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3, SOLID STATE, AND THEIR CLASSIFICATION, :4 icis defined as that form of matter which possesses rigidity and, A solid defined, hence possesses a, definite, shapeanda definite volume. The solid are divided into two types, namely, crystalline and, amorphous., LIDS, , 31., , a, , Crvstalline Solids. A, , solid is said to be, , crystaline ij the various ions,, , atoms or molecules of, ., sOlid is made up, are arranged in a definite geometric pattern within the solid., All solid, ents and compounds exist in this form. The crystalline solids are further classified into a number of, , elemo, , hich have been discussed in sec. 3.3 along with examples of each type., , 2. Amorphous Solids. A solid is said to be amorphous if the constituent ions, atoms or molecules, f the, , substance, , are not, , arranged, , in any, , regular fashion (although it possesses rigidity,, , definite shape, and definite volume), e.8. glasS,pitch,rubber, polymers of high molecular mass etc. In fact, the amorphous, substances are not regarded as true solids; rather they are considered to be highly supercooled liquids of, , very high viscosity., 3.2. POINTS OF DIFFERENCE BETWEEN CRYSTALLINE AND AMORPHOUS sOLIDS, ) Arrangement of particles. In a crystalline solid, the constituent particles are arranged in a, definite geometric pattern whereas in an amorphous solid, they are not arranged in any regular fashion., , (i) Melting points. The crystalline substances possess sharp melting points whereas the amorphous, , substances melt gradually over a temperature range., , (in) Isotropy and Anisotropy. In case of amorphous substances,, , properties like electrical conductivity, refractive index, thermal, etc. are identical in all directions just like in case of gases, , O, O/0, , CApansion, This property is called isotropy and the substances showing, 0s hiquids., property are called isotropic. On the other hand, in case of, ne, , called, , Opic in nature, the crystalline substances are anisotropie. 1ne, due to the, xhibited by crystalline substances is obviously, , faP, ct that, , O, , O, , have different, substances, the properties mentioned above, , v4ues in different directions. This type of behaviour is are, behaviour, LLSotropy and the substances exhibiting this type ofsubstances, are, nsotropic. * Thus, whereas amorphous, , in making measurements in different directions, different, , types of particles, , fall, , on, , the way,, , as shown, , in, , Fig., , 3.1, , or, , O, , crystals, , are, , have the, isotropic because they, , O, , 3/1, , O, , O, , O, , FIGURE 3.1., , Anisotropy exhibited by, crystalline substances., , the, , same, , O, O, , arangement of articles is different., Cubic, , O, , structurc u a

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3/2, , Pradeep's PHYSICAL CHEMISRY Vol. n, , (iv) Regular and irregular, , cut. A, , crystalline solid on being cut with a sharp-edged, knife, , gives, , a, , clean, , cleavage whereas, , an, , amorphous solid undergoes an iregular breaking, as shown in Fig. 3.2., b, , FIGURE 3.2., , (v) Cooling curves. When a molten, , Cutting of solids, , crystalline solid is cooled and temperature, , gives a clean cleavage, (a) A crystalline solid, solid gives an irregular cut,, (b) An amorphous, , is plotted against time, the cooling curve, , obtained has breaks at the points where, solidifcation, , starts, , and, , where, , the, , solidifcation is complete (Fig. 3.3). The heat, evolved, , during, , temperature, , solidifcation, , constant., , keeps, , BSOLIDMELT, , SOLID, , amorphous solid gives a smooth cooling, , SOLIDIFICATION, , STARTS, , curve without any break., , The main points of difference between, , crystalline and amorphous, , COMPLETE, , the, , molten, , Cooling of a, , SOLIDIFICATION IS, , MELT, , TIME, , solids may be, , FIGURE, , |Cooling curve, , summed up as follows:, , of, , 3.3., a, , k, , molten crystalline solid, , TABLE 3.1. Comparison of characteristics of crystalline and amorphous solids, Amorphous solid, , Crystalline solid, 1., , The constituent particles are arranged in a, , regular fashion containing short range as, , 1. The constituent particles are not arranged in|, , any regular