7/28/2019 Alumina-Based Composites Strenthened With Titanium and Titanium Carbide Dispersions

1/3

l ?*':la$ Tai"'*'i1*l-{3&,!, At 2! ae'!E' :+lr}tl|"',)!.'3 i

f:.i:a!! itL] {:l'|'ltl,i* [L ' L ' ]l!] l']],]] j|l' ,.l .l, *] ! r il ]..V]ir i]|illti*[l'sl!-!.a ' ln ]]:r i.l'' ,J]l] .]l ] i;]:' ] !l i. ']j'Li] l i'.] !]'jAtlD,:1-{fiair5'*jli ' -]L)ilrL.l1 ]]]'l''jls.l]]]||lln|jtri]!LIltjl-ji].'l'li .],'l']F!1l]'. $(BT!lt[:-l:lt}i{cs' 1 ]i |]]|l's.-flAsllit] |}i :.l}LA'I*s*r,l] .' ] i_l.in l] rl,] i), ]1.'.]L]l,' l l]l. .]ll ]i lr1 |].]]]]|']'']il..i.lAl.]]l]::....nl]]]]!ilj.jijv]']1 ]]iJ!!.l]l ,.]]]!ri.] al:|ii|il](|] nl]nii]]r]]|]ij.:l;|:,jl] |nltnll] liltil]lit]!l]l']iL !trlL,j.:j l]j:r i].] ].]!].lljli' l]]l':i]. ||i..U!!:'l|.:'|r]1]:.!1f.l L]i].]illii,:!; ]l_])i ,''.1 i j]]].i;l]l'.1 ll -':] ]j:]l]i]l] ir.l!,ai|: !f ].ii s.]! t| D ]l.]lr:!:i irri ]rlr.: ir a r ri,.i.;:! ir'i i rr i ,r:t, l),15! i .rxri!: iri. .,-i .rfri 1i,,)! anr llr! s,i.o.xl :i1{]; i i, i:l.rlL{ir': :irr.lir .J ll rlirrr .iir i)nr,:i1 l)').t t: t (ir,r i.i.rn.t.f irl.ir rt rt!.r.:r. !i:rrl-j;r. '.ll' .] l ]t] i] l..]il..lrl..j!i]ii]rri:.1:;]l]l'j|L]J. l)! |!e ] i]l]jl.'l]](](i |]i]i|i] t.l,.\!1i. .rr(.1 !i lrr. r.lif:iiii.i,: irn r Lii|rl l! u.r[r iii r 1]r il rrLroiifrijLri ir !i I ri,.i rrr ior r;r.i:.lIl],l] li j|:..]ii. ll lll:.b!].]1!. rhn1 ,r ii.Nl!i]].:]i']].!] !,-]';t.: 1]tt)iii, ,: ] 1l:,.' j|] f!i] ']t1r!:i.i i.;frli..(lrldiii!iirlr'.1.r1,.:rt, lir! u,r..inrtri rriil..iiiti,rri-r,i.ririi..i.l]d:|.il!.1ipr'i1].li]'tt..s']]::l:(i]i!l|ll]j]-t]i].l.!l:Iii]!l]llr] .i|iiii)i.!ajl]i]..|itl:]'ii] ]L!. .]! r],]:,.: ,:. ]]:|.l '..j!|l.5'.flj. l].t ]! tl1ilr |]l'i j|!].1!] :'i'i]:]l: iij:i.

Alumina-based compositesstrengfthened with titanium andtitanium carbide dispersions

Irrtloductionl'O. is. Njd.l.d a \!luable idustrial |1.l.rill xnll l]r. ost wcl}' Us.d .cranri.' 11 }rosscs!(s sooll nlcchati.lprop$Li.s s(.h as: hign h..d!css,ligh .onprcssl\c s{rcnglh,good chenrcal nnd th n3l st )illt} l1 2]' L]oi!c\ct, itsaPPli.rtions Js r ructu nlhJ(crial hale been ]ilniled by its]olv lii.l!l. louglucss arlrl J,N!'inct .e slrc glh. ]h!s isbe.xuse .la.lts .nsi]I pioPlgatc in tlrjs ccl.]lnics and th.l.!b elh!y.1igill lail unP .dj{jt'bl.! in selv]cc''l1re 1.oiporation ol

