amorphous solids, liquids and gases atoms or molecules are C A indentical and all properties are same in all directions.

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1 THE SOLID STTE 1. INTRODUCTION : Mtter cn exist in three physicl sttes nmely ; solid, liquid nd gs. Mtter consists of tiny prticles (toms, ions or molecules). If the prticles re very fr off from one nother, they behve like gses; nerer, they behve like liquids, nd nerest, like solids. The three sttes of mtter re thus known s the three sttes of ggregtion from Ltin word mening "Flcking together". The fundmentl difference between the three sttes of ggregtion lies essentilly in the difference of the reltive mounts of energy possessed by the prticles in the three sttes. The reltive energies in the different sttes of mtter re governed by two universl opposing tendencies ssocited with the prticles : (i) (ii) They hve tendency of mutul ttrction. They hve tendency of escpe from one nother which is known s escping tendency. Whether given system would exist s solid, liquid or gs depends upon the reltive strengths of these opposing tendencies. If the escping tendency is greter thn the ttrction between them, the molecules will be crried fr from ech other to distnces which re lrge s compred with their dimeters, the system will exists in gseous stte. But in the liquid stte the moleculr ttrction exceeds the escping tendency nd in the solid stte the forces of ttrction re so much greter thn those of escping tendency tht ech prticle is bound into definite plce in rigid position by the mutul ttrction of molecules. In other words, in the solid stte, the system possesses the mount of energy of motion i.e. kinetic energy.. THE SOLID STTE : The solid re chrcterised by incompressibility, rigidity nd mechnicl strength. The molecules, toms or ions in solids re closely pcked i.e. they re held together by strong forces nd cn not move bout t rndom. Thus solids hve definite volume, shpe, slow diffusion, low vpour pressure nd possesses the unique property of being rigid. Such solids re known s true solids e.g. NCl, KCl, Sugr, g, Cu etc. On the other hnd the solid which loses shpes on long stnding, flows under its own weight nd esily distorted by even mild distortion forces re clled pseudo solids e.g. glss, pitch etc. Some solids such s NCl, Sugr, Sulphur etc. hve properties not only of rigidity nd incompressibility but lso of hving typicl geometricl forms. These solids re clled s crystlline solids. In such solids there is definite rrngements of prticles (toms, ions or molecules) throughout the entire three dimensionl network of crystl. This is nmed s long-rnge order. This three dimensionl rrngement is clled cr ystl lttice or spce lttice. Other solids such s glss, rubber, plstics etc. hve rigidity nd incompressibility to certin extent but they do not hve definite geometricl forms or do not hve long rnge order re known s morphous solids. 3. DIFFERENCES BET WEEN CRYSTLLINE ND MORPHOUS SOLIDS : ( i ) Chrcteristic Geometry : In the crystlline solids the prticles (toms, ions, or molecules) re definitely nd orderly rrnged thus these hve chrcteristic geometry while morphous solids do not hve chrcteristic geometry. ( i i ) Melting Points : crystlling solids hs shrp melting point i.e. it chnges into liquid stte t definite temperture. On the contrry n morphous solid does not hs shrp melting point. For exmple, when glss is heted, it softens nd then strts flowing without undergoing ny brupt or shrp chnge from solid to liquid stte. Therefore, morphous solids re regrded s "liquids t ll tempertures". ( i i i) Cooling curve : morphous solids show smooth cooling curve while crystlline solids show two breks in cooling curve. In the cse of crystlline solids two breks points '' nd 'b' re pper. These points indicte the beginning nd the end of the process of crystlliztion. In this time intervl temperture remins constnt. This is due to the fct tht during crystllistion process energy is liberted which compenstes for the loss of het thus the temperture remins constnt.

2 Temperture Temperture c c indicte super cooled liquid stte b Time Cooling curve of n morphous solid Time Cooling curve of crystlline solid ( i v ) Isotropy nd nisotropy : morphous solids differ from crystlline solids nd resemble liquids in mny respects. The properties of morphous solids, such s electricl conductivity, therml conductivity, mechnicl strength, refrctive index, coefficient of therml expnsion etc. re sme in ll directions. Such solids re known s isotropic. Gses nd liquids re lso isotropic. On the other hnd crystlline solids show these physicl properties different in diferent directions. Therefore crystlline solids re clled nisotropic. The nisotropy itself is strong evidence for the existence of orderly moleculr rrngement in crystls. For exmple, the velocity of light pssing through crystl is different in different directions. ry of light entering in crystl my split up into two components ech following different pth nd trvelling with different velocity. This phenomenon is clled double refrction. In the figure two different kinds of toms re shown in two dimensionl rrngement. If the properties re mesured long the direction CD, they will be different from those mesured long the direction B. This is due to the fct tht in the direction B ech row is mde up of one type of toms while in the direction CD ech row is mde up of two types of toms. It is importnt of note tht in the cse of B D morphous solids, liquids nd gses toms or molecules re C indenticl nd ll properties re sme in ll directions. nisotropic behviour of crystls ( v ) Cutting : Crystlline solids give clen clevge while morphous solids give irregulr cut, due to conchoidl frcture on cutting with shrp edged tool. 4. CRYSTLLINE STTE : " crystl is solid composed of toms (ions or molecules) rrnged in n orderly repetitive rry". Most of the nturlly occuring solids re found to hve definite crystlline shpes which cn be recognised esily. These re in lrge size becuse these re formed very slowly thus prticles get sufficient time to get proper position in the crystl structure. Some crystlline solids re so smll tht pper to be morphous. But on exmintion under powerful microscope it is lso seen to hve definite crystlline shpe. Such solids re known s micro crystlline solide. Thus the crystllinity of crystl my be defined s " condition of mtter resulting from n or orderly, cohesive, three dimensionl rrngement of its component prticles (toms, ions or molecules) in spce". This three dimensionl rrngement is clled crystl lttice or spce lttice. The position occupied by the prticles in the crystl lttice re clled lttice sites or lttice points. The lttices re bound by surfce tht usully plnr nd known s fces of the crystl. "T he sml le st geometricl posit ion of t he cr ystl which cn be used s repet it ive unit to bui ld up the whole crystl is clled unit cell."

