Rev. Mex. Fis. S 45(1) - Revista Mexicana de Física
Transcripción
Rev. Mex. Fis. S 45(1) - Revista Mexicana de Física
REVISTA MEXICANA DE FislCA 45 SUPLEl\IENTO 1,74-77 JUNIO 1999 Surface effects on the sintering behavior of nanometrie metallie particles OClavio Domingucz E Instituto de Metaltugia, U"iversidad Autónom{/ de San Luis PofOS/ 550 Sierra Leona, 78210 San Litis PotOSI: SLp, Mexico Yannick Champion and lean Bigot CECM-CNRS, 15 me G. Urbaill, 94407 Vit,.)'sllr Seine, Frallce Recibido el I de marzo de 1998; aceptado el 26 de mayo de 199R Nanome(ric re nmJ Cl! powdcrs (NP) were sinlercd in H2 nfter uniaxial cold pressing. The sintering behavior of samples wns studied using dilntomctric nnd cnlorimetric Icchniques. The sintering tempernture T,¡ and the self-dilfusion nctivation energy Qu. ob(aincd in ~h for Pe were :lSO°C and 60 kJ/molc respectively. nnd those oblained in H2 for Cl! wcre af 220°C and 43 kJ/molc. According to thc present results. lile activation energies oblained from both NP in lh could be associated 10 (hose for self-diffusion in (he liquid stn(e (Fe 65 kJ/mole and Cu 41 kJ/rnole). Assuming T,¡ rclated (o (he surface me1ting tempefílture, Ihe sile dependence of surface melting of nanometric melallic particles is proposeJ un the hasis 01' a simple Dcbye model togcther with the Lindemann law. by rhenomenologically taking inlo account a surface phonon softening process. Ke)"words: Nanoparticles: sintering; surface me1ting Polvos nanométricos de re y eu fueron sinterizados en H2 despues de hnber sido compactndos. Se determinaron las temreraturas de densitlcación T,¡ y las energíns de activación (¿" de la autodifusión por rneJio de lécnicas dil<ltométricas y calorimélricas. En el caso del Fe sc encontró una temperatura de densiticación T.I de 350°C y una cncrgía de activacicín Q" dc 60 Id/mole mientras que en el C;'Iso del Cu se ohluvicron los v,dores de 220°C y de 4:1 kJ/mole. respectivamente. Estns energías no corresponden a las conocidas pnra la nutodifusion de estos elementos en estado sólido y rarecen corresponder más a las cnergías asociadas a la aUlodifusión en estado líquido (65 kJ/mole y 41 ".l/mole para el Fe y el ClI. respectivamente). Considerando a la superficie de las p,lrLículas nanomélricas como la región en donde se produce una prefusión como resllltndo del rehlandecimiento lonónico, h1lcrnperalura de ucnsi ficacióll 7:/ pLlcJe scr justilicadJ quanlitativamente considerando la ley de Lindemanl1 y el modelo de Dchye. IJcscrip/ol"es: Nanopartkulas: sintcril.ado; fusión en superficie PACS: H1.20. E: 61.46 1. lntroduction Illetric particles, initiating in this way the liquid phase sinter- ing process. Thc principal intcrcst ahoul hlllk material s presenting nanocrystallinc structurcs slems "rom the strong modiflcalions 01' Iheir sol id slnlc properties compared lo convcntional polycryslalline solids r 11. At present, a eommon approach to hulk produelion is prcssing lhe powders in lhe sallle synlhesis apparatlls [21. Correel sinlering is of parumounl imporlanee (o the powdcr mClallurgieal proecss, to ensure lhc physicoehemical properties needcd ror the partlo fulflll ils inlended role as iln cngincering componenl. Nevertheless, sintering