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60 Solid State 197 E3 Chapter 5 Solid State property in all directions There is a sudden change in volume when it melts. There is no sudden change in volume on melting. These possess symmetry Not possess any symmetry. ID show different property in different direction D YG U The solids are the substa...

60 Solid State 197 E3 Chapter 5 Solid State property in all directions There is a sudden change in volume when it melts. There is no sudden change in volume on melting. These possess symmetry Not possess any symmetry. ID show different property in different direction D YG U The solids are the substances which have definite volume and definite shape. In terms of kinetic molecular model, solids have regular order of their constituent particles (atoms, molecules or ions). These particles are held together by fairly strong forces, therefore, they are present at fixed positions. The properties of the solids not only depend upon the nature of the constituents but also on their arrangements. Types and Classification of solids (1) Types of solids Solids can be broadly classified into following two types, These possess angles. interfacial U Crystalline solids Amorphous solids They have short range order. They have definite melting point Not have point They have a definite heat of fusion Not have definite heat of fusion They are rigid incompressible Not be compressed to appreciable extent ST They have long range order. and definite melting any They are given cleavage i.e. they break into two pieces with plane surfaces They are given irregular cleavage i.e. they break into two pieces with irregular surface They are anisotropic because of these substances They are isotropic because of these substances show same interfacial (2) Crystalline and amorphous silica (SiO 2 ) Silica occurs in crystalline as well as amorphous states. Quartz is a typical example of crystalline silica. Quartz and the amorphous silica differ considerably in their properties. Quartz Amorphous silica It is crystalline in nature (i) Crystalline solids/True solids, (ii) Amorphous solids/Pseudo solids Not possess angles. All four corners of SiO44  It is light powder The SiO44  (fluffy) white tetrahedra are tetrahedron are shared by others to give a network solid randomly joined, giving rise to polymeric chains, sheets or three-dimensional units It has high and sharp melting point (1710°C) It does not melting point have sharp (3) Diamond and graphite Diamond and graphite are tow allotropes of carbon. Diamond and graphite both are covalent crystals. But, they differ considerably in their properties. Diamond Graphite It occurs naturally in free It occurs naturally, as well state as manufactured artificially A Unique Book For Competition 198 and electricity. of heat and electricity substance known. It burns in air at 900°C to It burns in air at 700°C to It has high relative density give CO2 give CO2 It is the hardest natural It is soft and greasy to touch Its relative density is 2.3 (about 3.5) It It is transparent and has It has black in colour and crystals high refractive index (2.45) opaque It is non-conductor of heat Graphite is a good conductor occurs as octahedral It occurs as hexagonal crystals (4) Classification of crystalline solids Types of Solid Constituents Bonding Examples Physica l Nature Ionic Positive and negative ions network systematically arranged Coulombic NaCl, KCl, CaO, MgO, LiF, ZnS, BaSO4 and K2SO4 etc. Hard but brittle Covalent Atoms connected in covalent bonds Electron sharing SiO2 (Quartz), SiC, C (diamond), C(graphite) etc. Hard Hard Hard Polar or nonpolar molecules (i) Molecular interaction s (intermole cu-lar forces) (ii) Hydrogen bonding I2,S8, P4, CO2, CH4, CCl4 etc. Soft Cations in a sea of electrons Metallic Sodium , Au, Cu, magnesium, metals and alloys Ductile malleabl e High High (≃800K to 1000 K) (≃1500K 2000K) Atoms London dispersion force Noble gases Soft Very low Very low Metallic Atomic B.P. Very high (≃4000K) (≃5000K) ID U Crystallography ST “The branch of science that deals with the study of structure, geometry and properties of crystals is called crystallography”. (1) Symmetry in Crystal : A crystal possess following three types of symmetry, (i) Plane of symmetry : It is an imaginary plane which passes through the centre of a crystal can divides it into two equal portions which are exactly the mirror images of each other. Conductor (in molten state and in aqueous solution) Insulator except graphite High (≃2000K) Very high Low to Soft Low U Starch, sucrose, water, dry ice or drycold (solid CO2) etc. Electrical Conductivit y E3 High (≃1000K) (≃300K 600K) (≃400K) D YG Molecula r M.P. 60 Table : 5.1 Some characteristics of different types of crystalline solids Low Insulator (≃ 450 to 800 K) Insulator Low (≃373K to 500K) Conductor to Poor thermal and electrical conductors (ii) Axis of symmetry : An axis of symmetry or axis of rotation is an imaginary line, passing through the crystal such that when the crystal is rotated about this line, it