3 The ngle between the two perpendiculrs to the two intersecting fces is termed s the interfcil ngle which my be sme s the ngle between the unit cell edges. Goniometer is used to mesure the interfcil ngle. It is importnt to note tht interfcil ngle of substnce remins the sme lthough its shpe my be different due to conditions of formtion. Interfcil ngles of crystl This is known s lw of constncy of interfcil ngle or lw of crystllogrphy. 5. TYPES OF THE CRYSTLS : Crystl re divided into four importnt types on the bsis of chemicl bonding of the constituent toms. ( i ) Ionic Crystls : These re formed by combintion of highely electro-positive ions (ctions) nd highly electronegtive ions (nions). Thus strong electrosttic force of ttrction cts with in the ionic crystls. Therefore, lrge mount of energy is required to seprte ions from one nother. The type of the crystl Cl lttice depends upon (i) The size of the ion (ii) The necessity N + for the preservtion of electricl neutrlity. Therefore lternte ctions nd nions in equivlent mounts re rrnged in the ionic crystl e.g. NCl, KF, CsCl etc. Crystl structure of NCl ( i i ) Covlent Crystls : These re formed by shring of vlence electrons between two toms resulting in the formtion of covlent bond. The covlent bonds extend in two or three dimensions forming gint interlocking structure clled network. Dimond nd grphite re the good exmples of this type. (iii) Moleculr Crystls : In these crystls, molecules occupy the lttice points of the unit cells, except in solidified noble gses in which the units re toms, where the binding is due to vnder Wl's' forces nd dipole-dipole forces. Since vnder Wl's forces re non-directionl hence structure of the crystl is determined by geometric considertion only. Solid H, N, O, CO, I, sugr etc. re well known exmples of such crystl in which vnder Wl's forces re cting. Ice is the common exmple in which dipole-dipole forces of ttrction (hydrogen bonding) re ctive. Mny orgnic nd inorgnic crystls involve hydrogen bonds. lthough these re comprtively weker but ply very importnt role in determining the structures of substnces e.g. polynucleoides, proteins etc. ( i v ) Metllic Crystls : These re formed by combintion of toms of electropositive elements. These toms re binded by metllic bonds. It my be defined s : The force tht binds metl ion to number of electrons within its sphere of influences is known s metllic bond OR bond which is formed between electropositive elements OR The ttrctive force which holds the toms of two or more metls together in metl crystl or in n lloy.

4 We know tht the force of ttrction between metl ions nd vlency electrons is very strong. This force of ttrction is responsible for compct solid structure of metl. The importnt chrcteristics of the vrious types of crystls re given in the following tble: Some Impor t nt Chrcterist ics of Vrious t ype s of Cr ystls Chrcte ristics Ionic Crystls C o v l e nt Molecul r Metllic Crystls Crystls Crystls 1. Units tht Ctions nd toms Molecules Positive ions in occupy lttice nions "se or pond" of points electrons.. Binding Electrosttic Shred vnder Wls Electrosttic forces ttrction electrons or Dipole- ttrction between between ions dipole positively chrged ions nd negtively chrged electrons. 3. Hrdness Hrd Very hrd Soft Hrd or soft Grphite is soft 4. Brittleness Brittle Interme- Low Low dite 5. Melting point High Very high Low Vrying from moderte to high 6. Electricl Semi cond- Non-con- Bd condu- Good conductors Conduction uctor due to ductor ctor crystl impe- rfections,con- ductor in fused stte Grphite is good conductor 7. Solubility in Soluble Insoluble Soluble s Good conductors Polr solvents well s insoluble 8. Het of NCl(s) Grphite NH 3 (s) Cu(s) Vporistion (kj mol 1 ) 9. Het of NCl NH 3 (s) Cu(s) fusion (kj mol 1 ) 10. Exmple NCl, KNO 3 Dimond, H O(s), N, Cu, g, Fe, CsCl, N SO 4 grphite, CO (s), Pt, lloys ZnS Qurtz Sulphur, (SiO ), SiC Sugr, Iodine,noble gses