fashion. There may be at the most, , well, , some short range order only., , as long range order., , 2. They melt over a range of temperature., , 2. They have sharp melting points., , 3. They are anisotropic, i.e., properties like | 3. They are isotropic, i.e., properties like, electrical conductivity, thermal expansionetc.,, electrical conductivity, thermal expansion, etc., have different values in different directions., have same value in different directions (just, as in case of, gases and liquids)., 4. They undergo an irregular cut., 4 They undergo a clean cleavage., , 5. Cooling curves of molten solids have breaks., , 5. Cooling curves do not have breaks., , a * * w w w .w, * w., , wwwwww.wwwmowwmwm, , wwww, , Thus, to see that the given solid is crystalline in nature, it mustexhibit the following characteristics, , (i) Possess a definite geometry, , (iüi) Exhibit anisotropy, 3.3., , CLASSIFICATION, , (i) Possess a sharp melting point, (iv) Should give a clean cleavage., , OF CRYSTALLINE, , sOLIDS, , the lattice sites and hence the type of binding, Based upon the type of constituent particles occupying, are classified into the following different types, forces, the various crystalline solids

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3/3, ieCrystals., In, these, crystals,, the, constituent, particles, occupying, the, lattice, points, are, the, [onicCrystals. In, , S O L I D, S T A T E, , 1., , Nat and Cl ions in case of NaCl crystal). These ions are held, , (e.g.,, together bv, negative, posie and, electrostaticforces of attraction. Some of the important characteristics of these crystals are as, positive, ions, , follows, , Because of strong electrostatic forces of attraction existing among the ions, they have high, melting and boiling points., in They are good conductors of electncity in the molten state or in the solution (but not in the, , crystalline state where the ions are not free to move)., , GThey are soluble in polar solvents but insoluble in non-polar solvents., G)Because of strong electrostatic forces of attraction, the ions are closely packed and hence the, ionic crystals are hard. However, they are brittle because the stability of the, crystals depends, upon preservation of their geometric pattern., , 2. Molecular Crystals. The constituent particles occupying the lattice points in this case are the, , molecules. The intermolecular forces holding the molecules together in the crystal lattice are the weak van, der Waals forces. In case of polar molecules, (e.g., HCI, H,O0,, NH, etc., these van der Waals forces are, the dipole-dipole attractions as shown in Fig. 3.4 (a). In case of, non-polar molecules (e.g., H,, CI,, CH,, etc.) the van der Waals forces are the London dispersion forces., These forces are believed to arise due to, momentary dipole produced as a result of distortion of the, electron cloud of one molecule which produces an induced, dipole in the other molecule as shown in Fig., 3.4. (b). These have already been discussed in unit 2., HELIUM ATOM-1, , HELIUM ATOM-2, , C, FORCE OF, , ATTRACTION, , (LONDON-, , MOMENTARY DIPOLE, , FORCES), , b, , FIGURE, , (a), , INDUCED DIPOLE, , Ek, , Dipole-dipole attractions (b) London dispersion forces., The main, characteristics of the molecular crystals are as follows:, , AS the van der Waals forces are much weaker than the electrostatic forces existing in ionic erystals,, , C, , molecular crystals are soft and, , eny, present., , do not, , conduct, , have low melting and boiling points., , electricity in the solid or liquid state or in solution as there are no ions, , Cesolvents re less soluble in water and more soluble in non-polar solvents. Polar mole, for ionic, compounds., molecular cr, (v)As dipole-dipole attraction:, 1ons are stronger than London forces, therefore, polar, generally have higher 1melting points and boiling points than crystals ofnon-polar molecules, molecuiar gner, , act as, , or cov*, , molecular size, , and, , shape., , arable

