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UNIT 1
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✓ Topic:, • Amorphous and crystalline solids, • Crystal lattices and unit cells, • Number of atoms in a unit cell, • Close packed structures, • Imperfections in solids, , • Electrical properties, • Magnetic properties
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❑WHAT IS A SOLID ?, • Solids are substances having definite shape and definite, , volume., • In solids, the particles are closely packed and the force of, , attraction between the particles is strong., • solids are rigid and incompressible ., • Their constituent particles (atoms, molecules or ions) have, , fixed positions and can only vibrate about their mean, positions.
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Classification of solids, • On the basis of orderly arrangement of particles,, , solids can be classified into two –, , ➢ Crystalline solids, and, , ➢ Amorphous solids
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Amorphous Solids, , Crystalline Solids, • Highly ordered, arrangements of their, particles (atoms, ions, and, molecules) ., , • Particles are not arranged, in any specific order., •, , short range order, , • Long range order ., , • They have a definite, geometrical shape,, , • They have NO definite, geometrical shape,, , melting point and, , melting point and, , heat of fusion ., , heat of fusion .
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• Give regular cleavage on, cutting Nature ., , • Give irregular cleavage on, cutting., , • True solids ., , • Pseudo solids, , • Anisotropic in nature., , • Isotropic in nature., , • E.g.: Quartz, Diamond,, , • E.g.: Plastic, Glass (quartz, , Graphite, fullerene, NaCl,, , glass), Rubber, amorphous, , CuSO4.5H2O, ice,, , silica, coal, charcoal, coke,, , naphthalene, SiC etc., , PVC etc.
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• Like liquids amorphous solids, have a tendency to flow,, though very slowly., – Therefore, sometimes these are also called pseudo solids or, super cooled liquids., – Glass panes fixed to windows or doors of old buildings are, slightly thicker at the bottom than at the top., – This is because the glass flows down very slowly and makes, the bottom portion slightly thicker., , • Amorphous solids on heating become crystalline at, some temperature., • Some glass objects from ancient civilizations are found to, become milky in appearance due to some crystallization.
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❑Anisotropic and isotropic substances:, • Solids in which the physical properties like, electrical conductance, refractive index etc are, different when measured in different directions, are said to be anisotropic in nature., – This is due to the different arrangement of particles in, , different directions., – Crystalline solids are anisotropic..
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• Solids in which the physical properties are, same along any direction are said to be, isotropic in nature., – This is due to the irregular arrangement of, particles along different directions., – Amorphous solids are isotropic
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➢ Crystal lattices and unit cells :, Regular arrangement of constituent, particles of crystal in 3 dimensional space is called, space lattice ., ▪ The important characteristics of a crystal lattice are:, (a) Each point in a lattice is called lattice point or lattice, site.
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(b) Each point in a crystal lattice represents one constituent, particle which may be an atom, a molecule (group of, atoms) or an ion., (c) Lattice points are joined by straight lines to bring out, the geometry of the lattice., , There are only 14 possible three dimensional lattices., These are called Bravais Lattices.
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❑Unit cell :, A unit cell is the building block of a crystal., Or, It is the smallest portion of a crystal lattice which,, when repeated in three dimension to generate an, entire lattice.
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– A unit cell is characterised by its edge lengths (a, b and, c) and angle between the edges – α (between b and c), β, (between a and c) and γ (between a and b)., , • Thus a unit cell is characterised by 6 parameters, – a, b, c, α, β and γ.
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Classification of Unit cells :, Unit cells are broadly divided into 2 based on the position, of particles, - primitive and, - centred unit cells., (a) Primitive Unit Cells :, When constituent particles are present only on the, corner positions of a unit cell, it is called as primitive, unit cell., (b) Centred Unit Cells :When a unit cell contains one or, more constituent particles present at positions other than, corners in addition to those at corners, it is called a, centred unit cell.
