deseribe-general characteristics of solid state: distinguish-between amorphous and crystalline solids; classify crystalline solids on the basis of the nature of binding forces; define crystal lattice and unit cell: explain close packing of particles; describe different types of voids and Atene-packed : aleulate the packing eff diferent pes af en ey af sf cubie unit cells; correlate the density of a substance with its-unit cell Properties;_ "i > rr ic. describe the imperfectiogas in —PlanIs.st solids and their effect’ on properties; correlate the electrical and magnetic properties of solids and their structure, wor sord=> Zig S " Et vO “ aggebi? HO?) so aye (edaer™ ( SiO” Oe ek > BW HELE) structures; ~~ ~ ny Seated nov? SiEEpE ltetined bass ated nt 120 Ov (1 The-vast majority of'solid substances like high temperature ; superconductors, biocompatible plastics, silicon chips. etc. aredestined + 5 toplay an ever expanding role in future development of science. dlfen than liquids and gases. For different applicatidgs we need ‘Solids with widely Alifferent Properties. Rhese properties depend upon constituent particles and the binding forges operating between them. Therelore=siudy of the stmicture of solids 1S Important. “Tit From our earlier studieS{ we know that liquids and_ be gases are called fluids becaue of their ability to flow. ty ‘The fluidity in both of these stattg is due to the fact that, the molecules are free to move aby the constituent particles in solids have and can only oscillate ab mek explains the Hgidity in solids. in crystal Sonstituent particles are arranged in (te; i this Unit, we shall discuss differeht possible Yangemenits of particles resulting in several types of ‘ rructurés. The correlation between the ndture of ‘interagtions within the constituent particles and properties of solids will also be explored, How 0 Prpperties’ get“ modified due to the structul tos or by the presence of impurities in minut would also-be discussed.” Sao C0) scanned with CamScant: — Sn gee ye | , 7, tutors 0 q # : states namely, hn exist 11 ree Scratureant 1 General ou have learnt tnaé matter a ations. eee of, a Characteristies ( of Solid Stuate J Sntraleosoajore 9 eee Doles 7 pee al energy + 7 ste fpvMaster. At suX{ciently low temperature, ne / eat dev intermolecular Yorces bring the Fe about thelr meq! aay SF lodewind J occupy fixec\positions. ate a wingare| OC d the Sybst ; =) Om (i) Intermolecular distaxées are short. (iii) Intermolecular forces 4 strong. ve SF (iv) Their constifuent particlis (atom® molecules of tons) a ave fa ae position and can only ost late about their mean P’ TOA ‘ (vy aE are incompressible an rigid: ; | or 1.2 Hnuorphous classified as crystalline or amorphous on the basis of tht Fig. 1.2 cad Crystalline re of ordéx present in the arra gement of their constituent particles) ° Sulit A Gystalline soliq usually consists of a large number of small 3 Qo each ofthem having definite ope naa aa oail the arrangement of tenstituent particles (atoms, molecules oF fons) is ich means that there is aresegiatiem eats itself period ‘ofrregular shape. The arrakgement of constituent particles (atoms, molecules or ions) in such a solid has only short range order. In’ such an) ally repeating pattern is observed over. short distances only. Such portions’ lyre scattered and in between thé! ”~ atxangement is disordered. The © tures of quartz (crystalline) and Melting y glass famorphous)are shown, -1 (a) and (b) respectively Cleave two structures are almost) PrOPS hape arrat . eit Fig. 1.1: Two dimensional structure of particles, golids differ net rary + @) quartz and (b) quartz glass in their properties. ° fogs Re Scanned with CamScan)tbe Sorebuystlliym Crystalline solids have a sharp melting point. On the ther hand, amorphous solids soften over a range of temperatuyé and ean be moulded and blown into various shapes. On heatjig they become jass objécts from ancient crystalline at/some temperature. Some gl civilisations are found to/becs in appearance because of somé crystal in. Like liquids, amorphous solids 4 ndency to flow, though very slowly. Thergfore, sometimes these are called psctto Falls ‘or/super cooled liquids. Glass panes Tixed to windpWs or doors of old “buildings are invariably fo o_be_slightly thicker_al the _ hottom than at tf Th bees ethe glass. ows down vey slowly and makes the bottom portion slight thicker. —Gystalliye solids are/anisotropic )n nature. that is, some of their physical properties Tike electrica¥/ resistang? or refractive index show different values pherrmyasuredafongdiffcrent directions in the same 7 - _ Gysi This arises from diflerent arrangement of Ansty in estas ts dé partifes in diferent directions. This is usteated 19 Foe eee tone aijeres, Fig A-2. Since the arrangement of particles is diferent directions. alofe different diréctions, the value of same physical § SpoBEMyS Found to be dilferentalong each direetion. “Amorphous solids on the other hand are isotropic in nature. It is Gecause there Is no long range order in them and arrangement 1s frregular along all the directions. Therefore. value of any physical property would be sanie along any direction. These ferences are summarised in Table T.T- A, amend 9 cP * Ay: ble 1.1: Distinction between Crystallin€ an‘ ‘Aenorpions Solids 8 Adee 2 : c 4. The | Shape Definite characteristic geometrical shape | Irregular shape hejand | Melting point | Melt at a sharp and characteristic Gradually soften over a_range of } oo temperature Cpe temperature aan wtively. | Cleavage - When cut with a sharp edged tool, they | When eut with a sharp edged tool. they almost | Property spit nto two pieces an the newly cuit into two pleges with irregular 4 “generated surfaces are plain and surfaces Ate AbkGn per in | | smooth ea OO pansthedliney fo lors Omyptoty) Sire of | teat of fusion | They have a definite and characteristic | They do not have definite heat of fusion Sih | “heat of fusion | . dinatics | Anisotropy | Apisotrople in nature Isotropic in nature ele G/F? Soe teallobived