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3/4, , Pradeep's, 3., , these, , Atomic or Network or Covalent, Crystals., , [Vol., , n, , In, , crystals, the lattice points are occupied by atoms, , which are linked, to, , PHYSICAL CHEMISTRY, , form, , a, , together by a network of covalent bonds, , giant molecule., , One of the most common, examples of the crystals of this type is that of diamond in, , which the carbon atoms are linked together by covalent, bonds to give a three dimensional structure as shown in, , Fig. 3.5., , Substances of this type have high melting points,, high boiling, points low volatility and are extremely hard, because of the large number of covalent bonds that have, , A, FIGURE, , 3.5., , Diamond- A covalent crystal., , to be broken to destroy the crystal structure. Further, they, are non-conductors of electricity., , 4. Metallic Crystals. These crystals consist, , ofpositively charged metal ions (kernels) occupying, the lattice points which are held together by the, metallic bond. The metallic bond arises due to the, presence of mobile electrons (as the ionization, , energy of metals is low). These mobile electrons, undergo simutlaneous attraction by a number of|, , positive ions and hence the ions are held together, , Fig. 3.6)., Unlike ionic crystals, the positions of the, positive ions can be altered without destroying the, , UNIFORM ELECTRONDENSITY OF MOBILE ELECTRONS, , METAL IONS, , FIGURE 3.6., Metallic crystal., , crystal because of the uniform charge distribution, , provided by the freely moving electrons. Thus,, metallic crystals can be easily deformed. That is why the metals are malleable and ductile. The other, , properties of metals like lustre, thermal and electrical conductivity can be explained on the basis Or, free, , moving electrons. Further, as the positive ions are closely packed in the crystal lattice, most o, metals possess high melting points and, high densities., ltmay be noted that metallic bond differs from a covalent bond in the following two aspece, , ) Covalent bond is directional whereas a metallic bond is, non-directional., (i) Metallic bond is weaker than covalent bond., To sum up, the, , various types of crystalline solids, their constituent particles occupying, points, the type of attractive forces, their, and some, in labic, are, properties, , examples, , given, , the

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TABLE, , 3.2., , Classification of erystalline solids, , Constituent particles, , Crystal type, wwwwww., , ww., , Main binding, , Positive and negative, ions, , arranged, , definite order., , in, , a, , different tvDes, , 3/5, , Examples, , Strong, , like, conductors in the |Salts, aqueous solution | KNO,, LR, Nacil, fused state,, orBasO etc., of fusion high heats, , Small molecules, , 2. Molecular, , forces, , Properties, electrostatic Brittle, high, forces of attraction, m.p.,, good, , wwwww, , 1. Ionic, , into, , van, , der Waals forces, , Soft,, , low, , m.p., Solid, volatile, electrical, CO, and CH, wax, iodine,, insulators, poor |sulphur, ice, , thermal conductors,, , low heats of fusion, , Atoms chemically, bound together in the, , 3. Covalent, , Covalent bond forces, , Very hard, high m.p.,, poor conductors of |Diamond, silicon, quartz, , form of a network., , heat and electricity,, 4. Metallic, , Positive, , high heats of fusion, 1ons, , and, , Electrical, , mobile electrons, , attractions| Very soft to very hard,, , (metallic bond), , low to, , high, , conductors, , m.p.,, of, , All metals and, , | alloys, , some, , electricity and heat,, metallic, lustre,, malleable and ductille,, moderate heats of, , fusion, The branch, , of science which deals with the study of geometry, properties and structure of crystals, substances is known as "Crystallography'. This study is based, upon three fundamental, laws. These are :, (1) The law of constancy of interfacial angles., , and crystalline, , (2) The law of rationality of indices., (3) The law of symmetry., , Each of these laws will be discussed in the, , subsequent sections of this chapter., , urther, the study of crystal structure involves two important aspects. These are, h e shudy of the external shape or geometry ofthe crystal (also sometimes called the crystal habitn., , 2)The study of internal, structure of the crystal., , ,, , study o, , we shall proceed to describe briefly the various terms and aspects related to laws used in ine, the, and then we shall also describe briefly, and the internal structure of, , crystals, , methods, Unods nee, used to Snape, , investigate the internal structure of the crystaid, , 3.4. SOME TERMS USED IN, Face. The, surfaces of, Edge. plane, , STALLOGRAOPHY, , crystal are called the faces of the crystl., the eugc:, The line, intersect is called, d oalong, n g which the two adjacent faces of a crystal, , Form. Aset, , a, , SImilar, charactenstic, eriangles, sticangle, ang with, each other, , crystal is called, and with other faces., , faces of, , a, , a, , form., , The, , fáces of any given 10

