) c. Face centred cubic unit cell: The unit cell in which constituents particles are present at the centre of each face in addition to the particles at its corner. The 8 particles at the 8 corner of the cube and 6 at the centre of 6 faces, represent atoms or ions. (Total 8 + 6 = 14 points) d. Side centred or end centred unit cell: The unit cell in which consitutents particles are present at the centre of only one set of faces in addition to the particles at its corner. The 8 particles at the 8 corner of the cube and 2 at the centre of upper and lower faces, represent atoms or ions. (Total 8 + 2 = 10 points) (6) · Contribution of particles in unit cell: Contribution of a particles present at the corner of the cubic unit cell towards cell = 1/8. Contribution of a particles present on the face of the cubic unit cell towards the cell = 1/2. Contribution of a particle present within the body of the cubic unit cell towards the cell = 1 Contribution of a particle present at the end centre of the cubic unit cell towards the cell = 1/4 · Evaluation of IlUmber of atoms in per unit cell: Total number of constituent units (spheres) per unit cell = 1 1 1  occupied corners +  occupied face centres + occupied body centre +  occupied end centre 8 2 4 A. Simple cubic unit cell: 1 Number of atoms (spheres) in one simple cubic unit cell =  8 + 0 + 0 + 0 = 1 i.e. one atom per unit cell. 8 B. Body centred unit cell: 1 Number of atoms (spheres) in one simple cubic unit cell  8 + 0 + 1 + 0 = 2 i.e. two atoms per unit cell. 8 C. Face centred unit cell: 1 1 Number of atoms (spheres) in one simple cubic unit cell =  8 +  6 + 0 + 0 = 4 i.e. four atoms per 8 2 unit cell. · Co-ordination number (C.N.) : The number of particles surrounding a single particle in the crystal lattice is called co-ordination number that lattice or the number of nearest neighbours particles with which a given particle is in direct contact the crystal lattice of a substance is known as the co-ordination number of that lattice. Crystal Simple Cubic Body centred Face centred Hexagonal close packed system SCC BCC FCP HCP CN 6 8 12 12 Structural relationship for cubic lattices: Sr. lattices No. Particular entity Simple Cubic BCC FCC l. No. of particles per unit cell 1 2 4 2. Nearest neighbours or (CN) 6 8 12 3. Distance between nearest d = 2r a e j e j d  2 r a 3 / 2  0.866 a d  2 r a 2 / 2  0.707 a neighbours ( d ) and (r) a 4. Atomic radius (r) 2  0.5 a ea 3 j / 4  0.433a ea 2 j / 4  0.433a FG IJ 4 F a 3I 4 F a I 3 3 3 G J 4 a  G J 5. Volume of atom ( V ) 3 2 HK 3 H 4 K 3 H2 2K FG  IJ  0.524 or 52.4% LM e 3j OP L e 2 j OP Volume occupied by atoms  0.68 or 68% M 6. Packing  Volumeof unit cell H 6K MN 8 QP MN 8 QP  0.74 or 74% (7)  7. % of void 47.6 % 32 % 26 % M 2M 4M 8. Density 3 3 3 a  NA a  NA a  NA FG 8  4 IJ r 3  3.81 r 3 FG 4  8 IJ r FG 16 IJ H 3K 3  3.941 r 3 8 8   r 3  587. r3 9. Empty space H 3 3K H 3 K The characteristics and Examples of Difference Crystal Structure: Property hcp ccp bcc Arrangement of packing Close packed Close packed Not close packed Type of packing ABABA ABCABCA ABABA Available space occupied 74% 74% 68% Vacant space 26% 26% 32% Coordination number 12 12 8 Malleability and ductility Less malleable, hard, brittle Malleable and ductile · Radious ratio: Definition: The limiting value of a ratio of radius of cation to that of anion for given co-ordination number is called radius ratio. Expression: Let r+ and r– be the radius of cations and anions respectively then- Radius ratio = r+ / r- · Radius ratio rule for ionic compounds: The relationship between the radius ratio and co-ordination number and structural arrangement are called radius ratio rule. a. If the value of ratio of r+ / r- is equal to the expected value then ionic structure becomes stable. b. If the value of r+ / r- is less than or greater than expected then ionic becomes unstable. · Radius ratio and structural arrangement: Sr. Lumiting value of Coordination Structural Example No. radius ratio (r r ) + – no. of cation arrangement 1. o - 0.155 2 Linear - 2. 0.155 - 0.225 3 Planner triangular B 2O 3 3. 0.225 - 0.414 4 Tetrahedral ZnS 4. 0.414 - 0.732 6 Octahedral NaCl 5. 