the properties of materials

8/12/2019 The Properties of Materials

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The properties of

Engineering materialsSecond Edition

Raymond A. Higgins BSc (Birm), CEng,

Formerly Senior Lecturer in Materials Science, West Bromwich College of Commerce

and Technology; former Chief Metallurgist, Messrs Aston Chain and Hoo Co! Ltd!,Birmingham; and "#aminer in Metallurgy to the $nstitution of %roduction "ngineers, The

City and &uilds of London $nstitute, The 'nion of Lancashire and Cheshire $nstitutesand The 'nion of "ducational $nstitutes!

Viva Books Private Limited


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New Delhi. Mm!ai .Chennai

" R A Higgins

#irst Soth Asian Edition $%%&

'' A B*S +R'AE -MED /012/ Ansari Road, Daryagan3, New Delhi $$4 440 0$ New A5ollo ndstrial Estate, Mogra -ane, Andheri ("), Mm!ai 44 46% & A7i7 Ml8 #orth Street, hosand -ights, Chennai 644 446.

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All rights reser9ed. No 5art o: this !oo8 may !e re5rodced ortransmitted in any :orm or !y any means withot 5ermission :romthe 5!lishers,

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/012/ Ansari Road, Daryagan3, New Delhi $$4 440.+rinted at Re5li8a +ress +9t -td, Delhi $$4 44


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PREFACETo the First Edition

his !oo8 was written 5rimarily as an introdction to MaterialsScience :or those engineering stdents who !ecome in9ol9ed withthe s!3ect at ad9anced technical college le9el or, as :irst=yearndergradates, :eel the need o: an introdction to its !asic

5rinci5les, t may also 5ro9e se:l to those stdents o: metallrgywho :ind it necessary to e


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e


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Bromwich College, :or reading the :irst three cha5ters o: this !oo8and :or ma8ing hel5:l sggestions relating to the !asic chemistrythey contain.

R. A. HNS*i+ision of Materials Technology,West Bromwich College of Commerce and Technology,Wednesury, West Midlands!


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PREFACE

To the Second Edition

he Swedish scientist S9ante Agst Arrhenis died at a!ot thetime was recei9ing my :irst school lessons in 5hysics !t it isonly ?ite recently that his E?ation has :ond its way intocollege sylla!ses :or Materials Science. ther :ndamentalscienti:ic laws, hy5otheses and relationshi5s ha9e !eensimilarly assimilated. he science o: materials has ceased to dealwith s!stances on a mainly descri5ti9e !asis and now :ollows a

more ?antitati9e a55roach so that the stdent, in addition toretaining a !asic 8nowledge o: 5hysics and chemistry, mst !e5re5ared to se e


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a55lication o: some o: these 5ro!lems with cation. hs, whilstthe di::erential e?ations associated with #ic8s -aws indicate tos that di::sion in metallic solid soltions is not a sim5le linear@

5rocess and also e


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8ee5ing 5 with it all. n the words o: the +reacher some threethosand years ago=

. !!of maing many oos there is no end,! and much study is a

weariness of the flesh!

(Ecclesiastes, , $0)

R. A. HNS

Walsall,

West Midlands!


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oHE ;MEN # MI -#E=

My ;i:e, Helen and orDaghter, Alice.

;hate9er ha55ens, ha55ens as it shold. !ser9e care:lly andyo will :ind this to !e tre. Marcs Arelis (AD $0$=$&4), Meditations (', $4)

or, 5t another way

;hen the tree :alls, how can the shadow standJ Mary -a9in, n the Middle o: the #ields.


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1

The Atom

11Fntil a :ew hndred years ago==a mere !lin8 o: the eye in thetime scale o: the Fni9erse=edcated Man !elie9ed that or Earthwas the :i


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the 8nown elements, a system !y which he was a!le to 5redict the5ro5erties o: other elements at that time still n8nown.

Science deals largely with systems o: classi:ication. hs, the!iologist classi:ies li9ing things :irst as either animal or

9egeta!le. he :ormer he s!di9ides into 9erte!rate andin9erte!rate=and so on. Chemistry is, a!o9e all, a science o:classi:ication. Both elements and their com5onds are 5lacedinto gro5s de5ending 5on their chemical and 5hysical

5ro5erties. n this !oo8 we shall !e classi:ying s!stancesmainly !ecase, as engineers, we are interested in theirmechanical 5ro5erties, !t :irst it will !e necessary to see8reasons which e


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5articles throgh a condctor whilst, later, Sir ;illiam Croo8eshowed that cathode rays cold !e !ent !y an electromagnetic :ieldths sggesting that these rays consisted o: electrically=charged

5articles o: some 8ind. hese 5articles ltimately !ecame 8nown

as electrons and were in :act the :irst o: the s!=atomic 5articles to!e disco9ered. oday we ma8e considera!le se o: theelectromagnetic de:lection o: electrons, as :or e


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electricity. t also means that the electron 5ossesses anglarmomentm and this mst !e ta8en into accont in s5ectrogra5hicmeasrements.

1## The Proton n $&&6 Egene oldstein noticed lminosrays emerging :rom holes in a 5er:orated cathode which he hadsed in a cathode=ray t!e. hese rays were tra9eling in a directiono..osite to that o: the cathode rays. -ater it was shown that theywere de:lected !y !oth magnetic and electrical :ields !t in theo55osite direction to that o: a stream o: electrons (cathode rays).Conse?ently it was realised that the 5articles o: which these newrays consisted were 5ositi9ely charged. nitially they were 8nown

as canal rays since they 5assed throgh channels in the cathode!t in $%4> K. K. homson sggested the name 5ositi9e rays andwhen a determination o: the 9ale charge2mass (e2m) was made itshowed them to consist o: 5articles which were mch hea9ier thanelectrons. Fltimately it was :ond that the mass o: the lightest o:these new 5articles was roghly that o: the ordinary hydrogenatom ($./.0) when stri55ed o: its lone electron. he name .roton,deri9ed :rom the ree8 word meaning :irst, was sggested !yRther:ord in $%04.

he 5roton carries an e?al !t o55osite (hence 5ositi9e)charge to that o: the electron. ts mass is $.6>01 < $4=0> 8g($.44>06/ a.m..) ma8ing it some $&/6 times hea9ier than theelectron, t is re5resented !y a nm!er o: sym!ols sch as ., $Hand $$H the latter !eing the most commonly sed and indicatingthat it is the ncles o: the hydrogen atom with a mass o: one and a

5ositi9e charge o: one.

1#$ The !e"tron Dring my school days chemists got along?ite well with 3st two 5articles with which to e


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realised, howe9er, that all atoms with the e


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1#%Since Chadwic8s disco9ery o: the netron the nm!er o:elementary 5articles has 5roli:erated. hese can !e 9ery roghlyclassi:ied into three main gro5s

(i) aryons 5rotons and other 5articles o: mass greater than that o:the 5roton(ii) mesons any o: a gro5 o: 5articles ha9ing a rest mass !etweenthose o: the electron and the 5roton and ha9ing an integral s5in

(iii) le.tons which inclde electron, mon, 5ositron (5ositi9eelectron) and netrino (which 5ossesses neither mass nor charge=

!t only s5inG)

he term ?ar8 has !een ado5ted to descri!e anyone o: a nm!ero: hy5othetical elementary 5articles with charges o: 0e- or 10e-

(where e- is the charge on the electron) and considered to !e the:ndamental nits o: all !aryons and mesons. ncidentally the word?ar8 was coined !y Kames Koyce in Finnegan2s Wae3 Howe9er,the reader need not !e discoraged !y the com5le


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!e considered as a !eam o: 5articles or 5hotons.) Howe9er, instdying the strctres o: atoms it will !e more con9enient toregard the electron as a 5article e9en thogh this gi9es a restricted9ision o: the s!3ect.

The Str"ct"re of the Atom

1$ E9erything is !ilt 5 o: atoms. hey are 9ery tiny 5articlesand the co55er=nic8el alloy British 15 coin in yor 5oc8et containssome /4>44444444444444444444 atoms=gi9e or ta8e a :ewtrillions whilst, in America, the dime will contain roghly 0$ %44444 444 444 444 444 444 atoms=gi9e or ta8e a :ew ?intillions.

Each atom has at its centre a ncles consisting o: a gro5 o:5rotons and netrons whilst in or!it arond the ncles areelectrons. An indi9idal atom consists almost entirely o: em5tys5ace. Althogh most o: the mass is concentrated in the ncles

!oth the ncles and the indi9idal electrons in or!itals arond itare o: a55ro


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hs, sch diagrams !ear the same relationshi5 to the actal natreo: an atom as does a 5a5er street gide to the 5ictorial 9iew o: atown=it shows the locality o: the Coc8 and Mag5ie@ !t gi9es nohint o: the actal a55earance o: that e


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to the ne


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almost in the natre o: a resltant 5article (here the termresltant is sed in the mechanical sense) and the or!italinter5reted as denoting the statistical 5ro!a!ility o: :inding that

5article at any gi9en 5oint arond the ncles. Conse?ently it

mst !e stressed again that 5ictres showing an atom asconsisting o: a central ncles a!ot which a nm!er o: electronsare mo9ing in de:inite or!its mst not !e inter5reted too literally.hey are 5rely sym!olic and o::er a sim5le diagrammatic meanso: showing the electron com5lement o: the 9arios ?antmshells. Sch diagrams will !e sed in the 5ages which :ollow inorder to e


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atomic theory sccess:lly e


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already :illed (with the helim atom) the third electron in thelithim atom mst go into the second ?antm shell. n atoms o:each o: the elements which :ollow=!eryllim, !oron, car!on,nitrogen, o


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s!shells are created to hold the other si< electrons which aremem!ers o: this second 5rinci5al shell.

Each o: the scceeding shells contains two or more s!shellswhich are designated., d andf! he greatest nm!er o: electrons

in these s!shells is si


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The Atomic !"cle"s

1% he ncles o: an atom consists o: an association o: 5rotonsand netrons. Since these are 5articles some $&/6 times hea9ier


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than the electron it :ollows that the mass o: an atom tends to !econcentrated in its ncles. he nm!er o: 5rotons in the ncleso: a sta!le atom is always e?al to the total nm!er o: electrons inthe 9arios shells arond the ncles. Since the charge on a

5roton is e?al !t o55osite to that on an electron it :ollows that asta!le atom is electrically netral. he nm!er o: 5rotons in thencles o: an atom is called the Atomic Nm!er (7) o: theelement.


