1164 PRNORIES OF PHYSICAL CHOMSTRY 'o the other curve. We see that she tuo curves represent the wo stable sates ofa blsable system. (We ean, infact, liken bi-stabilty ofa chemical easton to supercool wherein a iguid tay be cooled below te freezing point without slidiying). It may be emphasized that the two states are not in equim states in the thermodynamic sense. They are in sendy sates which ae faraway from the eqiltrium, The concenirations of X and ¥ ate maintained as a result ofthe reactants continously ‘owing imo and ofthe products Rowing oit ofthe reactor) ‘Te presence of thie intermediate 7, capable of renting t with both X and, causes dramatic change. Suppose that in the absence of Z, the flows of the reacting species | «| | \e correspond tothe stable state ¢ on the upper curve (Fig 146). When, however, Z reacts with Yt produce X,Y decreases and X increases s0 thatthe slate ofthe system ‘moves. vards the right slong the curve until a sudden ttansion occurs to the lower curve. Therefore, Z reacts ‘Vth X producing Y, withthe result thatthe state ofthe system moves towards the left along the lower curve until il snoher suden transition occurs to the upper curve when the process stars again. The result is a periodic surge ant depletion of coicersation of Y, arising Out ofa sudden lespng from one stable sate to another in the bistability : occuring in an oscillatory reaction. Fig 15) Te Considerable research is going on to dover oxiltry ‘reactions of tds inpotance, The shih of te heartbeat is mained by oscillatory reactions. Fig 1S. Peiaicuge and depletion of onseatan ia bate Se [Review Questions | Ms wei of Gs te enery of tec oreo ya cay. Da carly he geal tracers fy reasons. 2 ict Kes fai alyad rein. 3. Diu the min stn of eanne-atyad eo 4. Te wing mei as en pool for eye exis ees poe, eee ins aun ES, 0 x een i ey 1 = ABT +18) tte bh ial meng. Das hen Ky >> (ly >> 8 5 ni ei tin a me a ai ers thas: este seer a te mil aes sal meming an E eee come foe tee enya pr ‘Wig wa eon, Sow a ° ACES) fe GT ilk + Cs RBI 6, Das Gees of (Ominous eins (bine sti won 1. bp fie ns fad eats. Wilt SN tins» Osa i ein hel mdi, aa Solid ae characterised by incompressibiliy, rigid Sl ressibility, rigidity and mechanical strength. This indicates Seon ete, ons o os that mike up a oi ar sly paied. Tare ie together by Re orl agen 80 ONE a radon, This, in sos we hve weeded say sl i, aan sap, ess ea msi ati ave also ck istic geometrical forms. Such substances are éai¢ to er line soli : ge Sis eve ‘Gt linearis mote eT A ere a ts pte ey 2. Melting Points. Consider’ a mote 2 eer eget vratosinctease and utinately bone gat yee, A cosine stsance ba sa pelea a ha aaa point, Ae it changes abruptly into liquid state. An sem bcs one conta, ds a veh nig pa a Ae crores fen od sar 0 for who sadapony setae Se fore ea €S terioe,tepned ae seal epee hs pe ane, Te wt say aN known from Xa ex Berea a anenon Spa Da cMaene or amie arangeneats Sy ela al Se. nla caine materi cn be cms ey a, THES. ny tgs RRR, 24 Acropy. Amorous sane die fom csi sie ad ese Cn pe Te pet eh eee ec ee soulucviy, metal seas od sie Pie ae ee pious ToS A, Gee, ido We oops tat weak ee, aT $86 i1168 PRNOPLES OF PHYSICAL CHEMISTRY ‘lids, onthe oer hand, are anisotropic, i, thee physical properties ave different in diferent directions. For example, the velocity of Tigh passing trough a crystal varies with the direction in which itis seasured, Thus a ray of light entering sucha crystal may split up ‘inno two components each folowing. ferent velocity. This pheaomenon iow a dob etacton, Ths anny Ca eg cvs fe xen of ore leu ode oe eeeeat hh cael Ta Care Eo toe cha simple two-dimensional arrangement of only «wo Aiferet kids of atoms is depicted. Ifthe properties