Chapter 4 Structures of Solids

8/10/2019 Chapter 4 Structures of Solids

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CHAPTER 4 STRUCTURES OF SOLIDS

4.1 Introduction1

4.2 Model Cryt!l Structure..2

4.2.1 Bonding in Solids24.2.2 Atomic Packing...34.2.3 The Unit Cell.. 44.2.4 Typology of Cystal St!ct!es.. "

4." T#e Ionic Model. #

4.3.1 The $adi!s $atio Paamete... #4.3.2 %lectonegati&ity and Cystal St!ct!e.1'4.3.3 (attice %negy...11

4.4 Cryt!l Structure1"

4.4.1 )etallic %lements and Alloys... 1"4.4.2 )etal Salts 1*4.4.3 )etal +,ides.224.4.4 )etal -ydo,o and -ydated 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... 33

4.".1 )olec!la +/itals and %negy Bands..334.".2 )etals0 ns!latos0 and Semicond!ctos... 344.".3 ntinsic and %,tinsic Semicond!ctos... .3"4.".4 The emi (e&el in a Solid... 3

4.( Electronic Structure o' Solid... 3*

4..1 )olec!la +/ital%negy Band )odels.. 3*4..2 %lectonic St!ct!es of )etal +,ides..34..3 %lectonic St!ct!es of )etal S!lfides41

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4.1 Introduction

n a6!eo!s pocessing0 o! pimay concen is 7ith sol!tion8/ased eactions0 and

the key eagents ae applied mostly in the fom of dissol&ed a6!eo!s species. t is

impotant to emem/e0 ho7e&e0 that in many of the eactions of inteest0 7e enco!nte

eactants ando pod!cts in the solid phase. n this connection0 it is 7othy of note that1


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the ma9oity of the elements :; #'e shall see that the

s!face popeties and eacti&ities of solids ae intimately connected 7ith the /!lk cystal

and electonic st!ct!es.

>e /egin this chapte /y consideing the types of /onding that e,ist in solids. >ethen t!n o! attention to the geometical aangements of the /onded atoms in space.

om a consideation of the !les that go&en the packing of e6!al8si?ed sphees0 7e

identify the /asic !nits that constit!te the /!ilding /locks fo cystal st!ct!es. >ith the

aid of these /!ilding /locks0 7e e&ie7 the cystal st!ct!es of epesentati&e solids.

inally0 7e disc!ss electonic st!ct!es of solids0 !sing molec!la o/ital theoy as o!

stating point.

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4.2 Model Cryt!l Structure

4.2.1 &ondin) in Solid

>e sa7 in Chaptes 2 and 3 that0 accoding to molec!la o/ital theoy0 a co&alent

molec!le o a metal8ligand comple, foms its molec!la o/itals /y com/ining the atomic

o/itals of the constit!ent atoms. Similaly0 7e can teat a solid paticle as a giant

molecule consisting of an e,temely lage n!m/e of molec!la o/itals. >e ecall

f!the fom Chaptes 2 and 3 that 7e can teat molec!la o/itals of a polyatomicmolec!le fom t7o e,teme points of &ie70 i.e.0 the locali?ed and delocali?ed /ond

models. Both models ae !sef!l in the disc!ssion of solid st!ct!es. >ith the locali?ed

/ond appoach0 7e can imagine a sit!ation 7hee one of the /onded atoms da7s the

shaed electons 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 solid0 7hee the thee8dimensional

st!ct!e is /ased on the electostatic inteaction :/onding= /et7een the constit!ent ions.

+n the othe hand0 if the /ond is completely co&alent0 7e get a thee8dimensional

co&alent solid s!ch as diamond0 7hee the st!ct!e consists of C8C /onds. At the othe

e,teme0 7e can conside the giant molec!le fom the &ie7point of the delocali?ed /ond

model. n this m!lti8centeed molec!la o/ital appoach0 the atomic n!clei of the solid

ae &ie7ed as em/edded in a sea of electons. This sit!ation is chaacteistic of the solids

of the metallic elements0 and this type of delocali?ed /onding has ac6!ied the name

metallic bonding. n some cases0 in addition to the ionic0 co&alent and metallic /onds0

othe intemolec!ala inteactions0 s!ch as &an de >aals foces and hydogen /onding

:see Section 2.4.4=0 conti/!te to the de&elopment of the thee8dimensional st!ct!e.

4.2.2 Ato*ic P!c+in)

n the pe&io!s section 7e s!ggested that a solid can /e !sef!lly consideed as a

giant molec!le. As egads the shape of this molec!le0 ho7e&e0 7e 7ee silent. n this

section 7e 7ish to t!n to this 6!estion@ -o7 ae the constit!ent atoms of a solid

ogani?ed spatially in the solid phase To /egin0 7e conside the n!m/e of 7ays sphees

can /e densely packed into space. Then 7e ela, the constaint on dense packing this

ena/les !s to teat the cystal st!ct!es of ionic solids. t is helpf!l to ogani?e o!

thinking ao!nd t7o8dimensional layes of sphees in contact. Then 7e /!ild thee

dimensional st!ct!es /y depositing these layes one on top the othe0 as ill!stated in

ig!e 4.1. >e can /egin the laye /y laye stacking /y allo7ing the sphees of the

second laye to fall in the ca&ities in the fist laye. >e then ha&e t7o 7ays to add a thid

laye. n one scenaio0 7e can !se an ABAB poced!e0 7hee the thid laye sphees ae3


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&etically colinea 7ith fist laye sphees. n the othe scenaio0 7hich is /ased on an

ABCABC patten0 the thid laye sphees ae &etically colinea 7ith the holes in the fist

laye. These t7o st!ct!es of ABAB and ABCABC ae called polytypes 8 they ae

identical in t7o dimensions 7hile they ae mismatched in the thid. o each of these

polytypes0 the coodination n!m/e is 12.

Fi)ure 4.1 L!yer %y l!yer %uild,u- o' t#ree,di*enion!l tructure S#ri/er0 -.11.

4.2." T#e Unit Cell

>hen disc!ssing the st!ct!e of a cystalline solid0 it is helpf!l to identify the

smallest thee8dimensional !nit0 i.e.0 the unit cell0 that epesents the epeat !nit fo the

t7o close8packed st!ct!es disc!ssed a/o&e. To help in &is!ali?ing the !nit cell0 it iscon&enient to epesent each atom position as a point. The es!lting system of points is

temed the lattice0 and /y connecting the lattice points 7ith staight lines0 7e can

const!ct the unit cell. >e see fom ig!e 4.2a that the ABAB aangement es!lts in a

he,agonal !nit cell the atoms ae desci/ed as hexagonally close-packed(hcp). +n the

othe hand0 the ABCABC aangement gi&es a face8centeed c!/ic !nit cell0 the atoms

/eing calledface-centered cubic (fcc).

4

:a= :/=


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Fi)ure 4.2 Cloe,-!c+ed cryt!l tructure3 ! He!)on!l cloe,-!c+ed #c-0 %

'!ce,centered cu%ic 'cc.

Fi)ure 4." Le cloe,-!c+ed cryt!l tructure3 ! %ody,centered cu%ic %cc0 %

-ri*iti/e cu%ic cu%ic,P.

>hile the !nit cells /elo7 in&ol&e close8packed e6!al8si?ed sphees0 7e can

imagine othe sphee packings 7hich ae not close8packed. A !nit cell in&ol&ing a

coodination n!m/e of eight is sho7n in ig!e 4.3a :Shi&e0 p.112=. This epesents a

body-centered cubic (bcc)st!ct!e and it is chaactei?ed /y a system of c!/e8cente

"

:a= :/=

:/=:a=

:a=

:/=


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pl!s c!/e8cone lattice points. Anothe non8close8packed st!ct!e0 the primitive cubic

(cubic-P) is sho7n in ig!e 4.3/. This st!ct!e is dei&ed fom the /cc st!ct!e /y

emo&ing the c!/e8cente lattice point.

E5AMPLE 4.1 Si6e contr!int on t#e occu-!tion o' intertiti!l #ole

Conside a close8packed system of sphees of adi!s . :a= Sho7 that the lagest atom that can

occ!py an octahedal hole 7ill ha&e a adi!s of '.414. :/= $epeat :a= fo a tetahedal hole0 and sho7 that

in this case the e6!ied adi!s is '.22".

Solution

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4.2.4 Ty-olo)y o' Cryt!l Structure

>hen 7e s!&ey the myiad of solids a&aila/le0 7hethe the &aio!s mateials ae

classified as metallic elements0 ionic solids0 o co&alent solids0 7e find that the &aio!scystal st!ct!es can /e consideed in tems of a small set of model cystal st!ct!es. n

these st!ct!es the coodination n!m/e anges fom t7el&e to t7o. )etals ae

geneally associated 7ith lage coodination n!m/es : 8 12=0 7hile molec!la solids

!s!ally ha&e lo7 coodination n!m/es :e.g.0 4=. o ionic solids0 a coodination of is

typically enco!nteed. o! of the model st!ct!es ha&e aleady /een disc!ssed a/o&e0

i.e.0 the face centeed c!/ic :fcc=0 the he,agonal close8packed :hcp=0 the /ody centeed

c!/ic :/cc=0 and simple o pimiti&e c!/ic :c!/ic8P=.

