Rev. Mex. Fis. S 45(1) - Revista Mexicana de Física

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.\". FiJ . ..tSSI (199lJ) 74-77
SURFACE EFFECTS UN TIIE SINTERING REHAVIUR UF NANOMETRIC
1. A,S. Edclstcin
and
~)'1lt¡'(,Jü.ProJll'rties
R.e.
Carnmarata
(1/1(/Aplica/iom.
(cds.), Nanol1Ulterials:
(I0P Publishers/lnslilUlc
01'Physics. 19(6).
13. O. Domingucl. Y. Champion, and J. Bigot. Me!. Mat. Trmu.
29A (l99R) 2941.
14. A.L. Grccr. Ml'Cllanical
2. H. Gleitcr. Prog. Mara. Sei. 33 (1989) 223.
.t. 01.. Rourcll ¡¡ntl \V.A. Kaysscr, ,\ft-tall. Mar. Trans. 25A (1994)
Properties
and Deformation
8ellal'ior
edited by M. Naslasi
('1 al., (Klu .•••.
cr Acadcmic Publishers. 1994) p. 53.
of Materiah
3. Y. Sakka. 1'. Uchikoshi. and E. OZJwa. J. Mater. Sci. 28 (1993)
203.
77
METALLlC PARTlCLES
/fal'ing
Ullrafme
StruclUres,
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255.
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677.
~. Y.H. ZhOll, ~1. Ihumelin.
antl J. Bigot. Scripta Met. 23 (1989)
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G.
o.
l.
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eh¡m. F,: 18 (1993) 369.
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am/ AlIlorl'/wlIs
lJiffral'tiOlI
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o.
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Re!'. Mi'x. Fú."¡S
SI (1999) 74-77
Res. 10 (1995)