ae measured alo the drstin indicated bythe slanting lise CD, they wil be iret fom those messued in the directo. indicated by he ‘erica ine AB. The reason i that while inthe fist case, each row is mae up of alent types of atoms, in the second case, cach ow s made wp of one typeof aon ‘ony. In amorphos sold, atoms or molecules are arranged at random ad ina disorderly manner and, teefre, all dections are enc and al properties are lt in all dresoas. Size and Shape of Crystal, Several naturally occuring sis have dette crystalline shapes which canbe recognise easly ‘here are many ober solid mle which ozur as powdets 0 daglomerates of fine particles and appear wo be amorphous. But when an individual parle is ‘xanlned unde a microscope, itis als seen wo have a definite eqs shape. Such solids, in Which the crys are so small tht they can be recognised only ude a powerfl microscope, are Sai o be mieroerytalline. The ofa costal depends on the cleat wich itis formed | the slower the rat, the bigger the cry Ths is Deane Une is needed y the alors Or ios or ET TAT TT proper Poston in the crystal structure. Ths, large wansparent esas of sodium cite, sive nate, ium chlrie, ec. can be prepared by meling these salts nd Allowing he: cool very slowly a uniform rts for ths eae that eystals of most of the ‘peas foned by glial proceses in ature ae often very large ‘pterfacial Angles. Crystals are bound by plane faces. The angle hetweeg any two faces is called au iterfaclal angle. Although the'size of the faces ot ‘even shapes of the crystals of one and te, same substance ‘may, vary widely with conditions of fofmation, et. yet ‘the interfacial angles between any two corresponding fees ‘of the erystal retain invariably the same throughout, This is illustrated in Fig. 2. Although the exteral shape is ferent yet the interfacial angles are the same. The ‘measurement of interfacial angles in erystals is, therefore, Iimportat ia the study of crystals. The Subject is known 26 censtallograpty, Fe. Anboope ain of evils Fit 2 retain crys SYMMETRY IN CRYSTAL SYSTEMS Besides the inertia angles, anther inoran propery of arya i thei symenety. There aud vais ger of symmetry. only thre of wish wl Be ceibed hee. These ate ©) Pe of Symmetry (ii) Axis of Symmetry and (iii) Centre of Symmetry. Pane of Symmetry. When an imigiary plan cn vide a ey it vo ats uch tat on is th exact mortage of the other, the cyt! sa to havea la mmr ‘xis of Smtr. An ais af syiméty isa line abo wih toys iy be rote such that it pen he se. slr. spesrance noe tan once dnb compl evo. For ei ie ae of cbs, ans ain peti oh centre sch x THe Soup stare 1167 fold or a diad axis (Fig. 35). In the if appearance: atl ther : ste se way, ifthe neo sna ppg esta 3 tae of 120 te ais cle & three tld or tad as ie. he oe ae = ae ofa horagoal ‘crystal the axis és valled a if the sane o Sir sypenatee of cy femdom roan tough an ele of 80°F, coun an nai ae a ele ae : 3 fll and fl sof ron The ape ated to pet the sane os appearance, eid, Thosieass whan Sets & & ray @ } @ Fg. 3. Varios as of ty. Gatre of Smtr. cence of of symmetry of eral sich a poi ta ay Une era Gogh i ese the sate of the ey at equ tPA any. tne dean Sian bt detons, 1 maybe pied out tat . vt that ergs may have a nb of ls o aes of sytney Bet as Oy ee E “G 0 cite of symmetry. Elements of Symmetry of a Ci of a Crystal. As mentioned above, there ae differeat types of sytnmeties which me sible ina crystal. A crystal may have diferent numbers of each te of symmetry. The total number of planes, |SHRRULPRE ST Diagonal plane of fue ad” cate offers posses oy att | See “ Sanaa elements of symmetry of the oma To!” : ‘ id olin stm fart, we may consider e ccnens a) ae of symmetry-possessed by a cubic crystal, such as