Chapter-2 SOLID STATE

Transcription

1 Chpte- SOLID STATE 1. We know solids e the substnces which hve definite volume nd definite shpe. A solid is nely incompessible stte of mtte with well definite shpe, igidity nd definite volume.. Clssifiction of Solids: Solids cn be bodly clssified into two types : (1) Cystlline () Amophous Diffeence Between Cystlline nd Amophous Solids S.No. Popety Cystlline solids Amophous solids 1. Geomety These hve definite egul geomety These do not hve definite odely which extends thoughout the cystls i.e., these solids hve long nge ode. ngment.. Melting Points These hve shp m.p. These do not hve shp m.p.. Symmety These possess symmety. These do not possess ny symmety. 4. Het of Fusion These hve definite het of fusion These do not hve definite het of fusion. 5. Intefcil Cystls e lwys guded by plnes These do not possess intefcil ngle. ngles so tht definite ngle exists between two plnes clled intefcil ngle. 6. Volume chnge Thee is sudden chnge in volume Thee is no sudden chnge in volume when it melts. on melting. 7. Isotopy nd These e nisotopes i.e., thei physicl They e isotopic i.e., thei physicl Anisotopy popeties such s efctive index, popeties such s efctive index conductivity etc. hve diffeent vlues in conductivity etc. hve sme vlue in. Types of cystlline solids: diffeent diections. ll the diections. On the bsis of the ntue of the constituent pticles, nd the intepticle foces, cystlline solids my be divided into fou clsses () Covlent netwok solids (b) Ionic solids (c) Metllic solids (d) Molecul solids

2 Chcteistics of Vious Types of Solids Chcteistic Molecul Solids Covlent Netwok Metllic Solids Ionic Solids 1. Units tht occupy Atoms o molecules Atoms Positive ions in Positive nd Lttice points se of electons negtive ions. Binding foces Vn de Wl s foces Covlent bonding Metllic bonding ionic bonding (wek intemolecul (shed pi of (exteme deloc- (electosttic foces) of following electons) lised bond) ttction two types positively chged between positive (i) London (dispesion) tomic coes nd negtive foces suounded by ions) (ii)dipole-dipole se of delocfoces lised electons. Physicl (i) Vey soft. (i) Vey hd (i) Hd o soft (i)quite hd Popeties (ii) Low melting (ii) Vey high (ii) Modete to nd bittle points melting points high melting (ii)fily high points melting (iii) Non conductos (iii) Non conductos (iii) Good points conductos 4. Exmples Solid Ne, Solid NH, Dimond, Cu, Fe, Ag NCl, KNO ice (solid H O), Cboundum(SiC), N SO 4 dy ice (solid CO ) qutz(sio ) 4. Spce Lttice : It my be defined s thee dimensionl ngement of points tht shows, how the toms o ions e yed in spce. Ech point is individully clled lttice point. Lttice point Unit Cell c b Spce Lttice y b z c Repesenttion of dimension of unit cell 5. Cystl Lttice : When the lttice points in the spce e eplced by ctul toms o ions then the spce lttice is clled cystl lttice. Unit Cell : The smllest epeting ptten in spce lttice is clled unit cell. Close Pcking in Two Dimension Let us conside the pcking of hd sphees of equl size (i) The sphees cn be nged side by side in ow (hoizontl lignment) s shown below x Close Pcking of Sphees in one dimension

3 (ii) The sphees e pcked in such wy tht the ows hve both hoizontl s will s veticl lignment. In this ngement the sphees e found to fom sque. This pcking is clled sque close pcking. Sque closed pcking lye (iii) The sphees my lso be pcked in such wy tht the second ow e plced in the depession between sphees of fist ow. Similly the sphees in the thid ow e plced in the depession between the sphees of second ow nd so on. This gives ise to hexgonl closed pcking of sphees. Hexgonl Closed Pcked Lye Closed Pcking in Thee Dimension 1. If in sque ngement of lyes with sphees touching ech othe, the second lye is plced ight bove the fist lye of sphees then the epetition of lyes become AAAA... Such -D pcking gives ise to simple cubic closed pcking stuctue. Simple Cubic Closed Pcking

4 . Whee in the sque pcking of lyes we hve sphees not touching ech othe i.e. Void I-Lye If the second lye sphees e plced in the voids of the fist lyes sphees nd the thid lye sphees e plced in the voids of the second lye sphees then the epetition becomes AB AB... I-Lye A A A A B B B II-Lye A A A A Such -D ngement leds to Body cented cubic closed pcking. () (b). If in the hexgonl ngement of lyes, the second lye is plced in the voids of the fist lye then we come coss two types of voids Voids - A Voids - B Octhedl Voids Tehedl Voids A B A A A B B B B B

5 Tethedl void : When the void of one lye is coveed by the sphee of othe lye then such void is clled tethedl void. e.g. Afte sliding slightly the blck sphee Afte sliding slightly the blck sphee Octhedl Void : When the voids of two lyes mix togethe, such voids e clled octhedl voids. I-lye II-lye Octhedl Vol. 4. When the thid lye is plced on the tethedl voids of the fist lye then the epetition become ABAB becuse the thid lye will be ight bove the fist lye. Such -D ngement is clled Hexgonl closest pcking s in fig () A B A () Hexgonl Closed Pcking (b) B A A 5. When the thid lye is plced on the octhedl voids of the second lye then the epetition becomes ABC... Such -D ngement is clled cubic closed pcking o fce cented cubic closed pcking.

6 Fce cented Cubic Close pking Cystl System : The unit cell in -dimensions lttices is chcteized by the length, b, c nd thei ngles,,. These e known s unit cell pmetes. An ngement of sphees s given bove leds to simple o pimitive unit cell, when thee e points only t the cone of the unit lttice. Howeve cetin unit cells hve lttice points t othe sides in dditions to the cones. Such unit cell e clled non-pimitive unit cells. Bvis (1848) showed fom geometicl considetions tht thee cn be only 14 diffeent wys in which simil points (sphees) cn be nged. These fouteen types of lttice e known s Bvis lttices. They cn be divided into seven cystl systems s shown below : Cystl Systems Tble S.No. Cystl System Axil Chcteistics Exmples 1. Cubic = b = c NCl, KCl, CsCl, zinc blende, = = = 90º Cu, Ag, dimond. Tetgonl = b c = = = 90º White tin, SnO, TiO. Othohombic b c = = = 90º Rhombic sulphu, KNO, PbCO, PbSO 4 4. Monoclinic b c; Monoclinic sulphu, CSO 4, H O, = = 90º; 90º N SO 4, 10H O 5. Rhombohedl = b = c; Clcite, qutz, o tigonl = 90º As, Sb, NNO, ICl 6. Ticlinic b c; K C O 7, H BO, CuSO 4, 5H O 90º 7. Hexgonl b c; Gphite = = 90º; = 10º In cse of cubic system which is the simplest cystl system, thee e thee types of lttices depending upon the unit cell. These e : (i) Simple Cubic Lttice. In this type of lttice, thee e lttice points only t cones of ech unit cell. (ii) Fce Cented Lttice (fcc) :- In this type of lttice, thee e points t the cones of the cube with dditionl points t the cente of ech fce. (iii) Body Cented Cubic Lttice (bcc) :- This type of lttice hs points t the cones of cube with n dditionl point in the cente of the cube.