)odel cystal st!ct!es fo compo!nds 7ith 1@1 stoichiomety :i.e.0 chemical

fom!la )= ae pesented in ig!e 4.4. n the rock-salt:DaCl= st!ct!e :ig!e 4.4a=0

chloide anions ae aanged in an fcc patten0 and the sodi!m cations eside in the

octahedal holes. The es!lting coodination is desci/ed as :0= since each ion has si,

co!nteions as neaest neigh/os. The cesium chloride :CsCl= st!ct!e :ig!e 4.4/=0

7hich is c!/ic0 is dei&ati&e of the ideal /cc st!ct!e0 7ith chloide anions at the cones

and Cs cations at the c!/e cente. The coodination is :0=. The sphalerite or

zincblende :EnS= st!ct!e :ig!e 4.4c= may /e &ie7ed in tems of an fcc aay of s!lfide

anions 7ith ?inc cations in one set of the tetahedal holes. The coodination is :404=. n

the case of thewurtzite:EnS= st!ct!e :ig!e 4.4d=0 the s!lf! anions ae aanged in an

hcp patten and the ?inc cations eside in one set of the tetahedal holes. The nickel

arsenide:DiAs= st!ct!e :ig!e 4.4e= is fo!nded on an hcp patten of As atoms0 7ith

nickel atoms filling the octahedal holes. The Di atoms ae aanged into a tigonal


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pism0 7ithin 7hich the As atom esides.

:a= $ock salt :DaCl= :/= Cesi!m chloide :CsCl=

:c= Sphaleite o ?inc/lende :EnS= :d= >!t?ite :EnS=

:e= Dickel asenide :DiAs=

Fi)ure 4.4 Model cryt!l tructure 'or M5 131 co*-ound.

ig!e 4." pesents model st!ct!es fo compo!nds 7ith 1@2 :o 2@1=

stoichiomety0 i.e.0 compo!nds of the type )2 :o )2=. Therutile:titani!m dio,ide0

Ti+2= st!ct!e :ig!e 4."a= is /ased on an hcp lattice of anions in 7hich only "'< of

the octahedal holes ae occc!pied /y the cations. The coodination n!m/e of Ti is si,0

7hile that of o,ygen is thee. n the fluorite :Ca2= st!ct!e :ig!e 4."/=0 the Ca2F

ions ae aanged as an fcc aay the fl!oide ions occ!py /oth sets of tetahedal holes0*


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gi&ing :04= coodination. o compo!nds 7ith the fom!la )20 the cation and anion

positions ae e&esed0 and the es!lting st!ct!e is called antifluorite. n -cristobalite

:Si+2=0 each Si atom is s!o!nded /y fo! + atoms0 7hile each + atom lies /et7een t7o

Si atoms :ig!e 4."c=. This st!ct!e may /e dei&ed fom the sphaleite st!ct!e /y

eplacing each ?inc and s!lf! atom 7ith a silicon atom and inseting o,ygen atoms

/et7een the silicon atoms. n the cadmium iodide:Cd2= st!ct!e :ig!e 4."d=0 a layeof Cd atoms is sand7iched in /et7een t7o layes of iodine atoms. Ad9acent sand7iches

ae linked only &ia &an de >aals foces.

:a= $!tile :titani!m dio,ide0 Ti+2= :/= l!oite :Ca2=

:c= 8Cisto/alite :Si+2= :d= Cadmi!m iodide :Cd2=

Fi)ure 4.$ Model cryt!l tructure 'or M52M25 co*-ound.


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:a= $e+3 :/= Peo&skite :CaTi+3=

Fi)ure 4.( Model cryt!l tructure 'or A&5"co*-ound3 ! ReO"0 % Pero/+ite

C!TiO".

The model st!ct!e fo many AB3compo!nds is theperovskite:CaTi+3=

st!ct!e. This st!ct!e0 in t!n0 may /e dei&ed fom the $e+3st!ct!e. As can /e

seen fom ig!e 4.a0 the $e+3st!ct!e is c!/ic $e atoms occ!py c!/e8cones0 7hile

+ atoms ae located at the edges of the !nit c!/e. >hen the st!ct!e is e,tended /eyond

the !nit cell0 it can /e seen that it is chaactei?ed /y octaheda 7hich ae linked at the

c!/e8cones. An impotant feat!e of the $e+3st!ct!e is the pesence of a lage

t7el&e8coodinate cental hole. By inseting a lage anion A into this hole0 one o/tains

the peo&skite st!ct!e :ig!e 4./=. n the peo&skite fom!la of AB30 is typically

+28o 8. n ode to maintain electone!tality0 the total chage caied /y the A and Batoms m!st add !p to si,.

)any metal compo!nds of geneal fom!la AB2+40 ha&e cystal st!ct!es that ae

modeled afte that ofspinel:)gAl2+4=. n this st!ct!e0 +28ions ae ogani?ed into an

fcc patten0 and 1 of the tetahedal holes ae occ!pied /y A ions0 7hile 12 of the

octahedal holes contain B ions. The identity of the octahedal ions may /e highlighted

/y !sing s6!ae /ackets0 as in AGB2H+4. n some cases0 an inverse spinelAGA0BH+4may

fom.

#


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4." T#e Ionic Model

4.".1 T#e R!diu R!tio P!r!*eter

>e sa7 in Section 4.2.1 that0 fom the &ie7point of the locali?ed /ond model0 the

/onding electons in an ionic solid0 )0 ae assigned entiely to the moe electonegati&e

atom :=0 7hich then /ecomes the anion. The less electonegati&e atom :)= /ecomes thecation. Th!s !nde s!ch cic!mstances0 the cystal st!ct!e can /e &ie7ed as a system of

chaged sphees held togethe /y attacti&e electostatic inteactions. Clealy0 not all

solids ae completely ionic. -o7e&e0 it is helpf!l to ass!me a thoo!ghgoing

electostatic &ie7 of solids. Then0 de&iations fom this ideal model po&ide an indication

of the elati&e impotance of co&alent and electostatic conti/!tions.

n co&alent /onding0 coodination n!m/es ae ationali?ed in tems of electonic

st!ct!e0 e.g.0 the symmety of atomic o/itals. n the case of ionic st!ct!es0 si?e

compati/ility /ecomes the g!iding pinciple. Also0 it 7as noted a/o&e that the cystal

st!ct!e of solids ae dei&ed fom close packed aays of one kind of atom and the holes

ae filled completely o patially /y anothe kind of atom. Th!s0 7e can conside0 in the

e,teme0 that thee 7ill /e si?e constaints on the si?e of the atom that fills the holes.

Altenati&ely0 fo a gi&en atom0 7e e,pect si?e constaints on the n!m/e of lage atoms

that can s!o!nd it. A !sef!l paamete that ena/les one to 6!antify the si?e constaint is

the adi!s atio0 F8. By consideing the coss8sections associated 7ith the &aio!s lattice

st!ct!es0 it can /e sho7n that the possi/le coodination n!m/es change as s!mmai?edin Ta/le 4.1.

T!%le 4.1 R!diu r!tio,coordin!tion nu*%er correl!tion

Coordin!tion nu*%er R!diu r!tio R!n)e

3 '.1"" I F8I '.234 '.23 I F8 I '.414 '.414 I F8I '.*32

'.*32 I F8I 1.''

E5AMPLE 4.2 Coordin!tion nu*%er o' *et!l !lt

Calc!late the ele&ant adi!s atios and pedict the coodination n!m/es of the ions in the

follo7ing solids@ :a= DaCl :/= Cs :c= CsCl :d= EnS.

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Solution

:a= $efeing to Ta/le 2.40 the adi!s of DaFis 113 pm fo CD J 4 and 11 pm fo CD J . Based on these

adii0 F8J 1131* o 111* J '.#" in eithe case0 the pedicted coodination n!m/e is 0

accoding to Ta/le 4.1.

:/= o a compo!nd s!ch as cesi!m fl!oide0 7hee the anion is smalle than the cation0 the adi!s atio is

detemined as 8F. Taking the ele&ant data fom Ta/le 2.40 8FJ 11#11 J '.". Th!s0 efeing

to Ta/le 4.10 7e e,pect a coodination n!m/e of .

:c= o CsCl0 7e ha&e 8FJ 1*11 J '.#23. Accodingly0 the pedicted coodination n!m/e is .

:d=

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Fi)ure 4.7 A tructure correl!tion *!- 'or M5 co*-ound S#ri/er0 -.122.

4.".2 Electrone)!ti/ity !nd Cryt!l Structure

>e ha&e seen that the /onding in a compo!nd AB is likely to /e ionic 7hen the

elctonegati&ity diffeence0 0 is lage. At the same time0 7e find that ionic compo!nds

tend to ha&e lage coodination n!m/es0 7hile co&alency es!lts in small coodination

n!m/es. Th!s0 it is not s!pising that thee sho!ld /e a coelation /et7een and and

the type of cystal st!ct!e. ig!e 4.* pesents a structure map7hich ill!states the

manne in 7hich the magnit!de of the electonegati&ity diffeence is elated to the

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coesponding st!ct!e. t can /e seen that 7hen is lage0 the tendency is to fom

compo!nds 7ith elati&ely high coodination n!m/es :e.g.0 the ock salt and !tile

st!ct!es=. +n the othe hand0 7ith small &al!es0 the es!lting st!ct!es tend to ha&e

smalle coodination n!m/es. :See also0 %. )ose and >. B. Peason0 Acta Cyst.0 120

1'1" :1#"#==.

