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2 MODERN PUBLISHERS (Producers of Quality Text & Competition Books)

3 UR ADDRESSES IN INDIA MBD PRINTOGRAPHICS (P) LTD. Ram Nagar, Industrial Area, Gagret, Distt. Una (H.P.)

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6 16 THE SOLID STATE Solids have definite volumes and definite shapes. The particles in solids are held together by strong forces and the solid state is the most ordered state. In terms of kinetic molecular model, solids have regular order of constituent particles (atoms, ions or molecules). These particles are held together by fairly strong forces and therefore, they are present at fixed positions. IMPORTANT TERMS, FORMULAE AND FACTS CLASSIFICATION OF SOLIDS Solids can be classified into two classes: 1. Crystalline solids The substances whose constituents are arranged in a definite orderly arrangement are called crystalline solids. For example, elements like copper, silver, iron, sulphur, phosphorus, iodine, sodium chloride, zinc sulphide, quartz, etc., are crystalline solids. The crystalline substances have definite regular geometry have sharp melting points have physical properties (electrical conductivity, thermal conductivity, refractive index, mechanical strength etc.) different in different directions i.e. crystalline substances are anisotropic. can be cleaved along definite planes. 2. Amorphous substances The substances whose constituents are not arranged in an orderly arrangement are called amorphous substances. e.g. glass, rubber, quartz glass, plastics, etc. Crystalline substances exhibit anisotropy i.e. they have different physical properties in different directions. Amorphous substances exhibit isotropy i.e. they have similar properties in all directions. Amorphous substances are also called PSEUDO SOLIDS. 16/1

7 16/2 MODERN S abc OF OBJECTIVE CHEMISTRY (NEET) The amorphous solids do not have regular arrangement of constituents do not have sharp melting points have physical properties (electrical conductivity, thermal conductivity, refractive index, mechanical strength, etc.) same in all directions i.e. amorphous substances are isotropic. cannot be cleaved along definite planes. It may be noted that some amorphous solids have some orderly arrangement but it is not extended to more than a few Angstrom units. Thus, amorphous solids are said to have short range order. On the other hand, crystalline substances are said to have long range order. TYPES OF CRYSTALLINE SOLIDS The crystalline solids may be classified into (i) molecular, (ii) ionic, (iii) covalent and (iv) metallic crystals. Their important characteristics are summed up in the following table: Table 1 : Important characteristics of crystals Types of Crystals Characteristics Molecular Ionic Covalent Metallic Constituent Small Positive and Atoms Positive ions in a particles molecules negative ions sea of electrons Binding Van der Waals Strong electro- Covalent Metallic bonds forces forces static forces bond forces (electric attraction between +ve ions and electrons). Properties Soft, low melting Hard and brittle, Very hard, Soft to hard, point, volatile high m.p., poor high m.p., poor moderate to good insulators, conductors of heat conductors of high m.p., good low heats of fusion and electricity, very heat and electri- conductors, metallic high heats of fusion city, high heats lustre, ductile and of fusion malleable, moderate heats of fusion Examples Solids CO 2, H 2,I 2, Salts like NaCl, Diamond, SiC, Common metals ice, SO 2, CCl 4 KNO 3, LiF, BaSO 4 quartz, SiO 2 (Cu, Na, Fe) and some alloys Space Lattice and Unit Cell Fig. 1. Three dimensional lattice UNIT CELL AND SPACE LATTICE Space Lattice The arrangement of points showing how constituent particles (atoms, ions or molecules) of a crystal are arranged at different positions in a three dimensional space is called space lattice. Unit Cell The smallest repeating unit in space lattice which when repeated over and over again gives the crystal of the given substance is called unit cell. The unit cell is characterized by the distances a, b and c along the three edges of the unit cell and the angles α, β and γ between the pair of edges. TYPES OF UNIT CELLS AND CRYSTAL SYSTEMS In all, there are seven types of basic or primitive unit cells or crystal systems. These are given in Table 2.