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he netrons, also 5resent in the ncles, ha9e little e::ect onthe chemical 5ro5erties o: the element since they carry noresltant electrical charge. hey !eha9e as a :orm o: nclear

!allast increasing the total mass o: the atom. he nm!er o:

netrons 5resent in the ncles may 9ary e9en :rom one atom toanother of the same element! Conse?ently when we measre therelati+e atomic mass o: an element we :ind that it is rarely awhole nm!er since we are in :act measring the a9erage mass o:a large nm!er o: atoms o: se9eral di::erent masses. riginallythe relati9e atomic massQ o: an element was the a9erage s5eci:icmass o: an atom o: that element as com5ared with the mass o: anatom o: hydrogen. #or 9arios reasons a car!on atom o: atomic

mass $0.4444 is now sed as the standard. Howe9er, in annderstanding o: the 5ro5erties o: the elements the atomicnm!er (7) is o: mch greater signi:icance than the relati9eatomic mass.

1%1soto5es whilst the nm!er o: 5rotons in the ncles o: anyatom o: a single element is :i 5rotons, !t a!ot >1 o: all chlorine

atoms contain $& netrons whilst roghly 01 contain 04netrons. hese two di::erent chlorine atoms are 8nown asisoto.es and chlorine is said to !e isoto.ic! he relati9e atomicmasses o: these two chlorine isoto5es will !e /1 and />res5ecti9ely (#ig. $.6) !t since the lighter isoto5e is the more

5lenti:l this e


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addition to the 5roton. he ncles o: isoto5e / (8nown astritium)consists o: two netrons in addition to the

Q +re9iosly 8nown as atomic weight.

his naming o: isoto5es is to !e discoraged=it may gi9e the im5ression that se5arate elementsare !eing descri!ed rather than isoto5es o: a single element, in this case hydrogen.

#ig. $.> he strctral ma8e=5 o: the three isoto5es o: hydrogen. he isoto5e o: helim,T0He, has a similar atomic mass to tritim !t is o: a 9ery di::erent natre !ecase o: its

:illed electron shell.

5roton. Althogh the relati9e atomic masses o: the three isoto5es

are $, 0 and / res5ecti9ely the a9erage relati9e atomic mass o:hydrogen is no more than $.44>%> !ecase isoto5es 0 and / aree


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1%# !"clear Binding Forceshe ncles o: an atom consists o:a collection o: 5rotons and netrons. Now li8e=charged !odiesre5el each other with a :orce which is in9ersely 5ro5ortional tothe s?are o: their distance a5art (the Colom! -aw). Since

5rotons are 5ositi9ely charged 5articles why does not the nclesdisintegrate de to re5lsion !etween these 5rotonsJ he answerto this ?estion is that :orces which !ind together the 5articles o:the ncles are not in :act o: an electrostatic natre. Neither arethey magnetic or gra9itational in character !t a55ear to !ese5arate :orces entirely and a!ot which little is yet 8nown. hese:orces act not only !etween the 5rotons !t also !etween thenetrons and are 8nown as nclear !inding :orces.

An atomic ncles may contain a large nm!er o: nucleons (i.e.5rotons and netrons) !ond together as a coherent nit. Ncleonsin the core are s!3ected to their s5ecial :orces o: attraction !y allneigh!oring ncleons !t those on the sr:ace are attractedinwards towards the core !y the !l8 o: the ncleons sitated there.his 5rodces something in the natre o: a

#ig. $.& Ncleons (i.e. 5rotons U and netrons V) at the sr:ace are attracted

inwards !y those at the core.

sr:ace tension e::ect at the oter limits o: the ncles so thatnclei can !e regarded as !eing constitted a:ter the :ashion o:dro5lets o: moistre.


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;hilst mch remains to !e disco9ered a!ot these nclear!inding :orces it is clear that they are e::ecti9e o9er an e


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ncles. At B, howe9er, the cr9e :lattens o:: at some 5otential

energy 9ale,",!ecase the 5roton now comes close enogh to!e nder the in:lence o: the nclear !inding :orce. Beyond Cthe nclear !inding :orce is mch greater than the electrostatic:orce o: re5lsion and so the 5roton is now attracted to thencles instead o: !eing re5elled !y it. Relati9e to its 5re9ioscondition it can now !e considered to 5ossess negati9e 5otentialenergy. he ca5tred 5roton is said to !e in a 5otential well o:de5th " W ; and this energy wold !e re?ired to remo9e it

:rom the ncles.

1%$ An im5ortant 5oint to a55reciate is that whilstelectrostatic re.ulsion acts o+er fairly large distances, the

nuclear inding force o.erates o+er +ery small distances!

here:ore a small nm!er o: ncleons can hold together !ecaseit is geometrically 5ossi!le :or the nclear !inding :orce too9ercome the electrostatic re5lsion !etween 5rotons, !t thereis a limit to this nm!er. A 9ery large ncles is certain to

5ossess many ncleons which are otside the in:lence o: theshort=range nclear !inding :orce !t any 5rotons will still !ein:lenced !y the mtal re5lsion !etween each others long=range electrostatic :ields. here:ore as a ncles !ecomes largethe total electrostatic re5lsion !etween 5rotons increases whilst

!eyond a certain si7e the total nclear !inding :orce !etweenncleons does not.

hs in a hea9y ncles the total !inding :orce is not strongenogh to hold the ncles together against the total re5lsion:orces !etween all o: the 5rotons. his is one reason why e


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ha9e no charge. Howe9er, these e


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Bt in :act the mass o: the helim ncles is .440>6 a.m.. hedi::erence !etween the e6 a.m.. P 4.40%4%0 a.m..

his di::erence is 8nown as the mass defect! t :ollows that in the:ormation o: the helim ncles :rom its constitent 5rotons andnetrons a 5ortion o: matter amonting to 4.40%4%0 a.m..iscon9erted into energy. his energy is 5resent in the :orm o: the

!inding :orce which holds the 5articles together as sggested in the5re9ios section. he amont o: energy released !y the con9ersiono: this amont o: matter may !e deri9ed :rom Einsteins mass=energy e?ation " P mc 0

where c is the 9elocity o: light (/ < $4& ms=l) m is the massin9ol9ed and " the energy 5rodced. Hence the s!stittion o:a!o9e 9ales in this e?ation indicates the energy released " P 4.40%4%0 < $.66$ < $4=0>< (/ $4&)0K

P ./1 $4=$0K

(;here $ atomic mass nit P $.66$ < $4=0>8g).

States o: Matter

1' All elements can e


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#ig. $.$4 he ncles o: the helim isoto5e 0He weighs less than the :or ncleons (0

5rotons and 0 netrons) ta8en se5arately.

#ig $.$$ #orces o5erating !etween single atoms.(i) Here the atoms are so :ar a5art that only wea8 :orces o: attraction o5erate !etweenthem. (ii)Now the atoms are close together and strong :orces tend to 5ll them closertogether. (iii) ;hen the electron or!itals are close or o9erla55ing a strong :orce o:re5lsion !ilds 5.

#orces o: attraction and re5lsion o5erate !etween atoms and thetotal :orce in9ol9ed may !e the resltant o: a nm!er o: :orces.#irst, :orces o: re5lsion will o5erate !etween the nclei o: twoatoms since !oth nclei are 5ositi9ely charged. Similarly theelectrons o: one atom will re5el those o: another atom sinceelectrons are negati9ely charged. 55osing these :orces o:re5lsion are :orces o: attraction in which the 5ositi9ely chargedncles o: one atom is attracted !y the negati9ely charged

electrons o: the other atom. At the same time there will !e agra9itational :orce o: attraction o5erating !etween the massi9enclei o: !oth atoms. ;hether the resltant :orce !etween the twoatoms is o: attraction or re5lsion de5ends 5on the distance a5arto: their centres.


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: the two atoms are an in:inite distance a5art then their.otentialenergy of interaction can !e assmed to !e 7ero. As the atomsmo9e closer together a :orce o: attraction !etween them increasesand 5otential energyfalls!ecase wor8 is !eing done !y the atoms

as they mo9e closer together nder the :orce o: attraction. As theyget 9ery close a short=range :orce o: re5lsion !ilds 5 andltimately tends to !alance the :orce o: attraction. At this stage the

5otential energy rises !ecase the atoms are now !eing 5lledtogether. his state o: a::airs is indicated in #ig. $.$0 where the

5otential energy de to :orces o: attraction (cr9e a), re5lsion(cr9e !) and the resltant (cr9e c) is shown in relation to theinteratomic distance !etween the atom centres. +otential energy is

at a minimm (+o) at the e?ili!rim 5osition (ro) and 9ore5resentsthe wor8 re?ired to se5arate the atoms com5letely. n a gas at relati9ely high tem5eratres the a9erage energy o: theatoms is s::icient :or the :orces o: attraction !etween them to !erendered negligi!le. hey a55roach each other on a collision 5athand only at short distances will strong :orces o: re5lsion lead tose5aration. As the tem5eratre o: the gas is decreased so is the8inetic energy o: each atom.#ig $.$0


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Conse?ently :orces o: attraction !etween atoms !ecome moresigni:icant. At some tem5eratre a stage is reached where largegro5s o: atoms are held together since their thermal acti9ation isins::icient to 5ll them a5art, i.e. the gas condenses to :orm a

li?id. At a lower tem5eratre still the :orce o: attraction5redominates to the e


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QRe:erence to A55endi< will show the accrate 9ale :or the atomic mass o: the o


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dioNm!er,=Aand=AP 6.40010 $40/atoms (etc.)2mole.


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#

The )olec"le

# 1 n the 5re9ios cha5ter we considered some o: the 5ro5ertieso: the atom as a single :ree 5article. Ne9ertheless, a5art :romthose o: the no!le gases, atoms rarely occr as single 5articles

!t are generally attached to other atoms :orming small or largegro5s. ;hich is 3st as well otherwise or Earth=i: it e


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one atom is strongly metallic (the element occ5ies a 5osition onthe le:t=hand side o: the +eriodic a!le) and the other stronglynon=metallic (the element is sitated on the e


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has a com5lete neon octet and the two atoms are held together !ythe electrical :orces in9ol9ed !y sharing electrons !elonging to theoter or!itals o: !oth atoms. #or this reason the co9alent !ond is astrong and sta!le chemical !ond.

wo hydrogen atoms com!ine in a similar way e


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manner is called a molecule! Molecles can contain more than twoatoms=in :act some molecles o: the more com5le< car!oncom5onds contain many thosands o: atoms. Most o: thecommon non=metallic gases, howe9er, e


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he strctre o: the water molecle is sch that the ond angle

!etween the two hydrogen atoms is $41Z (#ig. 0.1). As we shall seelater (0..), this 5articlar sha5e o: the water molecle o::ers an

e


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moleclar mass) has no nits since, li8e atomic mass, it is relati9eto the mass o: the car!on atom $06C ($0.4444) ($.).