4."." L!ttice Ener)y Ent#!l-y

A !sef!l paamete in assessing the sta/ility of a gi&en cystal st!ct!e is the

lattice enegy0 defined as the change in enegy associated 7ith the decomposition of a

solid into its gaseo!s ions@

) :s= )F:g= F 8:g= -( :4.1=

%negy is e6!ied in ode to degade the lattice0 and theefoe0 the lattice enegy is a

positi&e 6!antity. Th!s0 the highe the lattice enegy0 the geate the sta/ility of the

coesponding cystal st!ct!e. The lattice enegy also po&ides a means fo assessing

the degee of co&alency associated 7ith the chemical /onds in the solid. f an ionic

model is ass!med0 then a theoetical lattice enegy may /e calc!lated and this can /e

compaed 7ith the e,peimentally detemined &al!e.The lattice enegy can /e consideed as consisting of t7o main conti/!tions@ :1=

The electostatic co!lom/ic inteactions /et7een the ions :Kc=0 and :2= the electron

overlap repulsions:Ko=.

K(J KcF Ko :4.2=

o t7o ions A and B0 7hose centes ae sepaated /y a distance 0 the co!lom/ic

potential enegy is gi&en /y@

KABJ :?Ae= :?Be=:4oAB= :4.3=

7hee ?Aand ?B especti&ely epesent the chages on the ions0 and ois the &ac!!m

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pemitti&ity :." , 1'812 C2L81m81=.

To o/tain the total co!lom/ic potential enegy fo the cystal0 the s!mmation of

all the pai potentials is detemined. The es!lting e,pession has the fom@

KcJ DAGe24oHG?A?BdHA :4.4=

n this e,pession0 DA is the Avogadro number0 the second tem go!ps a n!m/e of

f!ndamental constants0 the thid tem contains paametes chaacteistic of the specific

ions and dimensions of the lattice :the paamete d epesents the neaest8neigh/o

distance=0 and the fo!th temAis called theadelung constantand is chaacteistic of

the patic!la cystal st!ct!e. Ta/le 4.2 pesents a selection of )adel!ng constants fo

some model cystal st!ct!es. n geneal0 the highe the coodination n!m/e0 the highe

the )adel!ng constant.

T!%le 4.2 M!delun) cont!nt

Structure Ty-e A

Cesi!m chloide 1.*3l!oite 2."1#$ock8salt 1.*4$!tile 2.4'Sphaeleite 1.3>!t?ite 1.41

>hen t7o ions 7ith closed8shell electonic st!ct!es appoach each othe0 they

7ill e,peience m!t!al ep!lsion fom the o&elap of thei electon clo!ds. The potential

enegy aising fom this ep!lsi&e inteaction can /e e,pessed as@

KoJ KcF DACM e8ddN :4."=

7hee CM and dN ae constants it is a !sef!l appo,imation to set dN J '.34" O.

n &ie7 of %6!ations 4.20 4.40 and 4."0 7e can 7ite@

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E5AMPLE 4." S-#!lerite /eru 9urt6ite 'or*!tion

+n the /asis of lattice enegy consideations0 detemine the chage and scale paamete constaints

that lead to the pefeential fomation of one o the othe polytypes of EnS.

Solution

Using the s!/scipts s and 7 to signify sphaleite and 7!t?ite especti&ely0 7e can 7ite that

sphaleite is pefeed o&e 7!t?ite po&ided that KmsR Km70 i.e.0

:?A?B=s :d=7 R A7J 1.41

:d=s :?A?B=7 As 1.3

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1"


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4.4 Cryt!l Structure

4.4.1 Met!llic Ele*ent !nd Alloy

t 7as noted a/o&e :Section 4.2.1= that /onding in solids of the metallic elements

is /est desci/ed in tems of delocali?ed /onds. As a es!lt of the non8diectional nat!e

of this kind of /onding0 the atoms of metals in the solid state can ac6!ie the ma,im!mcoodination n!m/es allo7ed /y adi!s atio consideations. Theefoe0 the st!ct!es of

the metallic elements tend to /e close8packed. This close packing acco!nts fo the

typically high densities of metals. >hat factos detemine 7hethe a gi&en metal pefes

the fcc o hcp st!ct!e A !sef!l !le of th!m/ is that a he,agonal st!ct!e is pefeed

if the n!m/e of &alence electons&alence o/itals is lo70 7hile c!/ic st!ct!es ae

pefeed 7hen the n!m/e is high. :>hy=

Besides hcp and fcc0 othe st!ct!es ae also kno7n. Th!s0 7ith incease in

tempeat!e0 it is not !ncommon fo metals to !ndego a tansition fom close8packed to

less close8packed st!ct!es. The onset of st!ct!al tansition can /e ationali?ed /y

ecogni?ing that geate atomic mo&ements ae moe compati/le 7ith a moe loose

cystal st!ct!e. At elati&ely lo7 tempeat!es0 the tendency of a gi&en metal to fom a

close8packed st!ct!e may /e elated to electonic st!ct!e. f a metal is &ie7ed in

tems of positi&e chages immesed in an ocean of electons0 then the highe the electon

density in this sea0 the highe the atomic packing. Accodingly0 the alkali metals 7hich

ha&e elati&ely lo7 &alence electons 7ill ha&e a geate tendency to adopt the /ccst!ct!e. The tempeat!e making the tansition fom close8packed to non close8packed

st!ct!es may /e a/o&e oom tempeat!e :e.g.0 Ca0 Ti0 )n=0 o it may /e /elo7 oom

tempeat!e :e.g.0 (i0 Da=.

>hen t7o o moe metals ae mi,ed in the molten state0 the es!lting solid

pod!ct is temed an alloy. At one e,teme0 an alloy may epesent a solid solution0

7hee the constit!ent atoms ae andomly intemi,ed. At the othe e,teme0 the atoms in

the mi,t!e com/ine to gi&e compo!nds 7ith specific compositions and st!ct!e. The

simplest alloy is a /inay mi,t!e 7hee the ma9oity atoms epesent the sol&ent and the

minoity atoms the sol!te. nsubstitutionalsolid sol!tions0 the sol!te atoms ae located

at sites nomally occ!pied /y the sol&ent atoms. n the case of intestitial solid sol!tions0

the sol!te atoms inset themsel&es in the spaces /et7een the sol&ent atoms. The

follo7ing set of conditions m!st /e met in ode fo a s!/stit!tional solid sol!tion to1


17/51

fom@ :a= the sol!te atom m!st ha&e a si?e compaa/le 7ith that of the sol&ent atom :

1"


18/51

7ith -0 B0 C0 o D as intestitial atoms.

:/= The late d8/lock mem/es of the fist o7 ha&e adii 7hich do not e,ceed 1.' O0 yet these metals ae

kno7n to fom intestitial solid8sol!tions 7ith -0 B0 C0 and D. -o7 can these o/se&ations /e

ationali?ed

Solution

:a= >e need to satisfy the condition D)I '.4140 the s!/scipt D) efes to nonmetal. Th!s0 fo -J 0 B

J 0 CJ 0 and DJ 0 )R D)'.414.

:/= i&en the condition D) I '.4140 B0 C0 and D atoms e6!ie metal atoms 7ith adii of 1.#"0 1.0 and

1.' O especti&ely. These adii e,ceed the 1.' O limit of the ele&ant tansition metals. Th!s it m!st

/e concl!ded that definite compo!nds fom0 athe than intestitial solid sol!tions.

555555555555555555555555555555555555555555555555555555555555555555555555

4.4.2 Met!l S!lt

n Chapte 3 7e enco!nteed the (e7is acid8/ase concept. $elated to this0 is the

!ronsted acid8/ase concept0 disc!ssed in geate detail in Chapte ". Biefly0 in the

Bonsted lang!age0 an acid is defined as a species :-A= that can donate a poton

:%6!ation 4.#= and a /ase as a species :+-= that ecei&es a poton :%6!ation 4.1'=. A

saltthen is a compo!nd 7hich foms 7hen a Bonsted acid is ne!tali?ed /y a Bonsted

/ase@

-A J -FF A8 :4.#=

+- F -FJ FF -2+ :4.1'=

+- F -A J A :s= F -2+ :4.11=

n this Section 7e conside t7o types of salts@ :a= simple binary salts0 ),Ay0 pimaily

metal halides0 and :/= complex metal salts0 pimaily salts of o,yanions. -ydo,ysalts

:i.e.0 salts 7hich contain +-8go!ps= and hydated salts :i.e.0 salts 7hich contain 7ate

molec!les= ae disc!ssed in Section 4.4.4.

1


19/51

etal halides. T7o key geneali?ations can /e made egading the cystal

st!ct!es of metal halides@ :a= o a gi&en metal0 the st!ct!e of the fl!oide tends to /e

diffeent fom that of the othe halides. Th!s fl!oides tend to cystalli?e into thee8

dimensional st!ct!es0 7heeas the chloides0 /omides and iodides pefe mostly laye

and occasionally chain st!ct!es. :/= l!oides and o,ides 7ith simila chemical

fom!las tend to ha&e the same cystal st!ct!es. +n the othe hand0 Cl0 B0 and salts

tend to /e isost!ct!al 7ith s!lfides0 selenides0 and tell!ides. Ta/le 4.4 pesents the

cystal st!ct!es fo selected metal halides.