mhous;| Nature “True solids” Pscudo solids or super cooled! liquids sin the)} Order in Long range order eons) Only short range order. ais item) | afrangement : | of constituent SE wapey _Gitiah i a r e f Meh Jateaniybw abuok Yoge oR ‘The Solid State Scanned with CamScan)aoghests but pmplhrenclainiGalyi Bry ber and Plastic, TIS One Gry 5 o tricity, ae ots [i ) | ye —hitest, Questions | <{ Why are solids rigid? y 2 2 do solids have a definite volume’ ids: Polyure 3 , erst the following as amorphous or crystalline c& hepa ee ‘ > 9 naphthalene, benzoic acid, teflon, potassium lyviny| 3 AO s chloride, fibre glass, copper. ed ar wgows a 1.4 Why is glass considered a super cooled liq ‘Reap bos £0 a “| ‘ Refrac index of a solid is observed to have the same i Sol cry | +e ernment onthe nature ofthis sold, Would itshow cleavage property?,, z, 4 m - * 1 Cons —~-Laodropit ica Acts nanos Sate AP ystandés =| 3 Classification In Section 1.2, we have learnt abdyt amorphéus sukst ty Ped ae Se they have only short range order. Hol acu of Crystalline BP : | Solids so Ras ue «4 wt] FEC BS, PoT Natt Wabtabone > Grugh- it C Mt se G0 le = . tide = picmmolecylar fore aperating im olay catego [es Vin, on bras» dnttruestioobs Pu*nolecular, ionic Metalic and covalent solids. Let us now learn abou foe } wast Conicy hese categories. ts cl 13,THolectiar — Molecules aré the constituent particles of molecular solids. These ay ong Solids further-stik divided into the following categories: tia Mon 9 hy > ekous(ce) i). Non par Molecular Solids: They comprise of either atoms, fq pu Hey, toll Ueodbed example gon and helium or the mol lag to; PUL Ty) seek Deprsion torc/ covalent bonds or example H, Ch and I}. In these solids, the atom: fo I jo]. . or molecules\gre held by weak dispersion forces or London fore bout Or 7 pea dot 4 gras. Wout which ydy have learnt in Class KI a ¢ e ese solids are soft an 57 Li pol diy < usually inti ' 1 borat ned (i) Polar Molecular Solids wr SO a Safe)! Pile 2th. ete. are formed by polar con ere plier, Sollee eet ules nS a nteractions.-These solids 4 example, = : AB ler countid bod thy drogen Bonded Molecular Solids yc Mlb ey ntain Is-betwr Q or N atom a oo ui ! ‘ogen bonding binds molec stich Sollde ies i ee F are NOn-cONGUCTORS Of clock po seNch Soltds Az H, ‘latte lgulds or soft sollds umderrene Cy~ Generally they a Unit Cells & S ot om TZ xe! Themainc ic of crystalline solids is-a-regularand_repeating pattern of constituent particles. If the three dimensional arrangement ‘Of constituent particles in a crystal Isrepresented ingrammnatlcaly in which each particle is depicted as a point, the arrangement 1s called crystaUTattice. Thus, a regular three dimensional arrangement of points in space s called a crystal lattice. Aportion ofa crystal lattice is shown in Fig. 1.5. Fig. 1.5: A portion of a’ three dimenstonal cubic lattice its unit cell. Lo io” ere are only{i4 are called Bravais ice: T | High [= Them). The following are the characteristics of a crystal lattice: | {a) Each point in a lattice is called lattice point or lattice site. ; (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. Unit cell is the[Smallest portion ‘of a crystal lattice which, when repeated in different directions. generates the entire lattice. A unit cell is characterised by: (0 its dimensions along the three edges. a, b and c. These edges may or may not be mutually perpendicular. (i) angles between the edges. « (between b and df (between p= and 9 and y (bet ). Thus, a unit cell is characterised by/six parameters. a. b. c. @. B and y._ ese parameters of a typical unit cell are shown in Fig. 1.6. 1.4.1 Primitive Unit cells can be broadly divided into two categories, primitive and and Centred centred unit cells. Unit Cells @) Primitive Unit Cells ‘When constituent particles are present only on the corner positions of : aunt cell, it is called as primitive unit cell. ! @) Centred Unit Cells reof . When a unit cell contains one or more constituent particles present at positions other than corner in-addition to those at comers, itis cated ’ geentred unit cell. Centred unit cells are of three types li} Body Centred Unit Cells: Such a unit cell contains gne constituent Stdes the on particle (atom, molecule or ion) at its body-centre be es thatare-at its comers. (ii) Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face. besides the ones Wat are at its comers. Very high Fig. 1.6: Illustration of parameters of a unit cell | ide, | oFea The Sole State Scanned with CamScan)ae one constituent partic, Sides the Ong Im all. there are seven types of primitive unit cells (Fig, Ln, () End-Centred Unit Cells: In such a unit cell ‘ ; 4s present at the centre of any two 0 Monoclinic ‘Triclinte Rhombohedral ee Fig. 1.7: Seven primitive unit cells in crystals | Ovihovhe , Rhowset Their characteristics along with the centred unit cells they can. for pte have been listed in Table 1.3. eae: ; Table 1.3: Seven Primitive Unit Cells and their Possible ; Sk Variations as Centred Unit Cells * ROGUGch th Geteesieeit { . t Primitive, NaCl, Zine blende, 2 Body-centred, cu — Face-centred ks Tetragonal Primitive, White tin, SnO,, Body-centred TIO, CaSO, Orthorhombic panies Rhombie sulphur, Face-centred, ve | End-centred | | Hexagonal Primitive Graphite, Zn0,CdS. Rhombohed Fhambohedral or | Primitive Calcite (Caco. HE (cinnabar) ee __Chemistry Scanned with CamScan)Tyee, OL partiey, athe ones ycan form Ny ea te ‘wo angles between faces all 90° | Monoclinic sulphur, Na;SO,.10H,0 K,Cr,07, CuSO,. SHO, Monoclinte a= y= 90° 290° a2Bpey490" ‘Triclinic for sim Redy-cent c iat) ‘The three cubic lattices: all sides of same length, angles between faces all 90° acpeco kefpe¥et Qe btCl L2pr1jK10 At bFAC D trp eer atte} pope e7 Que © ape tthe artic \ Lyre to Ad oA 44 bY es — Rhowsoticbnlgyc, Primitive ~Body-centred Cybie > Wes Ledrethe two tetragonal: one side different in length to the ot ch Ly ota df wack Ox End-centred Body-centred ‘The four orthorhombic lattices: unequal sides, angles between faces all 90" Yaa sy ¢ Primitive End-centred “The two monoclinic latices: unequal sides, ‘two faces have angles different to 90° The Solid State ————— ee a Scanned With CGMScanI1.5 Vlumber of |. We know that any crystal lat Atoms in a Unit Cell belongs to a particular unit cell. i 1.5.1 Primitive _ Primitive cubic unit cell has atoms only at its corner. Cubic Unit a corner is shared between eight adjacent unit Cell iB. Jess than 90° 1.5.2 Bi eo°o mombohedra atce- ‘alll sides. ao equal -~ sent ge a 9" Hexagonal lattice- ‘one side different in Jength to the other ‘two, the marked angles on two faces unteatloe- Tad eds aD. & Ripre are uneg eS etuh none equal t0 90° —~ ttice is made up of a very large number of int is occupied by one constituent particle d every lattice po! 0 Se anlar ‘ow work out what portion of each particle {atom, molecule or ion). Let us n¢ We shall consider three types of cubic unit cells and for simplicity assume that the constituent particle is an atom. Each atom at aeshown & 15S F 8, four unit cells in the same layer and four unit cells of the 1 upper (or lower) layer. Therefore, only "of an atom (or molecule or ion) actually belongs to a particular unit cell. In Fig. 1.9, a primitive cubic unit cell has been depicted aon in three different ways. Each small sphere in Fig. 1.9 (@) that position and not its actual size. Such structures | represents only the centre of the particle occupying are called open structures. The arrangement of particles is easier to follow in open structures. Fig. 1.9 (b) depicts space-filling representation of the —N unit cell with actual particle size and Fig. 1.9 (c) shows the actual portions of different atoms present in @ Fig. 1.8: Ina simple cubic unit cell, cubic unit cell. @ Chemistry ‘each comer atom is shared In all, since each cubic unit cell has between 8 unit cells. 8 atoms on its corners, the total number 1 1 atoms in one unit cell is 8x—=1 atom. Fig. 1.9: A primitive cubic unit cell (a) ope structure (b) space-filling structure . (6) actual portions of atoms belonging () to one unit cell. Scanned With CGMSCanISa 1.5.2 Body- Abody-centred cubic (bec) unit cell has an atom at each of its corners | Centred and also one atom at its body centre. Fig. 1.10 depicts (a) open ' Cuble Unit structure (b) space filling model and (c) the unit cell with portions of | Cell atoms actually belonging to it. It can be seen that the atom at the @) Fig. 1.10: A body-centred cubic unit cell (a) open structure (b) space- filling structure (c) actual portions of atoms belonging to one unit cell. body centre wholly belongs to the unit cell in which it is present. Thus in a body-centered cubic (bec) unit cell: () 8 corners x 3 per corner atom =8 ee = 1 atom (i) 1 body centre atom = 1 x 1 =1latom :. Total number of atoms per unit cell = 2 atoms + 1.5.3 Face- A face-centred cubic (fcc) unit cell contains atoms at all the corners and Centred at the centre of all the faces of the cube. It can be seen in Fig. 1.11 that Cubic Unit —_each atom located at the face-centre is unit cells and only 3 of each atom belongs to a unit cell. Fig. 1.12 depicts (a) open structure (b) space-filling model and (c) the unit cell with portions of atoms actually belonging to it. Thus, ina face-centred cubic (fec) unit cell: ( 8 corners atoms x 3 atom per unit cell =8 xy = 1 atom (ii) 6 face-centred atoms x 3 atom per unit cell = 6 x 3 3 atoms +» Total number of atoms per unit cell = 4 atoms Fig. 1.11: An atom at face centre of unit cell Fig 1.12: A face-centred cubic unit cell (a) open structure (b) space ts shared between Jilling structure (c) actual portions of atoms belonging to 2 untt cells ‘one unit cell. 11, The Solid State Scanned With CGMSCanIIutext_ Questions (2) a 1.10. Give the significance of a ‘lattice point’. i i S cel 1.11 Name the parameters that characterise a unt 1,12 Distinguish between () Hexagonal and monoclinic unit cells i (i) Face-centred and end-centred unit cells. na 1.13. Explain how much portion of an atom located at ac ot - (tt) body. centre of a cubic unit cell ts part of ts neight ce Jose-packed, leaving the fe § < 1.6 Close acked tn sotids, the constituent part ki . the constituent particles Im ienam vacant space. Let us conside! eal etructurt et Structures identical hard spheres sheres in a one dimensional close (a) Close and touching each ‘There is-only one a x packed structure, that other (Fig. 1.13). In this arrangement, each sphere 1s in contact COOK) YO) with two of its neighbours. The: of nearest neighbours of a particle is Calle ina Fig. 1.19: Close packing of spheres tn “number. Thus, in one dimensional Core packed cone dimension SeaTIenIeTt the coordination number 1s 2. () Close Packing in Two Dimensions | ‘Two dimensional close packed structure can be generated by stacking’ oS an be done in two y —— way of arranging sp) fis to arrange them in a row (placing) the rows of close packed spheres. ‘This ¢ different ways. (UW ‘The second row may be placed in contact with the first one such Co that the spheres of the second row are exactly above those of the s J first row. The spheres of the two rows are aligned horizontally as). OQ. os ‘well as vertically. If we call the first row as ‘A’ type row, the second > _ ‘ row being exactly the same as the first one, is also of ‘A’ type. imilarly, we maj ice more rows obtai e of | ' iP o c a as eae Fig, 1.14 (a). to obtain AAA wpe | € 'COCCOE | Lee ia | SEOCCOEO | | SEEREEES | | ECO | ee ° y. 1. fd Snare ar rl Fig. 1.15: Chemistry gy Scanned with CamScan)| e we AAA cl 07, In this arrangement, each sphere 1s in contact with four of its 3, neighbours. Thus, the “Also, {f the centres of these 4 immediate neighbouring spheres are joined, a square is formed. Hence this packing is called square close packing in_twa_dimensions. (ti) The second row may be placed above the first one in a staggered manner such that its spheres fit in the depressions of the first row. If the arrangement of spheres in the first row is called ‘A’ type, the one in the second row is different and may be called 'B’ type. When the third row is placed adjacent to the second in staggered manner, e its spheres are aligned with those of the first layer. Hence this layer Is also of ‘A’ type. The spheres of similarly placed fourth row will be aligned with those of the second row (‘B' type). Hence this £7) arrangement is of ABAB type. Ins arrangement bese se ee Sy gpace_and this-packing is more efitent then the savare css x packing. Each sphere is in contact with six of its neighbours and ‘i amenloalsocraton ners The eects tees six spheres are at the corners of_a regular hexagon (Fig. 1.14b) hence this packing {s called two dimensional hexagonal close- AGKY packing. It can be-scen in “Tf (b) that in this layer there ‘are some voids (empty spaces). These are| arin triangular two dill (c) Close Packing in Three Dimensions All real structures are three dimensional structures. They can be obtained by stackin fimensional lay bo} In 2 the last Section, we discussed close packing in two dimensions which y can be of two types; square close-packed and hexagonal close-packed. w i Let us see what types of ynal close packing can be obtained y from these. DISC Od | of x () Three dimensional close packing fromfio)dimensional_ square i 6 elose-packed layers: While placing the second square close-packed layer above the first we follow the Ss followed when one row was placed adjacent to the other. ‘The second layer is placed over the first layer such that the spheres of the upper layer are exactly above those of the first layer. In this arrangement spheres of layers are -perfectly aligned horizontall veitically as Fi ly, we may place more layers one above the other. If the arrangement of spheres in the first layer is called ‘A’ type, all the layers have the same arrangement. Thus this lattice has AAA. type pattern. The lattice thus generated is the simple cubic lattice, and its iinit cell is the primitive cubic unit cell [See Fig. * Eero ool (i) Three dimensional close packing from two fess + dimensional jonal close packed layers: Three |. 1.15: Simple cubte lattice formed dimensional close ‘packed structure can be generated arrangement by placing layers one over the other. A 23 69 30> AAA wide Te Sd" . Lda scanned with CGMSCcanIoa 7 7 zy oy (a) Placing second tayer over the first layer Let us take a two dimensional hexagonal close packed layer ‘,: x et (A Place a similar fayeraBove it such that the spheres of the Second it 6d yt x to 1aaeed i the depressions ofthe first layer. Since the spheres ae av phe ‘two layers are aligned differently, let us eall the second I HL ayer as 5 Ay Can be observed from Fig, 1.16 that not all the triangular vod: i» 0 fi j } a st layer are covered by the spherei’aT the secoret ayer. Ths got, KS {/ As iO-amerent SSS Whe ie second Jan } id Yh a” \PY~ above the void of the first Liver Tor viceversa) a tetrahedral wgy® | y ee ee Scrat a ct owe ge 10a f re, (ae formed. These voids are called t trahedral voids b tetrahedron ‘i L jecause a mee {eTormed when the centres of teeter re They have PY. 1-18 \ b ne SuERVOId ‘has been shown (Mex i . separately in Fig. 1.17. exploded v t ao} . showing st I N layers af ty CO) tetrad owe Swe 4 eet ow Bite stacked in he : < and (c) geo i on packing. 4 F 1.) A aN Teheton Fig. 1.19 ‘ (a) ABCAB aa | 8 oem \ ‘i layers whe Fig 1.17 - tahedral |} Tetrahedrat ere bi a oo ; Tevohedr na covered (b) | Rae etts SS _ofstnuctun (b) exploded side } ( ar view and () geometrical shape _ or face en the void, (ea src ak @ re Octahedron foe) struct Chemist eettY dy ic) Scanned with CamScan)iO At other places, the trlangular-velds-in the second_layer_are_abov re the angular voids n ne Ort layer, and the tlengulor shapes | donot overlap. One of them has the apex of the triangle pointing | ‘Ov in Fig. 1.16. | Such yolds are surrounded by sit SPhetes a “called octahedral voids. One such void has been shown separately in FES the wane of these two types of voids depend upon the number of close packed spheres. Let the number of close packed spheres be N, then: ' The SET aan tears ‘dL ogtahedral_volds generated = N ‘The number of tetrahedral voids gencrated = 2N & (@) Placing third layer over the second layer : When third layer is placed over the second, there are two possibilities. ( Covering Tetrahedral Voids: Tetrahedral vol er Bg =n this case, the t } layer. Thus, the pattern of spheres is repeated In “This pattern is often written as ABAB . pattern. This structure ure ee Se maak me | ae Pa : | Se 1 Ped aay Uh Q roa do Vv ; ote A Fig. 1.18 (@) Hexagonal cubic close-packing exploded view showing stacking of “layers of spheres () four layers stacked in each case Hexagonal Cubic close hep and (¢) geometry of packing packing packing. (a) Fig. 1.19 A oO (ii) Covering Octahedral Voids: The (@) ABCABC... third layer may be placed above arrangement of E ‘The second layer ina manner such layers when ‘Spheres! cover the octahedral void is voids, When placed in covered (b) fragment () / this manner, the spheres of the third layer are not aligned with those of either the first or the second layer. This arrangement is re type. Only_when_fourth_layer—is Placed, ts spheres are aligned with y15. The Solid State th Scanned With CGMSCcanIz yore A = 22 of the first rhe as shown in here and 1.19. This pattem, of layers is often written as ABCABC This structure is cj led cubic ced (cep) or Tace-verttred cuble (fec) structure. Meta, ‘Such aS topper am stallise in this caren , elficient and 745, Both these types of close Packing are En Tee space in the crystal {s filled. In either of them, each sph a TH contagy with twelve spheres. Thus, the coordination number is 12 in either o a these two structures. A hese two structure w 1.6.1 Formula ofa Earlier in the section, we have learnt that when particles are Close. Compound packed resulting in either ccp or hep struotus eevee oe ais a | and Number generated. While the number of octah is pres 7 \ of Voids e number of close packed parti © this number. In ionic solids, the bigger fir eee ee ene reag rion Tie close packed