Car*on and its Compo"nds#$he element car!on occ5ies a 5osition in the centre o: the+eriodic a!le. hs it may !e e


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:rom one com5ond to the ne


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#$#here is only one !asic 5attern in which the car!on atoms can!e arranged in the :irst three com5onds in the series, namely,methane, ethane and 5ro5ane. ;ith the com5ond !tane,howe9er, car!on atoms can !e arranged in two di::erent 5atterns asindicated in #ig. 0.%. n :act two di::erent s!stances do e&&41&/$ 5ossi!le isomers.

a!le 0.0============================================================================================================

somer Melting 5oint(oC) Boiling +oint(oC)============================================================================================================

n=Btane =$/& =4.1iso=Btane =$1% =4.0

============================================================================================================


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#$$he al8ane series descri!ed a!o9e consists o: hydrocar!ons;hich are said to !e satrated. Brie:ly, this means that car!onatoms are 3oined to their neigh!ors !y means o: single !onds.Another series e


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5olythene as it is commonly 8nown. he se?ence in this 5rocessis indicated in #ig. 0.$$.

#ig. 0.$$ he 5olymeri7ation o: ethylene to :orm 5oly(ethylene)or +olythene

+olythene is one o: a large nm!er o: these s5er=5olymers(commonly called 5lastics), which are :inding increasing se as

engineering materials. hey will !e discssed in more detail inCha5ter wel9e.

+ntermolec"lar Forces

#% he atoms in a molecle are, as we ha9e seen, held together!y co9alent !onds. hese are strong 5rimary !onds, which are

de5endent 5on relati9ely 5ower:l electrostatic :orces. At thesame time wea8er electrostatic :orces o: a secondary natre gi9erise to attractions !etween any one molecule and its neigh!ors.nly in this way can we e


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As early as $&>/ Kohannes Dideri8 9an der ;aals a Dtch5hysicist, soght to e


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tend to !e concentrated rather more densely in the region o: thechlorine ncles (which contains a larger 5ositi9e charge) thanarond the hydrogen ncles (which contains only a single 5ositi9echarge de to the 5resence o: one 5roton). he ne9en distri!tion

o: electrons in the moleclar or!ital is e?i9alent to a se5arationo: charges. #or this reason the hydrogen ncles tends to !e rathere


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+olar molecles will re5el each other or attract each otheraccording to the way in which they are orientated (#ig. 0.$).

he degree o: mtal di5ole alignment will go9ern the e


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#%$ -ispersion Forces Althogh. there are many molecleswhich a55ear to !e non=5olar, that is the centres o: 5ositi9e andnegati9e charges wold seem to !e coincident, all molecles=andthe single atoms o: no!le gases=ha9e time=9arying di5ole moments

the natre o: which will de5end 5on the 5osition o: the electronsat any 5articlar instant.

Consider the case o: two atoms o: the no!le gas, argon, in close5ro


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he dis5ersion e::ect is e9ident when considering therelationshi5 !etween moleclar mass and !oiling 5oint. Massi9emolecles contain more electrons than do light ones and so the

attraction de to dis5ersion e::ects is greater in the massi9emolecles. Heat o: e9a5oration is a measre o: the energy re?iredto o9ercome :orces o: attraction !etween molecles so that theycan se5arate. Since the !oiling 5oint is 5ro5ortional to the heat o:e9a5oration it is a con9enient criterion in assessing theseintermoleclar :orces. hs normal co9alently !onded com5ondswith massi9e molecles ha9e higher !oiling 5oints than those withsmall. molecles. An e


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Fig. 2.1/ !e &asis of t!e !'$roge &o$ (or &ri$ge) i t!e water molecule

his e::ect is a55arent in the case o: the water molecle. Herethe o


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atom casing a lesser concentration o: the electrons so that awea8er di5ole moment is 5rodced in the molecle. n the sameway the molecle o: hydrogen chloride, HC, does not e


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$

The Cr&stal

$1 ;hen sed in a non=scienti:ic sense the term crystal ,con9eys an im5ression o: a material which is geometricallyreglar in sha5e and which is !oth lstros and trans5arent=as the

e


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atoms are shared in sch a way that the a55ro5riate no!le=gasstrctres are attained in the oter electron shells concerned.Howe9er chemical com!ination can also ta8e 5lace !y the trans:ero: electrons :rom one atom to another sch that a no!le=gas

strctre is attained in the 9alency shells o: each resltant 5article.hs, a metallic atom which contains only one or two 9alencyelectrons tends to gi9e 5 these electrons to a non=metallic atomwhich already has a 9alency shell o: si< or se9en electrons. n thisway the oter electron shell o: each resltant 5article attains ano!le=gas strctre.

$#1he metal sodim reacts 9igorosly with the 5oisonosgas chlorine to 5rodce a 9ery sta!le s!stance, sodim chloride(common salt). n this instance the sodim atom which carries asingle electron in its oter shell donates this electron to a chlorineatom which 5re9iosly had se9en electrons in its oter shell. Bymeans o: this trans:er the sodim 5article is le:t with a com5leteoter shell (the neon shell) and the chlorine 5article also has acom5leted shell (the argon shell). Since an electron trans:er has

ta8en 5lace :rom one atom to another we can no longer re:er tothe resltant 5articles as atoms. he sodim 5article is o!9ioslysomething less than a sodim atom whilst the chlorine 5article issomething more than a chlorine atom. +articles 5rodced !yelectron trans:er in this manner are 8nown as ions.

+rior to the chemical reaction dring which the electron trans:ertoo8 5lace, the atoms were electrically netral !ecase in eachcase the nm!er o: 5ositi9ely charged 5rotons in the ncles was

!alanced !y an e?al nm!er o: negati9ely charged electrons in

or!itals arond the ncles. Dring the reaction the sodim atomlost an electron and the ion so :ormed mst there:ore carry aresltant 5ositi9e charge. Similarly, since the chlorine atomrecei9ed this electron the chlorine ion 5rodced mst carry aresltant negati9e charge (#ig. /.$).


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Since the two ions :ormed as a reslt o: this chemical reactioncarry e?al !t o55osite charges they will attract each other and itis this :orce o: colom!ic attraction which constittes theelectro9alent !ond. Althogh generally wea8er than a co9alent

!ond, this electro9alent !ond is mch stronger than any o: therelati9ely :ee!le 9an der ;aals :orces.

Fig 3.1 !e formatio of a electro#alet , or ,ioic , &o$ &etwee aso$ium atom a$ a c!lorie atom

Fig.3.2ac! a+ io is surrou$e$ &' si 3l, ios


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$##;hen sodim and chlorine react with each other e9en onthe la!oratory scale many ,millions o: atoms are in9ol9ed and ane?ally large nm!er o: ions is 5rodced. ;hilst there is mtalattraction o: sodim ions :or chlorine ions, :orces o: re5lsion

o5erate !etween all li8e ions. hat is, each sodim ion is re5elled!y all other sodim ions whilst each chlorine ion is re5elled !y allother chlorine ions. As a reslt the system attains e?ili!rimwhen each chlorine ion is srronded !y si< sodim ions and,con9ersely, when each ion o: sodim is at the same timesrronded !y si< chlorine ions (#ig. /.0)= n this instance therelati9e si7es o: the chlorine ions and sodim ions are sch that ac!ic ty5e o: 5attern is :ormed. Since each sodim ion is

srronded !y si< chlorine ions it is said to ha9e a co=ordinationnm!er o: Si


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when ions come into close 5ro


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and is e?al to ^A2rm whilst the 5otential energy (+E) de tore5lsion is e?al to B2rn. A and B are constants de5endent on thenatres o: the ions, i.e. sch :actors as nclear mass andmagnitde o: charge. m and n are 5owers (to !e determined)

where n is greater than m.he resltant 5otential energy, ', is gi9en !y

=A B

'P ===== W ==== rm rn

he relationshi5 !etween 5otential energy and interatomic distanceis indicated in #ig. $.$0 where cr9e ! re5resents the +E associatedwith :orces o: re5lsion, cr9e a the +E associated with :orces o:attraction whilst cr9e c re5resents the +E associated with theresltant :orce, each as a :nction o: the distance !etween nclei.he 5otential=energy well is dee5est at the e?ili!rim s5acing,, and its de5th, ' 4, the energy re_ired to se5arate ionscom5letely.

$#%he distances !etween the centre o: any chlorine ion and thecentre o: the si< nearest sodim ions is less than the distances

!etween the centre o: that same chlorine ion and the centre o: thesi< nearest chlorine ions. Conse?ently the :orces o: attraction

!etween any ion and its neigh!ors are greater than the :orces o:re5lsion, and the crystal is there:ore a sta!le strctre. he n3it strctre in the case o: the s!stance sodim chlorideis the crystal. Sodim chloride does not e


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$#'Sodim chloride will dissol9e readily in water, his is de totwo im5ortant 5ro5erties o: water(i) it :orms a 5olar molecle (0..)(ii) it has a high dielectric constant,

he hydrogen end o: the water molecle is attracted to thenegati9ely. charged chlorine ions and the o


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which is necessary to 9a5orise the solid 5hase and so com5letelyse5arate the

4!oug! I -ow of at least oe tet &oo- o material sciese i w!ic! t!e aut!or

$escri&es a 5so$ium c!lori$e molecule7

constitent atoms. n each case the heat o: 9a5orisation o: onegram=mole is measred so that we shall always !e dealing with thesame nm!er o: !onds, i.e.=AA9ogadros Nm!er.