5 6. ISOMORPHISM : The occurence of given substnce in more thn one solid crystlline forms hve different physicl properties is known s polymorphism. This property when occurs in elements is known s llotropy. Sometimes we come cross exmples of chemiclly different solids which crystllise in the sme crystlline shpe. Such substnces re sid to be Isomorphous (sme shpe). Their chemicl constitutions re very similr nd in some cses crystls of one substnce my continue to grow when plced in sturted solution of the other e.g. potsh lum nd chrome lum crystls hve the sme shpe nd cn be grown in ech other's solutions. Mitscherlich deduced tht isomorphous substnces hve similr chemicl formul e.g. phosphtes nd rsentes re sid to be isomorphous with one nother viz. 1. N HPO 4.1H O nd N 3 so 4.1H O. K SO 4, K CrO 4 3. ZnSO 4.7H O, MgSO 4.7H O, FeSO 4.7H O 4. KMnO 4, KClO 4 5. K SO 4.l (SO 4 ) 3.4H O, K SO 4. Cr (SO 4 ) 3.4H O. However, the lw is not without exceptions. 7. SPCE LT TICE/CRYSTLLINE LTTICE/ 3 D LTTICE : Spce lttice is regulr rrngement of lttice points showing how the prticles re rrnged t different sites in 3D view. Lttice Point Lttice point Lines re used to represent geometry of crystl " The three dimensionl distribution of component prticles in crystl cn be found by X-ry diffrction of different fces of the crystl. On the bsis of the clssifiction of symmetry, the crystls hve been divided into seven systems. These cn be grouped into 3 clsses which in turn cn be regrouped into 7 crystl systems. These seven systems with the chrcteristics of their xes (ngles nd intercepts) long with some exmples of ech re given in the following tble. The Seven Crystl Systems Nme of xes ngles Brvis Lttices System 1. Cubic = b = c Primitive, Fce-centred, Body centred = 3. Tetrgonl = b c Primitive, Body centred = 3. Rhombohedrl = b= c Primitive = 1 or Trigonl 4. Orthorhombic b c Primitive, Fce-centred, or Rhombic Body centred End centred = 4 5. Monoclinic b c Primitive, End - centred = Triclinic b c Primitive = 1 7. Hexgonl = b c Primitive = 1 Totl = 14

6 c b P I F = b = c ll sides re of equl length; ll ngles re 90 0 Three ngles chnged C u b i c Trigonl (Rhombohedrl) c b P = b = c ll sides re of equl length;ngles One side is chnged One side length chnged two ngles fixed t 90 0 one fixed t 10 0 c b P c l Te tr gonl = b c One side is of different length; ll ngles re 90 0 c b P Triclinic Generl cse : ll sides re different lengths; ll ngles re different c b P H exgon l Specil Cse = b c Three unit cells re shown to give the hexgon Length of nother side is chnged Two side lengths mde the sme; one ngle fixed t 10 0 c b P I F C Or t horh omb ic These crystl systems differ in length of unit cell edges (, b nd c) nd the ngles between the unit cell edges 4. In cubic nd trigonl (rhombohedrl) systems, the three unit edges re of equl lengths but for the rest five systems it is not so. The interfcil ngles re ll 90 0 in the cubic, tetrgonl nd orthorhombic systems but z it is not so for the rest four systems. 8. UNIT CELL (U.C.) : Unit cell of the crystlline substnce is defined s the smllest repeting unit which shows the complete geometry of the crystlline substnce. For eg. brick in wll. unit cell is the smllest picture of the whole crystl. unit cell is chrcterized by the edge lengths, b nd c long the three edges of the unit cell nd the ngles, nd between the pir of edges bc; c nd b respectively. 9. CO- ORDINTION NUMBER : x The number of nerest prticles round specific prticle in given crystlline substnce is clled s coordintion number of tht crystlline substnce PCKING EFFICIENCY OR PCKING DENSITY (P.E.) : Pcking efficiency is defined s the rtio of volume occupied by the toms to the totl volume of the crystlline substnce ie pcking efficiency is equl to- P.E.= P.E.= Volume occupied by toms present in crystl Volume of crystl Volume occupied by toms present in unit cell Volume of Unit Cell n (4 / 3) r P.E. = V 3 b c Three sides re of different lengths ; ll ngles re 90 0 One ngle chnged c P b C Monoclinic Where n = number of toms present in unit cell b c c ll sides re of different lengths; b y

7 1 1. GEOMETRY OF CUBE Number of corners = 8 Number of fces = 6 Number of edges = 1 Number of cube centre = 1 Number of cube digonls = 4 Number of fce digonls = 1 Contribution of n tom t different sites of cube : corner of cube is common in 8 cubes. So 1 8 th prt of n tom is present t this corner of cube. fce of cube is common is cubes. So 1 th prt of of n tom is present t the fce of cube. n edge of cube is common in four cubes, so 1 th prt of the tom is present t the edge of cube 4 cube centre is not common in ny nother cube, so one complete tom is present t the cube centre.

8 LNGTH OF FCE DIGONL ND CUBE DIGONL : Distnce between Distnce between djcent fce centres = djcent edge centre = Consider the tringle BC, with the help of pythogorous theorem C B BC (length of fce digonl.) Consider the tringle DC, with the help of phthogorous theorem DC D C = ( ) = 3 (length of cube digonl) 1. TYPE OF UNIT CELL (BR VIS L TTICE) : The distnce between sucessive lttice plnes of the sme type is clled the spcing of plnes or interplnr distnce between the plnes. On the bsis of this spect, the lttices my be divided in following clsses : ( 1 ) Simple/ Primitive/ Bsic Unit cell : unit cell hving lttice point only t corners clled s primitive or simple unit cell. i.e. in this cse there is one tom t ech of the eight corners of the unit cell considering n tom t one corner s the centre, it will be found tht this tom is surrounded by six equidistnt neighbours (toms) nd thus the co-ordintion number will be six. If '' is the side of the unit cell, then the distnce between the nerest neighbours shll be equl to ''.