7 The Bvis lttice ssocited with the seven cystl systems e shown below. c b Simple o Pimitive Body cented Cubic Fce cented CUBIC Simple o Pimitive Body cented End cented Fce cented ORTHORHOMBIC Simple Body cented Simple Body cented TETRAGONAL MONOCLINIC c c b B A G b B A c G b TRICLINIC HEXAGONAL RHOMBOHEDRAL Bvis lttices coesponding to diffeent cystl systemstble S.No. System Numbe of Bvis Desciption of the lttices lttices 1. Cubic Simple, Fce-cented, Body cented.. Tetgonl Simple, Body-cented. Othohombic o Rhombic 4 Simple, Fce-cented, End cented Body - cented 4. Monoclinic Simple, End-cented 5. Ticlinic 1 Simple 6. Rhombohedl o tigonl 1 Simple 7. Hexgonl 1 Simple

8 Types of symmety in cystl 1. Cente of Symmety :- Cente of symmety of cystl my be defined s n imginy point within cystl such tht ny line though it intesects the cystl t equl distnces in both diections e.g. stggeed fom of ethne possesses cente of symmety. The cente of symmety is lso clled the cente of invesion becuse if the cystl is inveted though the cente of symmety, it is distinguishble fom the oiginl. Evey Cystl Possesses Only One Cente of Symmety. Plne Of Symmety : Cente of Symmety It is n imginy plne pssing though the cystl which cn divide cystl into two equl pts such tht one pt is exct mio imge of the othe. These e theefoe lso clled mio plnes. Thee e two types mio plnes. () Rectngul mio plnes (b) Digonl mio plne H H H H H H Rectngul mio plne Digonl mio plne Axis of Symmety o Axis of Rottion An xis of symmety o xis of ottion is n imginy line, pssing though the cystl such tht when the cystl is otted bout this line, it pesents the sme ppence moe thn once in one complete ottion. i.e. though 60º. 60º When the sme ppence of cystl is epeted, on otting though n ngle of ound n n imginy xis it is clled n-fold xis of symmety whee n is known s ode of xis. Two-Fold Axis : If simil ppence occus two times in one complete ottion i.e. fte ottion though 180º, the xis is clled two fold xis of symmety o did xis. Thee-Fold Axis : If the oiginl ppence occus thice it is clled thee fold xis of symmety. Fou Fold Axis Two fold xis of symmety Thee fold xis () (b) (c)

9 Neest Neighbouing Distnce In Cse of Identicl Sphees : Neest neighbouing distnce is the distnce between the centes of ny two touching sphees. 1. In cse of SCC (Simple Cubic Lttice) d In simple cubic lttice the edge length () = Neest neighbouing distnce = d = = /. Body Cented (AB) = (AC) + (BC) Body Digonl) = (Fce Digonl) + (edge) = (edge) + (edge) = (edge) A C B ( Body digonl) (edge) Also Body Digonl = + + = 4 (4) = 4 = d Neest Neighboing distnce 4 d = d = neest neighbouing distnce. Fce Cented Cubic Lttice Hee (Fce digonl) = (edge) + (edge). Also fce digonl = + + = 4 (4) = (edge) 4 = d A C B D 4 1 d 1

10 Hence we cn sy Unit Cell Distnce between Rdius neest neighbou Simple cubic Fce Cented Cubic = 4 Body Cented Cubic 4 4. Pcking Fction in Cse of Identicl Sphees Pcking fction is the tio of volume occupied by sphees to the totl volume of the cube. Pcking Fction = Volume occupied by sphee Totl volume of cube whee = 4 = edge of cube z z = numbe of sphees pe unit cell Pcking fction fo SCC = z = 1 PF = 4 z = PF = 6 % volume occupied by sphees = = 5.4% % Fee spce = = 47.6% Pcking fction fo BCC = 4 z = PF = 4 4 = 4 64 PF = 8

11 % volume occupied = 68.04% % Fee spce = = 1.96% Pcking Fction fo FCC = 4 z = PF = 4 4 = 4 64 = PF = 6 % Volume occupied = 74.07% % Fee spce = 5.9% Clcultion of Density of System Cystl Cubic Cystl Let numbe of tom pe unit lttice = n Mss of unit cell = numbe of tom pe unit cell (n) Mss of one tom Mss of ech tom = Atomic Mss of Atom Avogdo' s numbe N A Mss of unit cell = n M N A 0 o n A N A 0 Density of unit cell = Mss of unit cell Volume of unit cell Length of edge = pm Volume of cube = pm = 10 0 cm Density = N o nm 10 0 gm/cc nm10 Density = N o 0 nm10 7 = 6.0 CRYSTAL STRUCTURES OF AB TYPE OF IONIC COMPOUNDS The thee bsic stuctue of this type e NCl, CsCl nd Zinc sulphide. The ionic compound of type AB hve one of these thee of stuctue

12 IONIC RADIUS AND RADIUS RATIO Ionic dius of n ion is the distnce fom the nucleus of tht ion upto which it hs its influence in n ionic bond. Co-odintion numbe. It is the numbe of oppositely chged ions suounding pticul ion in the ionic cystl. Rdius tio. In n ionic solid, the centl ction cn touch only tht numbe of nions which should led to mximum electosttic ttction nd minimum electoststic epulsions. These intections depend upon the sizes of the ction nd nion. Thus, the ngement of ions in cystl is getly influenced by the tio of dius of the ction nd the nion. Thus, Rdius tio is defined s the tio of the dius of the ction to tht of the nion. Rdius tio = Rdius of Rdius of the ction ( the nion ( ) ) Lge the ction, gete will be the numbe of nions suounding it nd gete will be its coodintion numbe. Significnce. Rdius tio helps to pedict co-odintion numbe nd the stuctue of the ionic cystl s follows : Rdius tio Co-odition numbe Stuctue Exmple Tigonl pln B O Tethedl ZnS Octhedl NCl Cubic CsCl () Rock Slt NCl type (i) N + = +96 pm Cl = 181 pm N Cl 96 = = 0.54 this tio lies between nd 0.7 nd coodintion numbe is 181 thus 6. (ii) Cl foms FCC type pcking (iii) N + ions occupy ll octhedl voids (iv) Coodintion numbe fo N + = 6 coodintion numbe fo Cl = 6 (v) Numbe of N + ions pe unit lttice = 4 numbe of Cl ions pe unit lttice = 4