presents the same appearance more than once in one complete revolution i.e., in a rotation through 360°. Suppose, the same appearance of crystal is repeated, on rotating it through an angle of 360°/n, around an imaginary axis, is called an n-fold axis where, n is known as the order of axis. By order is meant the value of n in 2 / n so that rotation through 2 / n, gives an equivalent configuration. Fig. 5.2 Plane of symmetry Rectangular plane of symmetry Fig. 5.1 Diagonal plane of symmetry Axis of two fold symmetry Axis of three f old symmetry Solid state Y Z Miller indices : Planes in crystals are described by a set of integers (h, k and l) known as Miller indices. Miller indices of a plane are the reciprocals of the fractional intercepts of that plane on the various crystallographic axes. For calculating Miller indices, a reference plane, known as parametral plane, is selected having intercepts a, b and c along x, y and z-axes, respectively. Then, the intercepts of the unknown plane are given with respect to a, b and c of the parametral plane. ID Centre of symmetry of a cubic crystal X (iii) Law of constancy of symmetry : According to this law, all crystals of a substance have the same elements of symmetry is plane of symmetry, axis of symmetry and centre of symmetry. E3 (iii) Centre of symmetry : It is an imaginary point in the crystal that any line drawn through it intersects the surface of the crystal at equal distance on either side. 60 (ii) Law of rational indices : This law states that the ratio of intercepts of different faces of a crystal with the three axes are constant and can be expressed by rational numbers that the intercepts of any face of a crystal along the crystallographic axes are either equal to unit intercepts (i.e., intercepts made by unit cell) a, b, c or some simple whole number multiples of them e.g., na, n' b, n''c, where n, n' and n'' are simple whole numbers. The whole numbers n, n' and n'' are called Weiss indices. This law was given by Hauy. Axis of six fold symmetry Axis of four fold symmetry Fig. 5.3 Thus, the Miller indices are : U Only simple cubic system have one centre of symmetry. Other system do not have centre of symmetry. D YG The total number of planes, axes and centre of symmetries possessed by a crystal is termed as elements of symmetry. A cubic crystal possesses total 23 elements of symmetry. Plane of symmetry =9 ( 3 + 6) Axes of symmetry ( 3 + 4 + 6) Centre of symmetry (1) = 13 U h a intercept of the plane along x - axis k b intercept of the plane along y - axis l c intercept of the plane along z - axis The distance between the parallel planes in crystals are designated as d hkl. For different cubic lattices these interplanar spacing are given by the general formula, =1 Total symmetry = 23 (2) Laws of crystallography : Crystallography is based on three fundamental laws. (i) Law of constancy of interfacial angles : This law states that angle between adjacent corresponding faces is inter facial angles of the crystal of a particular substance is always constant inspite of different shapes and sizes and mode of growth of crystal. The size and shape of crystal depend upon the conditions of crystallisation. This law is also known as Steno's Law. ST 199 d(hkl )  a h  k 2  l2 2 Where a is the length of cube side while h, k and l are the Miller indices of the plane. When a plane is parallel to an axis, its intercept with that axis is taken as infinite and the Miller will be zero. Negative signs in the Miller indices is indicated by placing a bar on the intercept. All parallel planes have same Miller indices. Space lattice and Unit cell Fig. 5.4. Constancy of interfacial angles Crystal is a homogeneous portion of a crystalline substance, composed of a regular pattern of structural units (ions, atoms or molecules) by plane surfaces 200 Solid State Lattic e c  Space lattice & unit cell Fig. 5.5 60 The crystals of the substance are obtained by cooling the liquid (or the melt) of the solution of that substance. The size of the crystal depends upon the rate of cooling. If cooling is carried out slowly, crystals of large size are obtained because the particles (ions, atoms or molecules) get sufficient time to arrange themselves in proper positions. Dissolved dissolved Atoms of molecules    cluster   dissolved embryo nucleus crystal Unit Cell b a Unit cell Formation of crystal and Crystal systems (unstable) (If loosing units dissolves as embryo and if gaining unit grow as a crystals). Bravais (1848) showed from geometrical considerations that there can be only 14 different ways in which similar points can be arranged. Thus, there can be only 14 different space lattices. These 14 types of lattices are known as Bravais Lattices. But on the other hand Bravais showed that there are only seven types of crystal systems. ID   (2) Body centred cubic (bcc) : Atoms are arranged at the corners and at the centre of the unit cell. (3) Face centred cubic (fcc) : Atoms are arranged at the corners and at the centre of each faces of the unit cell. (4) Side centered : Atoms