8 THE SOLID STATE 16/3 Table 2 : Seven types of basic crystal systems System Axial distance Axial angles Examples Cubic a = b = c α = β = γ = 90 NaCl, KCl, zinc blende, Cu, Ag Tetragonal a = b c α = β = γ = 90 White tin, SnO 2, TiO 2 Orthorhombic a b c α = β = γ = 90 Rhombic sulphur, KNO 3, PbCO 3 Monoclinic a b c α = γ = 90, Monoclinic sulphur, β 90 CaSO 4. 2H 2 O Rhombohedral a = b = c α = β = γ 90 Calcite, quartz, As, Sb or Trigonal Triclinic a b c α β γ = 90 K 2 Cr 2 O 7. H 3 BO 3 Hexagonal a = b c α = β = 90, Graphite, ZnO, CdS γ = 120 In addition to above seven primitive unit cells, there are non-primitive unit cells having points at other positions also. For example, a cubic system may be simple (or primitive), body centred cubic and face centred cubic as : THREE CUBIC SYSTEMS There are three common types of cubic systems: 1. Simple or primitive having points at all the corners of the unit cell. 2. Body centred cubic having points at all the corners as well as at the centre of the cube. 3. Face centred cubic having points at all the corners as well as at the centre of each face. It may be noted that there is another type of non-primitive unit cell known as end centred unit cell. This has points at all the corners and at the centres of two end faces. All systems do not have end centred unit cells. Only orthorhombic and monoclinic systems have end centred unit cells. BRAVAIS LATTICES If all types of space lattices are counted, there are fourteen in all and these are known as Bravais lattices. These are shown in Fig. 2. CLOSE PACKING OF PARTICLES There are two common types of close packing of particles in a crystalline substance : Hexagonal close packing. This type of packing is referred to as ABABA... arrangement. Cubic close packing. This type of packing is referred to as ABCABCA... arrangement. In both types of packing 74% of the available space is occupied by spheres. INTERSTITIAL SITES Two important interstitial sites are: (i) Tetrahedral site. When a sphere in the second layer is placed above three spheres which are touching one another, a tetrahedral site is formed. (ii) Octahedral site. This type of site is formed at the centre of six spheres and is produced by two sets of equilateral triangles which point in opposite directions. COORDINATION NUMBER AND RADIUS RATIO Coordination number The number of nearest neighbours with which a given sphere is in contact is called the coordination number. The coordination number in hcp and ccp arrangement is 12. Contribution of atoms in a unit cell Atoms at corners = 1 8 Atoms at edges = 1 4 Atoms in the face = 1 2 Atoms in the body = 1 No. of atoms in different unit cells Simple cubic = 1 Body centred cubic = 2 Face centred = 4 (fcc or ccp) hcp = 6 There are two tetrahedral sites for each sphere. There is one octahedral site for each sphere.

9 16/4 MODERN S abc OF OBJECTIVE CHEMISTRY (NEET) Cubic a = b = c α = β = γ = 90 c b a Primitive Body-centred Face-centred Tetragonal a = b c α = β = γ = 90 Primitive Body-centred Orthorhombic a b c α = β = γ = 90 Primitive Body-centred Face-centred End-centred Monoclinic a b c α = γ = 90 β 90 Primitive End-centred Hexagonal a = b c α = β = 90 γ = 120 Primitive Rhombohedral a = b = c α = β = γ 90 Triclinic a b c α β γ 90 There are seven types of crystal systems. There are 14 space lattices, called Bravais lattices. Primitive Primitive Fig. 2. Fourteen Bravais Lattices Radius ratio The ratio of the radius of the cation to the radius of the anion is called radius ratio. This is very important in determining the structure of ionic solids. The limiting radius ratios in different crystals and their coordination numbers are given in Table 3.