13 Hence totl numbe of ions = 8 Hence fo ech N + ions thee is only one Cl ions (A unit lttice consists of 4 fomul units of NCl o vice ves if N foms unit lttice (vi) Numbe of Cl ions used = 14 Numbe of N + ions used = 1 Othe exmples of this type e hlides of Li, N, K, Rb, fluoide of Cs oxides nd sulphides of Mg, C, S, B, AgCl, AlB, AgF (b) Cesium Chloide CsCl Type (i) Cs + = 169 Cl = 181 Cs Cl = 0.9 Hence lies between 0.7 to 1.0 thus coodintion numbe is = 8 CsCl hs BCC type stuctue (ii) Cl fom SCC pcking (iii) Cs + ions occupy the body cented void of (iv) Ech Cs + is suounded by 8 Cl ion ech Cl is suounded by 8 Cs + (v) Numbe of Cl ions Cs cl pe unit lttice = 1 Numbe of Cs + ions pe unit lttice = 1 (vi) A unit cell of cesium chloide hs one fomul unit of CsCl i.e. one Cs + nd one Cl ion. Othe exmples of this type n CsB, CsI, NH 4 B, NH 4 I, thllous cynide, thllous chloide. (c) Zinc Blende ZnS (Sphleite stuctue) (i) 74 s 184 zn zn s 0.4 this vlue lies between 0.5 nd hence tethedl void is occupies coodintion numbe = 4 (ii) S ions e nged in FCC type stuctue (iii) Zn + ions occupy hlf the tethedl void (iv) Numbe of Zn + ions = 4 Numbe of S ions = 4

14 The should hve been 0.5 but the vlue is The close pcked ngement of S ion opens up nd ccumultes the lge S ions (v) Coodintion numbe of Zn + = 4 Coodintion numbe of S = 4 (vi) The fomul unit fo ZnS type lttice = 4 othe exmples e CuCl, CuB, CuI, in which ctions is smlle thn nion. AgI, Beyllium oxides ll hve Zinc blende stuctue. Cystl Lttice of the Type AB & A B 1. Clcium Fluoide CF (Fluoite Type) (i) C + is nged in FCC type stuctue (ii) F occupy ll tethedl voids (iii) Ech C + suounded by 8 F ion Ech F is suounded by 4 C + ion. Thus gives 8 : 4 coodintion numbe. CF type unit cells n SF, CdF. Sodium oxide N O (Anti Fluoite Type) (i) O fom FCC (ii) N + occupies tethedl voids (iii) Coodintion numbe of O = 8; Coodintion numbe of N + = 4 Impefections in Solids The cystl stuctues of ionic compounds of the type AB nd AB discussed elie epesent idel stuctues in which thee is completely odeed ngement of constituent pticles. Howeve, in el cystls the ngement of constituent pticles is not egul nd thus cystls hve impefect stuctues. Such impefections e devitions fom the pefectly odeed ngement of toms. Thus ny devition fom the completely odeed ngement in cystl constitutes disode. The disode in cystl of n element depends upon : (i) Tempetue nd (ii) Pesence of impuities Electonic Impefections In pefectly covlent o ionic cystl such s silicon o gemnium o sodium chloide, the electons e pesent in the fully occupied lowest enegy sttes t 0K. The vlence electons e minly concentted ound the electonegtive component in ionic cystls. As the tempetue is ised bove 0K, some of the electons gin enegy nd move to highe enegy sttes. The electon-

15 deficient bond poduced s esult of the emovl of n electon is clled hole. As the electons hve moved wy fom thei noml positions ceting holes, the electons nd holes in solids e consideed electonic impefections o defects. Electons nd holes e genelly designted by the symbols e nd h espectively nd thei concenttions by n nd p espectively. So Si nd Ge behve s semiconductos o intinisic semiconductos. Thus the pomotion of electons cuses holes which esults in incesed electicl conductivity. The electicl conductivity of silicon inceses with incesing tempetue (this behviou is opposite to tht of metls). The electons nd holes cn lso be poduced by dding cetin impuities to covlent cystl. Fo exmple, electicl conductivity of silicon o gemnium cn be getly enhnced by dding tces of luminium o senic s n impuity. Atomic Impefections These cn be clssified into two ctegoies Lttice impefections nd point defects. Lttice Impefections These ise due to devition fom peiodic epetition of the lttice points ove lge section of the cystl. Lttice impefections my extend long lines known s line defects o disloctions o these my extend long sufce known s plne defects. Two common types of disloction e edge disloction nd scew disloction. Edge disloction is fomed when lye of pticles discontinues within the cystls. Points Defects These e cused by deptue fom the peiodic ngement in the vicinity of n tom o goup of toms. Point defects in cystls my be clssified s : () Defects in stoichiometic solids lso clled stoichiometic defects. (b) Defects in non-stoichiometic solids lso clled non-stoichiometic defects. (c) Impuity defects Defects in Stoichiometic Solids B B Stoichiometic solids e those in which the numbe of positive nd negtive ions e exctly in the tio B B B indicted by thei chemicl fomule. These e of types B (i) Schottky defect (ii) Fenkel defect B B

16 (i) Schottky defect : A pi of holes o vcncies exists in the cystl lttice due to one ction nd one nion missing fom the noml lttice sites. The cystl s whole emins neutl becuse the numbe of missing ctions nd nions emins the sme. This sot of defect occus in highly ionic compounds with high coodintion numbe nd whee the ions (both ctions nd nions) e of simil size. Alkli metl hlides such s NCl, KCl, KB, nd CsCl show this defect. In NCl cystl, t oom tempetue, thee will be one Schottky defect pe ions. Since the pesence of lge numbe of Schottky defects in cystl leds to decese in the numbe of ions in the lttice, this esults in loweing the density of the solid mkedly. (ii) Fenkel defect : When hole o vcncy exists in the cystl lttice becuse n ion occupies n intestitil lttice site, it gives ise to Fenkel defect. The cystl emins neutl. The defect occus moe fequently in solids which hve low coodintion numbe nd possess ions (ctions nd nions) of diffeent sizes. Since ctions e genelly smlle thn nions, it is moe common to find the ctions occupying the intestitil sites. Fo exmple, in AgB nd ZnS cystls, Ag + ions nd Zn + ions e missing fom thei noml lttice sites nd e pesent in the intestitil positions. AgB, AgCl nd AgI contins Schottky defects lso. Since the pesence of Fenkel defects does not chnge the numbe of ions in the lttice, the density of the solid emins the sme. The defect cuses incese in dielectic constnt of the cystls s simil chges come close. Defects in Non-Stoichiometic Solids B B B B B B B B Non-Stoichiometic solids e those in which the tio of positive nd negtive ions pesent diffes fom tht indicted by the idel chemicl fomul. In compounds such s FeO, FeS, CuO, TiO, ZO, VO nd Cu S the el composition of the constituent ions cn vy. Cupous sulphide, fo exmple, my contin nything between Cu 1.96 S nd Cu S. Similly, in vndium oxide, VOx, x cn be nywhee between 0.6 nd 1.. The blnce of positive nd negtive chge is mintined eithe by hving ext electon o ext positive chges pesent. Metl Excess Defects These defects my ise in two wys: (i) Metl excess due to nionic vcncies. A negtive ion my be missing fom its lttice site, leving hole which is occupied by n electon which ws ssocited with the negtive ion nd emins tpped in the vcncy theeby mintining the electicl neutlity. When NCl is teted

