THE SPACE LATTICE AND UNIT CELL

Transcription

1 6 Introution of Crystl Struture All the hlies MCl hve negtive enthlpies of formtion, whih inites tht thermoynmilly (tht is in terms of energy) it is fesile to form the ompouns MCl from the elements.. The most negtive enthlpies of formtion our with the fluories. For ny given metl, the vlues erese in the sequene fluorie > hlorie > romie > ioie. Thus the fluories re the most stle, n the ioies the lest stle.. The enthlpies of formtion for the hlories, romies n ioies eome more negtive on esening the group. This tren is oserve with most slts, ut the opposite tren is foun in the fluories. Ioni ompouns my lso e forme in solution, when similr yle of energy hnges must e onsiere, ut the hyrtion energies of the positive n negtive ions must e sustitute for the lttie energy. THE SPACE LATTICE AND UNIT CELL The regulr rrngement of n infinite set of points (toms, ions or moleule ) in spe is lle lttie or spe lttie. The spe lttie my e one imensionl, two imensionl n three imensionl epening upon the numer of prmeters require to efine it Tle Ltties n the Prmeters Require for Defining Spe Lttie Type of lttie Repet istnes Interfil ngles No. of prmeters require for efining the lttie -Dimensionl Only one repet istne -Dimensionl, 3-Dimensionl,,,, Two repet istnes n n interfil ngle Three repet istnes n three interfil ngles A spe lttie : The regulr rrngement of onstituent prtiles (i.e., toms, ions or moleules) of rystl in three imensionl spe is lle rystl lttie or spe lttis. Unit ell: The smllest three imensionl portion of omplete spe lttie when repete over n gin in ifferent iretions proues the omplete spe lttie is lle the unit ell. For esriing unit ell, we must know: () the istnes, n i.e; the lengths of the eges of unit ell. () the ngles, n etween the three imginry xes, Clssifition of Unit Cell : On the sis of the lotion of the lttie points within unit ell, we n lssify unit ells into the following types : Primitive unit ell Non-primitive unit ell () Simple or primitive: In this type, points (i.e, toms, ions or moleules) re present only t the orners of the unit ell. E.g. SCC (Simple Cui Cell). () Non-primitive : In this type of unit ell, the lttie points re present not only t orners ut lso t some other speifi positions. (i) Fe-entre: In this type, points re present t the orners s well s the entre of eh of the six fes.

2 Introution of Crystl Struture (ii) Boy-entre: In this type, points re present t the orners n n itionl point is present t the entre of the unit ell. 7 (iii) En fe entre : In this type, points re present t the orners n t the entre of the two enfes. (iv) Ege entre unit ell : Lttie points t ll orners + t eh ege entre. SOLVED EXAMPLES. The rystl lttie struture of soium, vnium n molyenum is BCC (Boy entere ui). Whih of the following metlli mixtures re most likely to form soli solution? [TIFR 00] () V n Mo () V n N () Mo n N () N, V, Mo Atomi rii : N = 0, V = 35, Mo = 45. Metlli mixtures of element hving omprle size form soli solution. Corret option is (). Whih of the prllelogrm in the figure elow re vile unit ells? [TIFR 00] i () i () ii ii iii () iii () ll of the ove Corret option is () Brvis lttie: Brvis showe tht the unit ells n e rrnge in regulr three imensionl orer in, the seven types of rystl systems in 4 ifferent wys. These rrngements re lle spe ltties orbrvis ltties. The 4 Brvis ltties my elong to either of the ove mentione four types of unit ells. Seon Clssifition of Unit Cell : On the sis of xil length n inter-fil ngle, the unit ells n e lssifie into the following 7 types whih re known s 7-rystl systems. Crystl Systems: At first sight there seems to e infinite numer of shpes of rystls. However, reful exmintion of severl thousn rystls of vrious sustnes hs revele tht only seven possile rystl symmetries re possile. The seven ifferent omintions of symmetry elements re lle rystls systems. These rystl systems iffer in the length of the unit ell eges (, n ) n the ngle etween the unit ell eges. Simple or Primitive (P) Boy-entere (I) Figure-() : Cui Spe Ltties Fe-entere (F)