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3/6, , Pradeep's PHYSICAL CHEMISTRY Vol. n, , ne, , Because of the, , regular shape of a crystal, faces are found to occur in sets wncn, paraiel edges or would meet in parallel edges if the planes of the faces were extended. Such a set eetin, or laces, is known as zone., , Crystal habit. The external shape of the crystal is called crystal habit., C a l angles. The angles between the adjacent faces of a crystal are called intertacial angles., , 3.5, STENO'S LAW OF CONSTANCY OF INTERFACIAL, ANGLES, The crystals of a substance are obtained by, cooling the liquid (or the melt) or the solution of, that substance. The size of the crystals depends, upon the rate of cooling. Ifcooling is carried out, slowly, crystals of large size are obtained because, the particles (viz., ions, atoms or molecules) get, , sufficient time to arrange themselves, , in proper, , position. Similarly, it is found that the shape of, , FIGURE 3.7., , the crystals of a substance also depends upon the, , crystals (crystal habits) of a, Shapes of, particular substance., , conditions under which the crystallization takes, place, i.e., in the absence or presence of any other, substance etc. For example, shapes of the crystals of a, , particular substance are shown in Fig. 3.7., of the same substance, the following, However, inspite of the different sizes and shapes of the crystal, , regularity is observed, , corresponding faces, called the interfacial angles of he crystals of a, the shape and size of the crystal. This is called, particular substance, are always the same independent of, The, , angles, , between the, , the law of constancy of interfacial angles. The instrument used for the measurement of interfacial angles, , is called a goniometer., A very simple and common form of a goniometer, is a contact goniometer. It has two flat arms pivoted, together on the centre of the straight portion of a, semicircular scale (usually called D) as shown in Fig., , 3.8. At the axis of their rotation, the two arms can be, , clamped at the desired angle with the help of a screw., , Thus the twoisarms are similar to that of a pair of scissors., The crystal placed between the two arms such that, its adjoining forces are touching the arms. The arms, them clamped and the, read from the scale., , are, , angle between the, , arms, , is, , OTTTUUTTm TUUITUT, , 30, E 20, , 150, , 160, , 170, , 10, , 180, , SCREW, , FIGURE3.8., , Principle of a contact goniometer, wever, , 1ne, , above technique is useful only when the crystals are large in size with clear cut faces. Howd, Tor, more precise work and for small crystals, an optical instrument called reflecting goniomee, or the best is an, X-ray goniometer., upon, it is found that the form or, Further,, shape (or habit) of the crystals of a substance also u, oher, the conditions under which the, of, crystallization takes place,, i.e., in the presence or aabsence, ahedral, from, from, Suostance, etc. For example, sodium chloride grows as, cubes from water solution but, as, 15%aqueous urea solution.,, , used, , A, , to, , largethevariety of shapes of the crystalline substances have been observed. One, , classity, , ore, tempted, , variety of shapes on some basis. Such classification is based upon the metries exhibi, , sy, , triesexhibited