17 with sodium vpous, yellow coloued non-stoichiometic fom of NCl is obtined in which thee is n excess of sodium ions. Sodium tom emoves chloine tom fom the nionic lttice site leving its electon tpped in the vcncy nd mkes the lttice excess of solid ions. Similly excess of potssium in KCl mkes the cystl to ppe violet nd excess lithium in LiCl mkes it pink. The electons tpped in nion vcncies e efeed to s F centes (F = Fben in Gemn mens colou). These electons bsob enegy of the white light, giving yellow colou to NCl, pink colou to LiCl nd violet colou to KCl. B B B e B B B B B (ii) Metl excess due to ext ctions. In this cse, the excess metl occus when n ext positive ion occupies n intestitil position in the lttice. The fee electon is tpped in nothe intestitil site close to the vicinity of the intestitil ction. This electon helps to mintin the electicl neutlity. When zinc oxide is heted t high tempetues, it loses oxygen evesibly nd tuns yellow in colou. The excess metl ion is ccommodted in the intestitil sites giving ise to electons tpped in the neighbohood. The highe electicl conductivity of the non-stoichiometic ZnO is due to these electons. 1 ZnO Zn O e ZnO is yellow when hot nd white when cold. B B B B e B B B Metl Deficiency Defects These defects occu in metls with vible oxidtion sttes, i.e., the tnsition metls. A ction my be missing fom its lttice site but the electicl neutlity is mintined when the djcent metl ion cqies highe oxidtion stte (fig.) Exmples include FeO, FeS nd NiO. metl deficient compounds conduct electicity thow positive hole conduction mechnism nd e theefoe p-type semi-conductos B B B B B B B B B B B B B

18 Impuity Defects These defects ies due to the pesence of foeign toms o ions t the lttice sites. Thus depending upon the ntue of impuity, two types of impuity defects e possible. (i) Impuity defect due to neutl toms : Foeign toms cn occupy intestitil o substitutionl sites in cystl. The electonic stuctue of impuity is of impotnce in the cse of substitutionl solid solutions while the size of the impuity tom detemines the fomtion of intestitil o substitutionl solid solution. Solid solutions of goup 1 o goup 15 s impuities with goup 14 elements such s Ge o Si (ct s host) e of get inteest in electonic industy in mking tnsistos. Goup 1 elements such s G nd Al nd Goup 15 elements such s P nd As ente Ge o Si substitutionlly. () Goup 15 elements such s P, As etc. hve one excess vlence electon (electon to Si o Ge) fte foming fou covlent bonds with Goup 14 element. The excess electons give ise to electonic conduction known s n-type semiconduction. (s the cuent is cied by electons in the noml wy). (b) On the othe hnd Goup 1 element such s G, Al o In which hs only thee vlence electons (i.e. one electon less thn equied fo foming fou covlent bonds) cetes n electon deficient bond o hole. Such holes cn move in the cystl giving ise to electicl conductivity known s p-type semiconduction. (ii) Impuity defect due to ions : This defect is bought bout by dding impuity ions in ionic solid. If the impuity ions e in diffeent vlence stte fom tht of the host ions, vcncies e ceted. Fo exmple, ddition of CdCl to AgCl (o of SCl o MgCl to NCl) yields solid solutions whee the divlent ction Cd + (o S + + Mg + ) occupies the Ag + (o N + ) sites nd poduces ction vcncies equl in numbe to tht of the divlent ions. The SCl doped NCl hs much highe electicl conductivity thn tht of pue NCl. N + Cl N + Cl N + Cl S + Cl N + Cl Cl Cl N + Cl N + Popeties of Solids Thee is close eltionship between the popeties of solid nd its stuctue nd composition. Some of these popeties e : (i) Electicl popeties (ii) Mgnetic popeties (iii) Dielectic popeties

19 Electicl Popeties (Electicl Conductivity) Bsed on thei electicl conductivity, solids cn be bodly clssified into thee types : (i) Metls o conductos : They e good conductos of electicity s the electons cn move feely without much esistnce. Thei conductivity vlue is of the ode of 10 8 ohm 1 cm 1 t oom tempetue which deceses with ise in tempetue. Some mono oxides of tnsition metls (which possess NCl stuctue) like TiO, VO behve like metllic conductos. CO lso behves s metl conducto. (ii) Insultos o Non-conductos: These solids do not llow the electicity to pss though them. Non-metls like dimond, P nd S, solutions of non-electolytes like sug nd ue, substnces like wood, ubbe nd plstics e ll exmples of insultos. Thei conductivity vlue is extemely low nd is of the ode of less thn 10 1 ohm 1 cm 1 t oom tempetue. (iii) Semi-conductos: These solids possess conductivity vlues which e intemedite between those of typicl metls nd insultos i.e. in the nge ohm 1 cm. The conductivity of such solids inceses with tempetue. Electicl conductivity of solids my ise though the motion of electons nd holes (electonic conductivity) o ions (ionic conductivity). Substnces such s pue solid lkli metl hlides whee the conduction is only though ions, e genelly insultos s thei ions cnnot move. Pesence of vcncies o othe impefections, howeve, getly incese the conductivity of ionic solids. Mgnetic Popeties Mteils cn be divided into diffeent clsses depending upon the effect of mgnetic fields on them. (i) Dimgnetic mteils : These mteils e wekly epelled by mgnetic field. Exmples e TiO, NCl nd benzene. (ii) Pmgnetic mteils : These mteils e ttcted by mgnetic field. Exmples e O, Cu +, Fe +. Pmgnetism is obseved due to the pesence of pemnent mgnetic dipoles s esult of unpied electons in toms, ions o molecules. Pmgnetic mteils, howeve, lose thei mgnetic chcte in the bsence of mgnetic field. Pmgnetic mteils sometimes show specil type of mgnetic behviou nd e clssified s: () Feomgnetic mteils : Unlike pmgnetic substnces feomgnetic mteils show pemnent mgnetic popety even when the mgnetic field is emoved. These mteils exhibit unusully lge pmgnetism. Exmples e Fe, Co, Ni, CO. () Feomgnet

20 (b) Antifeomgnetic mteils : These mteils show much educed pmgnetism (lmost zeo) thn expected fom thei electonic stuctues. Exmples e MnO, FeO, CoO, NiO, nd mny othe oxides. (b) Anti-Feomgnet (c) Feimgnetic mteils : These mteils show smll pmgnetic chcte. Exmples e Fe O 4 feites of the fomul M + Fe O 4, when M = Mg, Cu, Zn. In these mteils the lignment of mgnetic moments e in pllel nd ntipllel diections in unequl numbes. (c) Feimgnet As esult the mteil hs net mgnetic moment nd shows feimgnetism fig (c). All mgneticlly odeed solids (feomgnetic, feimgnetic nd nti-feomgnetic solids) tnsfom to the pmgnetic stte t some tempetue due to the ndomistion of spins. Thus feimgnetics, Fe O 4 becomes pmgnetic t 850 K. Mgnetic Popeties of Typicl Tnsition Metl Oxides Dimgnetic Pmgnetic Feomgnetic Antifeomgnetic Feimgnetic TiO TiO, Ti O CO V O, C O Fe O 4 V O 5 VO, VO MnO, MnO CuO Mn O Mn O FeO, Fe O, Co O 4 NiO, CoO Dielectic Popeties In insultos, electons e closely bound to individul toms o ions nd they do not genelly migte unde n pplied electic field. (i) These dipoles my lign themselves in n odeed mnne unde the influence of n pplied electic field such tht thee is net dipole moment in the cystls. (ii) They my lign themselves in such mnne tht the dipole moments cncel ech othe. (iii) It is lso possible tht thee e no dipoles in the cystl, but only ions e pesent. Popeties of Piezoelectic Cystls : Cystls whee sitution (i) is found, exhibit piezoelecticity. When mechnicl stess is pplied on such cystls so s to defom them, electicity is poduced due to displcement of ions.