As wold !e e44 8K2molede5ending 5on the material (#ig. /.1).Between these two e


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n any solid at tem5eratres a!o9e 4 * the atoms are in a stateo: constant 9i!ration and when a solid is heated these 9i!rationsincrease ntil a 5oint is reached where the !onds 3oining theseatoms are r5tred. Atoms then mo9e a5art, that is, melting occrs.

hs there is a relationshi5 !etween !ond strength and melting5oint. : we com5are a series o: li8e elements e.g. the Al8aliMetals o: ro5 , we note that melting 5oint (as a :nction o:

!ond strength) decreases as the atomic nm!er, O, ncreaseshere:ore one can assme that electrons o: higher 5rinci5al

?antm, :orm wea8er !onds so that smaller 9i!rational energiesat lower tem5eratres are s::icient to disr5t these !onds.

Space Lattices

$$ A s5ace lattice can !e de:ined as a distri!tion o: 5articles inthree dimensions sch that e9ery 5article has identical


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srrondings. t is generally con9enient to imagine a s5ace latticeas contining to in:inity in all directions, :or althogh crystalsthemsel9es are o: :inite si7e the nits :rom which they are !ilt aree


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Fig. ./ !e fourtee ra#ais s"ace lattices. (9 = "rimiti#e: 3 = cetre$ o ;a&face: I = &o$' cetre$ a$ F =face cetre$).


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hese are widely sed in =ray analyses and other methods sed inderi9ing crystal strctres.

Miller indices are 5ro5ortional to the reci5rocals o: theinterce5ts which the 5lane ma8es with the three 5rinci5al a


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5arallel to 5lane ABC and will !e re5resented !y the same millerindices.A 5lane on the o55osite side o: the rigin wold ha9e negati9einterce5ts on the a


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$$$Directions throgh a crystal can !e s5eci:ied in terms o: theindices which gi9e the integral co=ordinates o: a 5oint on a linedrawn !etween the 5oint and the origin. Direction indices arewritten in s?are !rac8ets b to distingish them :rom Miller

indices written in 5arentheses ( ) which re5resent a 5lane. n thecase o: the sim5le c!ic cell the direction normal to the.lane (h8l)

is bh8l. #igre !8< indicates some o: the im5ortant directions :ora sim5le c!ic cell. A generalfamily o: directions is written h8l.


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E/perimental -erivation of Cr&stallographic

Planes

$% nter5lanar distances :or crystalline materials are generallydetermined !y =ray methods. he =rays sed are o: shortwa9elength and hence great 5enetrating 5ower. hey are also asnearly as 5ossi!le monochromatic, that is, o: a singlewa9elength. he method sed de5ends 5on the :act that in acrystal, 5lanes occr which are occ5ied !y atoms according to areglar 5attern and that =rays will !e either re:lected ortransmitted at these 5lanes.

#igre /.$$ re5resents diagrammatically two layerso: atoms ina crystal strctre. he layers are distance d a5art. t is assmedthat two incident wa9es stri8e the crystal at and I. he wa9ewhich stri8es the :irst layer at will either !e re:lected ortransmitted to a 5oint I$in the second layer. Here the 5rocess isre5eated. he wa9e re:lected :rom I inter:eres constrcti9ely at++$ with the wa9e which is transmitted :rom to I$ ands!se?ently re:lected 5ro9iding that $I$O$ is an integral

mlti5le o: the wa9elength o: the incident =rays. sing sim5legeometry it can !e seen that

$I $P I $O $P d! sin

$%1 Bragg0s La, #or constrcti9e inter:erence o: =rays,Braggs -aw states that

nP 0d.sin

where is the incident angle o: =radiation. #or the 5rinci5aldi::raction, n P $ and so d can !e calclated

d520 sin

nter5lanar s5acings are 9ery small and since the ma


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sed so that is o: the same order as the inter5lanar s5acings, i.e.a55ro


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The )etallic Bond

$'A!ot three=?arters o: the elements are metals, only a!ot

one= eighth are non=metals, whilst the remainder, the metalloids,ha9e 5ro5erties which are intermediate !etween metals and non=metals. he non= metals are characterised !y relati9ely high electronegati9ities, !y !eing 5oor condctors o: heat and electricity and

!y ha9ing melting 5oints and !oiling 5oints which are generallylow. Metals, howe9er, ha9e relati9ely high melting 5oints and

!oiling 5oints and are good condctors o: heat and electricity.Moreo9er they 5ossess 5lasticity, the 5ro5erty which 5ermits

5ermanent de:ormation withot accom5anying :ractre. All o:these 5ro5erties are related to the natre o: the metallic !ond, and

are connected with the :act that metallic atoms ha9e only one ortwo electrons in theirhe atoms o: a metal are arranged sch that their ions

con:orm to some reglar crystal 5attern (#ig. /.$/) whilst their9alency electrons !eha9e as thogh they are mo!ile, :orming acommon clod@. srronding the ions. hese electrons can !edescri!ed as delocalised and no 5articlar electron !elongs to any

5articlar atom. Althogh the indi9idal electrons are !ond tometallic atoms mch less strongly than are those in non=metallic

elements, the shared electrons !ind metallic ions 9ery tightly intothe lattice since there is attraction !etween the 5ositi9ely chargednclear 5rotons and the delocalised electrons o: the commonclod@. his reslts in the high melting 5oints and !oiling 5ointso: metals, whilst the mo!ility o: the electrons con:ers highcondcti9ity o: !oth heat and electricity.


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$'1 t mst !e admitted that the a!o9e inter5retation o: themetallic !ond is o9ersim5li:ied and :ails nder more detailed?antitati9e e


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Cr&stal Str"ct"res in )etals

$( As we ha9e seen, the :orces !inding the atoms in a metal arenon=directional, and since in a 5re metal all atoms are o: the same8ind and si7e, they will arrange themsel9es in the closest 5ossi!le

5ac8ing 5atterns which are associated with 5ositions o: minimm5otential energy. Most o: the metals o: engineering im5ortancecrystallise in one o: three 5rinci5al ty5es o: strctre in all o:which the atoms are held together solely !y the metallic !ond. hes5heres sed in the illstrations which :ollow re5resent atomiccores !etween which the electron clod will !e distri!ted.

$(1 The Closepacked .e/agonal Str"ct"re 2CP.3;hen we 5lace the snoo8er !alls in the trianglar :rame at

the !eginning o: a game we are in :act 5ac8ing them in the closest5ossi!le arrangement in a single 5lane. he arrangement is thatindicated in #ig. /.$() and it will !e seen that any s5here, , istoched !y si< immediate neigh!ors. -ines 3oining the centres o:these s5heres :orm a reglar he


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here are two +ossi!le 5ositions in which s5heres o: a thirdlayer can !e 5laced either in those 5ositions mar8ed or in thosemar8ed I. : we 5lace them in 5ositions mar8ed , the centre o:each s5here in the third layer will !e 9ertically a!o9e the centre o:a s5here in the :irst layer. his is the close=5ac8ed he


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most metals with a C+H strctre are mch less dctile than thosewith a :ace=centred c!ic strctre.

$(# The Facecentred C"*ic Str"ct"re 2FCC3 n this strctre

the !asic 5ositions o: s5heres in thefirst two layers are the same asthose indicated in #ig. / .$(ii). #or the third layer, howe9er, thes5heres are 5laced in the hollows mar8ed I (#ig. /.$(ii)). hs inthis third layer the s5heres are in di::erent 5ositions :rom those inthe :irst layer (ths di::ering :rom the C+H strctre). : were5resent this third layer !y C then the !ilding order will !eABCABCABCABC... etc. his is the closest 5ossi!le 5ac8ing in ac!ic :orm (#ig. /.$1(i)).

: the nit cell o: this strctre is e


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#igre /. $1(i9) re9eals that the ($$$) 5lane is one o: close=5ac8ing. he direction o: closest 5ac8ed rows o: atoms is b$$4.

Altogether there are :or sets o: closely 5ac8ed ($$$) 5lanes in the:ace=centred c!ic strctre and twel9e sets o: close=5ac8eddirections. As already mentioned, 5lastic de:ormation o: metalliccrystals generally occrs !y the sli55ing o: close=5ac8ed 5laneso9er each other and in the close=5ac8ed directions. #or this reasonthe :ace=centred c!ic strctre wold !e e


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s5here (#ig. /.$6). hs 5ac8ing is not so close as in the other twosystems. So when iron, which is an allotro5ic (/.6.) metal,changes :rom a BCC strctre to one which is #CC on heating to%$4ZC, a measra!le contraction occrs s5ontaneosly

he most closely 5ac8ed 5lanes are ($$4) o: which there aresi


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>&4ZC %$4ZC lZC

=iron =iron =iron =iron

(BCC)

(BCC)

(#CC)

(BCC)

he allotro5y o: solids which relies soley on di::erence in crystalstrctre. is 8nown as .olymor.hism! Many metals are

5olymor5hic and sometimes two 5olymor5hs will !e :ace=centredc!ic and close=5ac8ed he


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nly one metal, radioacti9e 5olonim, is 8nown to crystallisein sim5le c!ic :orm, that is with one atom at each corner o: ac!e. Here any atom is toched !y si< nearest neigh!ors so thatthis 9ery loose 5ac8ing o: atoms has a coordination nm!er o: si(i)) a nit cell contains onecom5lete atom at its centre and one=eighth o: an atom at each o:the eight corners o: the nit c!e gi9ing a total o: two atoms 5ernit cell. Hence the total 9olme o: these atoms in terms o: their

diameter* is0< b2/(D20)/PD/2/

he internal diagonal AC (#ig. /.$>(ii o: the nit cell o:5arameter, a, is o: length e?al to two diameters o: the atomsconcerned.

all metallic strctres with the closest 5ossi!le 5ac8ing o: atoms. n the


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he diagonal AB o: a :ace o: the c!e is e?al to (a0Wa0)

Hence the internal diagonal AC is gi9en !y

(a0Wa0) P (/a0) P0D

a P0D2/

and the 9olme o: the nit cell !y aP b0D2//

'olme o: 0 atoms+ac8ing :raction P

'olme o: nit cell

P D/2/ 4b0D2//

P /2&P 4.46&4

n the #CC system (#ig. /.$>(iii)) each o: the eight comers o: anit cell contains one=eighth o: an atom, whilst each o: the si(i9)) is e?al to two atom diameters (6*) so that

0D P (a0Wa0)

or a P D0Hence

'olme o: 0 atoms

+ac8ing :raction P'olme o: nit cell

P


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P 4.>4his illstrates the magnitde o: the contraction which occrs

when BCC () iron trans:orms to #CC() iron at %$4oC and the5ac8ing :raction increases :rom 4.6& to 4.>.

n a nit cell o: the C+H system (#ig. /.$>(9)) hal: an atom atthe centre o: the 55er :ace is srronded !y si


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c!e). he 9olme o: the nit cell is D/since each side is e?al inlength to one atom diameter, Hence

+ac8ing :raction P b2/ (D20)/4D/

P 26P 4.10/

his con:irms the 9ery o5en 5ac8ing o: atoms in this system.