sludies on nanol1l~lric powders have shoWIl Ihat Ilanolllel- 2. Experimental details Powder compacts nI" nanoerystallinc eu amI Fe \\'cre prcpared fmm powders produced hy levitation Illclling in liquid nilrogen 17] ;tU then shaped hy die-colllpaclion as in prcviously reported studies from X-ray diffraction using lhe Seherrer alld lransmission [8,~)J. The grain sil.es werc delermincd (XRD) formula eleelron Iille hroadening Illcasurcments [10] and hy conventional lllieroseopy (SEM, TEM) scanning 18,9]. rie metallie particles lend to growlh quile easily during heating l3-D], making lIseless the material once Ihe grain growlh Thc sintcring hchavior 01" samples was studieJ lllelrie and dilatometrie tcchniques [G-111. SEM process images (Fig. 1) show Ihat Ihe as-prerared nanomctric Fe ami el! particles prcscnt sphcrieal shapc. This lllorphology is quite important due to Ihe f¿lCt that hasically, the Iheory oi" sintcring is hased in this assumplion [12J. The mean partiele sil.e of Ihe as-consolidated Fe samples was oi" 30 nm and conlained less Ihan 2 wcighl pet of Fe:lG.t. FOI"those samples nhlained from Cu, the mean particle size was 01" 50 nm and conlained Icss Ihan 4 weight pet of CU20. is eompleted. Thc prcscnl work is an allnlysis of lhe sinlering procL'SS <Iml the l1leehanisllls involvcd during lhe heJling nI" nallolllelric lllelalJic powdcrs. Thc principal purpose 01" this \vork was lo eOllsider the particle surl"acc as the respollsihle Illechanislll rOl" Ihe lllicroslrllcture evollltion in nanocrystallinc mClallic powders during lhe sintcring process. The hasic idea is that phonon softcning can takc places al thc surl~lce nI' Ihe nano- hy caloriand TEM SURFACE EFFECTS ()N THE SINTERING HEIIAVIOJ{ OF NANO\lETRIC METALLlC -- . •..- o o il ., , • J31~ ••<':>100 • e I O 50 nm (a) FUilJRE l. Imagcs (a) As-prcparcJ ric Cu ¡x)wdcrs. 100 200 \ o, nanomelric " :m «Xl 5 .-•. \, ~ '-0 J ~ •;; -;; - O Eal ~ T_urer<-) (h) oblaincd by transmissioll " " \ /J -..- '" \ .---~-f'" o " 1\ I I 1 \ \ 1 j ~ !~ 1--1 75 !'AHTleLES electron (,,) microscopy. Fe powdcrs. (h) As-prcparcd nanome(. 20 ~ ó ~ 3. R"slI!ts and discussion • " Figure 2a shows rcsults ohtaincd hy dilatolllclry (5°C/min) lIsing H:! logclhcr with Ihe grain sizc dcpcndcncc on Icmpcralurc. From thcsc rcsulls, il is clcar that dcnsification in nano4 Illclric Fe powdcrs occur al 350°C. which is ahout 600°C lowcr than Ihe dcnsification tempcraturc \Vllcn particles are in Ihe micromctric dOIll<lin. Calorirnclric studics [11] carricd out \'v'ilh Ihe sal1lc Fe NP llave shuwn cndolhcfmic pcaks at teJ11peralures 01' '-H)O°C. Under {he sarne experimental conditions, nanollletric eu powJcrs beha\'c in the sarnc way (Fig. 2h). In Ihis case, lhe densilkation temperature occurrcd at 220°C. which is a 1II11chlower tlcnsilication temperalure than lhe one observed in cOllvcntional Cu powders. Here again, endothermil' peaks are ohscrvcd by calorimelric lechniqllcs al approx¡malely lile dellsilication tcmpcraturc, 1¡.moc [11J. Thcn. rcsults Sl'CI1110 poinl out that in NP lllosl particle grO\vth ocurr at the dellsiJicatioll temperalure. Many ditTusional models havc hcell proposcd for sinlering 1121. Thc comll1on