"cvcl.L rcnrlor.cnr0r1 nlntcri..ls L.h N; c.lami.s' .rals aldinteln]tt!]}icsin{oan].o nul.i{ lol ninglcon1posite matel ialhds bct' prcved lo lrc an cili.t '. .rp.ri .nlil rcu|c \\,hic]]i 1p()!cs ltnlgh ness and nte.hJ ni..l s tlcngtir oI thc .onrPosiLcslll''l :; ll'''' ''t''|\':l. '' l''1 ll' l' '' 'l n..'-01 .ar bklc..rdilics, o\kicccrnhics and nrel!ls, a.d thc-'" cr! b.uscd' ld exinlpl ill |plicrtio! rL lrigh tcnrP.nrlul.s such lsin th. consl uclion (r1 gas l)in. cngines in ordel to incrcrs.lh.i. llr.rnul tvclc tliicitucy |.l 5l"lhereil' !il. e.naDi.r]and pli)si.al pmferti.s olsuch trpc ol .omPosiles halc Lrcc!sludjfd, as 'cLlas t|].il |fudu.t].n |rc.csscs l6 El. ]! sPil!o{ is' urc high lei]rPcrx{(lrc cenjenlrti.ll of nril Jis|elscdcrrb e.oDrpositcs hasnol bccn lnvcs(rgatedln d.uilind there.l( n.Jt srrtl]ci.nt reports on thc high LclrP.l a{ u n' cln1clitionoithermrl barri.r.onrt)orilc..orlingj [9].'lhe !'a.li a.mentxtlo! proccss lus trc.n uscd tu hrni yearsLo dc!.]op ]rn e.tn c.xlnlg ]D diliilcnl nlitcrix]s' }1.r. Lhcbod) is.sscntia]l} hcat Llc.l cl ir] a reicti\'e cnrilonn.nt asr. 1.. . i. ,1 ) .l'.. L n. l.'. r '.-,, ', rl - , 'n ,... ', r. '.conrpo(nds tlril inrprove.o.rcsnn lDd hcal ,csrsl:u,cehcha\,'.ir. \'r.ablrs thrr JHe.l i|e qurlitv ol co.ling in(ludcb( )d1' co|r P.sitio d' pojvLlcl bcd.or]!si{iolr, a.tl hcrt t!-exting(ol.liilons l.h as ten]Pefxnire, tnnc rnd li!na.f.Lnlosphelc

an. [rri!!. Rattil,.r l]UG.:t.l

D.' Dr]:d ilIRa;tlaa'$L n

Bl. aduald. J lF!s.a*']rj

!l' E4ljrj ' MIliiNl:.!:.;!it*aj$

Dr. s b.ia'* tl ;}a l lirBitli

si]rcc .lcDl.|Lll (a t]on fua\ djIflse throughout .n oider.ttllx at lri{h ttlrrpef?tures' the meta]li. pirticles di*r.rs.dil1 x nrrtrix.xn conscqlct1l]y ir...!ncnl' jl Lu j' lhecrystrllogrrphi. lolumc oi sucl rnclalli. oxidt s disfersionswill expa!rrl, ihus in.l(cilrg mi.ro strcss.s a.cum la{ion jrtlr surroundjn8 natrix' As llnj]t, 1is5urcs.{. .u.l.dt. in llltrc'chiroii.q ln.rrrix upor iht sb.sscs lrdction gene.ited by the!o]netxpi!lsi{'l''Ille lrl is Padic {arlIh!cialhemagnilul.ol .ompr.rsilc rrr.iscs rcr.hcs thc ullrnuk lrr.t!tre sn-ength.1nc\, lab]y. a]i.r nrulti|lc .ra.lls fttrn]itio!l, lhe co|lposiieundrrgoes cr tastrcf! i! ftactu.. I{ is thcn nnfor'.ant d.s ign ing.omf.sites for high t.lrpcntu.c applierilns,.nd so docslhcir anJi}s]s bc])1v!' il high lcltp..,1(!r. !!nlc lalion 'llrelrt ;s L|e expetirnental iil! oi this t'olL('Exper'inrtal procedure

Coir]poijlc lildiJls Wc. l)feladl sing t1vo .onse.trtivcstcps l]1 't' titaniunr disPersed oxid ahr!rinium .oDlposjlc!62 af' 3' szah.2{]1o' 3 ' pitny.c 75

7/28/2019 Alumina-Based Composites Strenthened With Titanium and Titanium Carbide Dispersions