[Q] The atomic radius of aluminium is 1.43 x 1010 m and itsatomic mass num!er is 26."#. $i%en that &%ogadro's (um!er)

(&) is 6.022 x 1023* mole calculate the densit+ of aluminium.!e atomic ra$ius of alumiium is 1.* 10,10m. Hece t!e

$iameter is gi#e &'> = 2.86 < 10,10m

For t!e F33 structure (alumiium) t!e legt! of oe si$e of t!e uitcell is e?ual to

D2= 2 < 2.86 10,10mHece t!e #olume of a uit cell of alumiium is e?ual to

(2 2.86 10,10)= 6.61/ < 10,2@m

uit cell of F33 alumiium cotais four atoms. 1 -Amole ofalumiium (atomic mass 26.@8) cotais atoms. !erefore% massof four alumiium atoms is

* 26.@8 * 26.@8

=

6.022 1026

Hece% $esit' of alumiium is

Mass of

* alumiium atoms * 26.@8

=

Bolume occu"ie$ &' 6.022 102 6.61/ 10,2@


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* alumiium atoms

= 2./08 10-gAm

i.e. relati#e $esit' = 2./08

!is #alue is slig!tl' !ig!er t!a t!at $etermie$e"erimetall' (2.6@@) $ue to t!e "resece of #arious small ca#itiesi la&orator' (or factor') "ro$uce$ metals. !is will &e $iscusse$ lateri t!is a$ su&se?uet c!a"ters (./.2: C.).

he Crystallisation o: Metals

$4 All 5re elements e


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are colliding continally with the walls o: their container. hecollisions gi9e rise to the 5ressre e


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ty5e o: cooling cr9e shown in #ig. /.$%(i). Howe9er, in mostcases there is some degree o:


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Fig. .1@ '"ical coolig cur#es for cr'stallie a$ amor"!ous soli$s. I (iii) t!erewas isufficiet molte metal to "ro#i$e latet !eat w!ic! woul$ ot!erwise !a#ecause$ a retur to e?uili&rium as i (ii).

nder cooling o: the li?id !e:ore the onset o: crystallisation.his is de to a lac8 o: ncleation o: the system (#ig. /.$%(ii) and(iii)). nce a crystal ncles :orms it 5ro9ides a solid2li?idinter:ace where crystallisation can 5roceed (#ig. /.04). Fnderindstrial conditions ncleation may occr on a 5article o: slag ordross, !t with 9ery 5re li?id metal some degree o: ndercooling will occr. ;hen ncleation ltimately ta8es 5lace the

greater the e


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latent heat may !e a9aila!le to allow the :ree7ing 5oint to !eregained (#ig. /.$%(iii)).

he nclei which :orm, will !e sim5le nits o: the crystal5attern in which the metal solidi:ies, generally C+H, #CC or

BCC. Crystal growth will tend to occr in the o55osite direction

to that in which heat is !eing condcted :rom the melt. hs as5i8e !egins to grow :rom the ncles into a region o: nder=cooled li?id, !t as this occrs, latent heat is li!erated and thiswarms 5 the li?id in :ront o: the growing s5i8e. Hence growtho: the s5i8e is retarded and as a reslt secondary s5i8es !egin togrow :rom the 5rimary one and these are :ollowed !y tertiarys5i8es (#ig. /.0$). hese 5rimary, secondary and tertiary !ranches:ollow crystallogra5hic 5lanes and gi9e rise to the general

reglarity o: the strctre. he crystal s8eleton which de9elo5s iscalled a dendrite, a re:erence to its tree=li8e growth (8. dendron,a tree), in which the 5rimary, secondary and tertiary armsresem!le the trn8, !ranches and twigs o: a tree.


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he main !ranches o: the dendrite contine to grow ntil theoter :ringes ma8e contact with those o: neigh!oring dendrites(#ig. /.0/). Since they are ths restrained :rom :rther otwardgrowth these ee$rites &egi to $e#elo"from ewl'forme$ uclei &' "uttig out "rimar' a$ seco$ar' arms. (ii) ertiar'arms form a$ meet ot!ers growig i t!e o""osite $irectio. (iii) >e$ritescotiue to grow util t!eir outer arms touc! t!ose from eig!&ourig $e$rites.istig arms t!e t!ic-e. (i#) D!e t!e metal is com"letel' soli$ t!ere is little


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e#i$ece of t!e $e$ritic met!o$ of growt! sice i a "ure metal all atoms aresimilar. !e ol' grai &ou$aries are #isi&le.

the atoms within anyone crystal are reglarly s5aced with res5ectto each other in a crystal lattice.

: the metal nder consideration is 5re only crystal !ondarieswill !e 9isi!le when a section o: the metal is e


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crystals. Iears ago this was 8nown as grain !ondary cement !r:ortnately this misleading term

has :allen into disse. he e


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chill crystals will reslt (#ig. /.06(ii)). As the mold warms 55rogressi9ely and the rate o:

cooling is redced a stage is reached when crystal growth inwardsis !alanced !y heat :low otwards. #resh nclei are not :ormed andso the e


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since there is little ndercooling. Conse?ently the resltantcrystals tend to !e large and @e?i=a


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molecles are nits relies on 9an der ;aals :orces o5erating!etween the molecles. hs water crystallises to :orm ice. Herethe :orces o: attraction are s55lied !y the hydrogen !ond (0..).

6iant )olec"les

$51 Threedimensional Cr&stals Althogh in a geometricalsense all crystals will !e three=dimensional, the term is sed hereas a re:erence to a


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Fig 3.2# !e cr'stal structure of $iamo$. (i) !e uit cell% i$icatig t!at !erecar&o !as a coor$iatio um&er of four: (iii) a$ (i#) s!ow !ow $iamo$ ca &ecosi$ere$ as a cubic structure.ote t!at i (ii) ot all #alecies are use$ u" i t!e frige atoms of t!e cr'stal%w!ic! will of course &e cotiuous i "ractice. (< re"resets t!e same atom i

t!e s'stem i eac! case.)

strctre. hs, in #ig. /.0&(i9), only :or ot o: the eight c!icnits has a car!on atom at its centre whilst many o: the cornersites are nsed.

Diamond can there:ore !e regarded as a three=dimensional giantmolecle (or macromolecle), Cn! n the Crystal so 5rodced thecar!on atom has a coordination nm!er o: :or. Diamond ismechanically strong and is the hardest s!stance 8nown.Moreo9er it has an e


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car!on atom is srronded !y three other car!on atoms (#ig./.0%(i)) so that the coordination nm!er o: car!on in thisinstance is three. As #ig. /.0%(ii) indicates each car!on atom

ses only three o: its oter shell electrons to :orm co9alent!onds. he :orth electron in each case can !e regarded as !eingshared to some e


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$5$ )olec"lar Cr&stals Molecles are se5arate sel:=containednits as are atoms so that it is 5ossi!le :or them to arrangethemsel9es in a crystalline :orm. ;hilst the atoms within amolecle are held together !y co9alent !onding, the molecles

themsel9es are !onded !y 9an der ;aals :orces. he elementtellrim :orms long=chain molecles and these in trn arrangethemsel9es in a 5attern with li8e molecles to 5rodce crystals.Many 5olymers are regarded as !eing amor5hos, that is,noncrystalline, yet many do 5ossess some crystalline regions8nown as fringed micelles! hese are o:ten lin8ed together !y achain molecle which [ e


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inclded at sita!le sites then the strctre can no longer remain:lat !t is drawn 5 into glo!lar :orm (#ig. /./$(ii)).

his is similar to the ty5e o: constrction sed architectrally in

geodesic domes sch as that hosing Science ;orld in'anco9er. n :act the name :llerene@ is deri9ed :rom that o: the,FS engineer and architect Richard Bc8minster #ller whode9elo5ed geodesic design. Nearer to home, the 5anels o: amodern soccer !all :ollow a similar 5attern. #llerenes contain

e9en nm!ers o: car!on atoms :rom 04 5 to as many as 644 !tthe more symmetrical and sta!le molecles are those with !etween0& and >4 car!on atoms . he :irst :llerene to !e 5rodced and isolated in any ?antitywas C64, 8nown as !c8minster :llerene. his can !eman:actred !y stri8ing a car!on arc in a low=5ressre argonatmos5here. he car!on 9a5or so :ormed condenses as a dstwhich contains a 5ro5ortion o: C64 molecles. his can !e

dissol9ed ot o: the reside with !en7ene in which it :orms amagenta colored soltion. he :llerene will crystallise ot :romthe !en7ene in the :orm o: magenta :ace=centred c!ic crystals. n the :llerene molecle the e9en nm!er o: car!on atoms isarranged o9er the sr:ace o: a closed hollow cage. Each atom is

!onded trigonally to its three neigh!ors (#ig. /./$(i)) !y !onds


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con:orming to a 5olyhedral networ8 consisting o: $0 5entagonsand n he


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!oncr&stalline S"*stances

$7 All tre solids are crystalline in natre. Howe9er, a nm!er o:a55arently solid materials are amor5hos, that is, their atoms ormolecles do not con:orm to any reglar geometrical 5atterns.Solids sch as glass and 5itch are com5arati9ely rigid and are

!ro8en !y sdden im5act, !t i: a steady load is a55lied o9er along 5eriod o: time the material will :low. A 5iece o: 5itch will:low 9ery gradally, o9er a 5eriod o: months, to ta8e the sha5e o: a9essel into which it has !een 5laced. A glass rod, s55orted at eachend, will sag nder its own weight i: le:t in this 5osition :or a long

time. he de:ormation 5rodced will !e .ermanent and nli8e thetem5orary elastic de:ormation 5rodced when an elastic solid islightly stressed within its elastic limit.

hese amor5hos solids do not melt at a de:inite tem5eratreas do 5re crystalline materials. nstead they so:ten gradally and

!ecome more mo!ile ths resem!ling li?ids o: 9ery high9iscosity. he 9iscosity of a li?id increases as its tem5eratre:alls and i: it is cooled !elow its :ree7ing 5oint withot

crystallisation ta8ing 5lace its 9iscosity may reach a 9ale asmch as $4$4 times that o: water. 'iscosity is related to 9an der;aals :orces. As tem5eratre :alls thermal 9i!rations o: themolecles are redced and so 9iscosity increases, since 9an der;aals :orces will also increase.