NaCl: e Sqr A abe coal pnenes ata ef Siemens | LO Symmetry, as will be clear from the discussion given, : below. Ths elements a samy ot y a a eonetee | ‘planes of symimetry. One rectangular L “+ pase of sutety is shova in Fig. da. There will be ; ; wore HIN pees, ach of whch whic age |. ©? ° angles tthe line shown inthe igre, This, there are 3 = Fectangular planes of symmetry inal ‘vs ot four fold” Anisof threefold . ‘yma ‘yet Diagonal planes of symmetry. One plane passing . @1168 PRINCIPE OF PHYSICAL Cty iagonally through the cube is shown fa Fig. 4b, There can be a total of 6 such planes passing iagoally through the cube, a6 a litle refetion will show. Aves of four-foid symmetry. One ofthe four-fold axes is shown in Fig, 4. Evidently, tere can bea total of 3 such four-fold axes at right anes to one another. <4 Axes of threesfold symmetry. One Such ans fasingthroegh opposite corners is shown in Fig. dd, There can be total of 4 such three-fold axes. . Axts of two-fold symmetry, One such axis emerging . ‘rox opposite edges is shown it Fig. 4e, There are, evidemly, | C19 sc aes of two-fold symmetry. 1. Centre.of symmetry. There is only one centre of symmereyIying atthe centre of the cube (Fg, 4. ‘Thu, the number of symmetry cements of vatious types ina cubic exystal are Panes of symmetry= 3 + 9 ements : co) Aves of sytimeuy = 3 +4 + 6 = 13 elements ' Asofewofld Caste of Centre of symmetry = 1 a eae ‘Toaal number of symmetry elements = 23 Cg o a 4 Var elien of yy 2 Point Groups aad Space Groups cic oys 1 can be shown from geometrical considerations that, theoretically, there can be 32 different combinaiors of elements of sjmmetry ofa crystal. These are called 32 point groups or 32 crystal systems. Some of the systems, however, have been grouped {ogetierso that we have only seven different categois, known asthe seven asic crystal systems. ‘These are cubic, onhorhombc, tetragonal, monoclinic, triclini, hexagonal and rhombohedral or trigonal ‘These systems together withthe marisium aumbers of plans of symméry and axes of symmetry and ther examples are given in Table 1 rane Cel Sans tad Man Syme Heat Tans Sa «tn =r ee 1) ae tne Neji pimny | WO, e, Rs, Thien stenty | Dana nA Se ND}, R304, BS 2. | ontatente The panes of smmery Mid Reames | Tie er of say 2 | tere Frei pteymeny | 88 Td 250 KPO, Frets ome fr 4 | meme Ove ce ef som Na. J00, No, 0, Ceecimmey | Gane tons ar 5 | ise Seriaw oye (320,380, K-00, HD, tlndomar mst py | 770, es, Ge Sletoretcigey |e bent Mere co Seren pes o symetry ‘Nalids, 1. ide, Magrsite Ssouedimey | Q'acs. 3 ‘Froups can Fhe pode 290 space groups as disused in Chapter 3 00 Grey ‘He SoU stATE 169 Space Lattice and Unit ll. A. space lace san aay of pins show bow mec, atoms or ions are arranged at different sites in three dimensional space. An array of points fi three-dimensional space latice is shown in Fig. 5. Esch point represents a molecule, an stom or an ion or a group of any of these consents, ‘The lace points can be broken up into a ‘umber of uit cells. Tis is done by conoecting the points by a regular network of lines, as shown in the figure. A unlt eel is che smallest ‘repeating unin space lace which when repeated over and over again results in a crystal ofthe given substance. Thus, space latce of a erytal has been tiene to a wall paper on which a single pater is contnuoasly repeated. Justas a pater the wall paper is repeated again and again, similarly, «unit cell (epresening a definite patter) ‘repeated agsin and again to build up 2 erysal. The only diference is that wile wall pape isin (0 Aimesions, space latice of a enystal isin three dimensions. The unit cell, in fact is the smallest ‘ample that represents the picute ofthe entie crystal, The crystal