2/3

s},jYA&Ti'!p{3,l!.'''!V. ",!'ilE :l-$ *i::*s{: i!!tle plc|.l.| Lls] l]plr.Uls.. |owdos ol ]\l.(). i99 91i,' ] gr.s]gnla, Us,\ ) lnd'L'i (99 9! l ]|l|l' ^ d] ich,L]s ]'] lrP]n].|lnlol poqder w.s s.l..trJ .s lo obhln nl O. bnscd .onrpos,tes]rlving {] 5' l' 2 aDd ] vol' ()l']'i ']hc poi!d.r nlirLur. Was bJllnr]ll.il in d lnnnre.cjll high.n0gv iiri]l (silt]lo}) usingZrO. .rlii(v'Lth Si,\. iDn.icontins1olrbid co.trnrinttidt,1 . ( l!jo..l sp..d o1'wlrich .ls s.l lo'l{]0 n]nr li' $ ]]"lh.1rx|l t.] powd.r \olU]]t. trti. \f.s sct lo ]0:l. Using .ril]ed+r$ .I niitLti.s' q1il].lri.rl san]Pl.j ol2 . r jn dlamet and0 ] cnr Lhicl \!tre ldrli.:lted b' uni.rr'l]t p essi.g ] g anls.t]](l NlP{ (]old }rlesj.d g.ccn 't\ plcs ll. e then |rcssur.lcsslintered lrt.s in .].ctric lil jn.e using irgon aL osl)hcle.1l..tl!!! irll !'li set to : "(] lni. l' snilcllng lemp.laiw. \asl5()()'C anli ]rol.ling Li1nc i h. licl s]nte.ing' liLnu.c NajLlrrr.d .li and sdnrflc! \vcrc Lcli i,rs,de it tbr griduilcoohlg'l]le!l rol s.co!d skP 1hc !o|rposiles ! cl..cncnLCd irl !r. nrislolli r5. lh! c.nrt,osite porrder Produ..ri d.s{lib.db.brewas pla.rd inridc x grrph'1c nrrdi.ontilncr rs tl .r. lr. st.!rin lT' l' lnsid. the .ontriner tirc sinl.r(d (ompl.t snrples.s l.talll surroonded b,v rh..cnrcnling rned;{m (}rowrl.rcdJctilrtcd cxlbonJ aBd lh.n hc,lle!] ]n \x.uu] uP to 50()"C loi h 'j11( lil..5!l ,lrlJn!,ed in ordcl to |n1U.. .il\)n .lj fus]onnrlo lh. samlte andlo ccnient nct lli. pr,ti.les thal lr( laundnert the sr|]icc ol'{hc (ornposile' bci]re bcnrg JlL$\'.d to coo]doNr nrsidc lhe 1u,na.e.

N1r.lc K''_is |lle !'a.tu? louglrir.ss, H is lh. hlrdness' . !s d].lerlgih ol thr nrrlicc Lr.cc ol lle i)rli.rick nleasurcd iornt1rc.. tcr ol the i|dent ald n is tlrc le|!tL] .i i]lc inde tationResults and discussion'll,( .(xs se.lion yiew ol ir.plird cofitotite spe.lRrensis jiro$ r /:{. 2' s n luncl]on o1 lh.'fi (nrl.nl and ilielc!.1|lclj!lx thcil .emeltatir Prc..sr Jl 5l)1]'(] lbl 1 lr' 'th.scfrictographs icYli] genclal f.atu'e! ol'thc nri.rsLr!.tllre a d1.l gcl g .li.s 10. r]re 2 ind j rol% Ti sp,jcnn.lts ll is eYid.nl thcIor!rlior oaht'1rgeneoLLs spe.incDs, b.(aLlsc Llrc'lj plflicl.s(t)picalll .iis.los.d b\ SEl4 as lrny w}1le dots), whi.h iclrnrc(lLh.n vciy lin,r \irrs ('erc wellLlisl.ibut.d in Lhc rlunira rrl!ix(Sra,v .la!k ph.i.). n gcrcr,,l the resullnrg nricroslru.{u.csdis}rL!)'.d t'llv |.les l.ji ilr th. Dralr]r il]cl jiilfu ing In the 'picnu' il cln .lso trc obsrl\ed th.t the.. il. no Ti |Jl1].lcsiD llrc s(r.i,rc. region to i dcpLh oi aboirt 50, 8J, 107 rnd I l9yin lar sal1lles Nith {{l'5], (l )' (2l i(l (.r) \ol-ql' o titJtjlll, esP!.til!l). Thc lo l r.gion l1 wh i.lr 'l'i pxrtic1cs lra],c rclI l.dwiLh dil]iliilj] .all)on is d.1]rtcd to s Lllc c. rent.d ZoD.'lrhos. thiclnlss Lrn s in!' lx-vo del)cnding on thc !!rdicn(con.eniration and snrlcrin litrc ^ .onrnro ta.tol nr l]lpi.LLncs shl)}1 it f{ 2 lel.lcs lo th! ltlcL lhnL r\l.() bisedNn4rosit.s do nol ]tclur. b.v tilt'l'i cRrc!trt]on'