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he low mo!ility o: large molecles in relation to their thermalacti9ation was :irst in9estigated in glasses and so terms sch asglass and glassiness are sed to descri!e the 5ro5erties and

!eha9ior o: amor5hos solids in general. At high tem5eratresglasses :orm normal li?ids which :low nder the a55lication o:

shear stresses As the glass cools normal contraction in 9olmeta8es 5lace and, althogh crystallisation does not set in, a 5oint isachie9ed where a change in the rate o: contraction occrs (#ig././/). Below this tem5eratre, called the glass transitiontem.erature ($/.6), there is no :rther rearrangement o: atom

5ac8ing and any contraction as does ta8e 5lace is de only to aredction in 9i!rations o: the atoms as thermal energy is lost.


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%

)echanical Properties

%1Strctral materials sed in mechanical and ci9il engineering5ractice mst generally ha9e strength! his 9ale is a measre o:


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the e


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inclde elasticity, hardness, toughness and also cree. andfatigue5ro5erties ($6. $6.1). n each case the 5ro5erty is associated withthe !eha9ior o: the material towards the a55lication o: :orce andthe engineer is generally interested in the density o: :orce@ which

is necessary to 5rodce some de:inite amont o: de:ormation,either tem5orary or 5ermanent in the material

%1# Stressa measrement o: density o: :orces@ de:ined as :orce5er nit area o: cross section. he S nit o: stress is the +ascal(+a) which is e?i9alent to a :orce o: one Newton acting on an areao: one s?are metre, i.e. N2m0or Nm=0. Since the Newton is a smallnit o: :orce relati9e to the s?are metre we shall generally !e

dealing with stresses measred in the region o: millions o: +ascalsand the :orce re?ired to !rea8 in tension a steel mem!er ones?are metre in cross section is di::iclt to 9isalise. Howe9er,since

M9a = MAm2= Amm2

we can thin8 in terms o: the latter nit (=mm6) since it will !ee?i9alent to the nm!er o: nits re?ired to !rea8 in tension a

wire or :i!re slightly o9er $ mm in diameter. Numerically o:corse it will !e the same as that e


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P +2r0

P 44 2(4.44/)0 N2m0

P $$>4>0 N2m0

P $.$1 M+a

%1$ Strainre:ers to the 5ro5ortional derormation 5rodced in amaterial nder the in:lence o: stress. t is measred as the

nm!er o: metres o: de:ormation s::ered 5er metre o: originallength and is a nmerical ratio.

89: The original ga"ge length 2Lo3 marked on an al"mini"m

test piece is %; mm The test piece is strained in tension so

that the ga"ge length *ecomes %#$ mm Calc"late the

strain 238A:P ncrease in length2-o

P (0./ ^ 4)2 4 P 4.41>1Strain is sally ?oted as a 5ercentage, i.e.

P 4.41>1 < $44 P 1.>1

Strain may !e either elastic or .lastic! Elastic strain is re9ersi!le

and disa55ears when the stress is remo9ed. Atoms are dis5laced:rom their initial 5ositions !y the a55lication o: stress !t whenthis stress is remo9ed they retrn to their initial 5ositions relati9e totheir neigh!ors 5ro9ided that the strain has !een o: an elasticnatre. Strain is roghly 5ro5ortional to the a55lied stress (#ig..$(i)), and, :or 5ractical 5r5oses, the material o!eys Hoo8es

FnitsP (mm ^mm)2mm


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-aw. his states that, :or an elastic !ody, strain 5rodced isdirectly 5ro5ortional to stress a55lied.

%1%


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P $.6& < $4=/m 2$4m

P 4.444$6&

EP 2 P /$./ MN2m02 4.444$6&

P $&61> MN2m0

2 P $&6.1 5a

Alternati9ely" can !e deri9ed :rom the slo5e o: the linear 5ortiono: the

stress2strain diagram :or the material, i.e.

Slo5e < gage length

"5

Cross=sectional areahe so5histicated technology o: these closing years o: the

twentieth centry o:ten in9ol9es consideration o: the mass o:material re?ired to 5ro9ide the necessary strength and rigidity in astrctre. his is 5articlarly so in the aero=s5ace and othertrans5ort indstries and in :act in any sitation where wor8 doneagainst gra9ity mst !e 5aid :or in terms o: increasingly e


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*g2m/

*g2m/

P N2m0

%1' Plastic Strainhis reslts when a material is stressed to thee


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sectional area of the test 5iece i: reslts are to !e com5ara!le. Sincethe !l8 o: 5lastic de:ormation occrs at the nec8 (!etween O andI) it is clear that a 5ercentage elongation !ased on OI as the gagelength wold gi9e di::erent reslts :rom that !ased on I as the

gage length. Conse?ently tensile test 5ieces shold

!e geometrically similar and are 8nown as .ro.ortional test.ieces! hey are sally circlar in cross=section and BS+ laysdown (B.S.$& +art $ and 0Q) that :or 5ro5ortional test 5ieces

LoP 1.61 S4

where L


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%1( Stress=strain -iagrams;hen corres5onding 9ales o: stressand strain deri9ed dring a tensile test are 5laned gra5hically it is:ond that each ty5e o: material is re5resented !y a characteristiccr9e. Materials o: negligi!le dctility, sch as :lly hardenedsteels,cast iron and concrete, ndergo little or no 5lasticde:ormation !e:ore :ractre (#ig. .(i)). hat is, there is no yield

5oint and only elastic e


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%1(1 Secant modulus Many so:t materials 5articlarlythermo5lastics ($0.1.) do not o!ey Hoo8es -aw and the stress=strain diagram shows no region where a linear relationshi5 a55lies

so that it is not 5ossi!le to ma8e a sim5le measrement o: IongsModls, "! As a re5resentati9e alternati9e we can calclate the

secant modulus o: the material. his is the ratio o: nominal stressto the corres5onding strain at some s5eci:ic 5oint on the:orce2e


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Fig. *.* Ee"resetati#e stressAstrai $iagrams for #arious t'"es of material. (i)o,$uctile material. (ii) emi,$uctile material. (iii) a$ (i#) >uctile materials.T = tesile stregt!: B = &rea-ig stregt!: Y = 'iel$ stress a$ P = "roof stress.


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;here A is the initial cross=sectional area o: the test 5iece. #ormost materials the secant modls associated with a strain o: 4.0is measred,thogh in some cases a strain o: 4.l is s5eci:ied.

.$.6.0 Tangent modulus Sometimes the tangent modulus is called:or. his is determined !y drawing a tangent to the :orce2e


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The test piece had a crosssectional area of '; mm# and a

ga"ge length of '; mm

Plot the force=e/tension diagram for the material over the

range of readings given and determine>

2i3 the tangent mod"l"s at ;# ? strain>2ii3 2ii3 the secant mod"l"s at ;'? strain

bA (i) Tangent modulus at

PAB 4./ mm

P$$14N2mm

Hence modls at 4.0 strain is e?al to

$$14 < 14 mm P $$14 N2mm#

14 mm#

P $.$1 +a


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ii) Secant modulus at

// N

Slo5e o: S P4.01 mm

P $//6 N2mmHence

Slo5e o: S < gage length

Secant modls P Cross=sectional area

$//6 < 14 mm

P14 mm0

P $//6 N2mm0

P $.//6 +a

%14 The tensile strength o: a material is deri9ed !y di9idingthe ma


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wold !e necessary to ta8e into accont the diminishing cross=section !y measring the minimm diameter at the nec8 with eachreading o: the :orce sed (#ig..>)

enerally measrement o: tre stress in this manner isim5ractica!le and the 9ale re:erred to as the engineering stress iso: more se in 5ractice. Force

Engineering stress P

riginal area o: cross=section

Howe9er, it shold !e a55reciated that the ordinate sally la!eledstress in the ma3ority o: 5!lished diagrams nearly always re:ersto this engineering stress rather than to tre stress. he redctionin cross= section o: dctile materials dring 5lastic :low leads tothe a55arent anomaly that the !rea8ing strength is less than thetensile strength. n :act o: corse the true !rea8ing stress is the

greater as indicated in #ig. .>.


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89: The follo,ing res"lts ,ere o*tained d"ring the tensile

testing of a heattreated nickelchromi"mmol&*den"m steel>

#orce (*N) $14 $44 $14 $>1 044

E/tension 2mm3 ;;;7 ;17 ;#5 ;$$ ;$7##' #'; #4' $;; $1; $1; #7;

;%4 ;'7 11; $%; ';; (%; 4%;2Break3

The original diameter of the test piece ,as 1( mm and the

ga"ge length 5; mm The diameter at fract"re ,as 1#% mm

-etermine

2i3 Tensile strength@

2ii3


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%ma#(8N)

(i) T5

Ao(mm0)

P/$$204$ 8N2mm0

P $.1> 8N2mm0 P $.1> 5a

(ii) EPSlo5e o: E 3-2A

$14 (8N) < &4 (mm)P

4.0& (mm) 304$ (mm0)

P 0$/.00 8N2mm0

P0$/.00+a

(iii) 8N wold

5rodce this amont o: 5ermanent e

P04$

5ma


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P $.0>% 8N2mm0

P $.0>% +a

E.4mm < $44 &4mm

P %.01

AR(9) ARP < $44 Ao

P (04$ = 3($0.)0 )

mm03$44 04$ mm0

P /%.%$

%15 he 5henomenon descri!ed a!o9e may !e e


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wor-hardening, the natre o: which is discssed later (1.>), setsin. he stress=strain cr9e :ollows an a55ro


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- -

nP =$ or n W$PL< L1#or annealed co55er

logP $.61 (interce5t with coordinate at a)

Hence


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P .>

#or ;or8 hardened co55er

logP $.%& (interce5t with coordinate at !)