are arranged at the centre of only one set of faces in addition to the atoms at the corner of the unit cell. E3 making definite angles with each other giving a regular geometric form. A regular array of points (showing atoms/ions) in three dimensions is commonly called as a space lattice, or lattice. Each point in a space lattice represents an atom or a group of atoms. Each point in a space lattice has identical surroundings throughout. A three dimensional group of lattice points which when repeated in space generates the crystal called unit cell. The unit cell is described by the lengths of its edges, a, b, c (which are related to the spacing between layers) and the angles between the edges, ,  , Space . D YG U Types of units cells A units cell is obtained by joining the lattice points. The choice of lattice points to draw a unit cell is made on the basis of the external geometry of the crystal, and symmetry of the lattice. There are four different types of unit cells. These are, (1) Primitive or simple cubic (sc) : Atoms are arranged only at the corners of the unit cell. Table : 5.2 Bravais lattices corresponding to different crystal systems Crystal system Cubic ab c,       90 o Space lattice Simple : Lattice points at the eight corners of the unit cells. c ST ab c ,       90 o   a SnO 2 , TiO 2 , ZnO 2 , NiSO 4 white Sn etc. b c  CsCl, NaCl, Cu 2O, CaF2 and ZrSiO 4. PbWO 4 , c Simple: Points at the eight corners of the unit cell.  Body centered : Points at the eight corners and at the body centre  a abc, Au, Cu, ZnS , diamond, KCl , b Simple : Points at the eight corners of the unit cell.  Pb, Hg, Ag, alums. etc.  a       90o Orthorhombic (Rhombic) Examples Face centered : Points at the eight corners and at the six face centres.  U  Tetragonal Body centered : Points at the eight corners and at the body centred. b End centered : Also called side centered or base centered. Points at the eight corners and at two face centres opposite to each other. Body centered : Points at the eight corners and at the body centre Face centered: Points at the eight corners and at the six face centres. KNO 3 , K 2 SO 4 , PbCO 3 , BaSO 4 , rhombic sulphur, MgSO 4. 7 H 2 O etc. Solid state Rhombohedral Simple : Points at the eight corners of the unit cell 201 NaNO 3 , CaSO 4 , calcite, quartz, As, Sb , Bi etc. or Trigonal ab c,       90 Simple : Points at the twelve corners of the unit cell out lined by thick line. abc, or Points at the twelve corners of the hexagonal prism and at the centres of the two hexagonal faces.     90 o HgS , graphite, ice, Mg, Zn, Cd etc. Monoclinic Simple : Points at the eight corners of the unit cell End centered : Point at the eight corners and at two face centres opposite to the each other. ID abc, E3   120o U     90 o ,   90 o Triclinic Simple : Points at the eight corners of the unit cell. o D YG a  b  c,       90 ZnO, PbS, CdS , 60 Hexagonal Analysis of cubic system (1) Number of atoms in per unit cell U The total number of atoms contained in the unit cell for a simple cubic called the unit cell content. ST The simplest relation can determine for it is, n nc n f   i 8 2 1 Where n c  Number of atoms at the corners of the cube=8 n f  Number of atoms at six faces of the cube = 6 n i  Number of atoms inside the cube = 1 Cubic unit cell nc nf ni Total atom in per unit cell Na 2 SO 4.10 H 2 O, Na 2 B4 O7.10 H 2O, CaSO 4.2 H 2 O, monoclinic sulphur etc. CaSO 4.5 H 2 O, K2Cr2O7 , H 3 BO3 etc. (2) Co-ordination number (C.N.) : It is defined as the number of nearest neighbours or touching particles with other particle present in a crystal is called its co-ordination number. It depends upon structure of the crystal. For simple cubic system C.N. = 6. For body centred cubic system C.N. = 8 For face centred cubic system C.N. = 12. (3) Density of the unit cell (  ) : It is defined as the ratio of mass per unit cell to the total volume of unit cell. ZM  a 3 N 0 Where Z = Number of particles per unit cell M = Atomic mass or molecular mass Simple cubic (sc) 8 0 0 1 body centered cubic (bcc) 8 0 1 2 N 0  Avogadro number (6.023  10 23 mol 1 ) Face centered cubic (fcc) 8 6 0 4 a  Edge length of the unit cell= a pm  a  10 10 cm 202 Solid State a 3  volume of the unit cell ZM g / cm 3 a 3  N 0  10 30 The density of the substance is same as the density of the unit cell. Let radius of the atom in the packing = r Edge length of the cube = a Volume of the cube V = a 3 Volume of the atom (spherical)   4 3 r Z  3 3 Packing density  V a Bodycentred cubic r a 2 2 r 4 3  4 a   3 2 3  a   2 2     6 3 % of void ID a 2 Packing density 3a 4 4 3  3a    4    3  (i) Square close packing : In which the spheres in the adjacent row lie just one over the other and show a horizontal as well as vertical alignment and form square. In this arrangement each sphere is in contact with four spheres. 11 100–52 = 48%  0.52 U Facecentred cubic r Volume of the atom ( ) 2  0. 74 6 100 – 74 = 26% 3  0. 