may be considered to consist of infinite number of unit ces. Each unit cell in 2 thret-dimensional space ins, evidently, three vectors, a, band ¢, as shown in Fig. 5 : ‘anay'be noted that these are the points and not the line which construe te spac latice. The lines joining the points are drawn simply to cepresen tite axes by means of which the relative Positions ofthe points can be described. For example, in Fi. 5, thre imaginary axes, OX. OY and (02, which may be used to represent the unit cell, have been showja. In order to describe a unit cell, vee should know ie distances a, b and c which give the lengths ofthe edges of the unt ell and the anges , B and 7, which give the angles between the three imaginary axes, as shown. Knowing ‘he unit cell dimensions, the theoretical density of a crystal can te ealtlted from the relation p= nMtiNgh) “0 ‘here mi the umber of molecules or atoms or foas inthe uit call; M isthe molar mass of the substance and V isthe volume of the uit cell Brava Lattices ‘The Freach erysallographer Auguste Bravais in 1848 showed from geometrical considerations that there can be tly 14 different ways in which similar points can be arranged in a theee- imersional space. Thus, the total umber of space latices belonging 1 all the seven basic crystal systems put gether is oly 14, a5 given in colur 2 of Table 2, ‘The cysts belonging tothe cubic system have thee kinds of Bravais latices depending. upon the shape ofthe unit eel, These are |, The simple or primitive cubic lat cach unit cll Fig 62). 2, The foce-centeed cubic lattice (Fin which ere are points atthe coors as well as at the cals f-cch ofthe six faces of the eve (Fig. 60). 3. The body-centred cubic lattice in which there ae points i, 5. Soe ine awit et. ¢ (P) in which there are pots only atthe corners of AA) Be By Fg. 60) Fasncmmed Fg. Boye ‘be tatee cde lance) ig a Single rive abe ce)1170 PRINCIPLES OF PHYSICAL CHEMISTRY at the comers as well asin the body centre ofeach cube (Fig, 6). The Bravais space latices associated with vaious crystal systems are shown in Figs. 72, 7, Te and 7d. The parameters of unit cell, the cell dimensions a,b, andthe interfacial angles &, 6 and y até also shown in each case. The actual Latice in a cestal of 2 given kind consists of a repetition ofa wit ell ofthat kind allover in three-dimensional space. LOA Ae 7 ody cen) Paseo F) Fig. Ya Cubic Spe Lanes, i NY Yar V7 Speen) Beja) Eel © Fete One ats AN ADA AYN AY nal Ye a7 ee a a a) ig, Ye. Tesora ait Moon pce Lats rash ese). Renter Tap) Fi. Tei, Hn inthe | Se Cr San he ies fv en eo ie 3 i gi ad 4 ‘splGe Lek ta seven exyoal systems. ‘Some detaled descriptions of these seven ems oes ti ay pons yt ay Single oe Pinitve ®) “THeSOUD STATE a7 TABLE2 Seven Crystal Systems Tiina Paras of Cal Cal P cy ten Beals Late ‘mney ‘cat a ] wey [tg etic Ane 1 Cac | Pie, Faeceaned, Fr Sd as Endycenre re nr \ 2, Ortartemtie| Prine, Facer, Body-eared Thee mit eres Earned Satur es i 3. Tetragoal | Priitv, Body-centred One fol axis 4% Monaise | Prnive, En- = $0x10™ He Mola miss __i2<1igeat Masso ne moll of Fe = Mola mast Tost bg tel Of FeO = Rrapsrasaunber "6.022510 ol = 95x10 ag 50x10 ig oer oR meres pet al cll = 4ipe6 Nene f FO males se Trap here ar four Fe fons sn four OF ons in ech en cl sail 3 Clelate the number of atoms contained within () centred cabic (sic) ent cell (i) a face-cntred cable (Cc) It (i) a ody Shain : 6) The primitive cblc ut cel cons af oe atm at each of the 8 comes. Bah ta i ths117 PRINCES OF PHYSICAL CHEMISTRY stan by 8 ui cals. Hesse, m= BX(U) = i) The tc wt ell consis of 8 atoms athe 8 corer and ne a athe exe. At each come only {Wk of tesa i within ce ui cell. Tus, the coaton ofthe 8 comets fe BX while at ofthe edycented wom & I. Hens, aL = 2. {id Toe 8 ams at the corners comb 8X1) = I, There i os stom eth ofthe 6 fae which is ‘at by 2 ui els exch, Tht, te combo of 6 taxed some = 6X{I) =3. Rene, ne Tod = 4 ly) we cose the si cell of dion late, we find tt tee ie sos 0 the 8 cas, each sary 8 unk els, Also, there ae 6 sos onthe fae hated by 2 en cell In ata, thee re Moms ide they cl. Hone, n= Bx) + 6342) +4 5 ramp ¢Caclate the conrinatin number (C.N) ofan toa, ‘bndycetrdP cic ult cell a) face-cetred cubic wal el Sdn: (A ite cosideratioe shows that in enitve cubic wit cl, each atom bas 6 eqely-pced nest neighbour ana. Tan CN = fi) Coiering we wom atte cen of the ut el, we fn ht iti sucounded by 8 nearest seghboer sows stu atte core: of the ee Thas, CN (i) CN. fra e-em tan (8 viel i evidey,equa 1. (0 primitive cable ust cal i) Eomple 5 At room temperature, pallu crystals in patie cable eit el. I 29336 A, cae te thst ety pl Molar of pleum=3 ma’ Selo A iv abi i ll ois ss cay eB cme i ah cmc 1h of at ao Hee t= i = Vane, ¥ =, = 636 A? = 35x10! a AM, 000107 ke) gigi ag MAY * Cea aor 0.36617 Fa From Ba 1. 9 Example 6 At roam temperate, sod cys in» body-coned cai cl with a Colette hoe deny fs. Moar at Mot sam = 59 gmt Sano As sown in Bape 3, Be va of far a be wit 2. 24 4? = 20210" wy? iM 2.430 x10eg mar KY” 60221 mor et aE unl 7 Lion trys, LB, ryan sa krone sen vt 4 moles er wit Gul, The vical dineaoas ae 4 = 681A, B= 643 A ans'e= PHT Ate lat macs Bf of LBs 2046 gmt eae he deny ofthe ea i) 45176 co gmar POE)” Gea TP mor ear aasraT IOP) aml 8; Aa ori ompound cyl ina ahorhombic ge ih cls perl cl. Te ut cl ineins are 1265, 1543 and 209 he It the Sly elie cya W Pal te, aaa She dar mf te ora compound. Seon Fam Be, 2 = Vie (1419.00 kg) 6022.16 mo (12.05 1505 269 110° wh 7 Pranpl 9 bon (ae) cylin in ce: tn wth « su Clty of on Volune, ¥ 00 x 10 kg From Be 1.9 Sala 68x10 eg 020 vg met! 2861 AMolr mass Mf iron S585 § Suton: From Bg. 1, p = MH 2a S55 10 eg at 8 aon. ag wd AY C022 «1% mor 861 x10 emP THe Soun stare 173 Lattice Energy ofan foni@Crystl. tis defined as the aout of energy eased when cations and ania inthe ans Saar rout ogee fo infinite separation fm ey. MG) + X@) + MX(); U = latice energy Tee teres testment of ini Iatice oer was sven by M. Bom and A. Lande. This resin at born dase blo Consider he potent energy ofan ion pir, M?,X° ina crystal spate by a dsnce r. The couloic clematis etry o atvaton gen by > zie uate) = SEE Since 2. is weave, the electestatic energy is opave (with reget to energy at nite sean) and becomes iresoly 0a he vin tne decrees, a shown by the doted line in Fig. 8. Note tht the charge on the eaton is {ye and at othe aon i In acrylate here are ore itertion ween the os than the inl on in an lst on pair, Tus, in NaC) lace, cach sodium on experiences aracton fo the sik meats cherie ‘ns, eubin y tenet twelve nearest sodiam ages tothe ex eh coi fons and epson by tenet etm ins and son. The summation ofa ese geomet mergers is own ste Madelung ennstant, MT energy of aration sn pa acta is has given by 4 - Maze ald * “Faeer @ The vale of Madelung, constant depends ony onthe geometry of telat andi independent of lone radius an charge. Ths, the vale of Madelung cosa it Na ate is ten by wag BE, : i Ta 1 sate latice can result nly. it teres ako repulsion enery wo balance the stractve coulombic energy. The atactive eneray becomes ttn at inftesinaly smal distances. However ions are at pin charges but comitof eleton charge clouds wich rea enc oer al very close sans Ts reuon shown by the broken ten Fig. 8. is ape at large dtc bot ines very rapidly asthe fons aptoach each eer closely. According to Boru the repulse energy is given by Ung) = Birt 6 Were B isa constant. Experimentally, the Born exponent m