r1! 1 s,',l]]l, l]li!{,i]]llll i/i] un{ill.' llldli/ll njll!'i]l.]Jliil4!L]lr'r.:1i]nr ]lt{]r'].rlJl1rc spccimenls.hdra.te.iZarion \V!' condu.ltd as r]Io$'s.Ilcnsity' ot ]lcdsPeci$.ts lvrs delelhined using th.

^ chin]edei nr.llrod' CcIn.nled srmplel wc e anih Zcd usings.r!ning cLc.Lron tui.roscopl Slli\,l (Xt.j(r FSll\'1, P|ilips)rnd en. rgi' dlst.rsivc spcctros.opr Illls (N".rrm).10 obicrvetheir microslruclurc arrd ch.micrl co.ly)sition, t lp.cli!eh.1hi.]or.ss ol' Lhe .rltjd. (..lncnl.d) lal!r is a fnctnnrol Lhc litan]trnr.fu e .onlcDL rn c.reh sanrfle ri.as alsodetennined trr Us rg lllcsc l.j.|lliqu 'ui.rrh.rJ!cs! (Jl theobtain.d spc.inrcns u,as elrl ried tr\ing \ri.l.^ rndcnt.tioni! x nri. ol).irdene. (8te]rlci '\'ii.ronl.1 :0 ]j)' s.lrerexs Llreii{ouSh,rcs\ wxs csttrnnle.l lollo{ing lhc litlurc 1!rdent.lion]Iet]rod' tlre nro wid.l)' uscd lech.iqu. n] thc lllcit!Lurc ijrasscssing lhc liacture toughness dir..tl) l.onr irldeni.ra.ksUlili7cs th. 1'i.]'.^ id.ntel' ]]i.st Plo]'osed nr t]re litc l970'!.thistechniquei'as dcvcLoPcl |o c i]ltcthe jj'a.t0 c loghD.s\oi ceranri. matcnals b! nrea!urin{ thc lcngtbs ol cri.lselrrnatlrg llonr li.t./\ indefltr 1101. ia?rs rr,11. nlodeledth! cllst]. |hst]c trehiarcl U|de] lh! n ent' .s nnitlg tli.t .,nedian/radlal .ra.k slsLctr ls ca1.d due 10 tcnsilc d csscs.1,"'.r'. I !, .-.1 ,'i ..\.lp,i\,Jrh..\t , ulKl( - 0'l6 ./a) '(lla''']76 ' p tahyag.20103'{]2 V{ 3 suin]

f(2 r..,jJllirr rir !,rln, r'ir]ll'Al !|trl. l] l l|']jn]''lI.iJ] l(r'!! 'i.l i].|.i]] i] ']Jl. [l|i .] )llll ii 1Lj l|,i 1t,'rl.! iiJ|l, ,!..l{ .1,\]] i]l].'ll lji,'] ^'1' i]r l 'iJ ]l/ ]]',].l].rrxlril'1']l]l l li lJl r) r|l)kr| l | ,nn i r,\, i1,) l i j 2 !: nl ]FL{. J vtrl.s r cross j..tiur sE\'l !1e , ol th. 2 !0190 1'i+]..in]en n]'l.! sinte g' Ll]s'mi.roanaL\si-r con,l'LjPn lr,rn]at tlre Nhite pa.ri.l$ .L lhc cdgc ,i,rd in tle core o1 ihc sampLe.on i.mcd ihc c'istcll.e of el.rn.nta] crrbon' palti.u]allvbe rgmo' .o'.fnLra{.d al t]lc speci!re|'s edge' r].s ]o gas lh( quilrlitn! r.al,vsis is .onlu.tcd il ,nr),:. 7!rrts ol the.ol posltc thc c.rlnnr colrlcnlratio! djnri1risired' Nol |IilcnLliom Lhj! pi(tur. butth.re is r.cilanr sl|1fu c Ia1'!l,1is|la'.g