T!%le 4.4 T#e cryt!l tructure o' *et!l #!lide :ell0 -.4;

Ty-e o' tructure For*ul! Ty-e M C


20/51

$omplex Salts. +n the /asis of the electonegati&ities of the atoms A and B0

compo!nds of the type A,By+?may /e classified into t7o main go!ps0 i.e.0 complexoxides0 and oxysalts. >hen A and B ha&e simila electopositi&e chaacte0 the solid may

/e &ie7ed as a system of A0 B0 and + ions0 and the compo!nd is called a complex oxide.

+n the othe hand0 if the cystal st!ct!e compises a metal ion A and a comple, anion

B+m0 then the compo!nd is called an oxysalt. n this case0 A is electopositi&e0 7hile B

is electonegati&e0 and the compo!nd is called a salt /eca!se it may /e synthesi?ed /y

eacting to a /asic o,ide :A8containing compo!nd= 7ith an acidic o,ide :B8containing

compo!nd=. n an o,ysalt0 B is typically a nonmetal0 ho7e&e0 in some cases it can /e a

highly chaged tansition metal cation. t m!st /e noted that this di&ision of comple, o,y

compo!nds into o,ysalts and comple, o,ides may /e am/ig!o!s in some cases.

Comple, o,ides ae disc!ssed in Section 4.".3. Ta/le 4." pesents a selection of

o,yanions 7ith thei coesponding shapes.

T!%le 4.$ Oy!nion !nd t#eir #!-e :ell0 -.$12

Don8linea D+28 Cl+28

Plana B+338 C+328 D+38

Pyamidal S+328 Cl+38

B+38

+38

Tetahedal Si+448 P+438 S+428 Cl+48

As+438 +48

K+438 )n+48

Tetagonal pyamidal +"38

$e+"38

+ctahedal Te+8 +"8

>hen an o,yanion inteacts 7ith a metal ion0 the /onding atom is the o,ygen. t

is fo!nd that the cationo,ide atio can /e !sed as a pedicto of the cystal st!ct!es of

o,ysalts. This is ill!stated in Ta/le 4. fo a go!p of !ni&alent nitates0 di&alent

ca/onates0 and teta&alent /oates. :Pa!ling0 p."4*=. t can /e seen that the adi!s atio2'


21/51

of '.* epesents a tansition /et7een the calcite :C.D. J = and aagonite :C.D. J #=

st!ct!es of calci!m ca/onate.

21


22/51

T!%le 4.( R!diu r!tio,tructure correl!tion 'or elected oy!lt !'ter P!ulin)0 -.$47

Calcite st!ct!e (iD+3 '.34 )gC+3 '.4* ScB+3 '.'

DaD+3 '."4 EnC+3 '."' nB+3 '."#CdC+3 '." B+3 '.

CaC+3 '.*

Aagonite st!ct!e D+3 '.* CaC+3 '.* (aB+3 '.*#SC+3 '.*"BaC+3 '.*

$/D+3 st!ct!e $/D+3 '.4CsD+3 '.#

555555555555555555555555555555555555555555555555555555555555555555555555555

A !sef!l concept in e,amining the sta/ilities of comple, ionic cystals is theelectrostatic bond strength :%BS=. Conside a cation of chage F?e and coodination

n!m/e n :i.e.0 the cental metal ion is engaged in n )8+ /onds=. Then 7e o/tain the

electostatic /ond stength /y disti/!ting the total cation chage among the n )8+

/onds0 i.e.0

%BS J ?n :4.12=

555555555555555555555555555555555555555555555555555555555555555555555555

E5AMPLE 4.( T#e electrot!tic %ond tren)t# o' M,O %ond in MOn -oly#edr!.

etemine the %BS fo the )8+ /onds in the follo7ing polyheda@ :a= Si+40 :/= Al+0 :c= )g+.

Solution

:a= o Si+40 ? J 40 n J 40 and theefoe0 !sing %6!ation 4.1"0 %BS J ?n J 11 J 1.

:/= o Al+0 ? J 30 n J 0 and th!s0 %BS J ?n J 3 J 12.

:c= o )g+0 ? J 20 n J . Th!s0 %BS J ?n J 2 J 13.

555555555555555555555555555555555555555555555555555555555555555555555555

Conside an anion +m?8 7e ass!me that the total anionic chage :?8= is shaed

22


23/51

among the m o,ygen atoms. Accodingly0 the patial chage on each o,ygen atom is :8

?m=. (et !s f!the conside a metal ion0 )?F0 7hich foms a salt )+m. >e e6!ie

that the patial chage caied /y each metal8ligand /ond :i.e.0 the electostatic /ond

stength0 %BS= /e /alanced locally /y an e6!al /!t opposite chage on the /onded o,ygen

atom this is the pinciple of local charge balancing. Th!s0 if a gi&en o,ide anion +28

:/elonging to the o,yanion +m?8= paticipates in 9 coodination polyheda0 then 7e

e,pect that the %BS of the coesponding 9 )8+ /onds sho!ld add !p to the patial chage

on the specific o,ide ion. That is0

:?m= J %BSiJ :?n=iJ 9:?n= :4.13=

555555555555555555555555555555555555555555555555555555555555555555555555

E5AMPLE 4.7 T#e electrot!tic /!lence rule.

:a= o each of these comple, anions0 detemine the patial chage on each o,ygen atom@ Si+4480 P+4380

S+4280 Cl+48.

:/= The follo7ing compo!nds adopt the calcite st!ct!e@ DaD+30 CaC+30 nB+3. etemine the n!m/e

of )+npolyheda associated 7ith each o,ygen of the especti&e anions.

Solution

:a= :i= Si+428@ o +m?80 mJ4 and ?J2. Theefoe0 patial chage J :8?m= J 824 J 812.

:ii= P+438@ mJ40 ?J3 :8?m= J 834.

:iii= S+428@ mJ40 ?J2 :8?m= J 824 J 812.

:i&= Cl+48@ mJ40 ?J1 :8?m= J 814.

:/= The calcite st!ct!e in&ol&es octahedal coodination0 i.e.0 )+. Th!s0 fo the gi&en metal cations0 the

coesponding %BS ae ?n J F1 :Da8+=0 F2 J F13 :Ca8+=0 F3 J F12 :n8+=. The patial

chages on the anionic o,ygens ae@ :813= :D+38=0 :823= :C+328=0 :833 J 81= :B+338=. Th!s0 efeing to

%6!ation 4.130 fo chage ne!tali?ation0 7e e6!ie@

:813= :D+38= F 9G1 :Da8+=H J ' i.e.0 9 J2.

23


24/51

DaF

DaF

D +

+

+

Ca2F

Ca2F

C +

+

+

n3F

n3F

B +

+

+

131823 81

12

1213

813

1

:823= :C+328= F 9G13 :Ca8+=H J ' i.e.0 9 J 2.

:81= :B+338= F 9G12 :n8+=H J ' i.e.0 9 J 2.

The coesponding st!ct!es ae as ill!stated /elo7.

:Also see >ells0 p.32*=

555555555555555555555555555555555555555555555555555555555555555555555555

4.4." Met!l Oide

The eathMs c!st consists of ; #'< o,ygen0 and inoganic mateials a/o!nd 7ith

o,ygen8containing compo!nds. n this section0 7e conside :a= binary metal oxides0 i.e.0

compo!nds that compise o,ygen and a metallic element0 and :/= complex metal oxides0

i.e.0 compo!nds that contain t7o o moe metals in com/ination 7ith o,ygen. The elatedhydo,o compo!nds0 hydo,ides0 ):+-=n0 and o,yhydo,ides0 )+:+-=0 ae disc!ssed

in Section 4.4.4.

!inary etal %xides& Ta/le 4.* pesents a ta/le of the st!ct!es of selected

/inay metal o,ides. A s!&ey of the /inay metal o,ides leads to a n!m/e of

geneali?ations@

:a= n most metal o,ides the /onding is ionic.

:/= The metal atom typically has a high coodination n!m/e0 o .

:c= The cystal st!ct!es adopted /y metal o,ides tend to /e the same as those

fo the coesponding fl!oides.

:d= The ionic adi!s of +28 is typically lage than that of the coesponding

metal ion $/F0 CsF0 and TlFae the e,ceptions.

24


25/51

:e= The cystal st!ct!e !s!ally consists of a close8packed aay of +28 ions0

7ith metal ions typically in the octahedal holes.

:f= n some o,ides0 the metal may /e pesent in moe than one o,idation state0

e.g.0 ):=0 ):=0 and ):K= in )3+4.

:g= )any tansition metals e,hi/it de&iations fom stoichiomety0 and this es!lts

in semicond!cti&ity :see Sections 4." and 4.=.

T!%le 4.7 T#e cryt!l tructure o' %in!ry *et!l oide :ell0 -.$"4



26/51

Chain st!ct!es -g+0 Se+20C+30

S/2+3

)olec!la st!ct!es $!+40 +s+4

555555555555555555555555555555555555555555555555555555555555555555555555

2


27/51

$omplex %xides. n tems of stoichiometic fom!la0 7e can identify se&eal

diffeent types of comple, o,ides0 e.g.0 0 AB+20 AB+30 AB+4 0 AB2+4. $epesentati&e

st!ct!es ae pesented in Ta/le 4..