9 ( ) Reltionship between edge length ' ' nd tomic rdius ' r' : r = r i.e. r = (One fce of SCC) ( b ) Number of toms present in unit cell : In this cse one tom or ion lies t the ech corner. Hence simple cubic unit cell contins totl of = 1 tom or ion/unit cell. ( c ) Pcki ng efficienc y (P. E.) : 4 3 Volume occupied by toms present in unit cell n r P.E. = Volume of tom r Volume of unit cell V For SCC : P.E. 3 3 [ r nd V, n 1] = 0.54 or 5.4 % 6. Body centred cubic (b.c.c.) cell : unit cell hving lttice point t the body centre in ddition to the lttice point t every corner is clled s body centered unit cell. Here the centrl tom is surrounded by eight equidistnt toms nd hence the co-ordintion number is eight. The nerest distnce between two toms will be 3 1/ 8 TOM ( ) Reltionship between edge length ' ' nd tomic rdius ' r' :- r r r

10 In BCC, long cube digonl ll toms touches ech other nd the length of cube digonl is 3. So, 3 = 4r 3 i.e. r 4 ( b ) Number of tom pre sent i n unit cel l : toms/unit cell (Corner) (Body centre) In this cse one tom or ion lies t the ech corner of the cube. Thus contribution of the 8 corners is =1, while tht of the body centred is 1 in the unit cell. Hence totl number of toms per unit cell is = toms (or ions) ( c ) Pcki ng efficienc y : n r P.E = 3 3 = = 0.68 [ n =, r = V , V = 3 ] In B.C.C. 68% of totl volume is occupied by tom or ions. 3. Fce centred cubic (f.c.c.) cell : unit cell hving lttice point t every fce centre in ddition to the lttice point t every corner clled s fce centred unit cell. i.e. in this cse there re eight toms t the eight corners of the unit cell nd six toms t the centre of six fces. Considering n tom t the fce centre s origin, it will be found tht this fce is common to two cubes nd there re twelve points surrounding it situted t distnce which is equl to hlf the fce digonl of the unit cell. Thus the co-ordintion number will be twelve nd the distnce between the two nerest toms will be. ( ) Reltionship between edge length ' ' nd tomic rdius ' r' : In FCC, long the fce digonl ll toms touches ech other nd the length of fce digonl is. So 4r = i.e. r = 4 r

11 ( b ) Number of toms per unit cell : = = 4 toms/unit cell Corner fces In this cse one tom or ion lies t the ech corner of the cube nd one tom or ion lies t the centre of ech fce of the cube. It my noted tht only 1 of ech fce sphere lie with in the unit cell nd there re six such 1 fces. The totl contribution of 8 corners is 8 8 = 1, while tht of 6 fce centred toms is 1 6 = 3 in the unit cell. Hence totl number of toms per unit cell is = 4 toms (or ions). ( c ) Pcki ng efficienc y : 4 3 n r P.E. 3 [ for FCC n =4, r = V, V = 3 ] = 3 3 = 0.74 or 74 % i.e. In FCC, 74% of totl volume is occupied by toms. 4. End Centered Unit Cel l : unit cell hving lttice point t the centres of only one set of opposite fces in ddition to the lttice point t every corner clled s end centered unit cell. Note : This type of Brvis lttice is obtined only in orthorhombic nd monoclinic type unit cell. Number of toms per unit cel l i n cubic close pcked str ucture of toms Unit cell Number of toms t No. of toms Volume occupied C o r ne r s C e nt re s F c e s per unit cell by prticles (%) Simple cube Body centred cube (BCC) Fce centred cube (FCC) CRYSTL DENSITY OF THE CRYSTL : If the length of edge of the unit cell is known we cn clculte the density of the crystl s follow : Let length of edge of the unit cell be. Volume of the unit cell = 3 = V cm 3 Mss of unit cell Density of the unit cell = Volume of unit cell Mss of the unit cell = Number of toms present in unit cell Mss of one tom = n m g tomic mss M But mss of one tom (m) = = vogdro Number N

12 Mss of the unit cell = M n g N, Density of the unit cell = M n N V gm cm 3 Density of the unit cell = (C.D.) = n M g cm V N 3 n M g cm V N E x. n element (tomic mss = 60) hving fce centred cubic crystl hs density of 6.3 g cm 3. Wht is the edge length of the unit cell (vogdro constnt, N = mol 1 ) :- S o l. Since element hs fcc structure hence there re 4 toms in unit cell ( or n = 4), tomic mss is 60 (or M = 60), N = nd = 6.3 g cm 3. or V = n M = V N n M N = 3 1) (4) 60 g mol 3) g cm mol = cm = cm 3 = cm 3 E x. S o l. Let be the length of the edge of the unit cell. 3 = V = cm 3 or = cm The density of KBr is.75 g cm 3. The length of the edge of the unit cell is 654 pm. Show tht KBr hs fce centred cubic structure. Length of the edge of the unit cell = 654 pm = cm volume (V) of the unit cell = ( cm) 3 Moleculr mss of KBr = = 119 g mol 1 Density of KBr =.75 g cm 3 or n M V N V N n M g cm cm mol = 119 g mol 1 = (6.54) (6.03)(10 ) 119 = 3.9 = 4 Since number of toms (or ions) in unit cell is four hence the crystl must be fce centred cubic.