can be determined from the compressibility «data because the later measure the-fesistance which the ions exhibit when foreed to approach each other very closely ‘Ths, for a crystal latice consisting of Avogadro's number of ions, the total energy is given by ® MN, MB ” foal) = Unt?) + Ung(t) = A =e es Yaak) = Ua) + Url = MOE Me 6 _ The total energy is shown by the solid line in Fig. & At the minimum in the curve tesponing othe equlrium latice configuration, (r= 1) (2 ASS eA 4)1174 PRINCIPLES OF PHYSICAL CATR In this lanie configuration, the atwactve forces between the ion balance the repulsive forces Let Uy represent the eneray atthe eqilibeium distance r,. From Ea. 7, apt Bg Mate 8) cos . Mia Meee ie a eee generE ee i i a“ : Mize, 1) x Mise, @ ‘ae Ud . - ‘This isthe Born-Lande’ equation for the latce energy ofan ionic crystal. The Born exponent depends upon te typeof te in involved. Large ios having relatively higer electron densities have larger vais of n. ample 10 Cele the late energy of Nl rsa fom the flowing ta: . M = LI j= 28 AG eS Solin + Sobting fe given data an he vale of he ater con 10, we Rave = GBI 0 ary AGF (1) GE BITE ON aA OAT t = = 775d mot Exernenalvalse » 7 Kt) We see'that the agreement of Bora-Lande eqation with experiment is satisfactory Subsiution ofthe various constants in Eq. 10 peste following equation = se naomi Experimentally, the Latice enthalpy ofan ionic compound can be aemined by using the Bora Haber eyele which can be represeted diagrammatically ab shown below : Jn to Ma ite ___yuty) xo ie ai a le . wo «fh 2p We find that i Ally = OH + BHex + Hie + Ags +.Uo ' Here the terms Affgy and AHax ae the entapies of atomization of the metal and the non— amet, respectively ; AH and AAfpy are the loaizaton energy of the metal and electron affinity of J - —ieaoo-met, respectively. | 175 ‘He Soup staTE Lay of Raton nfo, Tis ste at he ees of aay tae of cys log the cryonics se che equal w be vt inereps (D6) OF ne singe Stic umber mali of em, ©, 09, 85, C8, re aaa", dees sine who timbers Lt OF, OF nd 7 repent he thee eryeallogahic sue nd 6 ABC i pane (FT al ners il te bea, b nt Accrng te tove lav, be Tmecep of ay ft such KEM om te sume ee ate wi be single we met nll of Dal epee scan be on fom the grey the single maps ins cae we h Dad 3 Mller Indes. Miler indices are a set of ings (hk sch ae ued to sere a iven pane in a | PE 2 Comyn dn ‘crystal. The miller indices of a face of a crystal are inversely seis brooch fates of tat face oe vas ues, The procedure for dering he Mite ites fos pane flows 1. Prepare atiee-luma able wih uni cel aes th ops of ie clus. 2 aur in each cant inerep exes as € mile ofa, bo) ofthe plane with tex ue 2: Tae al sues 4 Clear factions obs bE and Esme I Clete the Mier inde of coal plier wh x hegh the crv ao ces tat a @y Ee Sate Flv poe Ger vee ps eee ow Omar we 231 erepe 1 ines 2 1 rapocals 1 reipoals 326 dla fratins. 1 eat ftons ere, the Miler Talos are (26. Hence, the Miler indes a (11D, omens om « 633 ieee 2 iereps W613 BS epoeals @ peat P22 lear fins 3 de Tatons Hear, the Miler aos are (122) nce, he Mile indices are (373) Nate, The ngtve nin the Miler ines i indice by placing bar on he ier. The Miler indices ‘eels wie parce, Tnterplanar Spacing in a Crystal System. It can be shows that in a crystal, the interplanar desance dis, piven by day? = (ra)? + cio}? + (ie? A) where, f, Hare the Miler indices of the planes and a,b,c ae te dimension ofthe cell. For atublc uzem, a = b = c so that from Ea. 12, yy = af +B + BY oy For a teragonal sytem, a = be so that ‘Wide? = 2 + a + Bice 4,1176 PRINCIPLES OF PHSICAL CHEWSTRY Foran onhorhonbi system, a 2b #6 shat Ud? = Wied + Bae + Bre 9) 12. The grates ofa ortoromble wit cl te 6°50 pm 5100p, ¢=15) pt