stricture and the Smalieres < don > CCP - (uStaiy-taonsl accupy Ure vor. 1 tre Tater on 1s-small eit. \ - d _ the % | Qiven>V0K i (ahaa se acon OS ten aad ash ruled Not all octahedrat-ortetrahedral ‘vords ina given te |}, p&nder si ae Soa the fraction of octahedral = oxt Ly aOcbatod ccupled, depends upon emical formula of the compouné, ax) mtu a ; Couple LA compound is formed by two elements X and Y. Atoms of the element! t - Y (as anions) make ccp and those of the element X (as cations) gecupy » ept “Wek | all the octahedral voids. What is the formula of the compound? uit Fey ‘The cep lattice is formed by the element Y. The number of octahedral | wact al Es voids generated would be equal to the number of atoms of ¥ present in read | it. Since all the octahedral voids are occupied by the atoms of,X, their {7 bag j number would also be equal to that of the element Y. Thus, the atoms | Ortiy t of elements X and Y are present in equal numbers or 1:1 ratio. Therefore, the formula of the compound is XY. : _Gsumple_1.2 Atoms of element B form hep lattice and those of 2/Srd of tetrahedral voids. What is the formula of by the elements A and B? Sulutiou The number of tetrahedral volds fo the element A occupy, f the compound formed (@) Locating Tetrahedrat Let us consider a unit cell of into eight seal co cP or fee lattice [Fig. 1(a)}. The unit cell is divided Voids Scanned with CGMScanIEach small cube has atoms at alternate corners [Fig. 1{a)]. In all, eagh_small Subs _has-4 atoms. When joined to each other, they make a regular tetrahedron, ” ‘Thus, there is one tetrahedral void in each small cube and eight tetrahedral voids in total. Each of the eight small cubes have one void in one unit cell of ecp structure. We know that cep structure has 4 atoms per_untt cell, Thus, the umber of tetrahedral vold@isetwiGe The number of Mem w 1: (a) Eight tetrahedral voids per unit cell of cep structure (b) one tetrahedral void’ showing the geometry. () Locating Octahedral Voids Let_us again consider a unit cell of cep or fee lattice [Fig. 2(a)]. The body centre of the cube."C is not occupied but it {s surrounded by six atoms on face centres. If these face centres are joined, an’ octahedron is generated. Thus, this unit cell has one octahedral vold at the body centre of the cube. Besides the body centre, there is one octahedral void at the centre of cach of the 12 edges. (Fig. 2(b)]. It is surrounded by six atoms, four belonging to the a same unit cell (2 on the corners and 2 on face centre) and two belonging to two i adjacent unit cells. Since each edge of the cube is shared between four adjacent Le unit cells, so is the octahedral vold located on it. Only 4" of each void belongs to a particular upit cell. Fig. 2: Location of octahedral voids per unit cell of ecp or fec lattice (a) at the body centre 5 of the cube and () at the centre of each edge (only one such void is shown). ok e Solid State . - Scanned with CamScani\ | ‘Thus in cubic close packed structure: Efficie =i Octahedral void at the body-centre of the cube 7 Loe 12 octahedral volds located at each edge and shared between fourcunit cays | po4s 1 Centre = 12x 2-3 = a Struct s40ee + Total number of octahedral volds = 4 = We Know that in cep structure, eagif unit cell has 4 atoms. Thus, the number - of octahedral voids is equal to toms, molecules or ion, fever way the constituent particles (at od packed, there is always some free space in the form of votdy Packing efficiency is the percentage of total space filled by 4) particles. Let us calculate the packing efficiency in different types structures. 4° 1.7.1 Packing Both types of close packing (hcp and ¢cp) are equally efficient. Lety wy Efficiency in calculate the efficiency of packing in ccp structure. In Fig. 1.20 let th C7 hep and cep unit cell edge length be ‘a’ and face diagonal AC = b. ‘Structures In A ABC . $e AC* = b?= BC? + AB? +a? = 2ator If ris the radius of the sphere, we find * ~ 4 €cC 7 b=4r= (0a ely 4r oraz = 2N8r re 24 dl eee acleiny In efficiency (we can also write, r= _9_) z D 22 a Fig. 1.20: Cuble close packing other We know, that each unit cell in cep structut (ies re tox rot ah has effectively 4 spheres. Total volume of fot epheres for sake of clarity. Spheres is equal to 4x(4/3)mr? and volume of th ws cube is a° or (vr), WF, Therefore, Packing efficiency = Volume occupied by four ‘spheresin the unit cell x1 Effic Total volume of the unit cell Simy Lat X(473)m 100 (2vary = (6/3)m? x100 = 6/8)" 100 , 1eV2r° Vee] Chemistry 18 Scanned with CamScan) %.2 Efficiency of From Fig. 1.21, it is clear that the Packing in = atom at the centre will be in wuch Body- with the other two atoms dityous atoms diagonally Centred _ arranged. Cubi mak a" EFD, ‘The length of the body diagonal G ex C1 equal to 4r, where ris the radius Ne ot = sphere (atom), 4s all the three body diagonal are shown a spheres along the dixon touch with solid boundaries). gv cach other. wee Therefore, VSa = 4r cca’ 4 4r y& SOTA rsowecanwne, In this type of swucliire, total number of atoms ts 2 and their volurne is 2x(3)me’ recaryy eel a (y 68Y. Volume of the cube, #° will be equal to | # 6 ed SDH) Therefore, ~ . —~_ Volume occupied by wwospheres i the unit cell <100 y_ Racking Rees “Total volume of the unit cell . _ 2x(4/3)mr? x100 , [@/8)F} _ (8/3)ar* x100 A — 64/(3V3)r* 7.3 Packing Ina simple cubic lattice the atoms are located only on the comers of the Efficiency in cube. The particles touch each other along the edge (Fig. 1.2 Simple Cubie ‘Thus, the edge length or side of the cube a, and the radius of each particle, Lattice rare related as 2 -ffevorumec of the cubic unit cell = a° = (2r)* = 8r* Since a simple cubic unit cell contains only 1 atom ‘The volume of the occupied space = Scanned With CGMSCGahI[ . Packing efficiency t . Volume of one atom xtoVotume of 208 g¢ } = Volume of cubicunit cell mee { density ‘Simpl «100 Aacinber. aii ae i = 52.36% ¢ 52.4 %| ‘ The spheres are in crus, we may Gnchide thal “Z3Sxi contact with each and hep structures Rave maxigs other. e tency. ether along the edge of packing efficiency. of atoms in 208 . = 24.16% 1.8 Calculations From the unit cell dimensions, tt 1s posstble to calculate the volun, the unit cell. Knowing the density of the metal, we can calculate X-1 Lif furateing ihe nt eel (anne tn the unit cell. The determination of the mag.