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SOLID, STATE, , and their internal structure. In the next, section, we, symmetryPOSsessedby, by crystals and molecules., t h e crystals and, , OF, ELEMENTS, , 36., , SYMMETRY, , of the various substances, possess the, of symmetry. It is defined as an, this point intersects the, , The crystals, , shall, therefore,, , discuss the, , 3/7, , elements of, , following, , types of symmetries, imaginary pointdifferent, thin, the, opposite faces of the crystalwithin, crystal such, such that, symmetryis also ealled the centre of inversion, that any line, at, because, if the, equal, distances., it, or, gives, crystal, The, results, equivalent* to the original and hencethe molecule is inverted centre of, centre of symmetry, cente of, the, inversion, ne.For example,, of afew molecules are, through the, indistinguishable, from the, given below, (represented by solid original, Centre, rough, , H, , dots) :, , H, , H, , H, H, , H, , HH, , H, , H, H, , FIGURE, , H, , cIC, , H-C3EC-H, , 3.9, , Centres of inversion of a, , few molecules., imaginar plane passing, des the crystal into two parts in such a, way that one part is the mirror through the crystal such that it, of symmetry are, therefore, also called mirror, image of the other. The planes, planes., (3) Rotation axis of symmetry. The, rotation the, aris of symmetry or simpBy called the axis of, ie defined as the, imaginary line passing through, symmetry, such that when the, this line, exactly similar appearance occurs more thancrystal, crystal is rotated about, once in one, complete revolution, i.e., in a rotation, through 360°. If similar appearance occurs twice in one, revolution (i.e., after every 180), the, complete, axis is called two-fold axis of symmetry or a diad axis., the other possibilities found for, Similarly, similar, appearance in one complete revolution are thrice, four times or six times, after, (i.e.,, rotation, through 120°,, 90 or 60°). The corresponding axes are called, three-fold, and sir-fold (hexad), (tetrad), (triad),, four-fold, axes of symmetry., Plane of symmetry. It is defined as an, , The, , above type of rotation which leads to equivalent, configurations, which are congruent as well,, is called proper rotation and the axis is called, rotation, axis. Further, it may be pointed out that, proper, we have only 2-fold, 3-fold, 4-fold and 6-fold axes of rotation and we do not have 5-fold, 7-fold,, 8-fold or, higer-fold axes of rotation, as will be explained later in section 3.13., 4 Rotation-reflection axis of symmetry. When the rotation of a molecule or a crystal about an, -fold axis of proper rotation is followed by reflection through a plane perpendicular to the axis, the axis, is called an n-fold rotation-reflection axis. The new configuration, is, , araomorphous., T, , obtained not congruent, but is, the numeral, , For example, rotation followed by reflection of an asymmetric object like, , is shown in, Fig. 3.10., , molecule or a, , crystal is followed, , the rotation of, new, Koation-inversion axis of symmetry. When, rotation-inversion axis. 1he, by i, axis is called ann-fold, the, symmetry,, of, the, centre, n through, a, , The, , is indictin, , term, should not be confused with the, , quivalent', Snable from the original, , ndistingu, , further of two, , one, , types, , ) Those cquivalent configurations, equivalent, hand an0Se, and right hand., and, , since the, ence is 0n,, hence, , configurations, , identical, but is not necessarily, , which, which, , relative positions, , enantiomorpous., , e n t i c a l configuration, , is, , identical'. The former, , perimposable., , are, are, , These, , not superimposable., , of the atoms change,, , the, obtained when, , means, , that the new configuraion, re, , with it. The equivalent, are, , called congruent, , These, , conigurauons, , configurations., , are called enanOmop, , the new configurationobtalne, , object is rotated through 5oUr., , sable