Deenlae the gc Bae te 2) plan ‘Seton >. Form oar nigh apn na, dy, ten by Meda? = OP) + Be) + CHA) Mtdys? = Ud? = (50 pm? + @2100 pai? + G3 pd ay = 5 /stpm 10 tat dn = Sopa YF = 29 pm ‘sample 13. The deny of LA metal is 0-53 g cw and the separation of the (00) planes of te ntl 350 pm. Determine whether the lice i ees or he. MCLI=OS gma (64.18) U5 po? Suton Tey, @ = O83 gen? = 5 tg? Forde abe sem dy = af + 8 + BY 1 = Se = 1 om = 390x107? “o Peo +o? ” We tow om 4.1 hat i B= AMINAY) = mMtitiya vee ati. Ss0eg 06022 «1 woly050 x10 a? _ ag 2g ue 6-941 « 10 ky mor ‘As shown in Brome 3. 0 a Ce ato, a= ad fora be, lc, n=2, Heme, it bs @ ee tates. X-RAY DIFFRACTION, a a, ermal tne ee oe cal mae ) tse Romesh Seg oe diy eee ee ie eve oe a oe | ‘crystal and the angle of reflection, is mene es Deron ofthe Brage Bavaton. Goose Fg, Ts hor ef this Faure reeset parlt planes in the ery sre separated frm one ape bythe diance &. Supone a beam oP Xa fala on the crystal at plancing angle 8, 5 sw, Some of tes: ays Pee ‘trom the pper plane at Figs 10, X-y ees fr ay ‘same angle 8 while some others wil THE SoUD stare ww be stsrbed nd et eee inthe successive layers, awa. Let he planes ABC and DEF be tava peptic ice and reflected beans, respective The waves releted by om uw 2 mw ue & & we Ww rca ey « « 35% large being abou 3:35 A. This rues out the posibiity of coralea boing beween the layers. Such crystals in which the varibu sheets of atoms are separated from one another by a dtanc larger than the maximum petinssible forthe | Fo formation of chemial bond are said to have layer tates, | tak Since a chemical bond is not posible between cabo |__Fe 7 Smurf wai ston in fret layers, the fourth yaleney remains unsaisted, de, some electrons renin fee ot unpaired. This peril he pasige of eleticiy trough graphite makig ita good coaductor of electricity the cobesive forces between diferent layers of Sheets are relatively feeble, ruptuve between the various layerscan occur easily. Such substances, therfore, are sof. Tey ae used a lubricants because one plane of atoms can readily sip over anther. Tate Crystals ‘8 Bionic crystals, the units occupying lative points are postive and negative ions. In sodium chloride, for example, the units are Na* ions and CI” ions. Each ias of a given sign in beld by oulombic forces of traction to all ions of opposite sign, Thee forces are very strong and therefore the amount of energy required to separate ion from one another is very high. Accordingly, Fi, 16, Sra oon,1190 PRINCPLES OF PHYSICAL CHEMISTRY the ionic erytals have the following characterises |. The beats of vaporisation of fone crystals are high, 2. The vapour pressures of ionic erystals at ordinary temperatures are very low: 3. The melting and boting points of ionic crystals are very high 4 Tone xystals are hard and brite 5. onic erystls are insulators in the solid state, The reason is that fons are ctrapped in fixed places in the crystal latice and cannot move when elect field is applied, However, Whea melted, they become good conductors of electricity. This i dve tothe fact that inthe maken state, the well ordered arrangement of ion inthe erystas is destroyed and the fons ae in a position to move about in the liquid medium when an electric field is applied 6. onic crystals are soluble in water and also in other polar solvents, They are insoluble or very slighty soluble in non-polar solvents such as benzene and carbon tetrachloride. 