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NUMBER OF PARTICLES IN UNITCELL, , Primitive cubic (Simple Cubic) unit cell:, Here atoms are present only at the corners of the cube., Each corner atom is shared by 8 unit cells. Therefore, contribution to, one unit cell = 1/8, Since each unit cell has 8 atoms at the corners, total number of, atoms in one unit cell = 8×1/8 = 1, So for a primitive (simple cubic) unit cell, z = 1
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• Body-centred cubic (bcc) unit cell:, Here the particles are present at the corners of the cube and also, one atom at the body centre., , The number of atoms at the corner = 8×1/8 = 1, The atom present at the centre of the body is not shared by other, atoms., , So the number of atoms at the body-centre = 1, Therefore, total number of atoms in the unit cell = 1+1=2, , So, for a bcc, z = 2
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• Face-centred cubic (fcc) unit cell:, Here the atoms are present at the corners and also at the centre, of each faces., Each corner atom is shared by 8 unit cells and each face, centre atom is shared by 2 unit cells., Number of corner atoms = 8×1/8 = 1, , Number of face-centre atoms = 6×1/2 = 3, Therefore, total number of atoms = 1+3 = 4, So, for an fcc, z = 4.
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Seven types of crystal systems :
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Close packing in solids :, Solids are three dimensional and the 3 D structure can, be obtained by the following three steps:, , 1., , Close packing in One Dimensions :, , Here the spheres (particles) are arranged in a row, touching each other., -In this arrangement each sphere is in contact with 2 adjacent, spheres., -Therefore, co-ordination number of each sphere is 2.
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2. Close packing in Two Dimensions :, Here the spheres are arranged in two directions – length-wise, and breadth-wise. This can be done in two different ways ., , Square close packing in two dimensions:, -Here each sphere is in contact with four adjacent spheres., So the co-ordination number of each sphere is 4., Here the spheres of second row are placed, exactly above those of the first row. In this, arrangement, each sphere is in contact with, four adjacent spheres. So the co-ordination, number of each sphere is 4. When we join, the centres of these spheres, we get a, square. So this close packing is called, square close packing in two dimensions
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Hexagonal close packing in two dimensions:, - Here each sphere is in contact with six adjacent spheres., So the co-ordination number of each sphere is 6., : Here the spheres of the second row are, placed in the depressions of the first row,, the spheres of the third row are placed in the, depressions of the second row and so on. In, this arrangement, each sphere is in contact, with six adjacent spheres. So the coordination number of each sphere is 6., ✓In 2D close packing, hexagonal closeWhen we join the centres of these spheres,, we get a hexagon. So this close packing is, packing is more efficient since the, called hexagonal close packing in two, maximum space is occupied by, dimensions, , spheres.
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▪ Three Dimensional close packing :, Here the particles are arranged in layers. This can be, possible in two ways., i. Three dimensional close packing from two dimensional, square close-packed layers:, Here the spheres of the each layer are placed exactly, above those of the lower layer., • In this arrangement, all the layers are identical., • So if we call the first layer as A, then all the layers are of, ‘A’ type. So this arrangement forms AAA….. type pattern., • The lattice thus generated is the simple cubic lattice and, its unit cell is the primitive cubic unit cell.
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ii. Three dimensional close packing from two dimensional hexagonal, , close-packed layers:, • Here the first layer is arranged as hexagonal manner. The second layer is, placed above the depressions of the first layer., , • On placing the second layer there arises two types of voids (vacant, spaces) above the second layer – tetrahedral voids and octahedral voids., Thus when we place the third layer over the second there are two, possibilities.
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❑Covering tetrahedral voids:, Here the spheres of the third layer are placed above the, , tetrahedral voids of the second layer., • In this arrangement, the spheres of the 3rd layer are vertically, , above those of the 1st layer., • Similarly the 4th layer is a repetition of the 1st layer. This will form, , the pattern ABAB……, •This type of close packing is called Hexagonal close packing (hcp), in three dimensions., , •This type of arrangement is found in metals like Zn , Mg etc.
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❑ Covering octahedral voids:, • Here the spheres of the third layer are placed above the octahedral, voids of the second layer., •, , In this arrangement, the 1st, 2nd and 3rd layers are different., , •, , But the 4th layer is identical to the 1st layer, the 5th layer to the, 2nd layer and so on., , • This will form the pattern ABCABC……, , • This type of close packing is called cubic close packing (ccp) or, face-centred cubic(fcc) packing in three dimensions., • This type of arrangement is found in metals like Cu, Ag etc
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Both hcp and ccp are equally, efficient since 74% of the, available space is occupied by, spheres.
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• Co-ordination Number :, , o In a close packed arrangement the number of nearest, neighbours with which a given sphere is in contact is, called the co-ordination number of that sphere., o In both hcp and ccp, co-ordination number in both hcp, and ccp is 12., • Interstitial voids :, o The vacant space in close packed arrangement is called, voids., o These are of two types- tetrahedral voids and, octahedral voids.