feature is (hal equations can he formulatcd at constanl lempcralure in lcrms 01' simple variahles, Ihcrcfore prcdicting lhe hont!ing beha\'ior 01' particles in fUIlCliofl 01' experimcntal paramelers. Figure 3 rcpresenls lhe curves ohtainetl fmm isothcrlllal experimcnls lIsing Fe NI'. The self.tlilfllsioll activalioll ellcrgy obtained from Ihis proccdure givcs Ihe values fiO :f: G kJ/molc in H1 [131. This activallon cllergy does not agrec wilh the lIleasured values rol' Fe sclf~dilfllsion in lhe micfOlllclric tlomain 1121 whcre honding (lCcurs hy \'OlllI1lC (213 kJ/mole) or grain houndary diffusion Illechanisllls (1 JO kJ/molc). Using thc salTlCproccdurc as hcfllrc. Ihe self-dilTlIsion activalion cnergy of Cu NP was ("alcuhlll..'d frolll isoll1erma! cxperilllcnts r l:q. The rcsults (Fig.]) gave tht.::valuc 01' ,l:~:f:.f kJ/molc in H2. Once again, the activalioll cncrgy docs nol agrcc wilh lhose associaled lo volullle (21] kJ/llIo!c) or grain boundary dilTusioll (11 R kJ/molc) in Rl'I'. Ml'X. ~ 10 :) S ;!!. 5 Temperature (oC) lh) FI(;URE 2. Grain sizc and shrinkage rate dependcncc on tcmpera. tme in Fe and Cu NP hcat trcatcd in 11'2. The dcnsificution alures me (a) 350°C rm Fc ane! (h) 220"C rm eu. tcmpcl'- -2 _3 o 6OkJ/mole -6 a -2 Cu F. a -6 1,6 1.7 FI(iUln: J. Anhcnills-Iype heal tre,llcd 18 19 ohtained 20 Fú'. 45 SI (1999) 74-77 2,2 hy dilalomctry. in 112. Thc activati{Jll cllcrgy Fe was (iO:f:: G kJ/molc 21 ami for nanornclric (lhscrved 2.3 Samplcs were for nanometric Cu was 43:f:: 4 kJ/mok. 76 OCTAVIO DOMINGUEZ E., YANNICK CIIAt\WION. sol id el! [12]. Thcrcforc. Ihe sclf-diffusion act¡vatioo cncrg:y fOlllld in lllclallic llanolllctric particles c~mnol he cxplaincd Oll Ihe hasis 01' convcntiollal solid-statc llifussional mollcls. According to Ihe prescnl r('sults, Ihe sclf-iJilTusioll aClivatioll cncrgics obtained frolll hoth NI' in H:! ((luId he associatcd lO Ihose for Ihe ¡¡quid statc (Fe 65 kJ/molc and el! 41 kJ/lllOlc). hOIll lhe lhermodynamical point 01' vicw, nanol11ctric partiele si/e can JIlodiflcd Ihe Illcl!ing tcmpcraturc 01' lhe material [1.1] al1<.I according lo salid statc physics, surfacc Illclting plays a relevan! role in Ihe solid-liquid transitiol1 [151. Thcrcfore, Ihe prcscllcc 01'a liquid-likc pllase could he assullled and this phase eould silllullaneously explain lhe high JilTusivity (slllal1 0(1), the kinelical behavior ane! lhe enhanced partiele growlh al Ihe densifkation tcmpcrature (TI!). Thc idea of so me 100v temperaturc ¡iquid phase during lhe sintering process in nanollletric Illetallic powders is at present arisillg 11G. 17J. Cnnsidering a simple Illodel for Ihe surfacc lIleltin-gof nanolllelric particles with spherical shape, il is possihle lo express Ihe fraelioll of atoms 18 allhe surface in tcrllls of Ihe particle sin.~ 118], ¡.l' . . _1',[ ( "'')"] j,-- 1- {J/¡ 1-R , (,,' ) 1/ '2 Irr'i\'J¡ ¡= {N(W) ./0 [~ w_ + -l'X-P-(.'-;'.