T!%le 4.8 Structure o' elected co*-le oide

Ty-e C


28/51

cylindically symmetic :i.e.0 dipola= species0 and :c= a 6!ad!pola species. As the

cation deceases in si?e and inceases in chage0 c8type /eha&io /ecomes moe fa&oa/le

in compaison 7ith /8type /eha&io. n its 6!ad!pola fom0 the +-8ion can !ndego

hydogen /onding the negati&e and positi&e egions of diffeent +- 8 ions inteact. As a

es!lt of the a/o&e consideations0 7e may di&ide metal hydo,ides into t7o main

go!ps0 i.e.0 those 7hich ha&e no hydogen /onds :a8 and /8type /eha&ios=0 and those

7ith hydogen /onds :c8type /eha&io=. Ta/le 4.# pesents st!ct!al infomation fo

selected metal hydo,ides and o,yhydo,ides.

T!%le 4.; T#e cryt!l tructure o' *et!l #ydroide !nd oy#ydroide

in'o 'ro* :ell0 -.(2( ''



29/51

(aye st!ct!es )+- (i+-0 Da+-

):+-=2 Cadmi!m iodide ) J )g0 Ca0 )n0 e0Co0 Di0 Cd

2#


30/51

T!%le 4.1 OH3M r!tio in #ydroy,oy!lt

OH 3 M S!lt OH 3 M S!lt

1" Ca":+-=:P+4=3 " En":+-=:C+3=212 C!2:+-=P+4 32 C!2:+-=3D+3

11 C!:+-=+3 21 Th:+-=2S+4=======================================================================

'ydroxysalts. The metals 7hich tend to fom /asic salts incl!de Be0 )g0 Al0

se&eal of the A s!/go!p tansition metals :e.g.0 Ti0 E=0 3d metals :e.g.0 e0 Co0 Di=0 4f

and "f metals :e.g.0 Ce0 Th0 U=0 a ma9oity of the B s!/go!p elements :e.g.0 n0 Sn0 P/0

Bi=. n nat!e0 some impotant oe mineals occ! as /asic salts0 e.g.0 /ochantite0

C!4:+-=S+40 and atacamite0 C!2:+-=3Cl. Coosion pod!cts may also occ! as /asic

salts0 e.g.0 hydo?incite0 En":+-=:C+3=20 foms 7hen metallic ?inc is e,posed to moist

ai. +the e,amples of /asic salts incl!de 7hite lead0 P/3:+-=2:C+3=20 !sed as a pigment0

and )g2:+-=3Cl4-2+0 a eaction pod!ct in the hydation of Soels cement. Thee is a

7ide &aiation in the +-@) atios enco!nteed in hydo,ysalts0 as ill!stated in Ta/le

4.1' fo a seies of hydo,y8o,ysalts.

:a=:/=

Fi)ure 4.8 Structure o' #ydroy#!lide3 Cloed,-!c+ed -#ere o' ! 5OH0 % 5OH".

3'


31/51

-2+ +-

Al

-2+

-2+

-2+

-2+-2+ +-

Al

-2+

-2+

4Fl

+-

:-2+=

4E

+-

:-2+=4E

+-

E:-2+=

4

+-

E:-2+=4

+-

+-

+-

+-

Fl

'ydroxyhalides. The st!ct!es of hydo,yfl!oides tend to follo7 those of

o,yhdo,ides o o,ides. Th!s0 fo e,ample0 En:+-= has the diaspoe st!ct!e0

Cd:+-=0 the CaCl2st!ct!e0 -g:+-=0 a !tile8type st!ct!e0 and n2:+-=0 a $e+38

type st!ct!e. The most common hydo,ychloides and hydo,y/omides ae those of

the types0 )+- and )2:+-=30 7hee ) J )g0 )n0 e0 Co0 Di0 C!:=. n the )+-

st!ct!es0 and +- ions fom a close8packed laye0 as sho7n in ig!e 4.a :>ells0

p.1'=. The metal atoms eside in 2"< of the octahedal sites. n the case of the

)2:+-=3st!ct!es0 and +- ions fom a close8packed laye0 as sho7n in ig!e 4./

:>ells0 p.1'=. The metal atoms eside in "'< of the octahedal sites.

Fi)ure 4.; Structure %!ed on 'inite M,OH co*-lee3 ! >Al2OH2H2O8?4@0

% >r4OH8H2O1(?8@

'ydroxy-oxysalts. t is helpf!l to think of the st!ct!es of hydo,y8o,ysalts in

tems of the nat!e of the )8+- comple,. Th!s the )8+- comple, o s!/!nit may /e

:a= finite0 :/= infinite one8dimensional :chain=0 :c= infinite t7o8dimensional :sheet=0 and

:d= infinite thee8dimensional. n the case of the fist thee sit!ations0 the o,yanions play

the impotant ole of 9oining the s!/!nits into thee8dimensional st!ct!es. An e,ample

of a st!ct!e /ased on a finite )8+- s!/!nit is the /asic al!min!m s!lfate 7ith the

empiical fom!la Al2+3.2S+3.11-2+. The st!ct!al fom!la can /e e,pessed as

GAl2:+-=2:-2+=H:S+4=2.2-2+. As can /e seen fom ig!e 4.#a0 thee ae t7o +-

/idges linking t7o Al3Fcentes0 i.e.0 a dimeic comple,. The finite )8+- s!/!nit can

also /e in the fom of a ing0 as e,emplified /y the st!ct!e of GE4:+-=:-2+=1HF:see

ig!e 4.#/=.

St!ct!es /ased on )8+- chains ae chaacteistic of many /asic salts of

stoichiomety +-@) J 1. The )8+- chains ae linked &ia o,yanions to gi&e thee8

dimensional st!ct!es. ig!e 4.1' ill!states the C!:+-=+3 st!ct!e. :>ells0 ig

31


32/51

a / c

d e

)F )F

1 221

21

o

oo

)2F

)2F

14.1a0 p.4*=. A n!m/e of st!ct!es /ased on t7o8dimensional )8+- s!/!nits can /e

&ie7ed as dei&ati&es of the Cd2st!ct!e. ist0 7e take the Cd2st!ct!e and eplace

Cd /y ) and 2/y :+-=2. Then 7e eplace 2"< of the +- go!ps 7ith o,ygen atoms of

o,yanions0 s!ch that the plane of the +n?8go!p is pependic!la to that of the laye.

! %

o Cu I O OH

Fi)ure 4.1 Structure o' #ydroy,oy !lt %!ed on t9o,di*enion!l M,OH

u%unit. CuOHIO"3 ! Pl!nB % Ele/!tion0 9it# t#e oct!#edr!l c#!in

-er-endicul!r to t#e -l!ne o' t#e -!-er. :ell0 -.(47.

Fi)ure 4.11 Inter!ction o' 9!ter *olecule in cryt!l. T#e l!r)er #!ded circle

re-reent M@0 OH,0 F,0 or oy)en o' oy,ion :ell0 -.((8.

'ydrated Salts. -ee 7e shall /e concened 7ith hydates of halides oxysalts0

32


33/51

and hydroxides. >e leaned in Chapte 2 that the o,ygen atom in a 7ate molec!le

possesses t7o lone pais of electons. These es!lt in t7o egions of negati&e chage on

one end of the molec!le. At the same time0 d!e to the polai?ation of the 7ate molec!le0

the t7o hydogen atoms ae elati&ely positi&e0 compaed 7ith the o,ygen atom. Th!s

the t7o hydogen atoms epesent t7o egions of positi&e chage. As a es!lt0 the 7ate

molec!le may /e &ie7ed as a "uadrupolarspecies0 7ith a tetahedal aangement of the

t7o positi&e and t7o negati&e egions. The manne in 7hich a 7ate molec!le is linked

in a hydate may /e ationali?ed in tems of the inteactions of anions0 metal ions0 o

othe 7ate molec!les 7ith these chaged egions0 as ill!stated in ig!e 4.11 :>ells0

p.=.

A con&enient classification0 /ased on the coodination of the cation0 is ill!stated

in Ta/le 4.11 fo a hydated salt ),Ay.7-2+0 7hee A sym/oli?es an anion s!ch as Cl80

S+4280 and n is the coodination n!m/e of the metal ion. n class A0 ) is f!lly hydated0

and thee is e,cess 7ate ::7,n= R 1=. This is a elati&ely small go!p. A epesentati&e

compo!nd is )gCl2.12-2+. -ee the cation and anion ae each octahedally s!o!nded

/y si, 7ate molec!les.

T!%le 4.11 Cl!i'ic!tion o' #ydr!ted !lt !'ter :ell0 -.(7

M Fully Hydr!ted M Inco*-letely Hydr!ted

9n Ece H2O I


34/51

1 C!S+4-2+

34


35/51

4.4.$ Met!l Silic!te

Silicon and o,ygen make !p a/o!t *"< of the eathMs c!st0 7hee they e,ist

pimaily as silicate mineals. The /asic /!ilding /lock in silicates is the Si+4

tetahedon0 and as ill!stated in ig!e 4.12a0 it is con&enient to epesent this as a

tiangle0 7hich sym/oli?es a top8do7n &ie7 of the tetahedon. The comple, st!ct!es

of silicates can /e esol&ed in tems of the manne in 7hich the Si+4 tetaheda ae

linked. %,amples of the possi/le linkages ae ill!stated in ig!es 4.12/8f especti&ely

fo the disilicate anion :Si2+*8=0 a ing :Si+328=0 an infinite single chain :Si+3=n2n80 an

infinite do!/le chain o /and0 :Si4+11=nn80 and a sheet o laye0 :Si2+"=n2n8. The chage

/alance in the linked st!ct!es can /e o/tained /y asci/ing !nit negati&e chage :81= to a

teminal + atom and ?eo chage to a shaed + atom. Taditional nomenclat!e@ the la/el

ortho is !sed to signify that a species is completely hydated0 7hile the la/el metaindicates the elimination of a mole of 7ate fom the otho species. Ta/le 4.12 pesents a

selection of silicate compo!nds0 7ith coesponding Si+4tetahedal linkages.