a siiglrth d l.rcn! (o1ot .(|it .jt ilitlr resplcl {o tlrc ^].o. !ulknldL i\ such conrl'st' in pla.licc cxhi])it.d sinrilal texlul. tothi ..nlfu!.J legion So thit ]'.ti{een thf ..nrcnlcd ldlcr ad enon .cmented l.gjon, Lhclc is Jn llleneditrle z,]ne lri.lrL)

7/28/2019 Alumina-Based Composites Strenthened With Titanium and Titanium Carbide Dispersions

3/3

$]fi11ll''$ *19:]!:l;,|',[l'jt!Lajl,_a'}*l*i1Y..,slsls of pir{i)ll,!.em.nl..l 1i p.rti(l.s llr.r(lorr, rnoringlio ] lhc 'LItelosL ! lla.. Pdl1 itt() the bul]t 01' raLcii], (h.s b.cD cl.t..t.d lhlc ] st1).-itl. !eg]]s' i.ittll]ns] (]) iul]'.en.!l!({ ncl.] Prr li.hs, 12] r'tt inll}_ .(nxr]lcd pa li.] a df l) nretillii prftlclcs noi bcl.S cenrcDl.J.

ob,ier!'c.l ihrl dens t-r' in.reN.,l as li .or1l.nt lvrs rlsc iIlhc con]pos!rcs' ]l ii $uLh Iolins llra{ rni.rxr.]ncss s',N.., .,1 . ,.1. ,I. .r,1:, 'r, ^,1.. r r.,,.Fi st test]n* \,is .xllii o!t at 1he .LLg. .1'thC srnrPLc whcrcrsothcis w.rc pir.{'.c(] r1(rl Li) ils corc' 11i.rohardljess .. 3l]sltlditd slPl.s !']d] '|i n |xlgel .t lhe cdgc oI +r..imcnsthi| that obsclv.d.t lh.ii.orc' l1r]5 b(hJvn]l is dllc l thcllrralillr 01'hrld _l'i(] neir io l]re ..lge oi s.!p]es' 'llrc |.{..1alt.s n]a.. li .ugh the r.i.t]ol]: 'l'i t (] )'l'lc' 'lhis.h.r'i.llecliot is th.l nrod)ninrj.alt) l:tlor.d sr!c.lls t]cr.h.tli'olfonnrt'o,ris li.2I(.al/rnol l8l. lh. li(ll.rntaiir)nhkespl.c.l'itlj . ]on r.as dilfuJing lluollgh thc sP..inrcn's i{g. nj((jtlrc b!lk. c.nrcnl.tlon dlgrcc dcpcnds on 1]j. len4)..xtl. nd.qls co..entfution 1 pri.t]ce' il ]s thus |ossib]c to abri.dl.Al.U;/l jCl/1i .oBrposil.s.

li. J. li])!' l{d]]l!,.!.ll.t ll'lli !l ild l]]/l']'(]llj.|_!li lll]ai!.]i.l |l!! l, 'l ]il| r]l,/!i ]]rir r r.\ '!t!,/rr r!,t L1 r.trir r..,iJJiir:rr rr,, l.1i,r{l,t!rIrr!t,,.,r':,r,,i'r:,,, !/r.,,,,,-!r.H '' s|bi\,s de h 01 lhe c.|rcn(.d ].).I as a li]|clio. oi lhctita.in co!td]t s+Tli.J in{o t1rc.lilniuJ_lr.scd.l.fu posiles_lhere is rn e\.i(t!nl in.r.nrent on th. h}!r's dcpth as Lhc l_i.dr.enll!n() l !s.s' lhi\oll g nt'ing ])eh avjol is not lLn..l i.d1hc curic's l !|J nlggcsls cfcntllll sJlillx(il of |ita jUnr rtihc suri!... $]rr| a.(ounLs ia, ils !ii)rpositt nalu.t |!! th.

