Detection of the onset of nanocrystallization by calorimetric and magnetic measurements
Abstract
It is generally accepted that measurements of the magnetic properties are more sensitive than measurements of the enthalpy changes in the detection of the onset of crystallization of ferromagnetic phases emerging from a paramagnetic amorphous alloy. In this work, it is shown that the formation of a very fine nanocrystalline microstructure can make this assumption incorrect. Under some circumstances, the nanocrystallization onset temperature obtained from magnetic techniques is higher than the one obtained from enthalpy changes. The phenomenon is explained in terms of the superparamagnetic behavior of the uncoupled nanocrystals at the very early stages of nanocrystallization
Full text
De ec ion o he onse o nanoc ys alliza ion by calo ime ic and magne ic
measu emen s
J. S. Blázquez, V. F anco, C. F. Conde, A. Conde, and S. Ro h
Ci a ion: Jou nal o Applied Physics 97, 044308 (2005); doi: 10.1063/1.1849826
View online: h p://dx.doi.o g/10.1063/1.1849826
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De ec ion o he onse o nanoc ys alliza ion by calo ime ic
and magne ic measu emen s
J. S. Blázquez
Depa amen o de Física de la Ma e ia Condensada, Ins i u o de Ciencia de Ma e iales de Se illa–Consejo
Supe io de In es igaciones Cien i ícas (ICMSE-CSIC), Uni e sidad de Se illa, P.O. Box 1065, 41080
Se illa, Spain and Leibniz Ins i u e o Solid S a e and Ma e ials Resea ch D esden (IFW-D esden), Ins i u e
o Me allic Ma e ials, Helmhol zs asse 20, 01069 D esden, Ge many
V. F anco, C. F. Conde, and A. Condea兲
Depa amen o de Física de la Ma e ia Condensada, Ins i u o de Ciencia de Ma e iales de Se illa–Consejo
Supe io de In es igaciones Cien i ícas (ICMSE-CSIC), Uni e sidad de Se illa, P.O. Box 1065, 41080
Se illa, Spain
S. Ro h
Leibniz Ins i u e o Solid S a e and Ma e ials Resea ch D esden (IFW-D esden), Ins i u e o Me allic
Ma e ials, Helmhol zs asse 20, 01069 D esden, Ge many
共Recei ed 13 July 2004; accep ed 22 No embe 2004; published online 24 Janua y 2005兲
I is gene ally accep ed ha measu emen s o he magne ic p ope ies a e mo e sensi i e han
measu emen s o he en halpy changes in he de ec ion o he onse o c ys alliza ion o
e omagne ic phases eme ging om a pa amagne ic amo phous alloy. In his wo k, i is shown ha
he o ma ion o a e y ine nanoc ys alline mic os uc u e can make his assump ion inco ec .
Unde some ci cums ances, he nanoc ys alliza ion onse empe a u e ob ained om magne ic
echniques is highe han he one ob ained om en halpy changes. The phenomenon is explained in
e ms o he supe pa amagne ic beha io o he uncoupled nanoc ys als a he e y ea ly s ages o
nanoc ys alliza ion. © 2005 Ame ican Ins i u e o Physics.关DOI: 10.1063/1.1849826兴
I. INTRODUCTION
A widesp ead echnique o ob ain nanoc ys alline alloys
is he con olled pa ial c ys alliza ion o a p ecu so amo -
phous alloy wi h a sui able composi ion. The op imiza ion o
he ma e ial p ope ies equi es an accu a e de e mina ion o
he onse empe a u e o nanoc ys alliza ion, TX. This pa am-
e e , which depends on he hea ing a e due o he he mally
ac i a ed cha ac e o he de i i ica ion p ocess, can be di-
ec ly measu ed om en halpy changes. Howe e , indi ec
measu emen s, like changes in he elec ical esis i i y o in
he magne ic p ope ies due o he o ma ion o a new phase,
a e claimed o be mo e sensi i e han calo ime ic measu e-
men s o he de ec ion o he eme ging c ys als.1This a ib-
u ed highe sensi i i y is in ag eemen wi h he ac ha he
onse empe a u e ex ac ed om magne ic echniques 共TX
mag兲
is usually lowe han he one ob ained om di e en ial scan-
ning calo ime y 共TX
DSC兲.1Magne iza ion measu emen s a e
especially use ul when TXis abo e he Cu ie empe a u e TC
o he amo phous phase. In his case, a ze o signal is ob-
ained p e ious o he onse o c ys alliza ion and he signal
inc eases as he c ys alline olume ac ion Xinc eases, al-
lowing de ailed kine ic s udies o he ans o ma ion.2
In his pape we epo expe imen al esul s indica ing
ha , unde some ci cums ances, he assump ion TX
mag艋TX
DSC
is no longe ue. Fo his pu pose, Fe-based nanoc ys alline
alloys ha e been s udied. Thei cha ac e is ic mic os uc u e
consis s o andomly dispe sed c ys alli es 共⬃10 nm兲o a
e omagne ic phase 共
␣
-Fe- ype兲embedded in a esidual
amo phous ma ix, also e omagne ic bu wi h a lowe TC.3
This mic os uc u e acili a es he a e aging o he magne o-
c ys alline aniso opy due o he exchange coupling o he
nanoc ys als ia he e omagne ic amo phous ma ix. The
educed alue o he o e all aniso opy is esponsible o he
ou s anding so magne ic p ope ies exhibi ed by hese
alloys.4The di e ence in he nanoc ys alliza ion onse em-
pe a u es ob ained om he calo ime ic and magne ic ech-
niques will be analyzed aking in o accoun he possibili y o
a supe pa amagne ic beha io o he eme ging monodomain
nanopa icles embedded in he pa amagne ic amo phous
ma ix.