3 Introution of Crystl Struture Simple or Primitive (P) Boy-entere (I) En-entere (C) Figure-() : Orthorhomi Spe Ltties Fe-entere (F) Simple (P) Boy-entere (I) Simple (P) En-entere (C) Figure-() : Tetrgonl n Monolini Spe Ltties Trilini Hexgonl Rhomoherl or Trigonl (R) Figure-() : Trilini, Hexgonl n Rhomoherl Spe Ltties Spe Groups : The olletion of totl numer of symmetry opertions of ll the symmetry elements in rystl is lle its spe group. Chrteristis of Seven types of Crystl Systems System No. of Brvis Ltties (4) Mximum symmetry elements. Cui 3 9 Plnes 3 xes. Tetrgonl 5 Plnes 5 xes 3. Hexgonl 7 Plnes 7 xes 4. Trigonl or 7 Plnes Rhomoherl 7 xes Axes n Angles = = = = = = = = = = Exmples NCl, KCl, CF, ZnS, Cu O, Dimon Alums, P, Ag, Au, Hg SnO, ZnO, TiO, NiSO 4, ZrSiO 4, White Sn ZnO, Pl, CS, HgS, Grphite, Ie Mg Zn C NNO 3, CSO 4, Clite, ICl, Qurtz, As, S, Bi Spe Group Orthorhomi (Rhomi) 4 3 Plnes 3 xes 6. Monolini Plnes xes 7. Trilini No Plnes No xes = = = = KNO 3, K SO 4, PCO 3, BSO 4, Rhomi Sulphur, MgSO 4 7H O N SO 4 0H O, N B 4 O 7 0H O, CSO 4 H O, Monolini Sulphur CuSO 4 5H O, K Cr O 7, H 3 BO

4 Introution of Crystl Struture SOLVED EXAMPLES 9. A rystl system hrterise y n 90º, 90º is [BHU-05] () trilini () monolini () rhomi () trigonl Corret option is (). Whih of the following is true for n orthorhomi lttie? [BHU 07] (), 90º (), 90º (), 90º, 90º (), Corret option is () 3. Wht is the unit ell hving imension n? [CUCET 07] () orthorhomi () monolini () trilini () rhomoherl Corret option is () 4. In tetrgonl rystl (), 90º (), 90º (), 90º (), 0º, 90º Corret option is () [DU 06] 5. Assign the Brvis lttie type for the following unit-ell struture [DU 07] () Tetrgonl I () Cui I () Orthorhomi I () Monolini 90 Therefore, tetrgonl rystl system. Corret option is () 6. One of ngle in monolini rystl system is [DU 07] () less thn 90 egree () greter thn 90 egree () less thn 30 egree () less thn 0 egree Monolini rystl system, Therefore, either greter or less then 90º. Corret option is (, ) Interplnr Distne: The perpeniulr seprtion etween jent plnes of rystl lttie is lle inter plnr sping, or the length of the perpeniulr from the origin on the unit plne represente y set of miller inies is lso known s interplnr sping. For n orthorhomi system, h k l So, hkl h k l ; hkl

5 0 Introution of Crystl Struture where h, k, l e Miller inies of the plne n,, re the imensions of the ell. For ui system, So, hkl h k l For tetrgonl system, So, hkl h k l SOLVED EXAMPLES. How o the spings of the three plnes 00, 0 n of ui lttie vry? hkl ( h k l ) ; 00 ( 0 0 ) 0 ( 0 ) ; ( ) 3 Thus, 00 : 0 : : : : : Potssium hlorie rystllises with oy entre ui lttie. Clulte the istne etween the 00, 0 n plnes. The length of the sie of the unit ell is 5. 34Å Sine we know tht for ui system, hkl ( h k l ) For 00 plne; 00.67Å ( 0 0 ) For 0 plne; Å ( 0 ) For plne,.54 Å ( ) 3. Consier rystl with simple ui lttie. If on heting, the unit ell volume inreses y 5% isotropilly (eqully in ll iretions), the perentge inrese in the (0) interplnr istne is [HCU 0] ().64 ().67 ().50 () % inrese 00

6 Introution of Crystl Struture Corret option is () %. 4. For simple ui system the sping of (00), (0) n () plnes re in the rtio of () : : 3 () : : 3 () :: () 3 : : [BHU-0] (00) (0) () Rtio : : : :. 3 3 Corret option is () LATTICE POINT The points representing the toms, moleules or ions in unit ell re known s lttie points. In the vrious unit ells, there re three kins of lttie points. () Points lote t the orners of unit ell. Sine suh point lies t the orner of unit ell, it is shre etween eight suh unit ells. Thus only (/) th prt of eh suh point ontriutes to ny one unit ell. () Points lote t the entre of fe of unit ell. Sine suh point is shre etween two suh unit ells, only / of eh suh point ontriutes to ny unit ell. Points lote t the entre of the unit ell. This point, eing present entirely within unit ell, wholly elongs to this unit ell. Contriution of lttie point t prtiulr lotion (per unit ell) : Lotion. Boy entre Contriution. Fe entre / 3. Ege entre /4 4. Corner / The numer of toms elonging to unit ell is lso terme s lttie sites n is enote y Z. Z = T.L.P. (Totl Lttie Points) Contriution Thus the totl numer of lttie points (or numer of toms) per unit ell in the four types of unit ells my e lulte s elow. () Simple or primitive: () Fe-entre: Z Z () Boy-entre: Z () En-entre : In ition to points present on the orners, suh unit ell lso hs points only on the en