68 8 100 – 68 = 32% D YG Simple cubic r related to a In the formation of crystals, the constituent particles (atoms, ions or molecules) get closely packed together. The closely packed arrangement is that in which maximum available space is occupied. This corresponds to a state of maximum density. The closer the packing, the greater is the stability of the packed system. (1) Close packing in two dimensions : The two possible arrangement of close packing in two dimensions. 4 3 r 3 Z Structur e Close packing in crystalline solids 60 (4) Packing fraction (P.F.) : It is defined as ratio of the volume of the unit cell that is occupied by spheres of the unit cell to the total volume of the unit cell. Where dhkl denotes the perpendicular distance between adjacent planes with the indices hkl. E3 i.e.   equal to 1. Thus Bragg’s equation may alternatively be written as   2 d sin = 2 dhkl sin X-ray study of crystal structure U Study of internal structure of crystal can be done with the help of X-rays. The distance of the constituent particles can be determined from diffraction value by Bragg’s equation. n  2d sin ST where,  = Wave length of X-rays, n = order of reflection,   Angle of reflection, d = Distance between two parallel surfaces The above equation is known as Bragg’s equation or Bragg’s law. The reflection corresponding to n = 1 (for a given family of planes) is called first order reflection; the reflection corresponding to n = 2 is the second order reflection and so on. Thus by measuring n (the order of reflection of the X-rays) and the incidence angle , we can know d/. d n   2 sin  From this, d can be calculated if  is known and vice versa. In X-ray reflections, n is generally set as 4 2 3 Fig. 5.6. Square close packing (ii) Hexagonal close packing : In which the spheres in every second row are seated in the depression between the spheres of first row. The spheres in the third row are vertically aligned with spheres in first row. The similar pattern is noticed throughout the crystal structure. In this arrangement 2 each sphere is in contact with1 six other spheres. 3 6 5 4 Fig. 5.7. Hexagonal close packing (2) Close packing in three dimensions : In order to develop three dimensional close packing, let us retain the hexagonal close packing in the first layer. For close packing, each spheres in the second layer rests in the hollow at the centre of three touching spheres in the layer as shown in figure. The spheres in the first layer are shown by solid lines while those in Solid state 203 second layer are shown by broken lines. It may be noted that only half of the triangular voids in the first layer are occupied by spheres in the second layer (i.e., either b or c). The unoccupied hollows or voids in the b b a a a a b a a c c c a a a a a Fig. 5.8. Close packing in three dimensions There are two alternative ways in which species in third layer can be arranged over the second layer, A A A ID (i) Hexagonal close packing : The third layer lies vertically above the first and the spheres in third layer rest in one set of hollows on the top of the second layer. This arrangement is called ABAB …. type and 74% of the available space is occupied by spheres. This arrangement is found in Be, Mg, Zn, Cd, Sc, Y, Ti, Zr, Tc, Ru. A 60 aa a a (iii) Body centred cubic : This arrangement of spheres (or atoms) is not exactly close packed. This structure can be obtained if spheres in the first layer (A) of close packing are slightly opened up. As a result none of these spheres are in contact with each other. The second layer of spheres (B) can be placed on top of the first layer so that each sphere of the second layer is in contact with four spheres of the layer below it. Successive building of the third will be exactly like the first layer. If this pattern of building layers is repeated infinitely we get an arrangement as shown in figure. This arrangement is found in Li, Na, K, Rb, Ba, Cs, V, Nb, Cr, Mo, Fe. E3 first layer are indicated by (c) in figure. B A A U B A A B A A A A B B A B A A A A B A A A A A A B B D YG A Fig. 5.11. Body centred cubic (bcc) close packing in three dimensions B B A A A Fig. 5.9. Hexagonal close packing (hcp) in three dimensions ST U (ii) Cubic close packing : The third layer is different from the first and the spheres in the third layer lie on the other set of hollows marked ‘C’ in the first layer. This arrangement is called ABCABC….. type and in this also 74% of the available space is occupied by spheres. The cubic close packing has face centred cubic (fcc) unit cell. This arrangement is found in Cu, Ag, Au, Ni, Pt, Pd, Co, Rh, Ca, Sr. B Property hcp ccp bcc Arrangeme nt of packing Close packed Close packed Not close packed Type of packing AB AB A... ABC A... Available space occupied 74% 74% 68% Coordinati on number 12 12 8 Malleabilit y and ductility Less malleable, hard, brittle Malleable and ductile ABC AB A... Interstitial sites in close packing Even in the close packing of spheres, there is left some empty space between the spheres. This empty space in the crystal lattice is called site or void or hole. Voids are of following types, A (1) Trigonal void : This site is formed when three spheres lie at the vertices of an equilateral triangle. Size of the trigonal site is given by the following relation, C A Triogona l void r  0.155 R C AB B A B Table : 5.3 Comparison of hcp, ccp and bcc C Fig. 5.10. Cubic close packing (ccp or fcc) in three dimensions Fig. 5.12 204 Solid State r = Radius of the spherical and anions say NaCl structure. Then, rc  ra  a / 2 trigonal void R = Radius of closely packed spheres where rc and ra are radius of cation and anion. The number of tetrahedral voids is double the number of spheres in the crystal structure. r  0. 