II. EXPERIMENT
Samples o Fe60Co18Nb6B15Cu1,Fe
60Co18Nb6B16
共Hi pe m- ype alloys兲, and Fe74Si16Nb3B6Cu1共Fineme - ype兲
we e s udied. They will be deno ed in he ollowing as
Cu-HT, HT, and FM, espec i ely. Ribbons 5–10 mm wide
and 10–20
m hick we e p oduced by mel spinning. TX
DSC
was measu ed by di e en ial scanning calo ime y 共DSC兲in
a Pe kin–Elme DSC7 calo ime e ; TX
mag was measu ed by
he momagne ic g a ime y 共TMG兲in a Pe kin–Elme TGA7
he mobalance using a small magne 共maximum ield
⬃20 mT兲. Bo h measu emen s we e pe o med a hea ing
a es o 10 K/min. A ib a ing-sample magno eme e 共VSM兲
was used o s udy quan i a i ely he dependence o he mag-
ne ic signal wi h he applied magne ic ield B=0.002, 0.02,
and 0.2 T, using a hea ing a e o 5 K/min.
a兲Au ho o whom co espondence should be add essed; FAX: ⫹34-95/461-
2097; elec onic mail: [email p o ec ed]
JOURNAL OF APPLIED PHYSICS 97, 044308 共2005兲
0021-8979/2005/97共4兲/044308/4/$22.50 © 2005 Ame ican Ins i u e o Physics97, 044308-1
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III. RESULTS
The mic os uc u e o he Cu-HT and HT alloys is simi-
la . Bo h de elop a nanoc ys alline
␣
-Fe,Co phase and
p esen he same c ys alline olume ac ion a he end o he
nanoc ys alliza ion p ocess 共X⬃0.65兲.5Howe e , he addi-
ion o 1 a . % o Cu in he Cu-HT alloy wi h espec o he
HT alloy p o okes a s ong e inemen o he mic os uc u e
h ough an enhancemen o he he e ogeneous nuclea ion due
o he o ma ion o Cu clus e s be o e nanoc ys alliza ion.6
Consequen ly, he mean g ain sizes a e e y di e en : D
⬃5 nm o Cu-HT and ⬃20 nm o HT.7In he case o he
FM alloy, he Cu-clus e ing phenomenon is also p esen , and
he mean g ain size o he
␣
-Fe,Si phase a he end o nanoc-
ys alliza ion is ⬃15 nm.2Al hough he Cu-clus e ing phe-
nomenon occu s in bo h he FM and Cu-HT alloys, a la ge
g ain size is ob ained in he case o FM.8A lowe Nb con en
共3 a . %兲wi h espec o ha o Cu-HT 共6 a . %兲and he
p esence o Si in he
␣
-Fe c ys als could be he o igin o his
la ge g ain g ow h in he FM alloys.
In o de o calcula e he c ys alline olume ac ion, bo h
calo ime ic and magne ic measu emen s can be used. In he
i s case, he c ys alline olume ac ion Xcan be associa ed
wi h he en halpy change 共X⬀⌬H兲, while o magne ic mea-
su emen s i is connec ed o he magne iza ion 共X⬀M兲.In
ac , he magne iza ion o he nanoc ys als depends on he
empe a u e bu , in he case o iso he mal expe imen s o o
small empe a u e anges 共p o ided ha he Cu ie empe a-
u e o he phase is dis an enough兲, easonable esul s can be
ob ained by conside ing a empe a u e-independen magne i-
za ion o he phase. Unde hese condi ions i can be assumed
ha he c ys alline ac ion is di ec ly p opo ional o he
magne iza ion signal. Ne e heless, he ela ionship in ol -
ing en halpy and c ys alline ac ion is also no exemp om
c i icisms,9as i dis ega ds he con inuous composi ional
change o he amo phous ma ix along he nanoc ys alliza-
ion p ocess. The signal measu ed in a DSC un co esponds
o he ime a ia ion o he en halpy o he sys em du ing he
ans o ma ion, dH/d .