Hence

P %1.1

%#$he /icer2s *iamond %yramid Test (or Diamond +yramidHardness est) ses a diamond 5yramid indenter o: geometricalsha5e indicated in #ig. .$0. his has the :ollowing ad9antageso9er methods which se a s5herical steel indenter

(i) the 5yramid is o: constant angle ma8ing the choice o: asita!le%*6 ratio nnecessary

ii) the diamond 5yramid is less li8ely to distort nder high:orces than is a steel !all.

he 'ic8ers Hardness,H+, is related to the a55lied :orce,%, andthe sr:ace area o: im5ression in the same manner as is BrinellHardness, 9i7

#orce (%

H+ PSr:ace area o: im5ression

6% sin 20 P

d0

$.&1 + P 8g:2mm0

d0

where is the angle ($/6Z) !etween o55osite :aces in the diamond5yramid and d is the mean length o: diagonals (d$ and d6) o: theim5ression (mm). Hardness indices, H+, 9ary !etween a55ro


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A nm!er o: other hardness tests sch as Roc8well (which seseither a diamond cone or a steel !all) are also in se. #or most metallic alloys tensile strength is a55ro


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nder the stress2strain diagram is related directly to the energynecessary to !rea8 a material . n :act some materials, when hardened and strengthened !y asita!le 5rocess, lac8 toghness whereas in their so:test and most

dctile state they are e


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ther )echanical Tests

%% Many other tests ha9e !een de9ised in order to assess s5eci:icmechanical 5ro5erties o: interest in 5ractical engineering. #ore


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t may ha9e !een noticed that no mention has !een made hereo: cree5 or :atige=testing. hese to5ics are associated with metal:ailre and will !e dealt with later in this !oo8 ($6. and $6.1).

'The -eformation of

)aterials

'1 A well=worn cliche o: yesteryear, mch too old to ha9eoriginated :rom any o: today@s 5sedo=scienti:ic 3ornalists,s5eclated 5on the 5ossi!le e::ect o: an irresisti!le :orce meetingan immo9a!le o!3ect. n :act any :orce may !e regarded asirresisti!le in so :ar that no o!3ect is com5letely immo9a!le, sinceall s!stances when s!3ected to mechanical stress s::er somechange in sha5e. Many retrn to their original :orm when the stressis rela


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5ossess high degrees o: !oth elasticity and 5lasticity. hey can !esha5ed !y com5ression and tension and a:ter sch treatment theirstrctres are s!stantially na::ected since they ha9e s::eredde:ormation !t ha9e retained their continity.

A sim5li:ied e


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res5ect to its neigh!or. here is no disr5tion, howe9er, at thisstage !ecase o: the mtal attraction !etween 5ositi9e ions andthe srronding electron clod. he 5lane along which mo9ementoccrs is called asli. .lane!

A crystal o: a s!stance sch as sodim chloride consists o:5ositi9ely charged sodim ions and negati9ely charged chlorineions arranged so that each ion is srronded !y those o: o55ositecharge. Any attem5t to 5rodce sli5 in the b$44 direction (#ig.

1.0(ii)) will :ail since this wold !ring li8e ions into closer contact.-i8e ions wold immediately re5el each other so that the twohal9es o: the crystal se5arate. hs the crystal shatters along aclea+age5lane.

Becase o: this se9ere restriction in the a9aila!ility o: sli5

systems in ionically !onded materials, sch materials tend to:ractre at :airly low stresses=lower than those at which sli5 woldotherwise occr. n ceramics !oth ionic and strong co9alent !ondsare 5resent. Conse?ently one might e


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tensile strengths tend to !e low. his is de 5rinci5ally to the5ro5agation o: micro=crac8s which act as stress raisers.

Plastic -eformation in )etals'#he :act that a metal can ndergo !oth elastic and 5lasticde:ormation is demonstrated dring a tensile test in which the test

5iece is tested to destrction. hat 5lastic de:ormation ta8es 5lace!y some :orm o: sli5 is o!ser9a!le sing an ordinary metallrgicalmicrosco5e (#igs 1./ and 1.).

#ig. 1./ he :ormation o: sli5 !ands in a metal stressed !eyond itsyield 5oint. (i) Be:ore stressing. (ii) A:ter stressing=!loc8s o:

sli55ed atoms some 4 atoms wide and 5 to 44 atoms high castshadows on the sr:ace o: the metal gi9ing an a55earance as in(iii).: a dctile metal or alloy is 5olished and etched to re9eal itscrystal strctre and is then s?ee7ed laterally in a 9ice, ta8ing carenot to damage the etched sr:ace, the shadows cast !y the ridges:ormed as sli5 occrs can !e seen as hair=li8e lines (#ig. 1./(iii)) ata magni:ication o: $44


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'#1 n #CC metals li8e co55er sli5 sally occrs along the$$$] 5lanes (#ig. /.$1(i9)) since the 5er5endiclar distance

!etween these 5lanes is greater than that :or any other set o: 5lanesin the crystal and the atomic 5o5lation in these 5lanes is denser

than in any other :amily o: 5lanes. hs the 5lanes o: easiest sli5are also those o: densest 5ac8ing.


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he sli5 directions in the #CC strctre are the $$4 :amily (:ace

diagonals). here are :or e::ecti9e sets o: 5lanes !t each 5lanehas three 5ossi!le sli5 directions, gi9ing a total o: twel9e directionsin which sli5 cold ta8e 5lace with e?al ease in a #CC crystal.n#ig. 1.1(i) only two o: the :or 5lanes are shown :or the sa8e o:clarity.'##n the C+H strctre the (444$) or !asal 5lanes are o: similararrangement to the ($$$) 5lanes in the #CC strctre. Howe9er, inC+H there is !t one sch set o: !asal 5lanes instead o: :or ($$$)

5lanes in #CC. Hence there are only three easy sli5 systems inC+H (#ig. 1.1(ii)). his is re:lected in the di::erences inmechanical 5ro5erties !etween the mallea!le and dctile #CCmetals li8e alminim and co55er, and the relati9ely !rittle C+Hmetals li8e 7inc where sli5 is restricted.As indicated in #ig. /.$6 the BCC strctre does not contain any

5lanes o: closest 5ac8ing as are 5resent in the #CC or C+Hstrctres. Howe9er, sli5 occrs along those 5lanes where the

density o: 5ac8ing is greatest. here are si< sch 5lanes ($$4)where sli5 can ta8e 5lace with two directions b$$$ in each, gi9inga total o: $0 sli5 systems.


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'#$Normally we are dealing with 5olycrystalline metals !tmch :ndamental in:ormation on the natre o: sli5 has !eeno!tained !y stdying the !eha9ior o:single crystals o: metals instress hese single crystals can !e grown nder care:llycontrolled la!oratory conditions and then machined as test 5ieces.

Dring a tensile test sli5 occrs along 5arallel sli5 5lanes (#ig.1.6) the 5recise direction o: which can !e o!ser9ed. Bydetermining the yield stress o: sch a crystal e


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CRP y.cos . cos n di::erent single crystals o: the same material 9ales o: and will 9ary, that is crystallogra5hic 5lanes will !e di::erentlyorientated with res5ect to the a


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magnitde less than that dedced :rom theoretical considerations!ased on instantaneos [!loc8 sli5.

he sggestion that atoms in a metallic Crystal are arranged in arigid 5attern :rom which there is no de9iation has long since !een

re3ected as e9idence to the contrary has accmlated o9er theyears. Crrently the metallrgist thin8s o: a metallic crystal asha9ing atoms arranged according to some general o9erall 5attern

!t in which all manner o: local :alts and de:iciencies can e and 1,&), whilst =ray= in9estigations (/.) will


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Fig. 5.#Furt!er cr'stal $efects. (i) Frenkel defect is a #acac' "ro$uce$ w!ea atommo#es (as a result of a icrease i t!ermal #i&ratio) ito a self interstitial"ositio within t!e cr'stal. (ii) Schottky defect is a #acac' forme$ i a similarmaer &ut t!e $is"lace$ atom ta-es u" a lattice "ositio o t!e surface of t!e

cr'stal.re9eal the general crystal 5attern o: a metal they cannot detectsingle lattice :alts and the e


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'$1 ne o: the most im5ortant o: these lattice :alts was5ostlated more or less inde5endently in $%/ !y aylor, +olanyiand rowan. n its sim5lest :orm it consists o: a region containingan e


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he arrangement o: atoms in the region o: an edge dislocation isshown in #igs 1.% and 1.$4. he 5resence o: dislocations in sch

diagrams is generally indicated !y the sign. Fnder the action o:ade?ate stress the dislocation will mo9e 5rogressi9ely throgh thecrystal to the right (#ig. 1.$$) ntil it ltimately :orms a sli. ste.as indicated. n 5ractice the mo9ement may !e halted !y some

other :alt or discontinity within the crystal or, alternati9ely, !ythe crystal !ondary.

'$#+ossi!ly +ro:. N. Motts classical analogy o: the methodsa9aila!le :or smoothing wrin8les :orm a hea9y car5et e


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Retrning to or car5et, one can with 9ery little e::ort coa< thewrin8le along with ones toe so that it mo9es, ste5 !y ste5, acrossthe :loor (#ig. 1.$0(ii) to (i9). nly local :riction in the immediate9icinity o: the wrin8le then needs to !e o9ercome. his is

analogos to the 5rogressi9e mo9ement o: an edge dislocationwhere the only inter=atomic :orces !eing o9ercome at any instantare those acting in the locality o: the dislocation. n this way

Fig.5.11!e mo#emet of a e$ge $islocatio u$er t!e ifluece of stress.!e uit sli"% &% is -ow as t!e urgers #ector of sli".

;e can e


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'$$Sli5 may also occr !y the mo9ement o: ascrew dislocation,the 5rinci5le o: which is shown in #ig. 1.$/. Fnder the in:lenceo: shear stress this ty5e o: dislocation also mo9es in the sli5 5lane.Howe9er, dislocations are generally o: a more com5le< natre,

which can ne9ertheless !e resol9ed into a com!ination o: the edgeand screw ty5es (#ig. 1.$).