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• Tetrahedral void:, o A void surrounded by four spheres in tetrahedral position is, called tetrahedral void., o In a close packed arrangement the number of tetrahedral, voids is double the number of spheres, i.e. there are two, tetrahedral voids per sphere., • Octahedral voids:, o A void surrounded by six spheres in octahedral position is, called octahedral void., o In a close packed arrangement the number of octahedral, voids is equal to the number of spheres, i.e. there is only, one octahedral void per sphere.
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• If there are N close packed spheres,, The number of tetrahedral voids = 2N and, The number of octahedral voids = N
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Q1. Atoms of element B form hcp lattice and those of the, , element A occupy 2/3rd of tetrahedral voids. What is the, formula of the compound formed by the elements A and B?, , Ans:, Here the B atoms form hcp and A atoms occupy 2/3rd of, tetrahedral voids., Let the number of B atoms be x., We know that in a close packed structure,, no. of tetrahedral voids = 2 x no. of close packed spheres, = 2x., No. of A atoms = 2/3 x no. of tetrahedral voids, = 2/3 x 2x, = 4/3 x, Ratio between A and B atoms = 4/3 x : x, =4:3, Formula of the compound = A4B3
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Imperfections in solids :, The deviation from the regular orderly, arrangement of particles of a crystal is termed as, imperfections or crystal defects., The crystal defects are broadly classified into two, – point defects, And, – line defects., •The defect around a point or an atom in a crystal is, termed as point defect., •If the defect extends along a line, it is termed as line, defects .
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1. Stoichiometric defects:, Defects that do not change the, stoichiometric ratio of a compound is termed, as Stoichiometric defects (intrinsic or, thermodynamic defects)., In ionic solids, there are two types of, stoichiometric defects, -Schottky defect and, -Frenkel defect.
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•Non-Stoichiometric defects:, These are point defects which change the, stoichiometry of a solid., These defects are of two types:, i) Metal excess defect and ii) Metal deficiency defect, Metal excess Defect :, Here the no. of cations is greater than the number of anions., This arises in two ways:, • Metal excess defect due to anionic vacancies, • Metal excess defect due to extra cations at interstitial sites, , .
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Metal excess defect due to anionic, vacancies:, •Here some of the anions are missing from, the lattice site., •The electrical neutrality is maintained by, occupying electrons in the anionic sites., •These electrons are called f-centres, because they give colour to the crystal., •This defect is shown by alkali metal, halides., -For example when NaCl is heated in an, atmosphere of sodium vapour, some, sodium atoms are deposited at the surface, of the crystal. The Cl- ions diffuse to the, surface of the crystal and combines with, Na atom to form NaCl., , Na + Cl-, , NaCl + e-, , • The electron so formed diffuse into the, crystal and occupies the anion vacancy., •These electrons absorb light energy and, get excited. As a result the crystal, becomes yellow in colour. So the colour, is due to the formation of f-centres., •Similarly, excess of Li makes LiCl, crystals pink and excess of K makes KCl, crystals violet .
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Metal excess defect due to extra, cations at interstitial sites:, Here some cations occupy the, interstitial sites. The electrical neutrality is, maintained by occupying some electrons in, adjacent interstitial sites., E.g. When ZnO crystals are heated, the white coloured crystals, becomes yellow. This is because on heating, the crystal loses oxygen as, follows:, ZnO, Zn2+ + ½ O2 + 2e., The Zn ions now move to the interstitial sites and the electrons to, neighbouring interstitial sites., , The anion sites occupied by electrons are, called F-centre.
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ii) Metal deficiency Defect:, Here the number of cations is smaller than the, number of anions. This is mainly arises due to, cation vacancies, This type of defect is commonly shown by, transition metal compounds., E.g. FeO
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c) Impurity Defects:, It is the defect arising due to the presence of, foreign particles in a crystal., E.g. when molten NaCl is crystallized in presence of small, , amount of SrCl2, some Na+ ions are replaced by Sr2+ ions and, some cationic vacancies are formed., -The no. of cationic vacancies produced is equal to the number, of Sr2+ ions. Another example is a solid solution of CdCl2 and, , AgCl.