0.732 - 1.00 8 Cubic csci · Ionic solid are hard and brittle : a. The ionic solids are formed by molecules containing positively charged, small in size cations and negatively charged relatively bigger atoms. b. Thus the electrostatic forces of attraction between nearest neighbouring ions are very strong. Which are responsible for holding very strongly particles together. Thus ionic solids are hard. c. When a force is applied, the layer of ions slip over one another and repel. This break the crystal. d. Thus ionic solids are brittle. · Solids ice is lighter than water. a. Ice has hexagonal three dimensional crystal structure formed by intermolecular hydrogen bonding, which leaves more empty space i.e.unoccupied. (8) b. The structure of liquid water and solid ice are almost identical. c. However on melting of ice some of the hydrogen bonds are broken and some of the empty spaces are occupied by the water molecule i.e. hexagonal crystalline structure of solid ice collapses while liquid water molecules becomes closed packed. d. Thus the density of liquid water is more than ice. Hence ice floats on water. · Packing in solids: The space occupied by constituents particles in unit cell is called packing in solids. · Volids or empty space: The unoccupied empty space in unit cell is called by void or empty in unit cell. In three dimensional closed packing of constituents particle shows following two types of voids. · Tetrahedral voids: Each sphere in the second layer rest on the hollow in the three following sphere in the first layer. i. The vacent space surrounded by four neighbours in tetrahedral disposition in the crystal lattice is formed, called a tetrahedral void. ii. In a close packed structure, the number of tetrahedral voids is doubled the number of constituents particles. This is because every void has four particles and there are eight voids around each particle. · Octahedral void : Three touching spheres in the second layer rest on the hollow in the three touching spheres in the first layer. i. Then vacant space surrounded by six nearest neighbours in octahedral disposition in the crystal lattice is called an octahedral void. ii. A close packed structure, the number of octahedral voids is the same as the number of constituent particles. This is because every void has six particles and there are six voids around each particle. · Voids of ionic compound: In case of ionic compounds, it is found that the bigger ions (usually anions) are present in the packing whereas smaller ions (usually cations) occupy the voids. Ex. i. If the cations are smaller in size, they may occupy tetrahedral voids (because they are smaller than octahedral voids) for all tetrahedral voids, the ratio of cations to anion is 2:1. ii. If the cations are bigger in size, they may occupy octahedral voids (because they are smaller than tetrahedral voids) for all octahedral voids, the ratio of cations to anion is 1:1. · Number of void filled and formula of the compound: i. Number of octahedral voids = Number of particles in the close packing = N ii. Number of tetrahedral voids = 2 x Number of particles in the close packing = 2 N · Deffect in crystal structure: Any deviation from the perfectly ordered arrangement of constituents particles, called defect or imperfection. · Types of defects: There are two types of defects (a) line defect and (b) point effect · Line defects: The defect is due to the irregularity in a complex line, a row of lattice point of constituents particles is called line defect. (9) · Point defects: The defect is due to a fault produced in the arrangement of a point i.e. constituent particles like atom, ions or molecule in a crystalline solid is called point defect. · Types of point defects: There are three types of point defects - a. Vacancy defect b. Interstitial defect c. Impurity defect. A. Vacancy defect: During the crystallization some of the places of the constituents particles remain unoccupied in crystal lattice and the defect generated is called vacancy defect (schottky defect). · Schottky defect: The defect was noticed by German scientist Schottky in 1930. The defect arises because of some vacancies are produced due to missing of cations and anions in the crystal lattice is called schottky defect. · Condition favouring Schottky defect: The schottky defect is noticed in ionic compounds, a With high co-ordination numbers. b. In which cations and anions have almost identical sizes. Ex: Alkali metal halides such as NaCI, KCl, CsCl, KBr etc. normally show this defect. · Consequence of Schottky defect : i. The defect increases the electrical conductivity of the crystalline solid. ii. The presence of holes because of the missing ions lowers the density of the crystal. iii. Que to the presence of the large number of holes, the stability of the crystal decreases. iv. It also lowers its lattice energy. v. It does not change dielectric constant. B. Interstitial defect or Frenkel defect: This defect in the ionic crystals was discovered Frenkel in 1926. · Interstitial or Frenkel defect: A defect occur when-cation or anion from ionic solid leaves its regular site and moves to occupy a place between the lattice site i.e. interstitial position, the defect is called interstitial defect of Frenkel defect. · Conditions