10 THE SOLID STATE 16/5 Table 3 Radius ratio Possible coordination Structural Examples (r + /r ) number arrangement Tetrahedral ZnS Octahedral NaCl Cubic CsCl 1 12 Close packing Metals Relationship between nearest neighbour distance (d) and radius of atom (r) (for crystals of pure elements) and edge of unit cells (a) For simple cubic d = a r = a/2 For face centred cubic For body centred cubic DENSITY OF A CRYSTAL d = d = a r = a r = Density of a crystal can be calculated by knowing the edge length of the unit cell. ZM Density = g cm a 3 3, N where a = length of the edge of unit cell in cm Z = number of atoms per unit cell M = atomic mass of element or formula mass of the compound N = Avogadro number STRUCTURES OF SIMPLE SUBSTANCES In simple ionic solids ccp or hcp types of arrangement are generally present. The large ions (anions) adopt these arrangements and the smaller ions (cations) occupy interstitial sites. The summary of some common crystals is given below: a a Packing Efficiency. It is the percentage of total space filled by the particles. Structure Packing efficiency 1. Hexagonal closed packed (hcp) 74% 2. Cubic close packed (ccp) or face centred cubic (fcc) 74% 3. Body centred cubic (bcc) 68% 4. Simple cubic 52.4% If a is in pm, then Edge length = a pm = a m = a cm and a 3 = a cm 3 Z is the number of atoms per unit cell or formula units per unit cell. e.g. for fcc, Z = 4 for bcc, Z = 2 for simple cubic, Z = 1 Some Common types of structures of ionic compounds Compound Description Coordination number Other Examples NaCl ccp arrangement of Cl, Na + Na + = 6 Li, Na, K in all the octahedral sites Cl = 6 halides, AgCl, AgBr, MgO, CaO ZnS ccp arrangement of S 2, Zn 2+ Zn 2+ = 4 BeS, CuCl, (Zinc blende) in alternative tetrahedral sites S 2 = 4 CuBr, CuI CsCl Simple cubic arrangement of Cs + = 8 CsBr, CsI Cl, Cs + in cubic sites Cl = 8 CaF 2 ccp arrangement of Ca 2+, F Ca 2+ = 8 SrF 2, BaF 2 (Fluorite structure) occupy all tetrahedral sites F = 4 Na 2 O ccp arrangement of O 2, Na + Na + = 4 Li 2 O, K 2 S (Antifluorite structure) occupy all tetrahedral sites O 2 = 8

11 16/6 MODERN S abc OF OBJECTIVE CHEMISTRY (NEET) POINT DEFECTS IN CRYSTALS Fig. 3. Ideal crystal A + B Ideal crystals with perfect arrangement of constituents are found only at 0 K. Above this temperature, all crystalline solids have some defects in the arrangement of its unit cells. An ideal crystal of A + B type may be represented as shown in Fig. 3. Defects in the crystals may give rise to (A) Stoichiometric and (B) Non-stoichiometric structures. (A) Stoichiometric structures The compound A + B is stoichiometric if it contains equal number of atoms A + and B as suggested by the chemical formula of the compound. There are two types of defects in stoichiometric structures : (i) Schottky Defect. This defect consists of vacancies at cation sites and equal number of vacancies at anion sites. It is predominant in compounds with high coordination number and where the ions are of similar size. (i) Schottky defect (ii) Frenkel defect Fig. 4 Schottky and Frenkel defects in crystals (ii) Frenkel Defect. This defect consists of vacancies at cation sites in which the cation move to another position in between two layers called interstitial sites. This defect is most predominant in compounds which have low coordination number and ions of different sizes. (B) Non-stoichiometric compounds. The compounds in which the ratio of the number of atoms of A + to the number of atoms of B does not correspond to a simple whole number as suggested by the formula are called non-stoichiometric compounds. The non-stoichiometric defects are of two types : 1. Metal excess defects. In these defects, positive ions are in excess and arise due to : (i) Anion vacancies. Vacancies at anion sites and their electrons remain trapped. The electrons trapped in anion vacancies are called F-centres. The electrons trapped in anion vacancies are called F-centres because they impart colour to crystals. For example. excess of Na in NaCl imparts yellow colour, excess of K in KCl imparts violet (lilac) colour, excess of Li in LiCl makes it appear pink. Electron remains trapped in anion vacancy Fig. 5. Metal excess defects due to anion vacancy