21 () Electicl mechnicl tnsduce : When such cystl is defomed by mechnicl stess, electicity is poduced due to the displcement of ions cystl, o convesely if n electic field is pplied to the cystl, thee will be tomic displcements cusing mechnicl stin. Thus, piezoelectic cystl cts s mechnicl electicl tnsduce. (b) Pyoelecticity : Some of the pol cystls, when heted, poduce smll electic cuent clled pyoelecticity.

22 SOLVED EXAMPLES Exmple 1: Metllic gold cystllizes in the fce-centeed cubic lttice. The length of the cubic unit cell is = Å. () Wht is the closest distnce between gold toms? (b) How mny neest neighbous does ech gold tom hve t the distnce clculted in ()? (c) Wht is the density of gold? (d) Pove tht the pcking fcto fo gold, the fction of the totl volume occupied by the toms themselves, is Solution: () Conside cone gold tom. The closest distnce to nothe cone tom is. The distnce to n tom t the cente of fce is one-hlf the digonl of tht fce, i.e., 1 ( ) = < Thus the closest distnce between toms is =.878 Å. Fig. (1) Fig. () (b) The poblem is to find how mny fce centes e equidistnt fom cone tom. Point A in figue my be tken s the efeence cone tom. In tht sme figue, B is one of the fce-cente points t the neest distnce to A. In plne ABD in the figue thee e thee othe points eqully close to A: the centes of the sques in the uppe ight, lowe left, nd lowe ight qudnts of the plne, mesued ound A. Plnt ACE, pllel to the plne of the ppe, lso hs points in the centes of ech of the sques in the fou qudnts ound A. Also, plne ACF, pependicul to the plne of the ppe, hs points in the centes of ech of the sques in the fou qudnts ound A. Thus thee e 1 neest neighbos in ll, the numbe expected fo close-pcked stuctue. The sme esult would hve been obtined by counting the neest neighbos ound B, fce-centeed point. (c) Fo the fce-centeed cubic stuctue, with 8 cones nd 6 fce centes, Mss pe uniot cell = 8 1 (8m) + 1 (6m) = 4 m whee m is the mss of single gold tom, mu. Conveting to gms, 1g m = (197.0) =.7 10 g 4m 4(.7 10 g) nd Density = = ( cm) = 19.4 g/cm

23 (d) Since toms t closest distnce e in contct in close-pcked stuctue, the closest distnce between centes clculted in (), /, must equl the sum of the dii of the two spheicl toms,. Thus, = / /. Fom (c), thee e 4 gold toms pe unit cell. Then, Volume of 4 gold toms = nd Pcking fction = = 4 volume of 4 gold toms vlume of unit cell 4 / / = = = Exmple : KCl cystllizes in the sme type of lttice s does NCl. Given tht = N Cl = 0.5 nd Solution : N K = 0.7, clculte () the tio of the side of the unit cell fo KCl to tht fo NCl, nd (b) the tio of density of NCl to tht of KCl. Since NCl cystllizes in the fcc unit cell, so N Cl Whee = edge length of unit cell. Now N Cl = 0.5 o 1 + N Cl = N K Cl Cl = Cl K N /0.5 = K = (1) 0. 5 N / = Cl N N K 0.7 o 1 + K Cl = o K Cl Cl Divide () by (1) K Cl Cl = N Cl Cl...() 1. = o K N Cl Cl = 1.14 o KCl/ NCl/ = 1.14 K nd N Cl Cl KCl KCl

24 o Whee KCl NcCl = 1.14 N M density (d) =. N0 N = numbe of toms pe unit cell M = Molecul mss N 0 = Avogdo numbe = Edge length of unit cell d d NCl KCl = N M / ( ).N N M / ( ).N NCl NCl A KCl KCl A = KCl NCl MNCl. MKCl 58.5 = (1.14) 74.5 = Exmple : Clculte the glncing ngle on the cube of ock slt ( =.814 Å) coesponding to second Solution : ode diffction mximum fo X-ys of wvelength Å. The distnce between two consecutive lttice plnes is.814 Å. Accoding to Bgg s eqution d sin = n Fom eqution (i)... (i) sin = sin = = 0.5 sin = 0.5 = sin 1 (0.5) o = 14º 640 Exmple 4: The neest neighbou Ag toms in silve cystl e m pt. Wht is the density Solution : of silve? Silve cystllizes in f.c.c. fom (At. mss Ag = 108) In f.c.c. stuctue, toms long the fce digonl of the unit cell touch ech othe. As thee e thee toms on ech fce digonl, theefoe, distnce between neest neighbou Ag toms, d = Fce digonl = = ( whee = edge length of cubic unit cell) = d = = m = 406 pm

25 In f..c.c. unit cell of n element (silve) numbe of toms pe unit cell = 4 Mss of unit cell 4 Atomic mss of Ag 4108 = Avogdo's numbe (N0) = g = g Volume of unit cell = = ( ) cm = Mss of unit cell Density = Volume of unit cell = = 10.7 g cm Exmple 5: Led (II) sulphide cystl hs NCl stuctue. Wht is its density? The edge length of the unit cell of PbS cystl is 500 pm. [N 0 = mole 1 ; At. msses Pb = 07. S = ] Solution : M = 9. mu = 500 pm = cm Z = 4 N 0 = So = 10 = 1.7 g cm (50010 ) Exmple 6: A metl cystllises into two cubic phses, fce cented cubic (FCC) nd body cented cubic (BCC), whose unit cell lengths e.5 nd.0 Å, espectively. Clculte the tio of densities of FCC nd BCC. Solution : We know tht Z Fomul mss of substnce = N Since fo FCC, Z = 4 nd fo BCC, Z = nd 4 Fomul mss of mll d FCC = N (.5) 4 Fomul mss of mll d BCC = N () Dividing d FCC by d BCC d FCC d BCC 4 = = () (.5) 0 0 Exmple 7: Chomium metl cystllizes with body cented cubic lttice. The length of the unit cell is found to be 87 pm. Clculte the tomic dius. Wht would be the density of chomium in g/cm? (At. wt. of C = 51.99) Solution : Fo bcc, we know tht = 4 = = 87 = pm