225 R where, r is the radius of the tetrahedral void of (2) Radius ratio : Ionic compounds occur in crystalline forms. Ionic compounds are made of cations and anions. These ions are arranged in three dimensional array to form an aggregate of the type (A+B–)n. Since, the Coulombic forces are nondirectional, hence the structures of such crystals are mainly governed by the ratio of the radius of cation (r ) to that of anion (r ). The ratio r to r (r / r ) is called spheres forming Radius ratio  r r ID radius 3a 2 For bcc lattice say CsCl. rc  ra  as radius ratio. or atom occupying tetrahedral void. R is the tetrahedral void. (a / 2)2  (a / 2)2 a  2 4 60 Fig. 5.13. Tetrahedral void Radius of Cl   E3 (2) Tetrahedral void : A tetrahedral void is developed when triangular voids (made by three spheres in one layer touching each other) have contact with one sphere either in the upper layer or in the lower layer. U (3) Octahedral void : This type of void is surrounded by six closely packed spheres, i.e. it is formed by six spheres. r+/r– > 0.732 r  0. 414 R D YG The number of octahedral voids is equal to the number of spheres. Fig. 5.14. Octahedral void (4) Cubic void : This type of void is formed between 8 closely packed spheres which cube. U occupy all the eight corner of Fig. 5.15. Cubic void ST r  0. 732 R r+/r– = 0.414 Coordination number Coordination decreases from 6 to number increases 4 from 6 to 8 Fig. 5.17. Effect of radius ratio on co-ordination number Table : 5.4 Limiting Radius ratios and Structure Limiting radius ratio (r+)/(r–) C.N. Shape < 0.155 2 Linear 0.155 – 0.225 3 Planar triangle 0.225 – 0.414 4 Tetrahedral 0.414 – 0.732 6 Octahedral 0.732 – 0.999 or 1 8 Body-centered The decreasing order of the size of the various voids is, Cubic > Octahedral > Tetrahedral > Trigonal Ionic radii and Radius ratio (1) Ionic radii : X-ray diffraction or electron diffraction techniques provides the necessary information regarding unit cell. From the dimensions of the unit cell, it is possible to calculate ionic radii. Let, cube of edge length 'a' having cations Cl– cubic Effect of temperature and Pressure on C.N. On applying high pressure NaCl structure having 6 : 6 co-ordination changes to CsCl structure having co-ordination. Thus, increase in pressure 8 :8 increases the co-ordination number. Similarly, CsCl structure on heating to about 760 K, changes to NaCl structure. In other words, increase of temperature decreases the co-ordination number. Pressur e Temp a/2 90° Na+ Cl– a/2 Fig. 5.16. Radii of chloride r+/r– < 0.414 Solid state 205 CsCl NaCl (8 : 8) (6 : 6 ) Structure of ionic crystals Table : 5.5 Types of ionic crystal with description Type AB Brief description Examples Coordination number Number of formula units per unit cell It has fcc arrangement in which Halides of Li, Na, K, Rb, AgF, AgBr, NH4Cl, Na   6 4  ions occupy the corners and Rock salt Cl (NaCl) type face centres of a cube while Na  NH4Br, NH4I etc. ions are present at the body and edge of centres. blende (ZnS) type It has ccp arrangement in which 2 CuCl , CuBr , CuI , AgI , BeS 2 ions form fcc and each Zn ion is surrounded tetrahedrally by S (CaF2) type ions form fcc with each Ca surrounded by 8 F F Caesium chloride (CsCl) type 2+ ions by 4Ca ions ions and each ions. F  4 Na 2O Na   4 U Here negative ions form the ccp arrangement so that each positive ion is surrounded by 4 negative ions and each negative ion by 8 positive ions It has the bcc arrangement with   Cs at the body centre and Cl ions at the corners of a cube or vice versa. Ca 2   8 SrCl 2 , CdF2 , PbF2 D YG Antifluorite type   2 BaF2 , BaCl 2 , SrF2 ID Fluorite It has arrangement in which Ca 2  4 S 2  4 four S 2  ions and vice versa. Type AB2 Zn 2   4 E3 Zinc Cl   6 60 Crystal structure type Cs   8 TlCl, TlBr , TlI and TlCN Cl   8 ST U Any deviation from the perfectly ordered arrangement constitutes a defect or imperfection. These defects sometimes called thermodynamic defects because the number of these defects depend on the temperature. (1) Electronic imperfections : Generally, electrons are present in fully occupied lowest energy states. But at high temperatures, some of the electrons may occupy higher energy state depending upon the temperature. For example, in the crystals of pure Si or Ge some electrons are released thermally from the covalent bonds at temperature above 0 K. these electrons are free to move in the crystal and are responsible for electrical conductivity. This type of conduction is known