7 Introution of Crystl Struture (two) fes. Sine eh point of the ltter type is shre etween two, unit ells, it ontriutes to to eh unit ell. Suh points re present only in en fe-entre unit ells. Thus the numer of toms per unit ell =. (e) Ege-entre : Z 4 4 The numer of prtiles immeitely jent to eh prtile in the rystl lttie is known s the oorintion numer for tht lttie. In other wors, oorintion numer is the nerest neighours surrounings prtiulr lttie point. It is hrteristi of given lttie. In simple ui lttie, eh prtile is joine y 6 other prtiles n so the oorintion numer of simple ui lttie is 6. Similrly, the oorintion numer for oy entre n fe entre ui ltties re n respetively. Lttie Z C.N.. SCC 6. BCC 3. FCC 4 4. En CC 4 5. HCP 6 SOLVED EXAMPLES. A ompoun hving BCC lttie struture is forme y elements X n Y Atoms X re present t the orners n tom Y t the entre of the ue. Derive the fornul of the ompoun? Sine orner toms re shre etween eight orners, therefore, the numer of toms, X t eight orners = tom The tom Y present t the entre of ue is not eing shre i.e. one tom; unit ue Hene the formul of the ompoun is XY.. A ompoun, forme y elements X n Y, rystllises in the ui struture, where Y toms re t the orner of ue n X toms re t lternte fes. Wht is the formul of the ompoun? Numer of toms Y t eight orners of ui unit ell = = Numer of toms X present on lternte fe of unit ell = = Formul of ompoun = XY 3. In rystlline soli nions A, re rrnge in p mnner. 50% of the otherl vois re oupie y B n 50% of the tetrherl vois re oupie y toms C. Wht is the formul of the soli? We know tht the numer of otherl vois re equl in numer to the toms forming p, while the numer of tetrherl vois re oule in numer. Rtio of the numer of otherl vois n tetrherl vois is : Now 50% of the otherl vois re oupie, therefore the rtio of A n B is A : B The 50% of the tetrherl vois re oupie y C so, the rtio of A n C is : i.e. A : C or A : C, Hene the rtio of A, B n C is A : B : C So, the formul of the ompoun is A BC.

8 Introution of Crystl Struture 4. Clulte the numer of toms present in the unit ell of monotomi sustne (element) of () simple ui lttie-() oy-entre ui () fe-entre ui. () Numer of toms in unit ell of Simple Cui Lttie. A simple ui lttie hs only eight toms on the orners. As ontriution y eh therefore numer of toms present in the unit ell = () Numer of toms in unit ell of Boy Centre Cui (BCC). This littie hs toms on the orners n one tom within the oy. Therefore, Contriution y toms present on the orners = Contriution y the tom present within the oy = Therefore, Numer of toms present in the unit ell = + =. () Numer of toms in unit ell of the Fe Centre Cui (FCC). This lttie hs toms on the orners n 6 toms on the fes (one on eh fe). Contriution y toms on the orners = Contriution y toms on the fes 6 = 3 Therefore, Numer of toms present in the unit ell = + 3 = Clulte the numer of toms in ui se unit ell hving one tom on eh orner n two toms on eh oy : igonl. There re four oy igonls. Thus there re toms within the oy of the unit ell whih re not shre y ny other unit ell. Contriution y toms unit ell t the orners =. Hene totl tom/unit ell = + = If three elements P, Q n R rystllize in ui soli lttie with P toms t the orners, Q toms t the ue entre n R toms t the entre of the fes of the ue, then write the formul of the ompoun. Atoms P per unit ell =. Atoms Q per unit ell = Atoms R per unit ell = 6 3 Hene the formul is PQR In fe entre rrngement of A n B toms. Where A toms re t the orners of the unit ell n B toms re t the fe entres. For eh unit ell, one A tom is missing from orner position n one B toms is missing from one fe position. The simplest formul of the resulting ompoun will e () A 4 B 40 () A 7 B 0 () A -x B 3-x () AB [TIFR 06] 7 One A tom is missing from orner position = 7. 5 One B tom is missing from one fe position = 5. A7/ B5/ Multiply y : A7 B 0. Corret option is (). A ompoun lloy of metls P n Q hs unit ell ontining P toms t the orners, while tom Q re present t the fe entres. The formul of the ompoun shoul e [BHU-0] () PQ () PQ () PQ 3 () P 3 Q P Corners Formul PQ3. Corret option is () Q Fe entres 6 3 3