13 E x. n element crystllizes in structure hving f.c.c. unit cell of n edge 00 pm. Clculte its density, if 00 g of this element contins toms. S o l. Length of the edge of the unit cell () = 00 pm = 10 8 cm Volume (V) of the unit cell = ( 10 8 cm) 3 = cm 3 Mss of the element (M) = 00 g Number of the toms (N 0 ) = the number of toms per unit cell (fcc) = 4 n M V N 0 (4) (00 g) (8 10 cm )(4 10 ) = = 41.7 g cm 3 E x. S o l. n element crystllizes into structure which my be described by cubic type of unit cell hving one tom on ech corner of the cube nd two toms on one of its digonls. If volume of this unit cell is cm 3 nd density of the element is 7. g cm 3. Clculte the number of toms present in 00 g of the element. Volume (V) of the unit cell = cm 3 Density of ( ) of the element = 7. g cm 3 Mss of the element = 00 g Number of toms (n) per unit cell = [The contribution of the 8 corner is (1/8) 8=1 nd two toms on one of the digonl is 1 = ] i.e. 1 + = 3 toms n M V N 0 or N 0 = n M V (3) (00 g) N 0 = (4 10 cm )(7. g cm ) N 0 = toms 1 4. CLOSE PCKING OF IDENTICL SOLID SPHERES : The solids which hve non-directionl bonding, their structures re determined on the bsis of geometricl considertion. For such solids, it is found tht the lowest energy structure is tht in which ech prticle is surrounded by the gretest possible number of neighbours. In order to understnd the structure of such solids, let us consider the prticles s hrd sphere of equl size in three directions. lthough there re mny wys to rrnge the hrd spheres but the one in which mximum vilble spce is occupied will be economicl which is known s closed pcking. Now we describe the different rrngements of sphericl prticls of equl size. When the spheres re pcked in plne i.e. There re two types of close pcking. ( ) Two diment ionl ly close pcki ng : ( i ) The centres of the spheres lie one below nother. This type of rrngement is clled squre close pcking. In such pcking one sphere touches four other spheres. In this cse 5.4% of the volume is occupied. The remining 47.6% of the volume is empty nd is clled void volume. In squre close pcking co-ordintion number is 4

14 Squre close pcking ( i i ) nother type of rrngement of toms is shown below. This type of pcking is clled hexgonl close pcking. In such pcking one sphere touches six other spheres. In this cse 60.4% of the volume is occupied. The remining 39.6% of the volume is empty nd is clled void volume.therefore this type of pcking is more stble thn the squre close pcking. Hexgonl close pcking ( b ) T hree Diment ionl ly close pcki ng : In hexgonl close pcking, there re two types of the voids (open spce or spce left) which re divided into two sets 'b' nd 'c' for convenience. The spces mrked 'c' re curved tringulr spces with tips pointing upwrds wheres spces mrked 'b' re curved tringulr spces with tips pointing downwrds. Now we extend the rrngement of spheres in three dimensions by plcing second close pcked lyer (hexgonl close pcking) (B) on the first lyer (). The spheres of second lyer my plced either on spce denoted by 'b' or 'c'. It my be noted tht it is not possible to plce spheres on both types of voids (i.e. b nd c). Thus hlf of the voids remin unoccupied by the second lyer. The second lyer lso hve voids of the types 'b' nd in order to build up the third lyer, there re following two wys :

15 ( i ) In one wy, the spheres of the third lyer lie on the spces of second lyer (B) in such wy tht they lies directly bove those in the first lyer(). In other words we cn sy tht the third lyer becomes indenticl to the first lyer. If this rrngement is continued idefinitely in the sme order this represented s B B B... This type of rrngement represent B B 6 fold xis B hexgonl close pcking (hcp) symmetry (or structure), which mens tht the whole structure hs only one 6-fold xis of symmetry i.e. the crystl hs sme ppernce on rottion through n ngle of ( i i ) In second wy, the spheres of the third lyer (C) lie on the second lyer (B) in such wy tht they lie over the unoccupied spces 'C' of the first lyer(). If this rrngement is continuous in the sme order this is represented s BC BC BC... This type of rrngement represent cubic close pcked (ccp) structure. BBB... or hexgonl close pcking (hcp) of spheres 3 fold xis C B C C B B BCBC... or cubic close pcking (ccp) of spheres This structure hs 3-fold xes of symmetry which pss through the digonl of the cube. since in this system, there is sphere t the centre of ech fce of the unit cell nd hence this structure is lso known s fce-centred cubic (fcc) structure. It my be noted tht in ccp (or fcc) structures ech sphere is surrounded by 1 spheres hence the coordintion number of ech sphere is 1. The spheres occupy 74% of the totl volume nd 6% of is the empty spce in both (hcp nd ccp) structures X Coordintion number of hcp nd ccp structure