siore tigu1c it js J]so .lcii lh. tlligh.l)ing c k.l (h.l! l es!Lits o1lthe o'poljl dcii\ed liom tlr. o nalion olTrC, i'.', as Iongrs tle .enrenl la1.r Sets thi.k. li .xphin tlNghcning nr thcr!conrposil.e we rssrin. tir. .rrch lrridglrg .1lacl opcrxlilg.$hi!h rfrr!r o.curs {h.n disfersirrg mLnils iuto..r.nr(mR(ji! I]]' l}us' ilhen cllougl eat.lnil en.lgl i5 co! 'errr, .,. It\' L "" l ,. ".' L , .-; '.. ',,|o..s a.t irr. ing il .nd avoj(l 1]a(l.e, 10 ynl. c1tcn|"Ihc'li llgdnre|ts Pfcs.llt id tlr. c.lxntic n trix absorL] P.l t o 'lh!

systeh R lat vege ha r|n*s cor htd ess li"(vot%Ti) density (%) (6Pa) {cPa) (MPa h$)O !4.9! 17.1.1i tt t)l, 119A , A5 32+.t.)t680 r. o3 .11 r, 029tTa l0ol l,/ 0.4 913 l, 03 ! L,0196!+ 0.4 .r r lJl101t-,,05 /09+r {].3 52+ o1

!i'r!!r,,,,'n r.11 rr rr!n!.rnJ

'lh. !rigniludc ol li..rur. t(jtjl]ncss l(l. ^ltal ed fu th.9Lu(lied rdlt.ii|s ls ltp..ted ilj ].blc l' |'ill s|Ud'ed rascs,this stlcnglh |ar.nrclcl is su}r.rior lo lha( (jl lhc p! e aluminr$hi.h i! o about ]] ] MI'. nr''l.]l' sc.'l'tb]. tL is.on.ludcd".r I r...1 ,. ', l. .l .Jr u!s cor]d .1ed i] this \tlk n]ly in.lease ils loughn.sJ' soujcNilho(|a\cr.port.dlh LLh(rcnrlincingrnc.h!nis .prfutingl,erc is $n)ciet.d to the ..e.k bridgi!g phenorrcra lrigg.lTdl)1 ducl 1. mclalli. liginr.n{! [8. I I ]. I}! hlitl! d.nsili.rlirnlcvcl .onicr ed l. the.onrpo.]lts is in.lll.t ta.iol tht glcltl}i!1lLlen.cj tIej! touglucss valru clLlsl.ophI. clJ.hn! l)W(:.itr.lls ll\LrJll} t]k.l ph.. is lllg vo]ds ilc lei't i! it'Conclusionsst|e.g1h.ned I o b.s.d con1|ostl(s c.r1 (ll'..(Iv(l) bct.l!li]rcCd b) il u.i .q tlne dis|elsio1js of'1i1]/'l'1' throtrghoUtd.or!l)nlrtir o !xpeliNe.tal te.hniques, such.si nrlra!i..]D]illing' Pr.ssor(l(ss snrl.ing lr].s (r\ nllno\l)hefc) .lnd..r cntati.nl Pfu.es! {vrlLltn)' ']hc Iatel prolided thdt A]'o ,I'i i d r.Liva{.d crlbol 1ilrc piccursor |rwdcrs a cbli|glog,jlh.r trs l{] reac! lLpot ljnting olnring a n.t]onajl],(ra.l.d .cD.nl.dlaycr. Ihisn? -\it s.,rn1h.sis nr.thod prxhr..scon]}rsi1cj tlrrl xi. grcdtl) \it1.blc rl]J do cxhibit .nlrn|ccdl. ghlless' lis ...lpiled to nrodolithic l.(). .clinli.!' Ihisrdlg]r.!ing xP!)!Cmor1 l.(h|jq|. l)l]il' Lh. |ros\ibilil)' 01 llt sylllh.sis.ost' fu!]illg int() ln rtl!..tive \)"nth.sjs loute k]lscal!.q the proc!s-c up loxpild pl.nt.lcv.l.

2 t,:, o'a '.i&riJ:ad!3

'irrn]h i!,.l' )i').!? r 1rrr,.,i.r,1/rrrrr rrf i f ir .i t! 4 l,\t' b' t'l i, .'t!'! lt ti! |i. l

Tilr]. ] surrntlJlLrcs lh! fclrL]\,! densit] ri.l sonre nrhJn!.ll ptoP.rtjl nr..$..!] on lljc sludicd n]tjtelil1. ll c.ll ire