%TaY diffractior Lit Cell Sigle‘atom gives an aceurate method of determination of Avog Cell with celled; Dimension: ‘dete constant, Suppose, edge length of a untt cell of a cubic crystal detemy (termined to ‘of copper. by X-ray diffraction is a, d the density of the solid substance anq 0" °PP&™ niolar mass. In case of cuble crystal: In case of feclat Volume of a unit cell = a’ Mass of the unit cell = number of atoms in unit cell x mass of each atom = z (Here zis the number of atoms present in one unit cell and mis mass of a single atom) 8.92g em? xt = 63.1 g/mol ‘Mass of an atom present in the unit cél> Atomic mass of M \ m = 5 (M is molar mass) Silver forms cer ee hdge length oF i Therefore, density of the unit cell ‘Atomic mass = = Massof unit cell pince the lattice volume of unit cell Molar mass of =2m_ 2M “aM Edge length of @ an, C8" BH . determine the ith.” @8Ra Ny. fe | 1 ody- rae a (bcc) structure with a cell edge—————__ a eee 10 208 g of the element? >”? &/em. How many stone SNE Volume of the unit eet = (28g pmy ) [144 What ‘ : pasrios s = 28810" ems 1.15 Nom numb. Scanned With CGMSCanI~ | om aa Teal *10¢ Volume of 208 g of the clement . ee } mass, 2089 _ 94. 8em* & ; “density 72gem> ‘Number of unit cells in this volume nao) | 28.88em* ide that = Fgoxd0P em? unit coll ~ 12-08%10" unit cells \ “tn since each beceubic unit cell contains 2 atoms, therefore, the total number of atoms in 208 g = 2 (atoms/untt cell) x 12.08 x 10" unit cells he voluy = 24.1610 atoms saleul; ee ate x-ray diffraction studies show that copper crystallises in an Jee unit ( suilt Lt ae Of ASS) cell with cell edge of 3.608x10* cm. In a separate experiment coppers Be “determinéd to have a density of 8.92 g/cm’, calculate the atomic mass deter, a density of 8.02 g/cm" ve and wy SPP In case of foclatice, number of atoms per unit cell. z= 4 atoms Therefore, M = SNsS om = 2x, _ 8.92g em? x6.022x10™ atoms: mol" x(3.608x10%cm)* and mis atoms * = 63.1 g/mol" Atomic mass of copper = 63.101 Silver forms ccp lattice and X-ray studies ofits crystals show that the {vi | edge length oT its unit cell 1s 408.6 pm. Calculate the density of silver —_—_— | Since the lattice is ecp, the number of silver atoms per unit cell ‘Molar mass of silver = 107.9 g mol! = 107.9x10° kg mol | Bdge length of unit cell = a = 408.6 pm = 408.6x10"m 4x(107.9x10°kgmol") Ae = 10,510" kg (408.6x10"%m)’ (6.02210 mol") ale 1edge-— : toms : Intext_(Questinus 1.14 What is the two dimensional cpexdination number of a molecule in square close-packed layer? 1.15 A compound forms hexagonal close-packed structure, ‘What is the total number of voids,in 0.5 mol of it? How many of these are tetrahedral voids? Scanned With CGMSCcanI= Ln 13 ‘A componind is formed by two elements Mand N. The clement, 57193 forms ecp and atoms of M occupy 1/3rd of tetrahedral voids, Wha, is the formula of the compound? 1.16 1.17 Which of the following lattices has the highest packing efficiency (sir Pe cubic (i) body-centred cubie and (Hi) hexagonal close-packed lattice CS 1.18 An clement with molar mass 2.710? kf, mol” forms a cuble unit cx ae with cdge length 405 pm. If its density is 2.710" kg m®, what is the nature of the cubic rit cll? Freatil> G ee, : Vatand a ae J, Tnnperfections. Although erystalline solids have_shont range at Wel tng a in Solid: order in the arrangement of theif constituent partic . vet age meet For TEreet. Usually a sollg/Consists of an agarogAte of large my 2 OVQG G00 gr amall crystals. ‘Thesp/small crystals have fects in fhem. 7 ” & Single crystals are of exystallisy ~ xt remely 6 are not free/of d oh gett cttenet wy Gefects are Bi g fhe arrangement of con jeoks dapetororg foi Particles. Bybadly speaking, the defects are ‘of two. foros detfced a : Tine defects. Point defects arc d point defects only. 9.1 Types of Point defects can be classified into three types : (i) stoichiometric d¢ Point Defects (it) Sap tects and il nan.satepometie dees hi iometric Defects Sagi oloweut offer sei fa) Stoich these are the point defects shat do not disturb the stotcigne Voce obput-> fy when bad ‘ol tine solid. They are also called intrinsic or thermodynamii Vacaney Oiteted gbastegie lend Basically these arc of two types, vacancy defects and interstitial dé Saeed Vacancy Defect: When some of the lattice sites are vacatt Jee f TA orp toa Hea crustal is sald to have vacancy defect (Fig. 1.23). This res lecreass sity of the substance. Qe alee he nae le defect can also. dé F Tis defect can aso tf v/4 Ven fous dip ae ) Gi Tater De Defect: When some constituent pat . [atoms or molecules) occupy an interstitial I © the crystal is said to have interstitial & (Fig. 1.24), This defect increases the density’ substance. > ) Vacancy and interstitial defects as ext above can be shown by non-ionic soit! C solids must always maintain cle: atherthan Simple vac; Aceretheys iS ni Fig. 1.23: Vacancy defects fottky defects. 7 mistry p20 Scanned with CamScani—— x = Pai; Bra} 330° ze BY we by . S903? 