as intrinsic conduction. The 4 O 2  8 CsCl, CsBr , CsI, CsCN , Defects or Imperfections in solids 4 1 electron deficient bond formed by the release of an electron is called a hole. In the presence of electric field the positive holes move in a direction opposite to that of the electrons and conduct electricity. The electrons and holes in solids gives rise to electronic imperfections. (2) Atomic imperfections/point defects : When deviations exist from the regular or periodic arrangement around an atom or a group of atoms in a crystalline substance, the defects are called point defects. Point defect in a crystal may be classified into following three types. (i) Stoichiometric defects : The compounds in which the number of positive and negative ions are exactly in the ratios indicated by their chemical formulae are called stoichiometric compounds. The defects do not disturb the stoichiometry (the ratio of 206 Solid State (b) Schottky defect : This type of defect when equal number of cations and anions are missing from their lattice sites so that the electrical neutrality is maintained. This type of defect occurs in highly ionic compounds which have high co-ordination number and cations and anions of similar sizes. e.g., NaCl, KCl, CsCl and KBr etc. (a) Metal excess defects due to anion vacancies : A compound may have excess metal anion if a negative ion is absent from its lattice site, leaving a ‘hole’, which is occupied by electron to maintain electrical neutrality. This type of defects are found in crystals which are likely to possess Schottky defects. Anion vacancies in alkali metal halides are reduced by heating the alkali metal halides crystals in an atmosphere of alkali metal vapours. The ‘holes’ occupy by electrons are called F-centres (or colour centres). (b) Metal excess defects due to interstitial cations : Another way in which metal excess defects may occur is, if an extra positive ion is present in an interstitial site. Electrical neutrality is maintained by the presence of an electron in the interstitial site. This type of defects are exhibit by the crystals which are likely to exhibit Frenkel defects e.g., when ZnO is heated, it loses oxygen reversibly. The excess is accommodated in interstitial sites, with electrons trapped in the neighborhood. The yellow colour and the electrical + – + A+ B– ZnOAis A+ B– B– conductivity of Athe non-stoichiometric dueBto these trapped A+ electrons. A+ B– A+ B– A+ B– A+ A– B– B– D YG A+ B+ U ID (c) Frenkel defect : This type of defect arises when an ion is missing from its lattice site and occupies an interstitial position. The crystal as a whole remains electrically neutral because the number of anions and cations remain same. Since cations are usually smaller than anions, they occupy interstitial sites. This type of defect occurs in the compounds which have low co-ordination number and cations and anions of different sizes. e.g., ZnS, AgCl and AgI etc. Frenkel defect are not found in pure alkali metal halides because the cations due to larger size cannot get into the interstitial sites. In AgBr both Schottky and Frenkel defects occur simultaneously. deficiency of metal ions. 60 (a) Interstitial defect : This type of defect is caused due to the presence of ions in the normally vacant interstitial sites in the crystals. either due to the presence of excess metal ions or E3 numbers of positive and negative ions) are called stoichiometric defects. These are of following types, A+ A+ B– B– Fig. 5.18. Schottky defect A+ B– B– A+ B– A+ B– A+ B– A+ B– A+ A+ B– A+ B– A+ e– A+ B– A+ B– Fig. 5.19. Frenkel defect Fig. 5.20. Metal excess defect due to extra cation Fig. 5.21. Metal excess defect due to anion vacancy Consequences of Schottky and Frenkel defects ST U Presence of large number of Schottky defect lowers the density of the crystal. When Frenkel defect alone is present, there is no decrease in density. The closeness of the charge brought about by Frenkel defect tends to increase the dielectric constant of the crystal. Compounds having such defect conduct electricity to a small extent. When electric field is applied, an ion moves from its lattice site to occupy a hole, it creates a new hole. In this way, a hole moves from one end to the other. Thus, it conducts electricity across the crystal. Due to the presence of holes, stability (or the lattice energy) of the crystal decreases. (ii) Non-stoichiometric defects : The defects which disturb the stoichiometry of the compounds are called non-stoichiometry defects. These defects are Consequences of Metal excess defects The crystals with metal excess defects are generally coloured due to the presence of free electrons in them. The crystals with metal excess defects conduct electricity due to the presence of free electrons and are semiconductors. As the electric transport is mainly by “excess” electrons, these are called n-type (n for negative) semiconductor. The crystals with metal excess defects are generally paramagnetic due to the presence of unpaired electrons at lattice sites. When the crystal