12 THE SOLID STATE 16/7 (ii) Cation occupying interstitial sites. Excess cations are present in The common example of this type interstitial sites and equal number of electrons trapped in neighbouring of defect is zinc oxide. It is white interstitial sites. in colour at room temperature. On heating, it loses oxygen reversibly at high temperature and turns yellow in colour. The crystals with metal excess defect are n-type semiconductors. Fig. 6. Metal excess defects due to extra cation 2. Metal deficient defects. This arises due to (i) Cation vacancies. Vacancies at cation sites and the extra negative charge is balanced by extra charge (higher oxidation state) of equal number of some cations. Metal deficient defect is found in ferrous oxide, ferrous sulphide, nickel oxide, etc. These crystals acquire metallic lustre. 2+ Cation vacancy Metal acquiring higher charge Because of metallic lustre of some minerals of iron pyrites, they shine like gold and have been nick named as fool s gold. Fig. 7. Metal deficient defect due to cation vacancy (ii) Anion occupying interstitial sites. Excess anions are present in interstitial sites and the corresponding increase in negative charge is balanced by oxidation of equal number of cations to higher oxidation states. Crystals with metal deficient defects are p-type semiconductors. Fig. 8. Metal deficient defect due to extra anion IMPURITY DEFECTS These defects in ionic crystals arise due to the presence of some impurity ions at the lattice sites (in place of host ions) or at the vacant interstitial sites. For example, if molten NaCl containing a little amount of SrCl 2 is allowed to crystallize, some of the sites of Na + ions are occupied by Sr 2+ ions. For each Sr 2+ ion introduced, two Na + ions are removed to maintain electrical neutrality. One of these lattice site is occupied by Sr 2+ ion and the other remains vacant. Therefore, these vacancies result in increased electrical conductivity of the solid. Similar defect and behaviour is observed when CdCl 2 is added to AgCl.

13 16/8 MODERN S abc OF OBJECTIVE CHEMISTRY (NEET) Introduction of a cation vacancy in NaCl by substitution of Na + by Sr 2+. ELECTRICAL PROPERTIES OF SOLIDS Solids exhibit an interesting range of variation of electrical conductivities extending from to 10 7 ohm 1 m 1. On the basis of electrical conductivity, solids can be classified into three types: (i) Conductors. The solids which allow the passage of electric current Fig. 9. Impurity defect. Range of conductivity Conductors : 10 4 to 10 7 ohm 1 m 1 Semiconductors : 10 6 to 10 4 ohm 1 m 1 Insulators : to ohm 1 m 1 With increase in temperature electrical conductivity of metals decreases semiconductors increases. are called conductors. They have conductivities in the range 10 4 to 10 7 ohm 1 m 1. For example, metals have conductivities of the order of 10 7 ohm 1 m 1 and hence are the best conductors of electricity. Conductors are of two types: (a) Metallic conductors are those which allow the electricity to pass through them without undergoing any chemical change. For example, copper, silver etc. Metals conduct electricity in solid as well as in molten state. In metallic conductors, the conductance is due to the movement of electrons. (b) Electrolytic conductors are those which allow the electricity to pass through them by undergoing chemical change. The conduction in ionic solids is due to the migration of ions or other charged particles under the applied field. (ii) Insulators. The solids which do not allow the passage of electric current through them are called insulators. They have very very low conductivities ranging between to ohm 1 m 1. For example, wood, sulphur, phosphorus, rubber etc. (iii) Semi-conductors. The solids whose conductivity lies between those of typical metallic conductors and insulators are called semiconductors. The semi-conductors have conductivity in the range of 10 6 to 10 4 ohm 1 m 1. The conductivity of semi-conductors is due to the presence of impurities and defects. Conduction of electricity in metals Metals conduct electricity in the solid as well as in molten state. The conductivity of metals depends upon the number of valence electrons available per atom. The atomic orbitals of metal atoms form molecular orbitals which are close in energy to each other and form a band. If this band is partially filled or it overlaps with a high energy vacant band (called conduction band), then electrons flow easily under an applied electric field and the metal shows conductivity. If the gap between filled valence band and the next higher unoccupied band (conduction band) is large, electrons cannot jump to it and such substance has very small conductivity and it behaves as an insulator. Fig. 10. The gap between valence band and conduction band is small in case of semiconductors. Therefore, some electrons may jump to conduction band and show some conductivity. The electrical conductivity of semiconductors