-;'7-) terrns of the surface Dchye Icmperalure (J{)s ancllhe particle sizc [18J. To eslimalc Ihe surfacc mclting tcmpcralure (hence tlle dcnsification lcmperature ohtained from sinlcring CXPCfiments) wc use the Lindclllann law [2.3J. which says tllal a solid will melt whcn Ihe root-mcan-square displacemcnt of atoms in lhc solid excceds a certain rraelion 6 of Ihc interalomic dislanee 0.. Using Eqs. (1) ami (2) and sorne approxirnations. the surface llleltillg tempcrature of nanoIlletric parlieles 1:/ as a runctioll 01"parlielcs si!.e is expresscd as 118]: f ¡\f k{26rril8b ---J } (2 ) dw. \vherc X(:...') is Ihe phonon frequency distrihution. n is the nUlIlher 01"atoms. Mis lhc alomic lIlass, and considering the alolllic fraclion at lhc surracc and lhe phonon rrcqucncy dislriblllioll 01' lhe surl"ace regioll in tcnns of the Dehye mode!. lhe mcan displaccllIent of surface alOms can he expresscd in (3 ) 3(;11'(1 - (1 - 11,,/11)'] 3 nr 4 and f} lJ.~ = mean particle si/.e is found lo he helwcen 20 (() 30 nm (Fig. 1), logelhcr with tlle laHice, alolllic mass amI Debyc Icmpcralurcs 01"Fe and Cu. El). (3) givcs the following densification Icmpcratmes: r5 = O.OS, r\laking Ihe asslImption 11 = OVb/2. and cOllsidcring Ihal lhe experimental CII: ( I) where (J" and [JI, are lhe corrcsponding densities at the surfacc and hulk. I/{/ lhe surface lhickness and R Ihe parlicle radii. It is \\/ell known from 10w-el1ergy e1eclron dilTractioll (I_EED) experiments [1!J] that the mean-square displacelllent of an a10m in the surface region (U'1)8 is larger lhan lha! of an alom in Ihe hulk region (u'2)/¡. Thcorelica1 investigalions 120.21] shO\ved that Ihe dcviatioll of (11'2)" from (U'1)1I is \"er)' Iarge in lhe two or three surl"ace layers and it decreases rapidly \,,'ilh the dislance from the surface. Onllle olher ham.l. surface Dehyc tempcrature f} n.~eSlilllaled fmm XRD experiments [22] usually are in tlle range O.G < e < n.s, where (-:-)= f}f).~/HJ)b Using the Illcan-square displacelllenl in Ihe harmonic appnlxilllalion as AND JEAN BIGOT T" = 170 to 2.j()OC. (4) Therefore. Ihese lemlK~ralurcs seem to agrec quitc reasonahly \vith Ihose expcrimental values uhtainco hy Jilatol11elde (Fig. 2) ano calorimetric techniqucs fll]. Thc ahove rcsults suggesl the preSClH.:e01"a quasi liquid phasc during heal Irealmenl of nanolTletric melallic particlcs. In our opinion, depe!lding 011 Ihe oxide surface conlent, surfacc mclting could he prcsellt or nol during sintering experimcnls. Ncvertheless, in order lO ohlain hellcr undcrstanding of Ihe phenomcna, !llore experimcntal ano thcoretical sludies have lo he done. 4. Cunc!usiun Thc se1r-dilTlIsioll aclivatioll ellies ohlained in tlle prescnt work rOl" nanomelric re amI eu powdcrs \\lere compared lo dilTusioll dala. Thc aClivation energy obtaincd rol' Fe NI' in 11"2 was 01' 60 kJ/m01e ami for Cu NI' was of 43 kJ/lllolc. Tllesc aClivalion energies do nol corresponJ to any cOllvenliotlal ditTusional solid-statc process. I\ccording 10 Ihc present results. Ihese cncrgies are more closely rclated lo Ihose normally associaled lo lhe self-dil'fusion of Fe (65 kJ/lllolc) ami Cu (41 kJ/lllolc) in thc liquid state. Thc ahoye dala suggcst lhe presence of a Iiquid phasc during sinIcring 01' nanollletric mClallic powclers al Ihe dellsilicalion tempcralure 1:/. Good agreclllcnt hClwcen experimental densif1calion lemperalure and Iheorelical surfacc melting temperature can be ohtaincd. Rel'. Me.\". 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