is irradiated with white light, the trapped electron absorbs some component of white light for excitation from ground state to the excited state. This gives rise to colour. Such points are called Fcentres. (German word Farbe which means colour) such excess ions are accompanied by positive ion Solid state 207 vacancies. These vacancies serve to trap holes in the same way as the anion vacancies trapped electrons. The colour centres thus produced are called V-centres. conductors. These are further of two types; Metallic conductors and electrolytic conductors. The electrical conductivity of these solids is high in the range (c) Metal deficiency defect by cation vacancy : In this a cation is missing from its lattice site. To maintain electrical neutrality, one of the nearest metal ion acquires two positive charge. This type of defect occurs in compounds where metal can exhibit variable valency. e.g., Transition metal compounds like NiO, FeO, FeS etc. 10 4  10 6 ohm 1 cm 1. Their B– A + B– – A+ B– B– A+ +2 – B A A+ B– A+ Metal having higher charge 60 (iii) Semiconductors : The solids whose electrical conductivity lies between those of conductors and insulators are called semiconductors. The conductivity of these solid is due to the presence of impurities. e.g. Silicon and Germanium. Their conductance increase with increase in temperature. The electrical conductivity of these solids is increased by adding impurity. This is called Doping. When silicon is doped with P (or As, group 5th elements), we get n-type semiconductor. This is because P has five valence electrons. It forms 4 covalent bonds with silicon and the fifth electron remains free and is loosely bound. This give rise to n-type semiconductor because current is carried by electrons when silicon is doped with Ga (or in In/Al, group 3rd elements) we get p-type semiconductors. D YG Fig. 5.22 B Cation vacancy of these solids is very low i.e., 10 12  10 22 ohm 1 cm 1. ID B– (ii) Insulators : The solids which do not allow the current to pass through them are called insulators. e.g., rubber, wood and plastic etc. the electrical conductivity U A+ increase in temperature. E3 (d) By having extra anion occupying interstitial site : In this, an extra anion is present in the interstitial position. The extra negative charge is balanced by one extra positive charge on the adjacent metal ion. Since anions are usually larger it could not occupy an interstitial site. Thus, this structure has only a theoretical possibility. No example is known so far. conductance decrease with Consequences of metal deficiency defects + Due to the movement of electron, an ion A changes to A+2 ions. Thus, the movement of an electron from A+ ion is an apparent of positive hole and the substances are called p-type semiconductor (iii) Impurity defect : These defects arise when foreign atoms are present at the lattice site (in place of host atoms) or at the vacant interstitial sites. In the ST U former case, we get substitutional solid solutions while in the latter case, we get interstitial solid solution. The formation of the former depends upon the electronic structure of the impurity while that of the later on the size of the impurity. Properties of solids Some of the properties of solids which are useful in electronic and magnetic devices such as, transistor, computers, and telephones etc., are summarised below, (1) Electrical properties : Solids are classified into following classes depending on the extent of conducting nature. (i) Conductors : The solids which allow the electric current to pass through them are called Superconductivity : When any material loses its resistance for electric current, then it is called superconductor, Kammerlingh Onnes (1913) observed this phenomenon at 4K in mercury. The materials offering no resistance to the flow of current at very low temperature (2-5K) are called superconducting materials and phenomenon is called superconductivity. Examples, Nb 3 Ge alloy (Before 1986) La1.25 Ba 0.15 CuO 4 (1986) YBa 2 Cu 3 O7 (1987) Following are superconductivity, (a) Electronics, supermagnets, the important applications of (b) (c) Aviation transportation, transmission Building (d) Power “The temperature at which a material enters the superconducting state is called the superconducting transition temperature, (Tc ) ”. Superconductivity was also observed in lead (Pb) at 7.2 K and in tin (Sn) at 208 Solid State (TMTSF)2PF6, where TMTSF is tetra methyl tetra selena fulvalene. 