:a= Si+4tetahedon

:c= Si+328ing

:/= isilicate anion :Si2+*8=

:d= nfinite single chain ::Si+3=n2n8=

3"

+ J o,ygen J silicon


36/51

:e= nfinite do!/le chain ::Si4+11=nn8= :f= Sheet ::Si2+"=n2n8=

Fi)ure 4.12 SiO4tetr!#edr!l lin+!)e.

T!%le 4.12 Silic!te co*-ound

&uildin) &loc+ Co*-ound

iscete othosilicate :Si+448= anions )g2Si+40 :)g0 e=2Si+4:oli&ine=Da4Si+40 4Si+40 Be2Si+4:phenacite=En2Si+4:7illemite=0 ESi+4:?icon=):=3):=2:Si+4=30 ):= J Ca2F0)g2F0 e2F0 ):= J Al3F0 C3F0 e3F:ganets=

iscete disilicate :Si2+*8= anions Sc2Si2+*:thot&eitite=

Tisilicate ings :Si3+#8= BaTiSi3+#:/enitoite=0Da2ESi3+#-2+ :catapleite=

-e,asilicate ings :Si+1128= C!Si+1-2+ :dioptase=0Be3Al2Si+1-2+ :/eyl=

Single Chains :Pyo,enes :Si+3=n2n8= )gSi+3:enstatite=0Ca)g:Si+3=2:diopside=0(iAl:Si+3=2:spod!mene=

o!/le Chains :Amphi/oles :Si4+11=nn8= Da2e":+-=2:Si4+11=2:cocidolite0 /l!e as/estos=:)g0e=*:+-=2:Si4+11=2:amosite=

Sheets ::Si2+"=n2n8

= Al2:+-=4Si2+":kaolinite=Al2:+-=2Si4+1':pyophyllite=)g3:+-=4Si2+":sepentine=)g3:+-=2Si4+1':talc=

Al8s!/stit!ted sheets ::AlSi3+1'="8= Al2:+-=2Si3Al+1':m!sco&ite0 7hite mica=)g3:+-=2Si3Al+1':phlogopite0 )g8mica=:)g0e=3:+-=2Si3Al+1':/iotite0 /lack mica=

3


37/51

ame7ok Si+2:6!at? tidymite0 cisto/alite0 coesite0 stisho&ite=)Al28,Si2F,+:feldspas=),nnFGAl,Siy+2,F2yH,8?-2+ :?eolites=

3*


38/51

t sho!ld /e noted that silicate st!ct!es can also /e consideed in tems of a

close8packed aay of +28ions0 7hee tetahedal holes ae occ!pied /y Si4Fions0 and

octahedal and tetahedal holes /y metal ions.

4.4.( Met!l Sul'ide

The electonegati&ity of s!lf! is less than that of o,ygen. As a es!lt0 )8S /onds

tend to /e less pola than )8+ /onds. Th!s0 7heeas the cystal st!ct!es of metal

o,ides tend to /e simila to those of the coesponding fl!oides0 metal s!lfides pefe the

st!ct!es of the moe co&alent chloides0 /omides0 and iodides. o e,ample0 laye

st!ct!es ae !n!s!al among o,ides and fl!oides0 /!t ae fe6!ently o/se&ed among

s!lfides and the hea&ie halides. )any of the s!lfides of inteest in a6!eo!s pocessing

ha&e st!ct!es 7hich ae moe comple, than those listed in Ta/le 4.13. -o7e&e0 the

st!ct!es of these moe comple, s!lfides :Ta/le 4.14= can often /e &ie7ed as dei&ati&esof the simple st!ct!es.

T!%le 4.1" Cryt!l tructure o' *et!l ul'ide !'ter :ell0 -.74;

Ty-e o' tructure M C


39/51

T!%le 4.14 Met!l ul'ide

Coppe S!lfides C!S :co&ellite=0 digenite :C!1.S=0 d9!leite :C!1.#S=0C!2S :chalcocite=0 C!1F,S :/la!/leinde co&ellite=0C!3AsS4:enagite=0C!"eS4:/onite=0 C!eS2:chalcopyite=0C!e2S3:c!/anite=0 C!3eS4:idaite=

on S!lfides e#S1':m pyhotite :"C==0 e11S12:m pyhotite :C==0e1'S11:m pyhotite :11C==0 eS2:pyite=0 eS2:macasite=0e1F,S :mackina7ite=0 e#S1'e11S12:Don8integal pyhotite :nC==0eS :toilite=0 e*S:monoclinic pyhotite :4C==0 e3S4:geigite=0eAsS :asenopyite=0 eDi2S4:&iolaite=0 :e0 Di=#S11:smythite=

Dickel S!lfides DiS2:&aesite=0 DiS :milleite=0 Di3S2:hea?le7oodite=0 8Di*S08Di*S:godle&skite=0 Di3S4:polydymite=0 :Di0e=#S:pentlandite=

Co/alt S!lfides CoS :9aip!ite =0 Co3S4 :linnaeite=0 CoS2:cattieite=0

Co#S:co/alt pentlandite=0 :Co0e=AsS :co/altite=

Sil&e S!lfides 8Ag2S :agentite=0 8Ag2S :acanthite=

Asenic S!lfides 8AsS :ealga=0 8AsS :8asenic s!lfide=0 As2S3:opiment=

Einc S!lfides 8EnS :sphaleite=0 8EnS :7!t?ite=

3#


40/51

4.$ Molecul!r Or%it!l T#eory !nd t#e &!nd Model o' Solid

4.$.1 Molecul!r Or%it!l !nd Ener)y &!nd

Conside the /!ild8!p of a cystal0 one atom at a time. As t7o atoms appoach

each othe0 a stage is eached 7hee the highe enegy o/itals :7hich e,tend f!thest

a7ay fom the n!cle!s= /egin to inteact. >hen the distance of appoach is s!fficiently

close0 the t7o o!temost o/itals 7ill com/ine to gi&e t7o molec!la o/itals. Addition

of a thid atom yields a thid molec!la o/ital0 and e&ent!ally n atoms gi&e n molec!la

o/itals. Typically inoganic solid mateials contain on the ode of " , 1'22atoms pe

cm3. Th!s fo a patic!la atomic o/ital0 the es!lting molec!la o/itals geneated fom

the inteaction of ; 1'22atoms 7ill /e n!meo!s and 7ill /e confined in s!ch a limited

space that they 7ill essentially appea as a band of closely8spaced molec!la o/itals.

4.$.2 Met!l0 Inul!tor0 !nd Se*iconductorf a /and is dei&ed fomso/itals0 then the es!lting /and is called ans/and.

Similaly0pand d/ands may /e const!cted fompand do/itals especti&ely. L!st ass

pand do/itals lie at diffeent enegy le&els0 so aes pand d/ands typically sepaated

/y enegy gaps. The /ands ae filled 7ith electons0 stating fom the lo7est enegy

/and. The occ!pied /onding o/itals constit!te the valence band0 and the empty o/itals

epesent the cond!ction /and. The enegy of the lo7est molec!la o/ital of the

cond!ction /and is denoted as %c 7hile the !ppe8most enegy le&el of the &alence /and

is denoted as %&.

n geneal0 the &alence and cond!ction /ands do not o&elap0 /!t ae sepaated /y

a band gap0 %g. The &al!e of %g detemines 7hethe a mateial is a metal0 an insulator0

o a semiconductor0 as ill!stated in ig!e 4.13. )etals ae chaactei?ed /y the

pesence of enegy /ands that ae patially filled0 o /y occ!pied enegy le&els that

o&elap 7ith !nfilled o patially occ!pied /ands. +n the othe hand ins!latos and

semicond!ctos ae chaactei?ed /y the pesence of enegy gaps %g R 2eK fo an

ins!lato0 and %gI 2eK fo a semicond!cto. Ta/le 4.1" pesents &al!es of the /and gapsfo selected mateials.

4'


41/51

:a= :/= :c=

%D%$ AP

C+DUCT+DBAD

KA(ADC% BAD

C+DUCT+DBAD

C+DUCT+DBAD

KA(ADC% BAD

KA(ADC% BAD

%D%$ AP

%

Fi)ure 4.1" &!nd *odel o' olid3 ! Met!lB % Se*iconductorB c Inul!tor

T!%le 4.1$ &!nd)!- o' Selected M!teri!l

Se*iconductor Ty-e o'

Conducti/ity

&!nd)!-

e

Se*iconductor Ty-e o'

Conducti/ity

&!nd)!-

e

e n0 p '. Ag2S n ; 1.Si n 1.1 Bi2S3 n 1.2

Bi2+3 n0 p 2. CdS n 2.4Cd+ n 2.2 C!2S p ;1C!2+ p 2.2 C!S p ;1C!+ p 1.* e18,S p e3+4 n0 p '.1 eS2 n0 p '.#

e2+3 n 2.2 )oS2 n0 p '.3 8 1)n+2:Pyol!site=

n '.2" P/S n0 p '.3*

Sn+2 n 3.* S/2S3 1.*Ti+2 n 3.' EnS n 3. V 3.#K2+" m 2.23 C!eS2 n '.>+3 n 2.* C!"eS2 p ;1En+ n 3.2 eAsS n0 p ;'.2E+2 n ".' aAs n0 p 1.3" V 1.43P/+ n 2. CdTe n0 p 1."