9 4 Introution of Crystl Struture 9. An element rystllizes in n FCC ltttie. How mny toms re there per unit ell? [BHU-0] () () () 3 () 4 For FCC lttie, Z = 4. Corret option is () 0. An element rystllizes in BCC lttie. How mny toms re there per unit ell? [BHU-03] () () () 4 () 9 For BCC lttie, Z =. Corret option is () NUMBER AND LOCATION OF VOIDS IN A CRYSTAL In lose-pke struture (p or hp), if there re N spheres (toms or ions) in the pking, then Numer of otherl vois = N, Numer of tetrherl vois = N For exmple, in the ui lose pking (p) i.e. fe-entre ui (f) unit ell there re 4 toms or ions, therefore, there re 4 otherl vois. () Otherl vois: One otherl voi is present t the oy entre of the ue n otherl vois re present on the entres of the eges of the ue. But eh voi on the ege entre is shre y 4 unit ells. Hene its ontriution in the unit ell = 4 Hene the effetive numer of otherl vois in the p struture () Tetrherl vois: The tetrherl vois present in the p rise from the ft tht there re spheres t the orners of the unit ell n eh sphere touhes three spheres present on the fe entres of the three joining fes, eh giving rise to one tetrherl voi. Note: (i) Numer of otherl vois = Numer of toms present in the lose pke rrngement n (ii) Numer of tetrherl vois = Numer of otherl vois = Numer of toms.

10 Introution of Crystl Struture 5 SOLVED EXAMPLES. Rtio of the numer of tetrherl vois to otherl vois in ui lose pking (p) rrngement is () : () : () : () 3 : [HCU-03] p rrngement (Z = 4) Tetrherl vois = Otherl vois = 4 Rtio = :. 4 Corret option is (). In rystlline soli, nions B re rrnge in ui lose pking. Ctions A re eqully istriute etween otherl n tetrherl vois. If ll the otherl vois re oupie, wht is the formul of the soli? Suppose the numer of nions B = 00 Then Numer of otherl vois = 00 Numer of tetrherl vois = 00 As otherl n tetrherl vois re eqully oupie y tions A n ll the otherl vois re oupie (given), therefore 00 tions A re present in otherl vois n 00 tion A re present in tetrherl vois. In other wors, orresponing to 00 nions B, there re 00 tions A i.e. tion A n nions B re in the rtio :. Hene the formul of the soli will e A B. 3. In orrunum, oxie ions re rrnge in hexgonl lose pking n luminium ions oupy two-thir of the otherl vois. Wht is the formul of orrunum. Suppose oxie ions = 90. Then otherl vois = 90. Hene A 3+ ions 3 90 = 60. Therefore, rtio A 3+ : O = 60 : 90 = : 3 i.e. formul is A O In soli, oxie ions re rrnge in p.one-sixth of the tetrherl vois re oupie y the tions A while one-thir of the otherl vois re oupie y the tion B. Wht is the formul of the ompoun? Suppose O ions = 90. Then otherl vois = 90 n tetrherl vois = 0. Ctions A 0 = 30 6 n tion B 90 = Therefore, rtio A : B : O = 30 : 30 : 90 = : : 3 i.e. formul is ABO A soli is me up of two elements P n Q. Atoms Q re in p rrngement while toms P oupy ll the tetrherl sites. Wht is the formul of the ompoun? Sol. Suppose numer of toms Q = n Then numer of tetrherl sites = n Numer of toms P = n Rtio P : Q = n : n = : i.e. formul is P Q. STRUCTURES OF IONIC COMPOUNDS It hs lrey een isusse tht ioni ompouns onsist of positive n negtive ions rrnge in mnner so s to quire minimum potentil energy (mximum stility). To hieve the mximum stility, ions in rystl shoul e rrnge in suh wy tht fores of ttrtion re mximum n fores of repulsion re minimum. Hene, for mximum stility the oppositely hrge ions shoul e s lose s possile to one nother n similrly hrge ions s fr wy s possile from one nother.