16 (iii) There is nother possible rrngement of pcking of spheres known s body centred cubic (bcc) rrngement. This rrngement is observed in squre close pcking (which is slightly opened tht hexgonl close pcking). In bcc rrngement the spheres of the second lyer lie t the spce (hollows or voids) in the first lyer. B lyer B lyer Thus ech sphere of the second lyer touches four spheres of the first lyer. Now spheres of the third lyer re plced exctly bout the spheres of first lyer. In this wy ech sphere of the second lyer touches eight spheres (four of 1st lyer nd four of IIIrd lyer). Therefore coordintion number of ech sphere is 8 in bcc sturcture. The spheres occupy 68% of the totl volume 3% of the volume is the empty spce. Some exmples of metls with their lttice types nd coordintion number re given in the following tble. Li Be Body-centre Cubic [bcc] N Mg l Simple Cubic Fce centrl cubic Hexgonl Closed pcked [hcp] K C Sc Ti V Cr Mn Fe Co Ni Cu Zn Rb Sr Y Zr Nb Mo Tc Ru Rh Pd g Cd Cs B L Hf T W Re Os Ir Pt u T hree dimensionl close pcki ng Contents B C C CCP/FCC HC P Type of pcking BB... BCBC... BB... pcking but not close pcking close pcking close pcking No. of toms 4 6 Co-ordintion no Pcking efficiency 6 8 % 7 4 % 7 4 % Exmples I, B C, Sr, l Remining V & Cr group Co group, Ni group, d-block elements Fe Copper group, ll inert Be & Mg gses except helium Note :- Only Mn crystllizes in S.C.C.

17 1 5. INTERSTICES OR VOIDS OR HOLES IN CRYSTL S It hs been shown tht the prticles re closely pcked in the crystls even thn there is some empty spce left in between the spheres. This is known s interstices (or interstitil site or holest or empty spce or voids). In three dimentionl close pcking (CCP & HCP) the interstices re of two types : (i) tetrhedrl interstices nd (ii) octhedrl interstices. ( i ) Tetrhedrl interstices : We hve seen tht in hexgonl close pcking (hcp) nd cubic close pcking (ccp) ech sphere of second lyer touches with three spheres of first lyer. Thus they, leve smll spce in between which is known s tetrhedrl site or interstices. or The vcnt spce between 4 touching spheres is clled s tetrhedrl void. Since sphere touches three spheres in the below lyer nd three spheres in the bove lyer hence there re two tetrhedrl sites ssocited with one sphere. It my by noted tht tetrhedrl site does not men tht the site is tetrhedrl in geometry but it mens tht this site is surrounded by four spheres nd the centres of these four spheres lie t the pices of regulr tetrhedron. Tetrhedrl void tetrhedrl interstices Tetrhedron geometry In FCC, one corner nd its there fce centres form tetrhedrl void In FCC, two tetrhedrl voids re obtined long one cube digonl. So in FCC 8 tetrhedrl void re present. In FCC totl number of toms = 4 In FCC totl number of tetrhedrl voids = 8 So, we cn sy tht, in 3D close pcking tetrhedrl voids re ttched with one tom. B C D Tetrhedrl void Cube digonl

18 ( i i ) Octhedrl - interstices : Hexgonl close pcking (hcp) nd cubic close pcking (ccp) lso form nother type of interstices (or site)which is clled octhedrl site (or interstices). or The vcnt spce between 6 touching spheres is clled s octhedrl void. In the figure two lyers of close pcked spheres re shown. The spheres of first lyer re shown by full circles while tht of second lyer by dotted circles. Two tringles re drwn by joining the centres of three touching spheres of both the lyers. Octhedrl void Octhedrl interstices Octhedrl geometry In FCC, 6 fce centres form octhedrl void The pices of these tringles point re in opposite directions. On super imposing these tringles on one nother octhedrl site is creted. It my be noted tht n octhedrl site does not men tht the hole is octhedrl in shpe but it mens tht this site is surrounded by six nerest neighbour lttice points rrnged octhedrlly. Octhedrl void (t the edge) ( 1 th prt of Octhedrl 4 void is obtined t ech edge Octhedrl void (t the body centre) In FCC, totl number of octhedrl voids re (1 1) + (1 1 4 ) = = 4 (Cube centre) (edge) In FCC, number of toms = 4 In FCC, number of octhedrl voids = 4 So, we cn sy tht, in ny type of close pcking one octhedrl void is ttched with one tom.

19 Ex. S o l. Element is every element of FCC, tom B is present t every Octhedrl void, tom C is present t 5% of Tetrhedrl void. Find out the possible moleculr formul of the compound? tom is every element of FCC = 4 toms of tom B is present t every octhedrl void = 4 toms of B tom C is present t 5% of tetrhedrl void = 5 8 = tom of C 100 So, the possible moleculr formul is 4 B 4 C = B C LIMITING R DIUS RTIOS : n ionic crystl contins lrge number of ctions nd nions. Generlly ctions re Smller in size thn tht of nions. The ctions re surrounded by nions nd they touch ech other. These ions re rrnged in spce in such wy to produce mximum stbility. The stbility of the ionic crystl my be described in terms of rdius rtio i.e. the rtio of the rdius of ction (r) to tht of nion (R) is (r/r). The rnge of (r/r) my be expressed s limiting rdius rtio. This vlue is importnt to determine the rrngement of the ion in different types of crystls. Evidently rdius rtio (r/r) plys very importnt role in deciding the stble structure of ionic crystl. Lrger ctions prefer occupying lrger holes (cubic etc.) nd smller ctions prefer occupying smller holes (tetrhedrl etc.) ( i ) Tringulr : ll nions touches ech other nd co-ordintion number is 3 Cos r Cos 30 = r r 3 r r r r + + r - 3r 3r r 3r 3 r r r r - 60 L.R.R. = = r 1 r ( i i ) Tetrhedrl void : ll nions touches ech other nd co ordintion number of ction is 4. Fce digonl C = r r or = r Tri ngle CD - D = C + CD D = D = 3 = + = 3 ccording to cube digonl D 3 r r