favourifrg Frenkel defect : Generally it is observed in the ionic compounds: a. Crystal structure possess low co-ordination number. b. The anions are much larger than cations. · Consequences of Frenkel defect : i. The presence of this defect does not alter the density of solid. ii. Frenkel are responsible for conduction of electricity in crystals. iii. They are responsible for phenomenon of diffusion in solid. iv. They decreases the stability of crystal. v. They are also responsible to increase the dielectric constant of a crystal. (10) · Keep in mind: AgBr has both Schottky as well as Frenkel defect. C. Impurity defect: When a regular cation of the crystal is replaced by some different cation or excess of cations sometimes occupy interstitial position then the defect is generated is called impurity defect. · Types of impurity defect: There are two types: i. Substution impurity defect: If the impurity cation is substituted in place of regular cation then it is called substitution impurity defect. Ex. Brass is a substitution alloy formed by substituting copper metal by zinc metal in the ratio 1:3. ii. Interstitial impurity defect: If the impurity cation is present in the interstitial positions then it is called interstitial impurity defect. Ex. Stainless steel is an interstitial alloy formed by introducing carbon atoms as impurity. · Electrical properties in solid: On the basis of electrical conductivity, solids can be divided into three types: i. Metals ii. Non-metal iii. Semiconductors. i. Metals: These are the good conductors of heat and electricity because of a presence of delocalised or free electrons. Their conductivity 104–107 ohm–1m–1. Ex. Na, AI, Cu etc. ii. Non-metal: These are poor conductor of electricity because of absence of free electrons. Their conductivity 10–20–10–10 ohm–1m–1. iii. Semiconductors: Their conductivity lies in between metals and insulators. Their conductivity 10–6–10–4 ohm–1m–1. Conductivity: a. In metallic crystals valence band and conduction band are close to each other and a very little energy is required to excite electrons from valence band into conduction band. In conduction the electrons are delocalised and are free to move from one end to end of the metal acts as a good conductors. b. In non-metals, the spacing between valence band and conduction band is relatively more hence large amount of energy is required to promote electrons valence band to conduction band. This realtively more amount of energy is not available. Hence electrons remain in valence band and thus cannot move freely, do not conduct heat and electricity, ads as an insulator. c. In semiconductor, the spacing between valence band and conduction band is very small hence the electrons from valence band can be excited to conduction band on slight heating. Thus conduction band contain free electrons to conduct electricity. As temperature increases, more and more electrons available in conduction band thus the conductivity of semiconductor increases. Secmiconductors : The solid whose conductivity lies in between metals and insulators, called semiconductor. Types: There are two main types of semiconductors: (11) 1. n-type semiconductor (Electron rich or donor impurities) : The conductor which are formed by adding impurity atoms containing more valence electrons than the atoms of the parent in insulator are called n-type semiconductor. · Explanation: a. As a Si atom is substituted by an atom of ‘As’ then four of the electrons in arsenic form covalent bonds with surrounding Si atoms and the fifth electron remains free. b. This extra electron delocalised and can conduct electricity. This type of conductivity is known as n-type semiconductor where ‘n’ stands for negative because electrons are responsible for semiconducting behaviour. Ex. Doping of a silicon (or Ge) with group-15 elements such as P, Sb or Bi also give n-type semiconductors. · p-type semiconductor (electron deficient impurities): The conductors which are formed by adding impurity atoms containing lesser number of valence electrons that the atoms of the parent insulator element called p-type semiconductor. · Explanation: a. As a ‘Si’ atom is substituted by atom of ‘B’ then three electrons in boron form three covalent bonds and is unable to form fourth bond to complete the network structure of Si. b. As a result, some sites are left empty and gives rise to electrons deficiencies, are called electron vacancies or positive holes because the net charge at these sites is positive. c. When electric field is applied, a valence electrons on adjacent Si atom, jumps in the hole and this migration of positive hole continues and current is carried throughout the crystal. This types of