11 6 Introution of Crystl Struture Among the two ions onstituting the inry ompouns, the lrger ions (usully nions) form lose-pke rrngement (hp or p) n the smller ions (usully tions) oupy the interstitil vois. Thus in every ioni ompoun, positive ions re surroune y negtive ions n vie vers. Normlly eh ion is surroune y the lrgest possile numer of oppositely hrge ions. This numer of oppositely hrge ions surrouning eh ion is terme its oorintion numer. The oorintion numer of positive n negtive ions of ompoun re sme when the two types of ions re equl in numer (e.g., NCl, ZnS, et.). On the other hn, when n ioni ompoun ontins ifferent numer of positive n negtive ions (s in CC, N S et.), the oorintion numers of positive n negtive ions re ifferent. For exmple, in CC sine Cl ions re twie the numer of C + ions, the oorintion numer of lium ion is twie the oorintion numer of hlorie ion. Simple ioni ompouns re of two types, i.e., AB n AB type. From the knowlege of losepke strutures n the vois evelope therein, we n hve n ie out the struture of simple ioni ompouns. () If the nions (B ) onstitute the rystl lttie n ll otherl vois re oupie y tions (A + ), then the formul of the ioni soli is A + B. () Similrly, if hlf of the tetrherl vois re oupie y tions, then the formul of the soli rystl eomes A + B. () When the nions (B ) re onstituting spe lttie n ll the tetrherl vois re oupie y the tions (A + ), then the formul of the soli rystl will e A B. () When the nions (B ) re present t the lttie points n ll the otherl vois re oupie y the tions (A + ), then the formul of rystlline soli will eome A B. AB type ioni solis NCl, CsCl, ZnS AB type ioni solis CF, SrF Ioni Compouns of AB Type:. Struture of soium hlorie (NCl) or Rok Slt rystl : It hs f rrngement lso lle ui lose pke (p). Slient fetures of NCl rystl struture re summrise elow: (i) The nions (Cl ) re present t the lttie points of fe entre ui lose struture. (ii) N + ions re oupying ll the otherl vois, so eh N + ion is surroune y six Cl ions. (iii) Sine there will e six otherl vois (holes) roun eh hlorie ion, so eh hlorie ion is surroune y six soium ions. (iv) The o-orintion numer of Cl s well s of N + ion is six. Therefore, it is terme s 6:6 o-orintion rystl. (v) On pplying pressure, NCl struture (6 : 6 oorintion hnges to CsCl struture ( : oorintion). (vi) The ioni rius of N + ion (r = 95 pm) n the rius of Cl ion (R = pm) gives rius rtio r/r = This vlue of rius rtio suggest n otherl rrngement of ions. (vii) The totl numer of N + tion n Cl nion present in one unit ell re lulte s elow. Numer of soium ions : In NCl, the N + ions hve een shown y rk spheres), = ( ions t the ege entre ) + ( ion t oy entre ) = 3 + = 4 4 Numer of hlorie ions : = ( ions t the orner ) + (6 ions t the fe entres ) = + 3 = 4 Therefore, the unit ell of NCl hs ontriution of 4 N + ions n 4 Cl ions i.e. 4 NCl formul unit per unit ell. The soium hlorie struture is lso lle s rok-slt struture. (viii) The ege length of the unit ell of NCl type of rystl (r + R). Ioni rius Ege length () of unit ell of the NCI type = of the tion Ioni rius of the nion

12 Introution of Crystl Struture 7 Or ( r r ) Thus the istne etween N + n Cl ions Exmples hving rok-slt struture i.e. NCl type of struture re Alkli hlies : NCI, LiCl, KBr, RI, AgCl, AgBr, AgI, NH 4 Cl, NH 4 Br, NH 4 I Oxies of lkline erth metls : MgO, CO, TiO, FeO, NiO N Cl. Potssium Chlorie (KCl): * KCl is metl hlie slt. * In its pure stte, it is oorless n hs white or olourless rystl pperne with rystl struture tht leves esily in three iretion. * It is fe entrere ui rystl. * Struture similr to tht of NCl. K + Figure 3. Cesium hlorie (CsCl) type struture : In this type of ioni rystl, the size of Cs + ion is quite ig s ompre to Cl ion. Therefore, it quires the oy entre ui lttie struture

13 Introution of Crystl Struture (i) The Cl ions re present t the orners of the ui unit ell n the Cs + ions re t the oy entre of the unit ell. (ii) Eh Cs + ion in this moe of pking is touhing hlorie ions n eh Cl ion is touhing eight Cs + ions. Therefore, this struture will hve : o-orintion. (iii) At high temperture, CsCl struture ( : o-orintion) hnges to NCl struture (6 : 6 oorintion). (iv)the ioni rii of Cs + n Cl ions re 69 pm n pm respetively. This gives rius rtio s r 69 pm 0.93 R pm (v) This vlue of rius rtio orrespons to BCC type of unit ell. (vi) Eh unit ell will hve the ontriution of one Cs + n one Cl ion s shown elow Numer of Cs + ion = (ion t the oy entre) = Numer of Cl ion = (ions t the orner) / = Therefore, the unit ell hs ontriution of one Cs + ion n one C ion per unit ell (vii) Reltion etween rius of tion, nion n ege length of the ue 3 r r Cs Cl The unermentione ioni rystls re the exmples of CsCl type of rystl lttie. CsCl, CsBr, CsI, TlCl, TlBr, CS. 4. Zin sulphie struture : Zin sulphie exists in two forms: (i) ZnS Blene (ii) Zns Wurtzite (i) zin lene or Sphlerite: Struture of zin lene is ui lose pking (p). (i) The sulphie ions (S ) oupy fe entre ui lttie points. n the zin ions (Zn + ) oupy hlf of the totl numer of tetrherl vois (ii) Eh sulphie ion is surroune y 4 Zn + ions n eh Zn + ion is surroune y 4S ions. Therefore, ZnS hs 4 : 4 oorintion. (iii) The ioni rii of zin ion (Zn + ) n sulphie ions (S ) re 74 pm n 4 pm respetively. Therefore, the rius rtio r/r = 0.40 It suggests the tetrherl rrngement of ions in the-rystl lttie. (iv) The ontriution of Zn + n S ions per unit ell is lulte s isusse elow. Numer of sulphie ions = ( ions t the orners ) + (6 ions present t the fes )= + 3 = 4 Numer of zin ions = 4 (ions within the oy of unit ell) = 4 Thus the numer of ZnS units per unit ell is 4. The following ioni solis re oserve to form ZnS type of rystl struture. ZnS, CuCl, CuBr, CuI, US, AgI, BeS (ii) Wurtzite Struture. The unit ell for wurtzite struture is shown in following figure in whih eh Zn + ion is represente y hollow irle n eh S ion is represente y soli irle. The wurtzite struture my e esrie s follows:. The sulphie ions re rrnge in hexgonl lose pke (hp) rrngement.. The zin ions oupy hlf of the tetrherl sites.