3.7K. The phenomenon of superconductivity in other materials such as polymers and organic crystals. Examples are (2) Magnetic properties : Based on the behavior of substances when placed in the magnetic field, there are classified into five classes. (SN)x, polythiazyl, the subscript x indicates a large number of variable size. Table : 5.6 Magnetic properties of solids Alignment of Magnetic Dipoles Diamagnetic Feebly repelled by the magnetic fields. Non-metallic elements (excepts O2, S) inert gases and species with paired electrons are diamagnetic Paramagnetic Attracted by the magnetic field due to the presence of permanent magnetic dipoles (unpaired electrons). In magnetic field, these tend to orient themselves parallel to the direction of the field and thus, produce magnetism in the substances. Permanent magnetism even in the absence of magnetic field, Above a temperature called Curie temperature, there is no ferromagnetism. Insulator O2 , Cu 2  , Fe 3  , TiO, Electronic At least one unpaired electron Dipoles are aligned in the same direction Fe, Ni, Co, CrO2 MnO, MnO2, Mn2O, FeO, Fe2O3; NiO, Cr2O3, CoO, Co3O4, Ferrimagnetic This arises when there is net dipole moment Fe3O4, ferrites D YG U This arises when the dipole alignment is zero due to equal and opposite alignment. U ST appliances Ti2O3 , VO, VO2 , CuO Antiferromagne tic (3) Dielectric properties : A dielectric substance is that which does not allow the electricity to pass through them but on applying the electric field, induced charges are produced on its faces. In an insulator, the electrons are strongly held by the individual atoms. When an electric field is applied polarization takes place because nuclei are attracted to one side and the electron cloud to the other side. As a result, dipoles are created. Such type of crystals shows the following properties, (i) Piezoelectricity : In some of the crystals, the dipoles may align themselves is an ordered way so as to give some net dipole moment. When mechanical stress is applied in such crystals so as to deform them, electricity is produced due to the displacement of ions. The electricity thus produced is called piezoelectricity and the crystals are called piezoelectric crystals. Examples, Quartz, Rochelle’s salt ( sod. pot. tartarate). Piezoelectric crystals act as mechanical-electric transducer. These crystals are used as pick-ups in record players where they produce electric signals by application of pressure. Applications TiO2, V2O5, NaCl, C6H6 (benzene) ID Ferromagnetic All paired electrons Examples 60 Description E3 Properties CrO2 is used in audio and video tapes – – (ii) Pyroelectricity : On heating, some polar crystals produce a small electric current. The electricity thus produced is called pyroelectircity. (iii) Ferroelectricity : In some of the piezoelectric crystals, a permanent alignment of the dipoles is always there even in the absence of the electric field, however, on applying field the direction of polarization changes. This phenomenon is called ferroelectricity and the crystals as ferroelectric crystal. Example, Potassium hydrogen phosphate (KH 2 PO4 ) , Barium titanate (BaTiO 3 ). (iv) Antiferroelectricity : In some crystals, the dipoles in alternate polyhedra point up and down so that the crystals does not possess any net dipole moment. Such crystals are said to be antiferroelectric. Example, Lead zirconate Ferroelectrics are used in the (PbZrO3 ). preparation of small sized capacitors of high capacitance. Pyroelectric infrared detectors are based on such substances. These can be used in transistors, telephone, computer etc. Solid state 5. 209 (a) Molecular crystal (b) Ionic crystal (c) Covalent crystal (d) Metallic crystal Value of heat of fusion of NaCl is (a) Very low  The reverse of crystallization is the melting of the (b) Very high solid. (c) Not very low and not very high  The slower the rate of formation of crystal, the (d) None of the above 6.  The hardness of metals increases with the number of electrons available for metallic bonding. Thus Mg is harder than sodium. Piezoelectric crystals are used in (a) TV (c) Record player 7. [AFMC 1997] which are not only similar in their crystalline form, but also possess an equal number of atoms united in the similar manner. The existence of a substance in more than one crystalline form is known as polymorphism. E3 (a) Diamond is a good conductor of electricity (b) Diamond is soft (c) Diamond is a bad conductor of heat (d) Diamond is made up of C, H and O NaCl is an example of ID 8. [AIIMS 1991] (a) Gases and liquids have viscosity as a common property (b) The molecules in all the three states possess random translational motion (c) Gases cannot be converted into solids without passing through the liquid phase U (d) Solids and liquids have vapour pressure as a common property A pure crystalline substance, on being heated gradually, first forms a turbid looking liquid and then the turbidity completely disappears. This behaviour is the characteristic of substances forming [BHU 2000] ST 2. (a) Isomeric crystals (b) Liquid crystals (c) Isomorphous crystals 3. (d) Allotropic crystals Which of the following is ferroelectric compound [AFMC 1997] 4. (a) Covalent solid (b) Ionic solid (c) Molecular solid (d) Metallic solid U The three states of matter are solid, liquid and gas. Which of the following statement is/are true about them D YG 1. (a) BaTiO 3 (b) K 4 [Fe(CN )6 ] (c) Pb 2 O 3 (d) PbZrO3 Solid CO 2 is an example of (d) Freeze Which of the following is true for diamond  Isomorphism is applied to those substances Properties and Types of solid (b) Radio 60 bigger is the crystal.