20 3 r r D Put the vlue of = r 3 r r r 3 r r r r r 3 r r 1 r 3 1 r r r (iii) Octhedrl void : ll the nions re touch ech other nd co ordintion number is 6. In BC C = B + BC = + C = - - r + + r = C = BC = = r r r r r r r r r 1 1 r = = ( i v ) Cubic void : ll the nions re touch ech other nd co ordintion number is 8. ccording to cube digonl D = 3 r r ( = r = BC) 3 r r r Dividing by r on both sides. r 3 1 r 3 1 = = 0.73 r r The preferred direction of the structure with increse in the rdius rtio is s follows : Plne tringulr 0.5 Tetrhedrl octhedrl 0.73 Cubic B - - r = r - C - - D Limiting rdius rtio for vrious types of sites Limiting rdius Coordi nt ion Structurl E x m p l e rtio = r/r Number of ction rrngement (Geometry of voids) Plne Trigonl Boron Oxide Tetrhedrl ZnS, SiO Squre plner Octhedrl NCl, MgO Cubic CsCl

21 E x. solid + B hs NCl type close pcked structure. If the nion hs rdius of 50 pm, wht should be the idel rdius for the ction? Cn ction C + hving rdius of 180 pm be slipped into the tetrhedrl site of the crystl + B? Give reson for your nswer. S o l. In N + Cl crystl ech N + ion is surrounded by 6 Cl + ions nd vice vers. Thus N + ion is plced in octhedrl hole. The limiting rdius rtio for octhedrl site = or B = r R Given tht rdius of nion (B ) R = 50 pm i.e. rdius of ction ( + ) r = R = pm or r = pm Thus idel rdius for ction ( + ) is r = pm. We know tht (r/r) for tetrhedrl hole is 0.5. r 0.5 R o r r = 0.5 R = = 56.5 pm Thus idel rdius for ction is 56.5 pm for tetrhedrl hole. But the rdius of C + is 180 pm. It is much lrger thn idel rdius i.e pm. Therefore we cn not slipped ction C + into the tetrhedrl site. NCl type : For NCl : Distnce between two nerest ions ( r + + r ) :- r + + r = i.e. r + + r = CsCl type : For CsCl : Distnce between nerest ions ( r + + r ) :- r + + r = 3 r + + r = 3 Cs + Cs + Cs + Cs + Cl Cs + Cs + Cs + Cs +

22 T Y P E S O F I O N I C C R Y S T L Type of Ionic G e o m e t r y C o-ordi nt ion No. of formul's E x m p l e s C r y s t l N u m b e r per U.C.C. 1. NCl (1 : 1) 6 : 6 4N + + 4Cl Hlides of (Li, N, K, Rb) (Rock Slt Type) 4NCl Oxides nd sulphides of (4) II (Some exception) gf, gcl, gbr, NH 4 X. CsCl Type (1 : 1) 8 : 8 1Cs + + 1Cl Hlides of 'Cs' 1CsCl TlCl, TlBr, CS (1) 3. Zns Type (1 : 1) 4 : 4 4Zn + + 4S BeS, (Zinc Blende Type) 4ZnS BeO, CO, gi, (Sphlerite) (4) CuCl, CuBr, CuI 4. CF Type (1 : ) 4C + + 8F BCl, BF (Fluorite Type) 4CF SrCl, SrF (4) CCl, CF 5. N O Type ( : 1) 8N + + 4O Li O, Li S (ntiflourine) 4N O N O, N S (4) K O, K S 6. ZnS Type (1 : 1) 4 : 4 6Zn + + 6S Sme s (Wurtzite) 6ZnS sphlerite nother geometry (6) of Zns Cl N + Cl Cs + Zn + S C + F O N +

23 1 7. Defect s or imper fect ions i n solids : Idel crystl : The crystl in which ll the lttice points re occupied by the component prticles or groups of prticles is clled n idel crystl. Solid stte is chrcterised by vibrtory motion bout the men position of constituent prticles. t bsolute zero, ll the types of motions cese, nd therefore crystls tend to hve perfectly ordered rrngement. s the temperture increses, moleculr motions (vibrtory mplitudes) increse nd therefore the ions my lose their usul sites nd either get missed or occupy interstitil positions in the crystl, ie., devitions from ordered rrngement tke plce. ny devition from the perfectly ordered rrngement gives rise to defect or imperfection in the crystl. Defect in crystls re produced either due to therml effects or by dding certin impurities in the pure crystls (doping). Defects in crystls my be discussed under two titles :. Stoichiometric defects B. Non-stoichiometric defects [ ] Defects in stoichiometric compounds : Stoichiometric compounds re those in which the number of positive nd negtive ions re exctly in the rtio s shown by their chemicl formule. Two types of defects re observed in these compounds. (i) Schottky defect, (ii) Frenkel defect ( i ) Schottky defect : This type of defect is produced when one ction nd nion re missing from their respective positions leving behind pir of holes. The crystl s whole remins neutrl becuse the number of missing positive ions (ctions) nd negtive ions (nions) is the sme Schottky defect ppers generlly in ionic compounds in which rdius rtio [r + /r ] is not fr below unity. For this defect, the ctions nd nion should not differ much in size. For schottky defect, co-ordintion numbers of the ions should be high, Exmples of ionic solids showing this defect re NCl, CsCl, KCI, KBr etc. Consequences of schottky defect : Density of the crystl decreses The crystl begins to conduct electricity to smll extenet by ionic mechnism. The presence of too mny 'voids' lowers lttice energy or the stbility of the crystl. Schottky defect