14 Introution of Crystl Struture 9 3. There re two tetrherl sites for eh S ion in the lttie. Sine only hlf of them re oupie y Zn + ions, the stoihiometry of the ompoun is :. 4. Eh S ion is surroune y four Zn + ions whih re ispose towrs the orners of regulr tetrheron. Similrly, eh Zn + ion is surroune y four S ions. The rrngement roun one Zn + ion n one S ion is shown in following Figure. Therefore, the oorintion numers of Zn + n S ions in wurtzite struture re 4 : The rius rtio r + / r in this struture is 0.40 whih lso suggests tht the oorintion numer is 4 n tht the rystl hs tetrherl struture. Thus, the rius rtio rule supports the ove struture. The ompouns suh s AgI, ZnO, NH 4 F n AlN hve wurtzite struture. It will e note tht the si ifferene etween zin lene n wurtzite struture is tht wheres in the former se the sulphie ions re rrnge in p type of pking, in the ltter se they re rrnge in hp type of pking. 5. Dimon Cui Strutures: The imon lttie n e onsiere to e forme y interpenetrting two f ltties long the oy igonl y (/4) th ue ege. One sulttie hs its origin t the point (0, 0, 0) n the other t point qurter of the wy long the oy igonl (t the point /4, /4, /4). The si imon lttie n the tomi positions in the ui ell of imon projete on ue fe re shown in figure elow. The frtions enote height out the se in units of ue ege. The point t 0 n / re on the f lttie, those t /4 n 3/4 re on similr lttie isple mong the oy igonl y /4 of the ue ege. The pking ftor of this struture is thus lulte s follows: XY 4 4 XZ XY YZ But, XZ r Therefore, r 3 6 (or) the nerest neighour istne, r Figure: Dimon Struture 3 4 Z

15 30 Introution of Crystl Struture Lttie onstnt, r 3 -Cristollite Struture : SiO Si 4+ = In DCC lttie. 4 3 r r Pking ftor v/v 0.34 or 34% r 6 O = Eh oxie ion in etween ny Si-Si on. 4 Z :Si 6 4. O 6 6. F. 4 Si 4+ O C.N.:Si 4 n O. Effet of Pressure on Crystl Struture: Inrese of pressure inreses the o-orintion numer uring rystlliztion e.g. y pplying high pressure, the NCl rystl struture hving 6 : 6 o-orintion numer hnges to CsCl rystl struture hving oorintion numer :. high pressure NCl type rystl CsCl type rystl (6:6 o-orintion) (: o-orintion) Effet of Temperture on Crystl Struture : Inrese of temperture, however, ereses the o-orintion numer e.g., upon heting to 760 K, the CsCl rystl struture hving o-orintion of : hnges to NCl rystl strutures hving o-orintion 6 : 6 high tempressure CsCl type rystl NCl type rystl (: o-orintion) (6:6 o-orintion) SOLVED EXAMPLES. Upon heting to out 500ºC CsCl rystl hnges its struture to rok slt struture. Wht hppens to the oorintion numer of Cs? [BHU-04] () hnges from 6 to () hnges from to () hnges from to 6 () oes not hnge high tempressure CsCl type rystl NCl type rystl (: o-orintion) (6:6 o-orintion) Corret option is () Ioni Compouns of AB Type: Fluorite struture (rystl struture of CF ) : The lium fluorie rystl is ompose of lium ions (C + ) n fluorie ions (F ).