14 THE SOLID STATE 16/9 increases with rise in temperature because more electrons can jump to conduction band. Silicon and germanium show this type of behaviour and are called intrinsic semiconductors. The conductivity of these intrinsic semiconductors is very low to be of practical use. Their conductivity can be increased by introducing an appropriate amount of suitable impurity. This process is called doping. The conductivity of Si or Ge increases drastically by doping it either with electron rich impurities or with electron deficit (or acceptor) impurities. For example, when Ge is doped with some electron rich atoms such as P or As containing five valence electrons, these will randomly replace Ge atoms. Four of the electrons in P or As will form four covalent bonds with surrounding Ge atoms and the fifth electron will remain free. The extra electron will be able to conduct and this type of conduction is called n-type conduction. On the other hand, when Ge is doped with electron deficit atoms such as Ga or In containing three valence electrons, the atoms of Ga or In will replace Ge atoms. Each In or Ga atom will use its three electrons for forming three covalent bonds with the neighbouring Ge atoms and the place for fourth bond will remain missing and is called electron vacancy or hole. Such holes can move through the crystal like a positive charge giving rise to conductivity. This type of conduction is called p-type conduction. Fig. 11. Arsenic doped germanium semiconductor Fig. 12. Indium doped germanium semiconductor MAGNETIC PROPERTIES Substances can be divided into the following types depending upon their response to the magnetic fields : 1. Diamagnetic substances. The substances which are weakly repelled by the magnetic fields are known as diamagnetic substances. For example, NaCl, benzene, TiO 2, V 2 O 5, etc. 2. Paramagnetic substances. The substances which have permanent magnetic dipoles and are attracted by magnetic field are known as paramagnetic substances. These consist of atoms, ions or molecules having unpaired electrons. The common examples are O 2, Cu 2+, Fe 3+, TiO, Ti 2 O 3, VO, CuO, etc. They lose their magnetism in the absence of magnetic field. 3. Ferromagnetic substances. These substances are attracted by the magnetic field and show permanent magnetism even when the magnetic field is removed. Once such a material is magnetised, it remains permanently magnetised. Iron is the most common example. Other examples are cobalt, nickel, CrO 2, etc. In this case, the magnetic moments are aligned in the same direction. 4. Antiferromagnetic substances. In these substances, the alignment of the magnetic moments is in a compensatory way so as to give zero net magnetic moment. For example, MnO, MnO 2, FeO, Fe 2 O 3, NiO, Cr 2 O Ferrimagnetic substances. These are the substances in which the magnetic moments are aligned in parallel and anti-parallel directions in Fig. 13. Alignment of magnetic moments in (a) ferromagnet (b) antiferromagnet (c) ferrimagnet

15 16/10 MODERN S abc OF OBJECTIVE CHEMISTRY (NEET) unequal numbers giving a net magnetic moment. For example, Fe 3 O 4, ferrites of the formula M 2+, Fe 2 O 4, where M = Mg, Cu, Zn, etc. X RAY DIFFRACTION STUDIES X-ray studies have helped to know the arrangement of atoms, ions or molecules in crystals. The phenomenon of X-rays by the crystals was studied by W.L. Bragg and W.H. Bragg. By analysing the diffraction patterns, Bragg deduced a simple relationship between the distance between the layers, the wavelength of X-rays used and the angle of diffraction. This relation is known as Bragg equation and is given as: nλ =2d sin θ, where 2 θ = angle made by a diffracted X-rays beam with the direction of incident beam. λ = wavelength of X rays used d = distance between the planes of the constituent particles in the crystal. n = positive integer (1, 2, 3..., etc.) which stands for serial order of diffracted beams. Using Bragg's law, we can calculate the distance between rows of constituent particles in a crystal. These distances are characteristic of a crystal and depend upon the size and geometry or arrangement of these particles. STRUCTURES OF METALS The crystal structures adopted by some metallic elements at 25 C and 1 bar pressure are : Crystal Structure hcp fcc bcc Primitive cubic Elements Be, Cd, Co, Mg, Ca, Ti, Zn Ag, Al, Au, Ca, Cu, Ni, Pb, Pt Ba, Cr, Fe, Ir, alkali metals Po Example 1. Which of the following statement is not true about crystalline solids? (a) Polar molecular solids have higher enthalpies of vaporisation than those of non-polar molecular solids. (b) Graphite, though covalent solid, is a good conductor of electricity. (c) Ionic solids are conductors in molten state. (d) Non-polar molecular solids have London forces between the constituents and have higher melting points than polar molecular solids. Strategy/Solution : It is a conceptual question and we are to select the wrong statement. Choices (a), (b) and (c) are true but choice (d) is not true. The non polar molecular solids have London forces or dispersion forces between their molecules. These are weak forces and therefore, the solids have low melting points. On the other hand, polar solids have strong dipole-dipole forces between their molecules and have melting points higher than those in non-polar solids. Correct Answer: (d) Example 2. A spinel mineral has the formula MgAl 2 O 4. In this O 2 ions are present in ccp arrangement, Mg 2+ ions occupy the tetrahedral voids while Al 3+ ions occupy the octahedral voids. The percentage of tetrahedral

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