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3/8, Pradeep's PHYSICAL CHEMISTRY [Vol. ), , COnnguration obtained is not, vCrs1on, , coneruent but is enantiomorphous, as in the, ented in Fig. 3.11., (through the centre of inverslon) of the numeral 7"above, is, represente, ROTATION, , THROUGH, , ROTATION, , 1800, , THROUGH, 180°, , AXIS OF, ROTATION, , AXIS OF, , i ROTATION, , VERSION, CENTRE OF, INVERSION, , L, FIGURE 3.10., , Rotation followed by reflection, of the numeral 'T., , FIGURE 3.11., , Rotation followed by inversion, , through the centre of inversion, of the numeral 7'., , Corresponding to each proper n-fold axis, there is a rotation-reflection axis represented as n-fold, axis and, , a, , rotation-inversion axis,, , represented as n -fold axis., , The above two types, , of rotation, viz., rotation-reflection and rotation-inversion which, give, enantiomorphous configurations are called inmproper rotation and the axes are called, rotation, improper, axes., The various types of, symmetries, as discussed above, are collectively called elements of, and the operations involved like rotation,, symmetry, reflection, inversion etc., are called, symumetry operations., Further, it may be mentioned that whereas a crystal, have many planes of, may, axes of, symmetry,, symmetry but it can never, have more than one centre of, , symmetry., symmetry at all because of the different development of the, , many, , In some cases, there, may be, , opposite faces during crystallization., , 3.7. LAW OF SYMMETRY, The crystals, called law of, , no, , centre of, , of a particular substance always, possess the same elements of, symmetry. For example, a cubic crystal always, symmetry. This is, ofsymmetry:, possesses the following 23 different elements, (a) Rectangular planes, (b) Diagonal planes of of, 6 9, symmetry, (c) Four-fold axes of, symmetry, -3, (d) Three-fold axes of, -4, = 13, (e) Two-fold axes of symmetry, - 6, , symmetry =9, , Centre, , symmetry, (located at the centre of gravity, , of symmetry, , of the cube), , = 1

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SOLID STATE, , wample of each type of symmetry poSsessed by a cube is shown in Fig. 3.12., , 3/9, , An example., , C, , FIGURE3.12., Elements of symmetry of a cube., , CRYSTALLOGRAPHIC AXES AND, , 28., , AXIAL RATIOS, , As already mentioned, a crystal has a regular, constituent particles. The points occupied, arrangement of its, within the crystal are called the lattice points., by these particles, a large number of lattice points, Any plane passing through, A very large number of sets of, is called the crystal plane., the crystal. Some such sets of, parallel planes exist within, within cubic crystals are shown in Fig., , parallel planes present, , 3.13., - -, , The plane surfaces ofa crystal are, , called the faces, , of|, , the crystal., , M, , relative directions, In order to describe the, , and|, , Y, , FIGURE 3.13., , within, orientations of the faces and also the planes present, chosen which meet at a, the crystal, three suitable axes are, selected in a number ofways, point, say 0. These axes can be, , Crystallographic axes and, , axial ratio., , best choice is usually the lines, coinciding, of the crystal. However, the, the, symmetries, choice of, depending upon, in a cubic crystal, the best, For, faces., example,, with or parallel to the edges between the principal, lines thus selected, other. The three (or four), each, to, unit, the axes is the three lines mutually at right angles, called the standard or, suitable, plane, a, axes. Now,, are called crystallograophic, the three axes are, Eung at a point, axes. For example, suppose, the, crystallograophic, pane 1s selected which cuts all the, C respectively, making, axes at A, B and, these, cuts, and OZ and the unit plane, Thus the axial ratio may, pCSEnted by OX, OY, called the axial ratio., b:cis, a, :, ares., ratio, It 1s, crystallograophic, OA = a, OB = b, OC= c. The, the, on, Cepts, unit plane, the, or, made, by, intercepts, the position, ne o, defned as the ratio of the, and c depend upon, b, a,, intercepts, the, the, of, describing, lengths, shape ora, in, significant, is, portant to note that the actual, which, aXIal, therefore, the ratio, tr, crystals, the, b, constant, It is,, sulphate, is, ratio, copper, for, e.g.,, unity,, to write 'b as, urther, it is convention, andY, , i, Is a : b:c=0-5715: 1:0-5575., , angle:, Tespectively. These ang, are, , a,, , b, , p, , represented by, the linescoinciu, ratios, chosen are, , c are, , the intercepts, opposite to, axial, if the axes, with, with the, interfacial angles, gether, together, same as the, These angles, angles are the, crystal., Se, faces of the, or, the principal, of, to the edges, parallel, edge, Plel, , The, , with, , ,, , and, , between the, , axes, , called the elements of the, , ystal.