16 Introution of Crystl Struture 3 It hs Cui Close pke (p) rrngement. (i) The C + ions re present s the fe entre ui lttie n the fluorie ions (F ) oupy ll the tetrherl vois. (ii) The rius rtio, lulte from the ioni rii of C + ion (99 pm) n F ion (36 pm), is This shows tht the oorintion numer of lium ion is eight, i.e. eh lium tion is surroune y eight fluorie nions in oy entre ui rrngement. Eh fluorie ion is in ontt with four lium ions. Thus CF hs : 4 o-orintion. (iii) Eh unit ell of CF rystl is oserve to hve 4C + ions n F ions. Numer of C + ions: = ( ions t the orners ) + (6 ions t the fe entre ) = + 3 = 4 Numer of F ions = ( ions within the oy ) = Therefore, eh unit ell hs 4 CF moleules. Solis forming fluorite type of struture re CF, SrF, BF, BCl, CF, HgF, PF, CuF, SrCl et. Ioni Compouns of A B Type Antifluorite struture (rystl struture of Li O): Antifluorite struture is hving rrngement of tions n nions opposite to fluorite struture. (i) In the rystl struture of Li O, the O ions onstitute ui lose pke lttie (FCC struture) n the Li + ions oupy ll the tetrherl vois (ii) Eh oxie ion, O ion, is in ontt with Li + ions n eh Li + ion is hving ontt with 4 oxie ions. Therefore, Li O hs 4 : o-orintion. Exmples forming ntifluorite struture inlue N O, K O, K S n N S. Struture of ferrite n relte ompouns: 3 Ferrite (Fe 3 O 4 ) n relte ompouns of generl formul M Fe O4 re ferrimgneti in nture. The M + n e Fe +, Mn +, Zn +, Mg +, Co +, Ni + or some omintion of these ions. Ferrite (Fe 3 O 4 ) is the oule oxie hving omposition FeO Fe O 3. This shows, tht the numer of Fe 3+ ions is twie the numer of Fe + ions. Their respetive rrngement in the rystl lttie my e illustrte s elow. (i) In, Fe 3 O 4, the oxie ions onstitute the ui lose pke (FCC) rrngement. (ii) All the Fe + ions n hlf of the Fe 3+ ions oupy otherl vois, while the remining hlf of the Fe 3+ ions oupy tetrherl vois. Struture of Titnium Dioxie, TiO (Rutile Struture) : The unit ell of Rutile struture is shown in following figure in whih titnium ions re represente y hollow irles n oxie ions re represente y soli irles. The struture my e esrie s follows : Ti 4+ = In istorte oy entere ui. O = oxie ions re present t the entres of the tringle generte y ny opposite eges t the oy entre Ti. 4 oxie ions re present in plne whih is perpeniulr to the plne initil oxie ions. These 4 oxie ions re present on opposite fes (two on eh fe). Eh of these 4 oxie ions is present t /4 th istne of the fe igonl from orner long the fe igonl. These 4 oxie ions generte squre plnr struture, n ll the 6 oxie ions generte n otherl struture t the oy entre Ti.

17 3 Introution of Crystl Struture Z 4 Ti F O C.N. Ti 6 n O 3. Struture of Clium Crie (CC ) : The unit ell of lium rie is shown in following figure. The struture of lium rie is similr to tht of soium hlorie. Here soium ions re reple y lium ions n hlorie ions y C groups. The ron toms re ssoite in pirs, s shown in following figure, forming the C groups. The C groups re ligne in prllels s shown. The ui symmetry oserve in soium hlorie is, however, istorte onsierly in the se of lium rie for ovious resons. The struture of FeS is similr to tht of CC. However, the S units re not ligne in prllels s re the C units in the se of CC. C + = At oy entre + t eh ege entre Oh voi. C At orners + t eh fe entres FCC C 4 Z 4 C 6 4 F 4 C.N. C 6 n C 6 Struture of Cmium Ioie (CI ) : The unit ell of mium ioie is shown in following figure in whih C + ions re represente y hollow irles n ioie ions re represente y soli irles. The slient fetures of this struture re esrie elow:. The ioie ions re rrnge in hexgonl lose pke (hp) rrngement while mium ions lie in otherl sites etween every two lyers of ioie ions.. Eh C + ion is surroune otherlly y six I ions, s shown in following figure. On the other hn, eh I ion hs three C + ions s nerest neighours. The three C + ions surroun the I ion in n rrngement in whih C + ions form the se of trigonl pyrmi whose pex is the I ion. 3. The rrngement of the three lyers orrespons to the omposition CI. This rrngement is ontinue s shown n the struture is referre to s lyer lttie. The fores operting in etween the I C I lyers to hol them together re wek. As result, this ompoun is flky n n e esily leve.

