Chapter 4 Structures of Solids

  CHAPTER 4 STRUCTURES OF SOLIDS4.1Introduction ………………………………………………………………………1 4.2Model Cryt!l Structure ………………………………………………………..24.2.1Bonding in Solids……………………………………………………………24.2.2Atomic Packing……………………………………………………………...34.2.3The Unit Cell………………………………………………………………..44.2.4Typology of Cystal St!ct!es…………………………………………….. 4. T#e Ionic Model ………………………………………………………………….#4.3.1The $adi!s $atio Paamete………………………………………………...#4.3.2%lectonegati&ity and Cystal St!ct!e…………………………………….1'4.3.3(attice %negy……………………………………………………………...11 4.4Cryt!l Structure ………………………………………………………………1 4.4.1)etallic %lements and Alloys……………………………………………...1 4.4.2)etal Salts…………………………………………………………………1*4.4.3)etal +,ides……………………………………………………………….224.4.4)etal -ydo,o and -ydated Compo!nds………………………………...244.4. )etal Silicates……………………………………………………………...314.4.)etal S!lfides……………………………………………………………...32 4.$Molecul!r Or%it!l T#eory !nd t#e &!nd Model o' Solid …………………...334. .1)olec!la +/itals and %negy Bands……………………………………..334. .2)etals0 ns!latos0 and Semicond!ctos…………………………………...344. .3ntinsic and %,tinsic Semicond!ctos…………………………………....3 4. .4The emi (e&el in a Solid………………………………………………...3 4.(Electronic Structure o' Solid ………………………………………………...3*4..1)olec!la +/ital%negy Band )odels…………………………………..3*4..2%lectonic St!ct!es of )etal +,ides……………………………………..34..3%lectonic St!ct!es of )etal S!lfides……………………………………41 555555555555555555555555555555555555555555555555555555555555555555555555  4.1Introduction n a6!eo!s pocessing0 o! pimay concen is 7ith sol!tion8/ased eactions0 andthe key eagents ae applied mostly in the fom of dissol&ed a6!eo!s species. t isimpotant to emem/e0 ho7e&e0 that in many of the eactions of inteest0 7e enco!nte 1  eactants ando pod!cts in the solid phase. n this connection0 it is 7othy of note thatthe ma9oity of the elements :; #'<= e,ist as solids at odinay tempeat!es. n se&ealof the chaptes that follo7 this one0 7e 7ill /e peocc!pied 7ith intefacial pocesses0e.g.0 dissol!tion0 cystal go7th0 adsoption0 and ion8e,change. >e shall see that thes!face popeties and eacti&ities of solids ae intimately connected 7ith the /!lk cystaland electonic st!ct!es.>e /egin this chapte /y consideing the types of /onding that e,ist in solids. >ethen t!n o! attention to the geometical aangements of the /onded atoms in space.om a consideation of the !les that go&en the packing of e6!al8si?ed sphees0 7eidentify the /asic !nits that constit!te the /!ilding /locks fo cystal st!ct!es. >ith theaid of these /!ilding /locks0 7e e&ie7 the cystal st!ct!es of epesentati&e solids.inally0 7e disc!ss electonic st!ct!es of solids0 !sing molec!la o/ital theoy as o! stating point.2  4.2Model Cryt!l Structure4.2.1&ondin) in Solid >e sa7 in Chaptes 2 and 3 that0 accoding to molec!la o/ital theoy0 a co&alentmolec!le o a metal8ligand comple, foms its molec!la o/itals /y com/ining the atomico/itals of the constit!ent atoms. Similaly0 7e can teat a solid paticle as a  giant molecule  consisting of an e,temely lage n!m/e of molec!la o/itals. >e ecallf!the fom Chaptes 2 and 3 that 7e can teat molec!la o/itals of a polyatomicmolec!le fom t7o e,teme points of &ie70 i.e.0 the locali?ed and delocali?ed /ondmodels. Both models ae !sef!l in the disc!ssion of solid st!ct!es. >ith the locali?ed /ond appoach0 7e can imagine a sit!ation 7hee one of the /onded atoms da7s theshaed electons completely to itself. This 7ill es!lt in a completely ionic /ond0 and thees!lting giant molec!le 7ill /e in eality an ionic solid  0 7hee the thee8dimensionalst!ct!e is /ased on the electostatic inteaction :/onding= /et7een the constit!ent ions.+n the othe hand0 if the /ond is completely co&alent0 7e get a thee8dimensionalco&alent solid s!ch as diamond0 7hee the st!ct!e consists of C8C /onds. At the othe e,teme0 7e can conside the giant molec!le fom the &ie7point of the delocali?ed /ondmodel. n this m!lti8centeed molec!la o/ital appoach0 the atomic n!clei of the solidae &ie7ed as em/edded in a sea of electons. This sit!ation is chaacteistic of the solidsof the metallic elements0 and this type of delocali?ed /onding has ac6!ied the name metallic bonding  . n some cases0 in addition to the ionic0 co&alent and metallic /onds0othe intemolec!ala inteactions0 s!ch as &an de >aals foces and hydogen /onding:see Section 2.4.4=0 conti/!te to the de&elopment of the thee8dimensional st!ct!e. 4.2.2Ato*ic P!c+in) n the pe&io!s section 7e s!ggested that a solid can /e !sef!lly consideed as agiant molec!le. As egads the shape of this molec!le0 ho7e&e0 7e 7ee silent. n thissection 7e 7ish to t!n to this 6!estion@ -o7 ae the constit!ent atoms of a solidogani?ed spatially in the solid phase To /egin0 7e conside the n!m/e of 7ays spheescan /e densely packed into space. Then 7e ela, the constaint on dense packing thisena/les !s to teat the cystal st!ct!es of ionic solids. t is helpf!l to ogani?e o! thinking ao!nd t7o8dimensional layes of sphees in contact. Then 7e /!ild theedimensional st!ct!es /y depositing these layes one on top the othe0 as ill!stated inig!e 4.1. >e can /egin the laye /y laye stacking /y allo7ing the sphees of thesecond laye to fall in the ca&ities in the fist laye. >e then ha&e t7o 7ays to add a thid3  laye. n one scenaio0 7e can !se an ABAB poced!e0 7hee the thid laye sphees ae&etically colinea 7ith fist laye sphees. n the othe scenaio0 7hich is /ased on anABCABC patten0 the thid laye sphees ae &etically colinea 7ith the holes in the fistlaye. These t7o st!ct!es of ABAB and ABCABC ae called  polytypes  8 they aeidentical in t7o dimensions 7hile they ae mismatched in the thid. o each of these polytypes0 the coodination n!m/e is 12. Fi)ure 4.1 L!yer %y l!yer %uild,u- o' t#ree,di*enion!l tructure S#ri/er0 -.11.4.2. T#e Unit Cell >hen disc!ssing the st!ct!e of a cystalline solid0 it is helpf!l to identify thesmallest thee8dimensional !nit0 i.e.0 the unit cell  0 that epesents the epeat !nit fo thet7o close8packed st!ct!es disc!ssed a/o&e. To help in &is!ali?ing the !nit cell0 it iscon&enient to epesent each atom position as a point. The es!lting system of points istemed the lattice 0 and /y connecting the lattice points 7ith staight lines0 7e canconst!ct the unit cell  . >e see fom ig!e 4.2a that the ABAB aangement es!lts in ahe,agonal !nit cell the atoms ae desci/ed as hexagonally close-packed    (hcp) . +n theothe hand0 the ABCABC aangement gi&es a face8centeed c!/ic !nit cell0 the atoms /eing called  face-centered cubic (fcc) .4:a=:/=