7, Tonic solids are good conductors when dissolved in water. The ions held by coulombic forces fall away from one anothet when dissolved in water or in any other solvent having high dietetic constant. This i in accordance with the Coulomb's Isw that forces of attraction between oppositely charged particles vary inversely a8 the dielectic constant. CCharicterstc Structures of Tonle Crystals. Th-ionic model treats a crystal 2s an assembly of oppositely charged spheres that interact primarily through coulombic forces. If the therme-dynamic properties of the erystal calculated onthe basis of the ionic model agree with experimen, the crystal ‘may be taken as ionic, We shall briefly discuss the characersic structures which are KOIypES of 1 wide range of oni erytals 1. The Rock Salt (ACD Structure. This structure is based on an fc. array of bulky anions in which the cations occpy all, the octahedral holes (Fig. 18). Attematively, it can also be treated as a structure in hich anidas occupy all the octahedral holes in an fc, array of cations, I is evjdet from the diagram that eich ion is sounded by an octahgron of sx counterions. ‘Tous, the coordination number (C.N.} of each type at ion is 6 and the structure is refered to as (6 : 6) coordination. In this ‘otation, the fst number in the parenthesis is the coordination ‘umber ofthe cation and the second number isthe coordination umber of the aon, order to determine the number of ions of each type ia a unit cell, the follwing eles should be borne in mind Fg 1, Te ek suc. (An ion in the body ofa unit cll belongs entirely to that unt cell and counts as 1. (An in in a face is shared by two unit ces and comtibutes 1/2 wo the wit el in queton, (ii) Anion onan edge is shared by four unit eels and Uns contributes 1/4 (Go) Am ion ata vertex is shared by eight unit ells that share the vertex and so contributes 1/8. Applying tie abaye-rules to the rock salt (NaCl) smctur, we fndthat here are four Na* fons ‘and: for CF on so that each unit cell conta four NaCl formula uni. The stintfine of KCI'a THe Soup state 1191 2, The Cesium Chloride Structure, This structure (Fig. 19) has a obic uit cell with each vertex occupied by an anion having a eation at the cenie of the unt ell (or vce versa). The coordination number for both types of ions is & and the stricture is referred to as (8 : 8) conninatia. i 19, Te cso core sue. Fp. 20. The pies Wen severe. 13. The Zine Bled (Sphalerite) Structure. This structure (Fig. 20), devving its nar from the mineral form of Za, is used on an expanded f..c. anionic Tatice where cations occupy one type of ecahedral hoes, ach anion is surounded by four neighbours, Thus the srue- ture as (4 : 4) coordination, 2 4. The Wurtate Structure. This structure (Fig. 21) differs from the zine bleade structure in being derived from an expanded hexagonally close packed array of anions rather than an fcc. array, However, as in the zinc blede structure, the cations oeeupy one type of tetrahedral holes. The structure, thus, has a (4: 4) coordination, 5. The Fnotte Structure. This stucrose (Fig. 22) takes its ame from CaF. In his structure, the cations occupy half the cubie holes ofa primikve cubic array of anions. Alternatively, the anlons.oceupy both types of tetahedril hoes in an expanded Ce. lace of cations. (In the antiuorite structure, an example ‘of which is K,O, the roles of the cations and anions are reversed) In tbe Morte structure, the coordination num- ber is. 8 for the cations eight fluoride ios forming a cube about each calcium ia) and 4 for the aaions (four Ca2* fons tetrahedrally arranged about each F> ion), Thus, the ‘oorte structare has (4) coondnaton, 6. The Rutile Structure, This strusture (Fig. 23) lakes its mame ftom rile, the mineral form of fig (Y) onige, 710s, The coordination aumbers are 6 forthe cations (x ore anions arranged approximately octahe- Ally about the TH fons) and 3 forthe aoa (three TH#* ‘ions arrange trigonally about the oxide ions). The rutile structure has, ths, (6 3) coordination,