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❑ Properties of solids, 1) Electrical properties:, , Conductors: They are solids, which allow the passage of, electricity through them. Their, conductivity ranges from 104 to, 107 ohm-1m -1 ., , Based on the, electrical, conductivity, solids, are classified into, three type., , Semi-conductors: They are, solids which allow the passage of, electricity only partially. Their, conductivity ranges from 104 to, 10-6 ohm-1m -1, , Insulators: They are solids, which do not allow the passage of, electricity through them. Their, conductivity ranges from 10-10 to, 10-20 ohm-1m -1 .
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➢ Conduction of Electricity in metals, semiconductors and insulators - Band Model :, , oAccording to this model, in metal there are two, types of bands – valence band and conduction band., oValence band is the lower energy electron occupied, , band and ,, oconduction band is the higher energy unoccupied, band.
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•In metals, the valence, band is either partially, filled or it is, overlapped with the, conduction band., •So electron can easily, flow from the valence, band to the conduction, band., , •In semi-conductors,, there is a small energy, gap between the valence, band and conduction, band and only a few, electrons can enter into, the conduction band., •So they conduct only, partially., , •In insulators, the gap, between the valence, band and the, conduction band is, large and, •so they do not conduct, electricity.
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Conduction of Electricity in semi-conductors:, The conductivity of semi-conductors can be increased, by adding some impurity. This process is called doping., •Doping can be done by the addition of either electron rich, impurity or electron deficit impurity., •When a group 14 element (like Si, or Ge) is doped with a group 15, element (like P or As) four electrons, are used for the formation of, covalent bonds and the fifth, electron becomes free., •The presence of this delocalised, electron increases the conductivity, and these types of semi-conductors, are called n-type semiconductor., , •When a group 14 element (like Si or, Ge) is doped with a group 13 element, (like B, Al, or Ga), three electrons, are used for the formation of, covalent bonds and the fourth, valence electron is missing., •This creates an electron hole which, increases the conductivity of the, semi-conductor. Such type of, semiconductors are called p-type, semiconductors.
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P-type, , N-type
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Magnetic, properties, , Diamagnetic Substances:, These are weakly repelled, by a magnetic field., They contain only paired, electrons. E.g.: H2O, NaCl,, Benzene (C6H6), 1, Paramagnetic Substances:, , Substances which are, weakly attracted by a, magnetic field are called, paramagnetic substances., Eg: O2,Cuo,Fe3+, 2, , Ferromagnetic, Substances: Substances, which are strongly attracted, by a magnetic field are, called ferromagnetic, substances .Eg: Fe, Co, Ni, , 3, , Anti - Ferromagnetic Substances:, Substances which are expected to, possess para magnetism or, ferromagnetism on the basis of, unpaired electrons but actually, possess zero net magnetic moment, are called, Anti-Ferromagnetic substance., Eg:MnO, 4, , Ferrimagnetic Substances: Substances which are expected to, possess para magnetism or ferromagnetism on the basis of unpaired, electrons but actually have small net magnetic moment are called ferri, magnetic substances. Eg: Fe3O4,MgFe2O4,ZnFe2O4., 5
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. 1. Diamagnetic Substances: These are weakly repelled by, an external magnetic field. Diamagnetism arises due to the, presence of only paired electrons. Pairing of electrons, cancels their magnetic moments and so they have no net, magnetic moment. E.g.: H2O, NaCl, Benzene (C6H6) ., 2. Paramagnetic Substances: They are weakly attracted by an, external magnetic field. Paramagnetism is due to the, presence of one or more unpaired electrons. They have a net, magnetic moment. They lose their magnetism in the absence, of external magnetic field. So they are temporary magnets., Eg: O2, Cu2+, Fe3+, Cr3+ etc.
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3. Ferromagnetic Substances: They are very strongly attracted by a, magnetic field and can be permanently magnetised. In solid state,, , the metal ions of ferromagnetic substances are grouped together, into small regions called domains. In the absence of an external, , magnetic field, these domains are randomly oriented. When the, substance is placed in a magnetic field, all the domains get oriented, in the direction of the magnetic field and a strong magnetic effect is, , produced. This ordering of domains do not change even when the, externalmagnetic field is removed and so they become permanent, magnets. Eg: Fe, Co, Ni, Gd (Gadolinium), CrO2 etc.
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4. Anti-ferromagnetic Substances: Here the, domains are oppositively oriented and, cancel each other. So they have no net, magnetic moment. Eg: MnO, 5. Ferrimagnetic Substances: Here the, domains are arranged in opposite, directions but in unequal numbers. So they, have a net magnetic moment. Eg: Fe 3O4, (magnetite) and ferrites like MgFe.