D/2+" n 3.4 CaP n0 p 2.24Ta2+" n 4.' nP p 1.3

BaTi+3 n 3.3 CdSe n 1.*4eTi+3 n 2. EnTe p 2.3Ti+3 n 3." SiC p 3.'STi+3 n 3.4

NBased on $.T. Sh!ey0 Semicond!cting +e )ineals0 %lse&ie0 1#*" A. L. Do?ik0WPhotoelectochemisty@ Applications to Sola %negy Con&esionX0 Ann. $e&. Phys. Chem.02#0 1#8222 :1#*= . $a9esh7a0 P. Singh0 and L. !/o70 W%negy Con&esion in

41


42/51

Photoelectochemical Systems V A $e&ie7X0 %lectochim. Acta0 230 111*81144 :1#*=.4.$." Intrinic !nd Etrinic Se*iconductor

>hen the magnit!de of %gis s!fficiently lo70 it is possi/le fo themal agitation to

pomote an electon fom the &alence /and into the cond!ction /and of a p!e mateial0

thee/y pod!cing an electron holein the &alence /and. This mateial is then temed an

intrinsic semiconductor. A mateial can also ac6!ie cond!ction /and electons and

&alence /and holes /y ecei&ing imp!ities. Conside the addition of phospho!s0 7hich

has fi&e &alence electons0 to gemani!m0 7hich has fo! &alence electons. n ode fo

P to fit into the e st!ct!e0 only fo! &alence electons ae e6!ied. The e,ta electon

fom P emains !nde the infl!ence of the F" chaged P n!cle!s and stays in an enegy

le&el 7hich is 7ithin the e /and gap. f the electon is e,cited o!t of this locali?ed /and

into the e cond!ction /and0 then the P /ecomes positi&ely chaged. At the same time

the e lattice /ecomes negati&ely chaged and is theefoe called an n-typesemicond!cto. Phospho!s is temed a donorimp!ity since it donates electons to the

e cond!ction /and.

+n the othe hand0 7hen a /oon atom0 7ith thee &alence electons0 is intod!ced

in the gemani!m cystal st!ct!e0 it is necessay to find a fo!th &alence electon in

ode to fit this imp!ity into the e st!ct!e. The needed electon is taken fom the e

&alence /and0 thee/y ceating a hole 7ith an effecti&e positi&e chage. The B8doped

mateial is called ap-typesemicond!cto since B has donated a positi&e chage to the e

enegy8/and st!ct!e.

4.$.4 T#e Fer*i Le/el in ! Solid

Conside a solid const!cted /y appopiating anselecton fom each of D atoms.

At a/sol!te tempeat!e :T J '= one8half of the lo7e8lying o/itals 7ill /e occ!pied.

The topmost occ!pied o/ital is designated the ermi leveland it is located mid7ay

/et7een the /and. At highe tempeat!es0 the po/a/ility :f= that an enegy le&el 7ith

enegy %0 is occ!pied /y an electon is gi&en /y the emi disti/!tion f!nction@

f J 1G1 F e,p:%8%=kTH :4.14=

7hee %is temed theermi energy0 and k is the Bolt?mann constant. The emi enegy

is tempeat!e dependent at T J ' it is simply the enegy associated 7ith the emi le&el.42


43/51

>hen % J %0 f J 12. That is0 the po/a/ility of occ!pancy is one8half 7hen a le&el is at

the emi enegy.

The position of the emi le&el is dependent on the nat!e of the mateial. o a

metal0 the enegies of /oth the occ!pied and &acant states ae located nea %. At oom

tempeat!e0 the emi le&el of an intinsic semicond!cto lies in the cente of the /andgap. +n the othe hand fo e,tinsic semicond!ctos0 % occ!s 9!st /eneath the

cond!ction /and in n8type mateials0 and 9!st a/o&e the &alence /and in p8type mateials.

>hen the enegy le&el %clies significantly a/o&e the emi le&el :i.e.0 :%c8 %= R

2kT=0 then the po/a/ility that it is occ!pied is gi&en /y %6!ation 4.14 as@

f J e,p8:%c8 %=kT :4.1"=

Th!s0 if the cond!ction /and is chaactei?ed /y a density of enegy le&els :i.e.0 n!m/e

of enegy le&els pe !nit &ol!me= of Dc0 then the electon density :n= in the cond!ction

/and is gi&en /y

n J Dce,pG8:%c8 %=kTH :4.1=

Similaly if :%8 %&= R 2kT0 then the density of holes :p= in the &alence /and is gi&en /y@

p J D&e,pG8:%8 %&=kTH :4.1*=

7hee D&is the density of enegy le&els in the &alence /and. t follo7s fom %6!ations

4.1 and 4.1* that@

np J DcD&e,pG8:%c8%&=kTH J DcD&e,p:8%gkT= :4.1=

43


44/51

4.( Electronic Structure o' Solid

4.(.1 Molecul!r Or%it!lEner)y &!nd Model

n light of the cystal st!ct!al chaacteistics e&ie7ed a/o&e0 the /asic /!ilding

/locks of o,ides s!ch as Si+20 Ti+20 and Di+ can /e taken as the Si+40 Ti+0 and Di+

polyheda especti&ely. Similaly0 in the case of s!lfides0 epesentati&e /!ilding /locksae EnS4:fo EnS=0 C!S40 and eS4:fo C!eS2=0 and eSfo eS2. The fomation of

these cl!stes can /e &is!ali?ed in tems of the inteaction /et7een the o!te atomic

o/itals associated 7ith the metal and o,ygen o s!lf! atoms. )olec!la o/ital enegy

le&el diagams fo the cl!stes can /e dei&ed fom 6!ant!m chemical calc!lations.

ig!e 4.14 sho7s the es!lts fo :EnS4=8and :C!S4=8 the enegy scale is taken elati&e

to the non8/onding S 3p type o/itals :i.e.0 1t1 fo the tetahedal cl!stes=. n solid

mateials0 the molec!la o/itals of the n!meo!s cl!stes o&elap to gi&e /ands0 and this

is ill!stated /y the coesponding /and diagam fo sphaleite. n tems of the /and

model0 the highest occ!pied molec!la o/ital :-+)+= epesents the topmost laye of

the &alence /and0 7heeas the lo7est !nocc!pied molec!la o/ital :(U)+= epesents

the lo7est enegy le&el in the cond!ction /and.

5

4

3

2

1

0

-1

-2

-3

-4

-5

OrbitalEnergy

(eV)

3a1

4t2

3t2

1t1

2e

2a1

1e2t

2

Antibonding M-S Conduction and

Cry!tal-"iel d-#y$e %e&el!

'onbonding Sul(ur and

onding M-S and

S$)alerite

ZnS4-6

(Zn )2+

1

CuS4-6

4t2

2e

lt1

3t2

1e

,

2t2

2a1

Fi)ure 4.14 Ener)y le/el di!)r!* #o9in) t#e electronic tructure o' t#e nS4(,

!nd CuS4(,cluter0 !nd t#e %!nd *odel o' -#!lerite !'ter !u)#!n !nd Toell.

44


45/51

4.(.2 Electronic Structure o' Met!l Oide

+n the /asis of the oigin of thei enegy gaps0 tansition metal o,ides may /e

classified into empty d8shell :d'0 non8d8/and= o,ides0 closed d8shell :d8/and= o,ides0

and open d8shell :d8/and= o,ides0 as indicated in Ta/les 4.10 4.1*0 and 4.1 fo selected

compo!nds. The metal o,ides that fall !nde the d' categoy come fom the ealie

tansition elements@ !p to )n0 $!0 and +s especti&ely fo the 3d0 4d0 and "d seies.

Among the tansition metal o,ides0 these mateials e,hi/it the simplest electonic

st!ct!es. To ill!state the geneal chaacteistics of the electonic st!ct!e of d'metal

o,ides0 7e t!n to !tile Ti+2. >e kno7 fom the cystal st!ct!e that Ti4F is

octahedally coodinated to +28. )olec!la o/ital calc!lations /ased on the Ti+8

cl!ste gi&e the enegy le&els sho7n in ig!e 4.1". >e can identify fi&e go!ps of

molec!la o/itals@ :1= the + 2s non/onding o/itals :"a1g0 4t1!0 1eg=0 :2= the /onding

o/itals :"t1!0 a1g0 1t2g0 2eg=0 :3= the + 2p non/onding o/itals :1t2!0 t1!0 1t1g=0 :4= thecystal8field o/itals :2t2g0 3eg= and :"= the anti8/onding cond!ction /and o/itals :*a1g0

*t1!=. The main feat!e 7e 7ant to note hee is the nat!e of the highest filled o/ital and

the lo7est !nfilled o/ital0 since these epesent %&and %cespecti&ely. The filled o/ital

7ith the highest enegy is the 1t1g0 and this epesents the top of the &alence /and. +n the

othe hand0 the 2t2gis the lo7est8lying !nocc!pied molec!la o/ital.

T!%le 4.1( &!nd )!- 'or elected d*et!l oide A'ter Co0 1;;2

&in!ry Co*-ound Tern!ry Co*-ound

Co*-ound E)e Co*-ound E)e

3d' Ti+2:!tile= 3.' )gTi+3 3.*Ti+2:anatase= 3.2 STi+3 3.4

BaTi+3 3.2(a2Ti2+* 4.'