The 6eneration of -islocations'%;e ha9e seen that when a metal is 5lastically de:ormed sli5ta8es 5lace on a nm!er o: 5lanes within any crystal (#ig. 1./).he :act that these sli5 5lanes are 9isi!le nder the microsco5e at:airly low magni:ication indicates that not only are the 5lanes?ite :ar a5art !t that the ste5s are o: considera!le thic8ness. QHowe9er. a dislocation mo9ing along a sli5 5lane and rnning otat the o!ser9ed sr:ace o: the metal can only 5rodce a sr:ace

ste5 o: one atomic s5acing in de5th (#ig. 1.$$) and it woldre?ire a large nm!er o: dislocations. all on the same 5lane, to

5rodce the resltant large ste5 o: 44 atoms o!ser9ede


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a 5lasi!le e


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Fig.5.15!e o"eratio of a Fra-,Eea$ source;

he stress necessary to 5rodce new dislocations is mch greaterthan that re?ired to mo9e those already 5resent. his relationshi5is illstrated !y the tensile 5ro5erties o: metallic whis8ers. heseare 9ery small hair=li8e single crystals grown nder care :llycontrolled conditions and generally containing only a singledislocation which rns along the central a


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Fig. 5.1, Gsig a sesiti#e micro testig mac!ie o a #er' small s"ecime

cotaiig a fiite um&er of $islocatio cetres re#eals t!e icremetal atureof sli" (i). I a ormal tesile test o a large s"ecime (ii) sli" is ta-ig "lacecotiuall' at a #er' large um&er of cetres so t!at a regular cur#e is o&taie$.

!eing se:l :or determinations on single whis8ers other small

diameter s5ecimens containing a limited nm!er o: dislocationcentres cold also !e tested. #igre 1.$>(i) shows the. stress2straindiagram :or a small thin s5ecimen tested in a Marsh machine. Herethe stress2strain cr9e is in the :orm o: a series o: ste5s since themachine is s::iciently sensiti9e to detect the generation o:dislocations :rom an indi9idal sorce. ;hilstsingle dislocations,


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cold not !e detected e9en !y the sensiti9e Marsh machine the5rodction o: a dislocation sorce releases a nm!er o: dislocationssimltaneosly so that the total amont o: sli5 associated with onesorce is measra!le.

;ith :rther increases o: stress there are 5otential dislocationsorces ready to generate dislocations and these are 5resma!lytriggered !y the in:low o: thermal energy. Sorces are triggered?ite erratically and the sli5 5rodced is 9irtally instantaneosgi9ing a series o: irreglar ste5s illstrated. n the case o: a largetest 5iece (#ig. 1.$>(ii)) so many centres o: dislocation are !eingtriggered continosly throghot the s5ecimen that the ty5icalsmooth cr9e o: a stress2strain diagram is 5rodced.

'%$nteraction !etween dislocations mo9ing on the same or onnear!y 5lanes mst !e considered 5articlarly in so :ar as theya::ect the distri!tion o: strain energy. he 5resence o: the e


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fig.C.1@ >islocatios of t!e same sig will re"el eac! ot!er.

Energy in the srronding wood in a manner similar to the eislocatios of o""osite sig will te$ to attract (i) a$ so ai!ilate

eac! ot!er.

close 5ro


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(#ig. 1.0$) !t the total strain energy will !e redced de to theannihilation o: the dislocations


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Fig. 5.22 grai &ou$ar' w!ere t!e agle of misfit is small. (i) I$icatig t!e"ositio of t!e cr'stal &ou$ar'. (ii) 3r'stals oie$ wit! e$ge $islocatios"reset. (fter Eea$% >islocatios i 3r'stals.)

-islocations ithin /r+stal oundaries

'' hat grain !ondaries are a region o: some disorder hasalready !een sggested (/.>./). Howe9er, when the angle o:mis:it !etween ad3acent crystals is small an atomic arrangementsimilar to that in #ig. 1.00 may !e 5rodced. Here the two crystalsare a!le to 3oin more or less continosly along most o: theircommon !ondary with, o: corse, a certain amont o: elasticstrain. Since ad3acent 5lanes in the two crystals are not 5arallelsome o: these 5lanes mst terminate at the !ondary gi9ing rise to

line im5er:ections 5assing throgh the crystal normal to the 5laneo: the 5a5er. hese :alts mani:est themsel9es as sim5le edgedislocations.

:* is the s5acing !etween these dislocations, the interatomics5acing and % the angle o: mis:it, then

6

Sin == P =====

0 *

=--

6*

hs B

*5----------------

0 sin (20)

since e is small

! DP=====


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as increases the 9ale o: * decreases, i.e. the dislocationsmo9e closer together ntil their indi9idal identity is lost and the

!ondary !ecomes a general disordered region (#ig. /.01).

''1he 5assage o: a dislocation across a grain !ondary mst !ee


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DE#RMAN BI ;NNN

'( Althogh sli5 is the more signi:icant 5rocess !y which5lastic de= :ormation occrs in metals !rie: mention mst !emade o: the 5henomenon 8nown as twinning! ;hilst sli5 is a

5rocess associated with a line de:ect (the dislocation), twinningis related to a.lane de:ect (the twin !ondary).

n sli5 all atoms in a !loc8 ha9e mo9ed the same distance whensli55ing is com5lete (#ig. 1.0i)) !t in de:ormation !y twinning(#ig. 1.0(ii))


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atoms within each sccessi9e 5lane in a !loc8 will ha9e mo9ed di::erent distances.;hen twinning is com5lete the lattice direction will ha9e altered sch that one hal:o: the twin is a mirror image o: the other hal:, the twinning line corres5onding tothe 5osition o: a mirror. winning, li8e sli5, also 5roceeds !y the mo9ement o:dislocations. he net reslt o: a twinning 5rocess on the lattice o: a crystal is

de5icted in #ig. 1.01.

he stress re?ired to 5rodce de:ormation !y twinning tends toDe higher than that necessary to 5rodce de:ormation !y sli5.winning is more li8ely to occr in metals which are shoc8 loadedat low tem5eratres. hs in BCC iron sdden loading at low,tem5eratres 5rodces thin lamellar twins which are generally8nown as Nemann !ands. winning is commonly encontered inC+H metals li8e 7inc, whilst when a !ar o: tin is !ent sddenly the:ormation o: twins can !e heard ta8ing 5lace. he Ancients 8new

this as the cry o: tin.

'(1win=:ormation ta8es 5lace dring the annealing o: somecold= wor8ed metals. n this case recrystallisation is initiated at a

5lane instead o: at a 5oint sorce and twin !ands are o!ser9edwithin the new crystals as a reslt. hese annealing twins arecommon in co55er, !rasses, !ron7es and astenitic steels==alloyswith low stac8ing :alt energies=and are di::erent in this res5ect:rom the mechanical nins nder consideration here. hey are

:ormed not !y mechanical shear !t as 5art o: the 5rocess o: graingrowth.


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ork .ardening

'4As de:ormation 5roceeds==whether !y sli5 or !y twinning=themetal !ecomes harder and stronger and a stage is reached when

:rther de:ormation is im5ossi!le. Any increase in stress lead onlyto :ractre. At this stage, when tensile strength and hardness are ata ma)solution hardening (>.1) and dis.ersion hardening (8:!8!Eand $./). n solid soltions the mo9ement o: dislocations is


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im5eded !y irreglarities in the lattice strctre cased !y the5resence o: solte atoms (#ig. 1.>), whilst the 5resence o: small!t strong 5articles dis5ersed as se5arate 5hases throgh the metalwill also halt the mo9ement or a dislocation j:ront.

Stressrelief and Recr&stallisation

'5 As we ha9e seen a cold=wor8ed metal is in a state o:considera!le mechanical stress reslting :rom elastic strainsinternally !alanced. Mch o: the loc8ed 5 strain energy isassociated with the 5resence o: dislocations. n the region o: +

(#ig. 1.06) the lattice is in tension and since atoms there aredis5laced :rther a5art the region will 5ossess 5otential energy.he high energy associated with the congregation o: dislocationsat grain !ondaries has !een mentioned as a reason why corrosionoccrs more readily there than elsewhere in the Strctre. hesehigh=energy regions also initiate recrystallisation dring anannealing 5rocess so that new seed crystals a55ear :irst at the oldgrain !ondaries o: the original distorted strctre (#ig. 1./4).

n the early stages o: an annealing 5rocess some degree o:stress relie: occrs as atoms mo9e o9er limited distances into

5ositions nearer to e?ili!rim. At this stage, howe9er, there is no

alteration in the distorted a55earance o: the strctre and in :acthardness and tensile strength remain at the high 9ale 5rodced

!y cold wor8.At low tem5eratres the mo9ement o: dislocations is restricted

to glide along sli5 5lanes, !t at higher tem5eratres in edgedislocation is a!le to mo9e ot o: its sli5 5lane !y a 5rocess


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8nown as clim! : the terminal row o: atoms (normal to the 5laneo: the 5a5er) in the e


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'51 he di::sion o: interstitial atoms towards an edgedislocation (#ig. 1.0&(i)) can gi9e rise to negati+e clim whilst thedi::sion o: atoms away

n this instance we are interested mainly in 5ositi9e clim! and the redction o: str

associated with it. t can ta8e 5lace most easily !y the di::sion (>.) o: 9acanc

towards the dislocation as sggested in #ig. 1.0>. Here atoms migrate :rom the end

the hal:=5lane to :ill 9acancies which a55roach them !y means o: the di::s

mechanism.


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:rom the hal:=5lane to !ecome interstitials will case.ositi+e clim(#ig. 1.0&(ii)). All o: these 5rocesses necessitate the mass migrationo: atoms !y di::sion and clim! is there:ore 5ossi!le only !ythermal acti9ation. he redction o: strain energy dring annealing

will most li8ely in9ol9e 5ositi9e clim! !y the di::sion o:9acancies.

he reader may 5ossi!ly !e worried !y the :act that in the a!o9edescri5tion o: the mechanism o: clim! the assm5tion has !eenmade that a whole row o: atoms is remo9ed (or added)simltaneosly, whereas in 5ractice, indi9idal 9acancies or smallgro5s o: 9acancies di::se to (or :rom) the dislocation. #igre 1.0%illstrates clim! in9ol9ing a short section


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o: a dislocation line, reslting in the :ormation o: two ste5sgenerally descri!ed asGogs!

Dring an annealing 5rocess elastic strains are :irst dissi5ated !ylimited mo9ements o: atoms in the manner of those mentioneda!o9e. hen, at a higher tem5eratre, wholesale recrystallisation o:the distorted strctre occrs and is accom5anied !y a :all in tensilestrength and hardness to a55ro


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dissi5ating local strain which might otherwise gi9e rise to stresscorrosion ($%.1).

'5$ Recr&stallisation Althogh low=tem5eratre annealing is

o:ten sed to relie9e internal stresses otlined a!o9e, mostannealing 5rocesses in9ol9e com5lete recrystallisation o: thedistorted cold=wor8ed strctre. A

the properties of materials

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