26 Futhe we know tht Density = Mss of Vol. of one unit cell one unit cell Atomic mss Z = N0 Volume of one unit cell Hee, Z =, = 87 pm = cm Vol. of unit cell = ( cn) Thus, Density = (8710 ) = 7.0 g cm Exmple 8 :A compound, fomed by elements X nd Y, cystllises in the cubic stuctue, whee Y toms e t the cone of cube nd X toms e t ltente fces. Wht is the fomul of the compound? 1 Solution : Numbe of toms Y t eight cones of cubic unit cell = 8 = 1 8 Numbe of toms X pesent on ltente fce of unit cell = Fomul of compound = XY 1 = 1 Exmple 9: A fcc lttice cube is fomed by toms A nd B. If tom A is pesent t the cone of the cube nd the tom B t the fces of the cube. Find out the fomul of the compound. Solution : Contibution of tom A t eight cones of the cube = = 1 tom Contibution of tom t ech fce = 1 tom The tom B t six fces of the cube = 1 6 = toms Fomul of the compound = AB Exmple 10: Cesium chloide cystllises with body cented cubic lttice. Clculte the inteionic distnce if the length of the side of the unit cell is 5.4 Å. Solution : If R is the dius of nion & is the dius of ction, then the inteionic distnce in bcc lttice is R + = 5.4 = 4.6Å

27 OBJECTIVE QUESTIONS 1. A compound fomed by element A nd B cystllizes in the cubic stuctue, whee A toms e t the cones of cube nd B toms e t the cente of the body. The fomul of the compounds is () AB (b) AB (c) A B (d) AB. The numbe of octhedl sites in cubicl close pck y of N sphees is () N (b) 4N (c) N/ (d) N. The dius of Ag + ion is 16 pm while tht of I ion is 16 pm. The co-odintion numbe of Ag in AgI is () (b) 4 (c) 6 (d) 8 4. The yellow colou of ZnO nd conducting ntue poduced in heting is due to () Metl excess due to intestitl ction (b) Ext positive ions pesent in n intestitl site (c) Tpped electons (d) All of these 5. The spce occupied by sphees in FCC ngement is () 46.4% (b) 5.4% (c) 74% (d) None of these 6. The numbe of spce lttices nd cystl systems e nd espectively () 7 nd 14 (b) 14 nd 7 (c) nd 7 (d) 7 nd 7. A biny solid B hs zinc blende stuctue with B ions constituting the lttice nd ions occupying 50% tethedl holes. Fomul of the solid is () A B (b) AB (c) AB (d) AB 4 8. Titnium cystllizes in fce centeed cubic lttice. It ects with cbon o hydogen intestitilly by llowing toms of these elements to occupy holes in the host lttice. Hydogen occupies tethedl holes but cbon occupies octhedl holes the fomul of titnium cbide nd hydide e () TiC, TiH 4 (b) TiC, TiH (c) Ti C, TiH (d) TiC, TiH 9. A solid ABC hs A, B nd C nged s below. The fomul of solid is : C B () ABC (b) AB C (c) A BC (d) None of these 10. In the Schottky defect () Some of lttice sites e vcnt (b) An ion occupies intestitil positions between lttice point (c) A lttice site is occupied by electon (d) The tio + / is low A

28 11. TiO is well known exmple of () Ticlinic system (b) Tetgonl system (c) Monoclinic system (d) None of these 1. LiF is /n () Ionic cystl (b) Metllic cystl (c) Covlent cystl (d) Molecul cystl 1. A solid hs bcc stuctue. If the distnce of closest ppoch between the two toms is 1.7 Å. The edge length of the cell is () 00 pm (b) / pm (c) 14. pm (d) None of these 14. The pcking fction is mximum in the cystl lttice of () FCC (b) BCC (c) SCC (d) None of these 15. An element cystllises in bcc lttice with unit cell length of 00 pm. Wht is the dius of coppe tom in pm? () 157 (b) 181 (c) 108 (d) A cystl in which dipoles lign themselves in n odeed wy so s to give some net dipole moment, on plying field the diection of poliztion chnges. Such cystls e clled () Feielectic cystls (c) Antifeielectic cystls (b) Feoelectic cystls (d) Piezoelectic cystls 17. Fo solid with the stuctue, the co-odintion numbe of point Z is Z () (b) 4 (c) 5 (d) Mtch list I with list II nd select the coect nswe using the codes given below the list : List I List II (Shpe) (Rdius tio + / - ) (1) Pln tingle () 0.7 () Sque pln (b) 0.5 () Body cented cubic (c) (4) Tethedl (d) Codes : (1) () () (4) () 1 4 (b) 1 4 (c) 4 1 (d) None of these

29 19. Feoelecticity is exhibited by () Bium titnte (BTiO ) (c) Potssium dihydogen phosphte (KH PO 4 ) (b) Sodium potssiumttte (Rochelle slt) (d) ll of these 0. A cetin cubic cystlline substnce hs ions of sodium, tungsten nd oxygen t the body cente, cones nd edge centes espectively of the cubic unit cell. Wht is the type of cubic lttice nd wht is the fomul of the substnce? () Simple cubic fo the tungsten toms, NWO (b) Body cented cubic, NWO (c) Mixed type, NW 4 O 1 (d) None of the bove 1. In compound, toms of element Y fom ccp lttice nd those of element X occupy / d of octhedl voids. The fomul of the compound will be () X Y (b) X Y 4 (c) X 4 Y (d) X Y. The wvelength of the x-ys which give diffction ngle of o fo cystl with intepln distnce of 0.00 nm will be (only fist ode diffction, sin = 0.890)? () m (b) m (c) m (d) None of these. Wht is the volume of fce cented cubic unit cell, when its density is.0 g cm nd the mol mss of the substnce is 60.g mol 1? () 4 10 cm (b) 10 cm (c) cm (d) 10 cm 4. CO nd NCl hve the sme cystl stuctue nd nely the sme dii. If is the lttice enegy of NCl, the lttice enegy of CO is vey nely () 4 (b) (c) (d) / 5. A metl hs fce centeed cubic ngement. If length of the edge of the cell is x cm nd M is its tomic mss, then density will be equl to (N O is Avogdo numbe) () M x N 0 gcm M N (b) x 0 gcm (c) 4M x N 0 gcm (d) M 4x N gcm 0 6. Stuctue of compound of the fomul A B in which ech B ion is co-odinted by eight ions nd ech ion by fou B ions is clled () dimgnetic stuctue (c) feomgnetic stuctue (b) nti-fluoite stuctue (d) pmgnetic stuctue 7. Sodium metl cystllizes in body cented cubic lttice with the cell edge = 4.9 Å. The dius of sodium tom is () Å (b ).8574 Å (c).8574 Å (d) None of these 8. The unit cell cube length fo LiCl (just like NCl stuctue) is 5.14 Å. Assuming nion-nion contct, the ionic dius fo chloide ion is () 1.815Å (b).8 Å (c).8 Å (d) None of these