K2+" 2.2C+3 2

4d' SE+3 ".4D/2+" 3.# (iD/+3 3.

D/+3 3.3)o+3 3.'

"d' Ta2+" 4.2 (iTa+3 3.DaTi+3 3.

>+3 2.

4"


46/51

T!%le 4.17 Electronic -ro-ertie o' elected cloed,#ell dn*et!l oide A'ter Co0 1;;2

Co*-ound Ionic For*ul! Elec. Con'i). Met!l Coordin!tion E)e

C!2+ :C!F=2+28 3d1' 2 :(inea= 2.1Ag+ AgFAg3F:+28=2 4d1'0 4d 2 :(inea=0 4 :S6.

plan.=

Pd+ Pd2F

+28

4d

4 :S6!ae plana= 1(aCo+3 (a3FCo3F:+28=3 3d :+ctahedal= '.1(a$h+3 (a3F$h3F:+28=3 4d :+ctahedal= 1.

T!%le 4.18 Electronic -ro-ertie o' elected o-en,#ell dn*et!l oide A'ter Co0

1;;2

&in!ry Co*-ound Tern!ry Co*-ound

Co*-ound S-in E)e Co*-ound S-in E)e

3d' (aK+3 1

C2+3 32 3.3 (aC+3 32 )n+ "2 3. (a)n+3 2 )n+2 32 e+ 2 2.4 (ae+3 "2 8e2+3 "2 1.# 3e"+12 "2 3Co+ 32 2.Di+ 1 3.C!+ 12 1.4

$losed d-shell metal oxides. The chaacteistic feat!e of this categoy of metalo,ides is the pesence of a closed shell of d8electons and the fact that the !ppemost

o/ital of the &alence /and has d8chaacte. n the case of the d1'compo!nd0 C!2+0 the

closed shell aises /eca!se all the fi&e d o/itals ae f!lly occ!pied0 7ith an electon8pai

in each o/ital. The /and gap is /o!nded /y the lo7e8lying filled C! 3d le&els0 and the

highe8lying /!t empty C! 4s le&el. The chemical fom!la0 Ag+0 easily gi&es the

impession that this compo!nd contains sil&e in the pl!s t7o o,idation state :Ag:==. n

fact0 this is a mi,ed &alency compo!nd0 7hose ionic fom!la in&ol&es Ag:=0 d1'0 and

Ag:=0 d. As fo!nd in the case of C!:= a/o&e0 in the Ag:= o,idation state0 the sil&e

atom is coodinated to t7o o,ygen atoms. Also0 as 7ith C!F0 AgFis closed8shelled since

all a&aila/le d o/itals ae filled. The Ag:= ion is tetahedally coodinated to fo!

o,ygens. The /and gap po/a/ly lies /et7een the filled AgF4d o/itals and the empty

Ag3F4d o/itals.

4


47/51

Fi)ure 4.1$ Molecul!r or%it!l di!)r!* 'or t#e TiO(8,cluter Toell !nd !u)#!n0

-.188.

%pen-shell dn metal oxides. The o,ides that fall !nde this categoy contain

!npaied electons and theefoe they ha&e magnetic popeties.

4.(." Electronic Structure o' Met!l Sul'ide

)olec!la o/ital enegy le&el diagams fo the tetahedal cl!stes of En2F0 C!F0

C!2F0 e2F0 and e3F0 and the octahedal cl!ste of e2F0 ha&e /een dei&ed fom 6!ant!m

chemical calc!lations /y Ka!ghan and Tossell. The es!lts ae pesented in ig!e 4.1.

n compaing the diffeent cl!stes0 the follo7ing o/se&ations can /e made@

4*


48/51

2e

5

4

3

2

1

0

-1

-2

-3

-4

-5

OrbitalEnergy

(eV)

3a1

4t2

3t2

1t1

2e

2a1

1e2t

2

Antibonding M-S Conduction and

Cry!tal-"iel d-#y$e %e&el!

'onbonding Sul(er and

onding M-S and

S$)alerite "erroan S$)alerite C)alco$yrite

ZnS4

-6(Zn )

2+

FeS4-6

(Fe )2+

1

t2e

3t2

1t1

2a1

1e2t

2

e

4t2

t2

t2

et

2

e4t

2

e

3a1

FeS4-5

(Fe )+3

CuS4-7

(Cu )+

Fi)ure 4.1( Ener)y le/el di!)r!* #o9in) t#e electronic tructure o' *et!l ul'ide

cluter !'ter !u)#!n !nd Toell.

:1= The highest occ!pied molec!la o/ital :-+)+= of the EnS4cl!ste :the 4t2

o/ital= is of pedominantly non/onding s!lf! 3p chaacte. n contast0 the

-+)+s of the othe cl!stes ae epesented /y anti/onding metal 3d8type

o/itals. The -+)+s of :C!S4=*8and :C!S4=8ae filled and patially filled

4t2 o/itals especti&ely. n the case of :eS4=8

0 the fo! !npaied 3delectons in this st!ct!e ca!se the enegy le&els to di&ide into spin8!p and

spin8do7n go!ps the empty 1't2 and patially occ!pied 3e molec!la

o/itals lie at the top of the &alence /and. The 2t2go/ital se&es as the

-+)+ and &alence /and fo :eS=1'8.

:2= o /oth :EnS4=8 and :C!S4=*80 the (U)+ is the anti/onding 3a1 o/ital.

-o7e&e0 since the 4t2o/ital of the :C!S4=8cl!ste is incompletely filled0 it

epesents the (U)+. n the case of :eS4=80 the empty anti/onding #a1

:mostly e 4s= and 11t2 :mostly S 3p= o/itals epesent the cond!ction

/and0 7hile the empty 3ego/itals se&e as the (U)+ fo the cl!ste0 and

theefoe0 fo eS2.

4


49/51

:3= n the :EnS4=8electonic st!ct!e0 the metal 3d8type o/itals ae /!ied fa

/elo7 the /onding )8S o/itals. This is in contast to the othe cl!stes0

7hee the opposite odeing is o/se&ed.

Antibonding M-S

Conduction Band

Crystal-Field-Type Levels

Nonbonding

Sulfur Band

BondingM-S Band

Chalcopyrite

e

t2

t2

e

!

"

2

#

$

-#-2

-"

-!

-

%rbital&

nergy'e()

"t2#t#

2a#

#e2t2

!t2

e

"a#

2e

!t2

FeS4

5-(Fe )

3+CuS 4

7-(Cu )

+

Fi)ure 4.17 T#e electronic tructure o' c#!lco-yrite CuFeS2!'ter !u)#!n !nd

Toell.

4#


50/51

Sphalerite

!

"

2

#

$

-#

-2

-"

-!

-

"a#

!t2

"t2

#t#2e

2a#

#e2t2

Antibonding M-SConduction Band

Crystal-Field-Type Levels

Bonding M-S

Band

Nonbonding

Sulfur Band

Crystal-Field-

Type Levels

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

Energy

(eV)

2gt

1gt1ut

ge2ut

1ut

2gt1ga

ge

*yrite

'FeS )2

'+nS)

,-BAN, S&MC%N,.CT%/ N%N-,-BAN, S&MC%N,0

Bonding M-S

Band

Fi)ure 4.18 Co*-!rion o' t#e electronic tructure o' -yrite FeS2 !nd -#!lerite

nS !'ter !u)#!n !nd Toell

"'


51/51

Furt#er Re!din)

1. A. . >ells0 Structural *norganic $hemistry0 "th ed.0 +,fod0 De7 ok0 1#4.

2. P. A. Co,0 +ransition etal %xides0 +,fod0 De7 ok0 1##2.

3. P. A. Co,0 +he ,lectronic Structure and $hemistry of Solids0 +,fod0 De7 ok01#*.

4. . L. Ka!ghan and L. $. Caig0 ineral $hemistry of etal Sulfides0 Cam/idge0De7 ok0 1#*.

". L. A. Tossell and . L. Ka!ghan0 +heoretical eochemistry. Application of /uantumechanics in the ,arth and ineral Sciences0 +,fod0 De7 ok0 1##2.

. (. Pa!ling0 +he 0ature of the $hemical !ond0 3d. ed.0 Conell Uni&esity Pess0thaca0 De7 ok0 1#'.

*. L. %. -!heey0 %.A. eite0 and $. (. eite0 *norganic $hemistry& Principles ofStructure and 1eactivity0 4th ed.0 -ape Colins0 1##3.

. A. . Shape0*norganic $hemistry0 3d. ed.0 (ongman0 (ondon0 1##2.

#. . %. Shi&e0 P. >. Atkins0 and C. -. (angfod0 *norganic $hemistry0 eeman0De7 ok0 1##'.

1'. B. >e/ste0 $hemical !onding +heory0 Black7ell0 +,fod0 1##'.

11. . A. Cotton and . >ilkinson0Advanced *norganic $hemistry0 "th ed.0 >iley0 De7ok0 1#.

12. (. %. +gel0An *ntroduction to +ransition - etal $hemistry. 2igand-ield +heory2nd ed.0 >iley0 De7 ok0 1#.

13. . (ie/a!0 Structural $hemistry of Silicates0 Spinge8Kelag0 De7 ok0 1#".

Documents

Chapter 4 Structures of Solids