18 Introution of Crystl Struture 33 The Ilmenite Struture: Ilmenite is the minerl FeTiO 5. Its struture is losely relte to the orunum struture exept tht the tions re of two kins. In ilmenite the tions re Fe + n Ti 4+, ut mny sustnes with the ilmenite struture hve tions with hrges of (+, +5) or (+3, +3). The Perovskite Struture: Perovskite is the minerl CTiO 3. Its struture, shown in following figure, is se on p rry of oxie ions together with lrge tions, similr in size to the oxie ion. The smller tions lie in otherl holes forme entirely y oxie ions. Agin, the iniviul tion hrges re not importnt so long s their sum is +6. The struture is opte y mny fluories with tions of ifferent sizes, suh s KZnF 3. C + = At oy entre Ti 4+ = At ll orners C O 4 = At eh ege entre Z Ti O 3 F Chrteristi properties of vrious types of ioni solis C.N. From C O C.N. 4 Ti 6 O 4 O Ti

19 34 Introution of Crystl Struture S. No. Struture Ction Anion Numer of ions F C.N. Ction Anion Totl Ction Anion. NCl,KCl Oh voi FCC CC Oh voi FCC CF, BF, FCC All T voi SrF 4. N O All T FCC voi 5. CTiO 3, C + : Ege entre 3 5 CTiF 3 Boy entre Ti 4+ : Corner 6 6. ZnS(B) Hlf T FCC voi 7. ZnS(W) Hlf T voi HCP ol new SiO DCC Si O Si 9. TiO Distorte BCC CsCl Boy entre Corner SOLVED EXAMPLES. Wht is the empiril formul for the following unit ell: [TIFR 00] Ti O () CTi O () CTi O () CTiO 3 () CTi O 3 C Boy entre Ti Corners 4 O Ege entre 3 4 CTiO 3 Corret option is ()

20 Introution of Crystl Struture 35. NCl, KCl, NBr n KBr rystllize in FCC ltties. Their noin n tion touh long the ege of the unit ell. The imensions of their unit ells re 56. pm, 67.7 pm, 596. pm n 65.6 pm, respetively. From these t, wht n you sy out the size of the ioni rii (within n error of out 5%)? () Ioni rii of the tions epen on the nture of the nions [TIFR 05] () Ioni rii of the nions epen on the nture of the tions () Both () n () () Ioni rii re inepenent of the ions Corret option is () 3. KCl rystllizes in ui unit ell with Cl ions t eh vertex n fe entre. How mny K + ions n Cl ions re there is eh unit ell of KCl? [HCU-0] () K + ion n Cl ion () K + ions n Cl ions () 4 K + ions n 4 Cl ions () K + ions n Cl ions Cl t eh vertex n fe entre K + is present in otherl vois = 4. 4K + ions n 4Cl ions re there in eh unit ell of KCl. Corret option is () 4. The Perovskite struture hs the formul A II B IV O 3. The A tions form primitive ui lose pking with the oxie ions oupying the entres of the fes n B tions t the oy entre. The totl numer of ions of A, B n O in the unit ell re, respetively. [HCU-04] (), n 3 (), n 6 (), n 3 (), n 3 Perovskite struture A II B IV O 3. A II tion = only orners s O oupy fe entre position. O ion = entre of fes 6 3. B IV tion = oy entre =. Corret option is () 5. Perovskite is the minerl CTiO 3. The Perovskite rystl struture is opte y severl oxies s well s some fluries. Whih one, mong the given formule; most likely represents known fluorie hving the perovskite struture? [BHU-0,5] () CTiF 3 () KZnF 3 () CTiF 5 () CMgF 4 Corret option is () 6. CsF opts the NCl rystl struture. If the unit ell ege is of length 4.0 A, wht is the shortest istne etween the tion n nion in the rystl? [BHU-0] ().0 A ().4 A () 3.4 A () 4.0 A 4.0 = 4.0,.0. Corret option is () 7. Perovskite is the minerl CTiO 3. The perovskite rystl struture is opte y severl oxies s well s some fluories. Whih one, mong the given formule, most likely represents known fluorie hving the perovskite struture? [BHU-04] () CTiF 3 Corret option is () () KMnF 3 () NMnF 4 () CFeF 3

21 36 Introution of Crystl Struture. A ompoun lloy Cu 3 Au rystllizes in ui lttie with Cu t the fe enters n Au t the orners. How mny formul units of the ompoun re there in eh unit ell? [BHU 0] () 4 () 3 () () Cu = Fe entre 6 3. Au = Corners. Therefore, nswer is AuCu 3. i.e., formul unit =. Corret option is () 9. How mny toms re there in unit ell for the imon lttie? [BHU 0] () () 4 () 6 () Corret option is ()