30 9. Lithium boohydide cystllizes in othohombic system with 4 molecules pe unit cell. The unit cell dimensions e = 6.8 Å, b = 4.4 Å nd c = 7. Å. If the mol mss is 1.76, then the density of cystls is () g cm (b) g cm (c).6708 g cm (d) None of these 0. Which of the following sttements is tue? () Cystls of pticul substnce hve the sme shpe no mtte wht the conditions of cystlliztion e. (b) Thee is no egulity in the shpes of the cystls of pticul substnce. (c) While diffeing in ppeence, diffeent cystls of the sme substnce hve identicl ngles between coesponding fces. (d) Any diffeence in the ppence of two cystls of the sme substnces known s polymophism. MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS 1. The intemetllic compound LiAg hs cubic cystlline stuctue in which ech Li tom hs 8 neest neighbou silve toms nd vice-ves. Wht is the type of unit cell? () Body -cented cubic (b) Fce-cented Cubic (c) Simple cubic fo eithe Li toms lone o Ag toms lone (d) None of the bove. Which of the following sttements e coect? () The lttice positions left vcnt by nion nd occupied by electons e clled F-centes. (b) The pesence of F-centes mke lttice electiclly neutl nd dimgnetic. (c) The pesence of F-centes give colous to the cystl. (d) F-centes contins unpied electons.. Which of the following e coect with espect to Zinc blende stuctue? () Zn + ions e pesent t cones nd t the cente of ech fce. (b) Only ltente tethedl holes occupied by Zn + ions. (c) The coodintion numbe of Zn + nd S is 4 ech. (d) The numbe of ZnS units in unit cell is Select the coect sttements mong following: () Neest neighbou distnce in NCl = / (b) Neest neighbou distnce in CF = /4 (c) Neest neighbou distnce in N O= /4 (d) Neest neighbou distnce in CCl= /

31 5. In the unit cell of NCl, which of the following sttements e coect? () N + ions hve six Cl ions in its neest neighbouhood. (b) Cl ions hve six N + ions in its neest neighbouhood. (c) Second neest neighbou of N + ion e twelve N + ions. (d) NCl hs 68% of occupied spce. 6. The numbe of neest neighbous with which given sphee of pcking is in contct, is clled coodintion numbe. The coect sttements bout co-odintion numbe e () Coodintion numbe deceses on heting. (b) Coodintion numbe inceses on pplying pessue. (c) CsCl cquies NCl type stuctue on heting. (d) Coodintion numbe of octhedl site is Which of the following is/e Bvis lttice? () Fce cented othohombic (c) Body cented tetgonl (b) Fce cented cubic (d) End cented monoclinic 8. Which of the following sttements e coect? () ccp stuctue hs -lyes (b) In ccp stuctue fist nd fouth lyes e epeted. (c) In hcp stuctue fist nd thid lyes e epeted. (d) In hcp stuctue fist nd thid lyes e epeted. 9. The coect sttement(s) egding defects in solids is(e) () Fenkel defect is usully fvoued by vey smll diffeence in the sizes of ction nd nion. (b) Fenkel defect is disloction defect. (c) Tpping on n electon in the lttice leds to the fomtion of F-cente. (d) Schottky defects hve no effect on the physicl popeties of solids. 40. The composition of smple of wustite is Fe 0.9 O Which of the following sttements e coect elted to this compound? () The pecentge of Fe(III) by mss is 11.5% (b) The tio of Fe(III) to Fe(II) ion is 0.17 (c) The pecentge of Fe(II) ion 11.5% (d) The mount of Fe + is 7.84 g

32 MISCELLANEOUS ASSIGNMENT Compehension-I Atoms in solid cn be closely pcked esulting into eithe cubicl close pcking (ccp) o hexgonl close pcking (hcp). Thee exists two type of voids tethedl nd octhedl. Atoms cn be closely pcked esulting ccp hving ngement ABC, ABC,... while in hcp it is AB, AB,... type 1. The numbe of tethedl void ound n tom in ccp is () 1 (b) 8 (c) 4 (d). Which is coect bout densities () ccp > hcp (b) hcp > ccp (c) ccp = hcp (d) ccp > o < o = hcp depending upon the ctul size of toms. The tio of coodintion numbes of toms of ccp : hcp is () 1 : 1 (b) 1 : (c) : 1 (d) : 4. The height of hcp unit cell, if dius of n tom is () 6 (b) 4 (c) > 4 but < 6 (d) less thn < 4 Compehension-II X-y cystllogphy evels mny spects of the stuctue of metl hlides. The dius tio ( + / ) is useful pmete to tionlize thei stuctue nd stbility. A tble of dius tio ( + / ) fo some lkli hlides is given below. The vition of the electosttic component of lttice enegy of lkli hlides with dius tio ( kept constnt) is shown schemticlly fo NCl-type nd CsCl-type cystl stuctues. Enegy 1.0 CsCl type NCl type + / Cl B I Li + N + K + Rb + Cs Which mong the hlides is likely to undego phse tnsition fom NCl type to CsCl type stuctue with chnge of tempetue nd / o pessue? () LiB (b) RbB (c) NB (d) none of these 6. The dius tio ( + / ) t which the enegy t CsCl-type stuctue levels off () 0.7 (b) 0.41 (c) 0.5 (d) 0.64

33 Compehension-III A cubic unit cell contins Mngnese ions t the cones nd Fluoide ions t the cente of ech edge. 7. Wht is the empiicl fomul? () MnF (b) MnF (c) MnF (d) MnF 4 8. Wht is the coodintion numbe of the Mn ion? () 4 (b) 6 (c) 8 (d) 1 9. Wht is the edge length of the cell if the dius of Mn ion is 0.65 Å nd F-ion is 1.6 Å? ().01Å (b) 4.0Å (c) 5.68 Å (d).89 Å 10. Wht is the density of the compound? (Mn = 55, F = 19) ().86 gm/cm (b) 5.7 gm/cm (c) gm/cm (d) 8.59 gm/cm MATRIX MATCH TYPE QUESTIONS 11. A. Rock slt stuctue (p) Co-odintion numbe of ction is 4 B. Zinc blend stuctue (q) C. Anti Fluoite stuctue () Coodintion numbe of ction nd nion e sme D. Bcc Stuctue (s) Distnce between two neest nions is / 1. Mtch the cystl system/unit cell mentioned in Column I with thei chcteistic fetues mentioned in Column II Column I Column II A. Zinc Blende (p) Anion nd Ction hve simil coodintion numbe B. Rock Slt (q) Voids long one fce plne e not occupied C. Fluoite () All the voids long one of the body digonl line e not occupied D. Anti fluoite (s) gm 4 mol mss d = cm volumeof unit cell Avogdo'snumbe INTEGER TYPE QUESTIONS 1. PbS hs NCl stuctue. Its density is 1.7 gm/cm. Mol mss if PbS is 9. Clculte inte ionic distnce in pm units, nswe divided by 50 nd expess the numbe. 14. Chomium (At. wt.= 5) cystllizes with bcc lttice. The length of the unit cell edge is found to be 90 pm. The vlue of density in gm/cm is. 15. Find tio of body digonl length to tht of neest distnce between centes of tethedl nd octhedl voids in fcc system.