31 pWo186 | Late: Ve6- nt N (win. Frenkel fect: What defect is Al © @ © @ | ; DB Ong? aoe >» @ ¢ "e | ait com of dO i O-o @® © t Fig, 1.24: Interstitial defects atjon defect. ~ OY geoniov)drios WB ange the density of, Zr MAAMST row b 9 re a8 Erion, for example: es wn o anand ae ne lw Scliottkey Defect: 1 is at ly aeacamcy deen tnt solids. In sf Sefiotty Deft jm electrical neutrality. {he HUMBSe 5 cations and-anions ae ~ ~ Like simple vacancy é also Temperacure- ‘are_about Fig, 120: Schottky defects \SCHORRY onic subsiances\in which th ilar sizes\. cation and anion are of almost st Caen ample NaCl RCT._CacT ane AaB Tt may be noted ‘Sat ARDT Shows both. Frenkel ‘as well as Schottky defects; | 2 rout 52 { &) Impurity psec) ROP ed If mol 1 cohtaining & wy uF BC is crystallised. some of the sites of hou Secupied by St (Fig.1.27)- gp jaces two Nat ions}it occupies STonion and the other site 3 cationic vacancies us gid LS 7 progiuced aTin number to that of 5: = Vee iced ar a Tee Te IN Fig, 1.27: Introduction af cation vacancy 1 “Solfd_ solution of Ca if b howte NaCl by substitution of Nav bySr* ah “bho 9 Furr cane of depot Gh ostre Bed rae aa __ eens rile cts eso Site pf Bett els tite genome ee” polite (tte ir [we ? tt Ft a Te tobe A ¢ Scanned with CamScan)disturb the stoichiometry g The defects discus However, a large number of ron, 01 7 th stalline subs ioe contain a 2, MMabecit the crstatine su are known whicb-cortan Sven ath” s : vee Oe gmt sent ni ae ope Bere cir cr fal stru S. ie pes exes defect and (ti) metal deficien Nat LCR) Metal Excess De Y sgr Bikat natal eee ore e Metal excess defeci/due to a! ge Alka halides WR Ot eS be Te ss defer ao “ “i like NaCl and KCI ant eee. fel in a aUIHOSP wn a by ang is An in a crystal a Fig. 1.28: An Fecentre in a crys ox (Cclowrbios) la eal Ba Mev Cyl). Wa 64, a gt = Chee 2B" +702 + Peg naighossy nse ys its formula begomes Sites. Lote bow, 7 (i) Metal Deficiency Defect C\ nV “igue love cts 7 There are many solids which are diteuit" 5 prepare in’ Ghe Fagg Oineyecas-r46%4) : stoichiometric composition and contain I FEE host yah compan d to the stoic lenpok ELE, Fe ane fet : ay 110 Electrical Draperties over 27 orders of Solids can be qt conductivities, tots rot © gpd landed, S$ rangi between 10) ductors. Metals hye conductivities, food cond rE ch Scanned With CGMSCGanIInsulators : These are the solids With very low ranging bepween 10% to 10" fim "m'. On. the <6 4 (i Bemicopductors : These are-the solids with condugyfites in the Bin (C10 to 10 1 .4,-) itepatediate range fromp10" to 16” ohm 'm". { stay . ‘ | 4. 30.1 conduction A conductor may conduct electricity through moyément of electrons or of ons. Metallic conductors belong to the formes OdudN OIA ag sosaue saben i end nce salen. Lop clonP? a f yb wt gy. Pe Various combinations of n-type and p-type semiconductors are used woes for making electronic components. Diode is“a_ combination of n-ts and is us rw : ar ‘and silicon are group 14 elepfnts and therefofe, have a characfefistic valence of four and form fgGr bonds as in djamond. A az. of gfoups 13 and 15 or 12 and 16 to Amulate average valence of four y? large yafiety of solid state materials have Keen prepared by obmbination | | | i "" GnSCdS, CdSe and HgTe are examples of groups 0 ; porids are not perleorly covalent and the 14 Aor | R a =n LAL Haguetic Drope } } ; i Magnet oe wpe oan sions} a ne . ruleus mn grbital magnetic Fig.1.31: Demonstration of the magnetic moment associated with (a) an orbiting electron and (b) a spinning electron. magneton. fp. [tis equal to 9.27 x —_—— = On the basis of their Magnetic properties, substances can be classificd into five categories: (i) paramagnetic (ii) diamagnetic (tii) y_(Teftomagnetic (iv) antiferromagnetic and (v) ferrimagnetic. » Sisthle () Paramagnet® ances dxefwealdy] by a magneti j meen rae t nip ae F (,) mére unpaired clectrons Which are attracted by the masnetic Dorhitelrotion aroud mut fila Os, CO", Fe™, Cr™ are sdme examples of such substant Dobitad mation around ilimscy, ei ene valet HY ES CP Or deertispiy orbital Mga 92 F010 71 pee Fam scanned with CGMSCGnIoa ly repelled by ‘some examples of such j and they | lose their magnetic character. sobatt, niet : AF Ferromagnetism: A few substances jie eon, cobalt niche { sgdolinium and CxO, are attracted very strondly BY a Maghe ; ield. Such substances-are called ferromagnetic Substances, j Besides strong attractions, these substances can be permanently Tons- of ferromagnetic ed- In solid state, {he ~mel Satta ore grouped together into small regions called A h domain acts,as a tiny magnet. In an WS Grains) Tes, ees ferromagnetic substance the gents nly orient their m: l. When theo petance is placed in a magnetic field all the domains get oriented in the direction of the magnetic field (Fig.- 1.32 a) and a strong magnetic effect is produced. This ordering of domains persist even when the magnetic field is removed and the ferromagnetic substance becomes a ayjent; magnet. (iv)_Antiferromagnetism: Substances like (MnO Showing anti =~ ferromagnetism have domain stru similar to Terromegnei substance, but their domain sre Gppiiny esto and cancel out each other's magnetic moment (Fig. 1.32 b)- % AY Ferrimagnetism: Ferrimagnetism is observed when the magnetic q moments of the domains iri the substanc@are aligned in-parallel ‘ and anti-parallel directions in unequal numb: ers (Fig. 1.320). They ' are: attracted etic field as compared to ferromagnetic substances. FeO, (magnetite) and ferrites like MgFe,O, and t 2nFe,0, are exanipres of such substarices. These substances also ; {oe lerrimagnetism on heating and become paramagnetic, ~- $CGnned with CGMScan)Intext_CQuestions: 1.19 What type of defect can arise when a solid is heated? Which physical property is affected by it and in what way? 1.20 What type of stoichiometric defect i shown by: ) Zns (ti) AgBr 1.21 Explain how vacancies are introduced in an fonic solid when a cation of higher valence is added as an impurity in it. 1,22 Ionic solids, which have anionic vacancies due to metal excess defect, develop colour. Explain with the help of a suitable example. 1.23__A group 14 element is to be converted into n-type semiconductor by doping it with a suitable impurity. To which group should this impurity belong? 