24 ( i i ) Frenkel defect : This type of defect is creted when n ion leves its pproprite site in the lttice nd occupies n interstitil site. hole or vcncy is thus produced in the lttice. Frenkel defect The electroneutrlity of the crystl is mintined since the number of positive nd negtive ions is the sme. Since positive ions re smll, in size, they usully leve their positions in the lttice nd occupy interstil positions. Frenkel defect is exhibited in ionic compounds in which the rdius rtio [r + /r ] is low. The ctions nd nions differ much in their sizes nd the ions hve low co-ordintion numbers. Exmples re ZnS, gbr, gi, gcl. Consequence s of Frenkel defect : The closeness of like chrges tends to increse the dielectric constnt of the crystl. The crystl showing frenkel defect conducts electricity to smll extent by ionic mechnism. The density of the crystl remins the sme. [ B ] Non- stoichiometric defect : These types of defects re observed in the compounds of trnsitionl elements. These defects rise either due to the presence of excess metl ions or excess non-metl ions. ( i ) Metl excess defect due to nion vcncies : compound my hve excess metl ion if n nion (negtive ion) is bsent from its pproprite lttice site creting 'void' which is occupied by n electron. Ionic crystl which re likely to posses schottky defect, my lso develop this type of metl excess defect. When lkli metl hlides re heted in tmosphere of vpours of the lkli metl, nion vcncies re creted. The nions (hlide ions) diffuse to the surfce of the crystl from their pproprite lttice sites to combine with the newly generted metl ctions. The e lost by the metl tom diffuse through the crystl re known s F-centres. The min consequence of metl excess defect is the development of colour in the crystl. For exmple, when NCl crystl is heted in n tmosphere of N vpours, it becomes yellow. Similrly, KCI crystl when heted in n tmosphere of potssium vpours, it pper violet. ( i i ) Metl excess defect due to interstitil ctions : This type of defect is shown by crystls which re likely to exhibit Frenkel defect. n excess positive ion is locted in the interstitil site. To mintin electricl neutrlity, n electron is present in the intrestitil site. n exmple showing this type of defect is ZnO. When ZnO is heted, it loses oxygen reversibly. The excess Zn ++ ions re ccommodted in the interstitil sites, the, electrons re enclosed in the neightbouring interstitils. The yelllow colour of ZnO when hot is due to these trpped electrons. These electrons lso explin electricl conductivity of the ZnO crystl.

25 Doping : The ddition of smll mount of foreign impurity in the host crystl is clled s doping. It results in n increse in the electricl conductivity of the crystl. Doping of group 14 elements (such s Si, Ge, etc.) with elements of group 15 (such s s) produces n excess of electrons in the crystls, thus giving n-types semiconductors. Doping of groups 14 elements with group 13 elements (such s Indium) produces holes (electron deficiency) in the crystls. Thus p-type semiconductors re produced. Then symbol 'p' indictes flow of positive chrge ELECTRICL PROPERTIES OF SOLIDS : Solids hve been clssified s metls, insultors (bd conductors) nd semi-conductors. Electricl conductivity of solids is due to motion of electrons nd holes or ions. Conduction of ionic solids is due to bsence of vcncies nd other defects. Thus conductivity of semi conductors s well s insultors is minly becuse of impurities nd defects present in them. Electrons nd holes produced by the ioniztion of defects contribute to conduction in these solids MGENETIC PROPERTIES OF SOLIDS : Solids cn be divided into different clsses. Depending on their response to mgnetic fields. ( ) Prmgnet ic (wekly mgnetic) : Such mterils contin permnent mgnetic dipoles due to the presence of toms, ion or molecules with unpired electrons e.g. O, Cu +, Fe +3 nd they re ttrcted by the mgnetic field. They however lose their mgnetism in the bsence of mgnetic field. ( b ) Dimgnetic : They re wekly repelled by mgnetic fields. dimgnetism rises due to the bsence of unpired electrons e.g. H, Li +, Be +, ( electron type), O, F, N +, Mg + (8 electron type), g +, Zn +, Cd + (18 electron type). ( c ) Ferromgnetic : It is cused by spontneous lignment of mgnetic moments in the sme direction. ( d ) Ferrimgnetism : It occurs when the moments re ligned in prllel nd ntiprlled direction in unequl number resulting in net moment e.g. Fe 3 O 4. ( e ) ntiferromgnetism : It occurs if the lignment of moments is in compenstory wy so s to give zero net moment e.g. MnO. ll mgneticlly ordered solids (ferromgnetic nd ntiferromgnetic solids) trnsform to the prmgnetic stte t some elevted tempertures. This is most probbly due to the rndomistion of spins. Ferromgnetic chrcter ntiferromgnetic chrcter Ferrimgnetic chrcter