34 16. In FeO cystl lttice, 4% of ctions sites e vcnt nd electoneutlity is mintined by oxidtion of some Fe(II) into Fe(III). The numbe of Fe(III) ions pesent pe hunded of O ions e. 17. An ionic substnce AB hs NCl like stuctue in which ions A occupy cones of the cubic unit cell. If ll the fce cented ions long one of xes e emoved. The totl no of ions A nd B in one unit cell will be. 18. Density of Lithium tom is 0.5 g/cm. the edge length of Li is.5 Å. The numbe of Lithium toms in unit cell will be... (tomic mss of Lithium is 6.94). 19. The concenttion of ction vcncies if NCl is doped with 10 mole pecentge of SCl is (x + y). If x is 10 they y is. 0. A cubic is mde up of two elements X nd Y. X is pesent t cones nd Y pesent t body cente. The Co. no. of X is. 1. In ABC, ABC pcking no. of tethedl voids pesent pe unit cell is.. How mny numbe of effective N + ions, pesent in unit cell of Rock slt stuctue is.

35 PREVIOUS YEAR QUESTIONS IIT-JEE/JEE-ADVANCE QUESTIONS 1. Which of the following FCC stuctue contins ctions in ltente tethedl voids? () NCl (b) ZnS (c) N O (d) CF. When I is oxidised by MnO 4 in lkline medium, I convets into () IO (b) I (c) IO 4 (d) IO. A metllic cystl cystllizes into lttice contining sequence of lyes AB AB AB... Any pcking of sphees leves out voids in the lttice. Wht pecentge of volume of this lttice is empty spce? () 74% (b) 6% (c) 50% (d) none of these 4. The coodintion numbe of metl cystlling in hexgonl close pcked stuctue is () 1 (b) 4 (c) 8 (d) 6 5. In solid AB hving the NCl stuctue, A toms occupy the cones of the cubic unit cell. If ll the fce-cented toms long one of the xes e emoved, then the esultnt stoichiomety of the solid is () AB (b) A B (c) A 4 B (d) A B 4 6. A subsnce A x B y cystllizes in fce cented cubic (FCC) lttice in which toms A occupy ech cone of the cube nd toms B occupy the centes of ech fce of the cube. Identify the coect composition of the substnce A x B y () AB (b) A 4 B (c) A B (d) composition cnnot be specified Pgph fo Question Nos. 7 to 9 In hexgonl systems of cystls, fequently encounteed ngement of toms is descibed s hexgonl pism. Hee, the top nd bottom of the cell e egul hexgons nd thee toms e sndwiched in between them. A spce-filling model of this stuctue, clled hexgonl close-pcked (HCP), is constituted of sphee on flt sufce suounded in the sme plne by six identicl sphees s closely s possible. Thee sphees e then plced ove the fist lye so tht they touch ech othe nd epesent the second lye. Ech one of these thee sphees touches thee sphees of the bottom lye. Finlly, the second lye is coveed with thid lye tht is identicl to the bottom lye in [IIT 008] 7. The numbe of toms in this HCP unit cell is () 4 (b) 6 (c) 1 (d) The volume of this HCP unit cell is () 4 (b) 16 (c) 1 (d) 64

36 9. The empty spce in this HCP unit cell is () 74% (b) 47.6% (c) % (d) 6% 10. The coect sttement(s) egding defects in solids is (e) () (b) (c) (d) Fenkel defect is usully fvoued by vey smll diffeence in the sizes of ction nd nion Fenkel defect is disloction defect Tpping of n electon in the lttice leds to the fomtion of F-cente Schottky defects hve no effect on the physicl popeties of solids 11. Mtch the cystl system/unit cell mentioned in Column I with thei chcteistic fetues mentioned in Column II. Indicte you nswe by dkening the ppopite bubbles of the 4 4 mtix given in the ORS. Column I Column II A. simple cubic nd fce-cented cubic (p) hve these cell pmtes = b = c nd B. cubic nd hombohedl (q) e two cystl systems C. cubic nd tetgonl () hve only two cystllogphic ngles of 90 D. hexgonl nd monoclinic (s) belong to sme cystl system 1. The coodintion numbe of Al in the cystlline stte of AlCl is 1. The pcking efficiency of the two-dimensionl sque unit cell shown below is () 9.7% (b) 68.0% (c) 74.05% (d) 78.54% L 14. Silve (tomic weight = 108 g mol 1 ) hs density of 10.5g cm. The numbe of silve toms on sufce of e 10 1 m cn be expessed in scientific nottion s y 10 x. The vlue of x is 15. A compound M p X q hs cubic close pcking (ccp) ngement of X. Its unit cell stuctue is shown below. The empiicl fomul of the compound is M = X = () MX (b) MX (c) M X (d) M 5 X The ngement of X ions ound ion in solid AX is given in the figue (not dwn to scle). If the dius of X is 50 pm, the dius of is () 104 pm (b) 15 pm (c) 18 pm (d) 57 pm

37 DCE QUESTIONS 1. How mny N + ions e pesent in the NCl unit cell () (b) 4 (c) 6 (d) 8. All cystls of sme substnce posess the sme elements of symmety. This is sttement of () Bgg s lw (b) Lw of cytls (c) Lw of symmety (d) None of these. Lithium metl hs body cented cubic stuctue. Its density is 0.5 g cm nd its tomic mss is 6.94 g mol 1. Clculte the edge length of unit cell of lithium metl () 15.6 pm (b) 51.6 pm (c) 57.4 pm (d) 6.7 pm 4. In solid lttice, ction is bsent fom lttice site nd pesent t n intestitil position, the lttice defect is () Fenkel (b) intestitil (c) Schottky (d) None of these 5. Monoclinic cystl hs dimension () b c, = 90, 90 (b) b c, = 90 (c) b c, = 90 (d) b c, Shine t feshly cut sodium is becuse of () osciltion of fee electons (b) wek metllic bonding (c) bsoption of light in cystl lttice (d) pesence of fee vlency t the sufce 7. Fo cystl system = b = c nd = = 90 () tetgonl (b) hexgonl (c) homohedl (d) monoclinic 8. Choose the incoect sttement fo ionic solids: [ () (b) The dius tio + / inceses s coodintion numbe inceses. As the diffeence in size of ions inceses, coodintion numbe inceses. (c) When coodintion numbe is eight, + / tio lies between 0.5 to (d) In ionic solid of the type AX (ZnS, wutzite), the coodintion numbe of Zn + nd S espectively e 4 & 4. AIEEE/JEE-MAINS QUESTIONS 1. An ionic compound hs unit cell consisting of A ions t the cones of cube nd B ions on the centes of the fces of the cube. The empiicl fomul fo this compound would be () AB (b) A B (c) AB (d) A B. Wht type of cystl defect is indicted in the digm below? N + Cl N + Cl N + Cl Cl Cl N + N + N + Cl Cl N + Cl Cl N + Cl N + N + () Intestitil defect (b) Schottky defect (c) Fenkel defect (d) Fenkel nd Schottky defects