1.24 What type of substances would make better permanent magnets, ferromagnetic or ferrimagnetic. Justify your answer. Stommary Solids have definite mass, volume and shape. This is due to the fixed position of their constituent particles, short distances and strong interactions between them. In amorphous solids, the arrangement of éonstituent particles has only short range order and consequently they behave like super cooled liquids, do not have sharp melting points and are isotropic in nature. In crystalline solids there is long range order in the arrangement of their constituent particles. They have sharp melting points, are anisotropic in nature and their particles have characteristic shapes. \ProPertles of Cry a sea an a ee between Tiel constituent particles) ‘On this basis, they can be divided into four -categories, namely: molecular, ionic, metallic arid covalent solids. They differ widely in their properties. vos The constituent particles in crystalline solids are arranged in a regular pattern which extends throughout the crystal. This arrangement {s often depicted in the form of a three dimensional array of points which is called crystal lattice. Each lattice point gives the location of one particle in space. In all, fourteen different types of lattices\are possible which are called Bravais lattices. Each lattice can be generated by repeating its small characteristic portion called unit cell. A unit cell fs characterised by its edge lengths and three angles between these edges. Unit cells can be either primitive which have particles only at thelr corner positions or centred. The centred unit cells have additional particles at their body centre (body- centred), at the centre of each face (face-centred) or at the centre of two opposite faces (end-centred)\fhere are seven types of primitive unlt cclls.yraking centred unit cells also into account, there gre fourteen types of unit cells in all, which result in fourteen Bravais tattices | Close-packing of particles result in two highly efficient lattices, hexagonal close-packed (hep) and cubic close-packed (ecp). The latter 1s also called face~ centred cubic (fec) lattice. In both of these packings 74% space ts filled. The remain! of es of volds-oc' I voids and tetrahedral voids. Other types of packing are not close-packings and have less 29, The Solid S Scanned with CGMS can68% space tc lattice (bee) 6 cllicient packing of particles. While in body-centred es ic lat 's filled, in simple cubie lattice only 52.4 % space is {types of imperfections Solids are not perfect in structure. There are sitrent (gps ‘ypes of defects, or defects in them. Point defects and line defects are con marity defects and Point defects are of three types - stoichiometric defects, iat defects are the Ron-stoichiometric defects. Vacancy defects aaa intersitie, these defects are two basic types of stoichiometric point defects. In Saale feten wie cacuedl by te Present as Frenkel and Schottky defects. ee oa the onde impurity has Presence of an impurity in the crystal. In fonic solids, when the avelereated:iNon® & different valence than the main compound, $01 ne way metal deficient type. Stoichiometric defects are of metal excess TPs introduced by doping in Sometimes calculated amounts of impu ‘Such materials are widely ” sal properties. onductors that change their electrical Bar math cis proposal Tass Sarwan Sas my ge me pers .etism, agnetism, ferromagnetism, 7 ; iinet, the fers te ls er cg devices. Al these properties can be correlated with their electronic contig or structures, Exercises 1-2 Deline the term ‘amarphous'. Give a few examples of amorphous solids, * AZ What makes a glass different from a solid such as quartz? Under what _ © conditions could quartz be converted into glass? B10K XE Classify cach of the following solids as ionte, metallic, molecular, network © (covalent) or amorphous. {) Tetra phosphorus decoxide (P,0,,) (vii) Graphite (i) Ammonium phosphate (H),Po, 4) sic 1) Rb wv cate &) Libr ¢ atomic mass of any unknown aston of its unit cell I? Explain, nitude of its melting ¥ Points’ ter, ethyl alcohol, diethyl ether you say about the intermolecular ne th metal if you know L6 ‘Stability of a crystal ts reflected in the Comment, Collect melting Points of Solid aa 2 data Book. What ean scanned with GamScani1.7. How will you distinguish between the following pairs of terms: ~ (®) Hexagonal close-packing and cubic close-packing? (i) Crystal lattice and unit cell? (iu) Tetrahedral void and octahedral void? 1.8 How many lattice points are there in one unit cell of each of the following lattice? () Face-centred cubic (i) Face-centred tetragonal _ (i) Body-centred 1.9 Explain () The basis of similarities and differences between metallic and tonic crystals. (i) Tonic solids are hard and brittle. 1.10 Calculate the efficiency of packing in case of a metal crystal for ( simple cubic (il) body-centred cubic (ti) face-centred cubie (with the assumptions that atoms are touching each other). 1.11 Silver crystallises in fec lattice. If edge length of the cell is 4.07 x 10* ; em and density fs 10.5 g cnr’, calculate the atomic mass of silver. 1.12 A cubic solid is made of two elements P and Q. Atoms of Q are at the comers of the cube and P at the body-centre. What is the formula of the compound? What are the coordination numbers of P and Q? 1.13 Niobium crystallises in body-centred cubic structure. If density ts 8.55 g cm*, calculate atomic radius of niobium using its atomic mass 93 u. 1.14 If the radius of the oct id is r and radius of the atoms in close~ packing js derive relation between r and R- 1.15 Copper crystallises into a fee lattice with edge length 3.61 x 10° cm, Show that the calculated dex.it; is in agreement with its measured value of 8.92 g cm. 1.16 Analysis shows that nickel oxide has the formula Nj,,,0,,,- What fractions of nickel exist as Ni and Ni fons? 1.17 What is a semiconductor? Describe the two main types of semiconductors and contrast thelr conduction mechanism. L Non-stoichiometric_cuprous oxide, Cu,O can be prepared in laboratory. KK is oxide, copper to oxygen ratio is slightly les 2:1. Can you ‘account for the ict that this substance is a p-type, semiconductor? 1.19 Ferric oxide crystallises in a hexagonal close-packed array of oxide ions with two out of every three octahedral holes occupted by ferric tons. Derive thé Ton fe. . Classify each of the following as being either a p-type or « n-type semiconductor: (0 Ge doped with In (u) St doped with B, ‘ re ee wd iy 3 S waii, The Solld S Scanned with UamScani