conduction is called p-type secmiconduction be case ‘p’ stand for holes (positive charge) appears to be responsible for the semiconducting properties. Ex. Doping of a silicon (or Ge) with group-13 elements such as In, Al or Ga also give p-type semiconductor · Some examples of ‘n’ and ‘p’ type semiconductors: i. B doped with Si : ‘B’ is 13 group element and ‘Si’ is a 14 group element. When B is doped with ‘Si’ then electron will free. Therefore it is a n -type semiconductor. ii. As doped with Si : ‘As’ is 15 group element and ‘Si’ is 14 group element. When ‘As’ is doped with ‘Si’ then electron will free. Therefore it is a n-type semiconductor. iii. P doped with Si : ‘P’ is a 15 group element and ‘Si’ is a 14 group element. Hence when ‘P’ is doped with ‘Si’ then electron will free. Therefore it is n-type semiconductor. iv. Ge doped with In: ‘Ge’ is 14 group element and ‘In’ is 13 group element. Hence when ‘Ge’ is doped with ‘In’ then an electron deficient hole is created. Therefore, it is p-type semiconductor. · Magnetic Properties: Due to the spining motion of electrons around the nucleus, a spinning charge generates a magnetic field and hence spinning electrons as like tiny magnets. a. Diamagnatism: Substances which are repelled by external magnetic field [diamagnetic (Ti02, NaCl)] b. Paramagnetism: Substances which are weakly attracted by magnetic field [paramagnetic (TiO, VO2] c. Ferromagnetism: Substances which a are strongly attracted by magnetic field [Ferromagnetic (Fe, CO, Ni)] (12)  Sr. Properties Information Magnetic Example Application Alignment l. Diamagnetic Repelled weakly in Benzene, Insulators. magnetic field. NaCl, TiO2, Such solids have only V2OS, etc. paired electrons 2. Paramagnetic Have unpaired electron, O2, VO, Electronic weakly attracted in CuO, TiO devise. magnetic field. They cannot be permanently magnetized. 3. Ferromagnetic Have unpaired electrons. Strongly attracted in magnetic Fe, Ni, COO, CrO2 is used field. crO 2 in audio video Such solids can be tapes permanently magnetized. - Determination of magnetic property (Guoy’s method) : The method consists of weighing the substances in and out of magnetic field. i. If the substance is diamagnetic then it weightless in the magnetic field. ii. If the substance is paramagnetic then it weight more in the magnetic field because the substance is pulled in magnetic field. iii. If the substance is ferromagnetic then its weight more than that of paramagnetic in the magnetic field because the substance is more pulled in magnetic field. Important Formulae 1. To calculate formula of compound: a. In a cube, there are 8 comers, 6 face centres, 12 edge centres and one body centres. b. Contribution towards unit cell : 1 1 1 corner = , face centre = , edge centre = , body centre = 1 8 2 4 c. Formula of the compound is same as the ratio of atoms in the unit cell. 2. To calculate the radius of cation exactly filting into the void. a. Radius of cation in the tetrahedral void = 0.225 x Radius of anion b. Radius of cation in the octahedral void = 0.414 x Radius of anion 3. To calculate the radius of the cation that can be slipped into the void: Radius ratio 0.155 - 0.225 0.225 - 0.414 0.414-0.732 0.732-1 C.N. 3 4 6 8 Structural Planer Tetrahedral Octahedral BCC arrangement triangular · Keep In mind: a. If the radius ratio for cation has exact value’[ike 0.225, 0.414 then cation fitted exactly in void. (13) b. If the radius ratio for cation has value intermediate between suppose 0.225 to 0.414 then cation can slipped into the void. 4. To calculate radius ratio: r Radius ratio = r 5. To calculate distance between nearest neighbouring atoms (d) : a a. For SCC: d = a and r  2 3 3 b. For BCC: d  a  0.866 a and r  a  0.433 a 2 4 a a c. For FCC: d   0.707 a and r   0.3535 a 2 2 2 6. To calculate density () of cubic system: A. For cubic crystal of an element: Z M Density,   g cm 3 a3  NA Where Z = number of atoms present per unit cell i.e. for SCC, Z = I, BCC, Z = 2 and FCC, Z = 4 M = Atomic mass of an element in gmol “, a = Edge of cubic crystal in cm. (Generally it is given pm, hence convert into cm) NA = Avogadro’s number = 6.022 x1023 B. For cubic crystals of ionic compounds: Z M  g cm 3 a3  NA Where Z = number of formula unit present in one unit cell. M = Formula mass. · Keep in Mind: For BCC structure of pure element, Z= 2 (molecular mass) of compound but for BCC structure of ioru compounds like NaCl, (Z = 4), CsCl, (Z = 1). 7. To calculate number of formula units: NA Number of formula units in 1 g of any compound = molar mass 8. Relation between’ d’ and’ a’ scc bcc fcc d  2r d  2r d  2r 3 a da d a d 2 r Where ‘d’ g distance between nearest neighbours and ‘a’ g edge length of cubic unit cell. (14)