Bo h echniques, TMG and DSC, allow a e y good con-
ol o he hea ing a e. The e o e, a compa ison be ween TX
ob ained a he same hea ing a e will gi e an idea o he
sensi i i y o he echnique wi hou being a ec ed by he
he mally ac i a ed cha ac e o he p ocess. Figu e 1 shows
he no malized DSC plo s 共peak a ea=1兲o he h ee as-cas
alloys, oge he wi h he no malized i s de i a i e o he
TMG cu es 共a a ield o ⬃20 mT兲wi h espec o he em-
pe a u e 共 he noise in hese cu es is due o he nume ical
de i a i es兲. The onse o c ys alliza ion is de ec ed a a
lowe empe a u e by TMG han by DSC. Howe e , whe eas
he di e ence in TXbe ween bo h echniques is only o 3 K
o he Cu-HT alloy, ha di e ence clea ly inc eases o he
o he wo alloys, being ⬎10 K.
To explain his e ec , he Cu-clus e ing p ocess be o e
nanoc ys alliza ion in he alloys wi h Cu could be aken in o
accoun . The o ma ion o his Cu- ich nonmagne ic phase
implies ha an ex a amoun o en halpy change would be
obse ed a a lowe empe a u e. This could make he onse
empe a u es de ec ed om DSC and TMG close , as ound
o he Cu-HT alloy. Howe e , i canno explain he di e -
ence be ween he TX alues obse ed by DSC and TMG o
he FM alloy, o which an e en highe densi y o Cu clus e s
han o he Cu-HT alloy is expec ed.10
To in es iga e hese di e ences in he c ys alliza ion on-
se de ec ed by DSC and TMG echniques o he s udied
alloys, he applied magne ic ield in he TMG measu emen s
was changed o es i s in luence on he obse ed alue o
TX
mag. Table I shows TX alues ob ained by DSC and by TMG
using wo applied ields con olled by he posi ion o he
magne a he he mobalance: he maximum achie able ield
共high兲and a ield which supplies a signal equal o 10% o he
maximum signal 共low兲. I can be obse ed ha whe eas o
he HT and FM alloys TX
mag is almos independen o he
ield, o he Cu-HT alloy, TX
mag is highe o low- ield mea-
su emen s han o high- ield ones. In he case o low- ield
measu emen , TX
mag is e en highe han ha obse ed om
he DSC measu emen s.
A quan i a i e s udy o he ield dependence o TX
mag was
done using a VSM. Figu e 2 shows M e sus empe a u e
plo s o he Cu-HT and HT alloys ob ained o di e en
FIG. 1. The momagne ic g a ime y 共TMG兲共dM/d 兲and di e en ial scan-
ning calo ime y 共DSC兲共dH/d 兲plo s a a hea ing a e o 10 K/min. The
TMG signal is ob ained as he de i a i e o he expe imen al M共T兲da a o
an applied ield o ⬃0.02 T.
TABLE I. Values o TXmeasu ed om DSC and TMG echniques a he
same hea ing a e, 10 K/min. High ield co esponds o he posi ioning o
he magne o ob ain he maximum signal a oom empe a u e 共⬃20 mT兲.
Low ield is ob ained o a signal equal o 10% o ha maximum.
Alloy Composi ion 共a . %兲TX
DSC 共±1 K兲
TX
mag 共±2 K兲
共high ield兲
TX
mag 共±2 K兲
共low ield兲
Cu-HT Fe60Co18Nb6B15Cu1727 724 731
HT Fe60Co18Nb6B16 759 741 740
FM Fe74Si16Nb3B6Cu1784 771 769
044308-2 Blázquez
e al.
J. Appl. Phys. 97, 044308 共2005兲
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applied magne ic ields. Samples we e hea ed a ⬃5 K/min.
Fo he highes ield 共B=0.2 T兲, e en he pa amagne ic ma-
ix gi es a nonze o signal. Howe e , i is possible o dis in-
guish a empe a u e a which he signal ises due o he onse
o nanoc ys alliza ion. In he case o he alloy wi hou Cu,
TX
mag=730±1 K and is independen o he applied ield. On
he o he hand, o he alloy wi h Cu, TX
mag inc eases as he
applied ield is dec eased: TX
mag=707, 712, and 722±1 K o
B=0.2, 0.02, and 0.002 T, espec i ely. A i s sigh , his
inc ease could be ela ed o he sensi i i y o he measu ing
equipmen . Howe e , his can be uled ou as he signal le el
o a gi en ield alue is he same o bo h he Cu-HT and
HT samples and he TXinc ease as he applied ield dec eases
is only obse ed o he Cu-HT samples.
IV. DISCUSSION
An explana ion o his e ec may be ound in he di e -
ences obse ed in he mic os uc u e o he s udied alloys. A
he e y beginning o nanoc ys alliza ion, e y small c ys als
a e o med, which can be conside ed isola ed and, he e o e,
in a supe pa amagne ic s a e. The magne iza ion p oduced by
a monodispe sed supe pa amagne ic sys em is desc ibed by
M=N
mL共mB/kBT兲,共1兲
whe e N
is he nume ical densi y o pa icles, m he mag-
ne ic momen o he indi idual pa icles, B he magne ic
ield, T he empe a u e, kB he Bol zmann cons an , and L
he Lange in unc ion.
Se e al assump ions may be made o ha e a iew o he
exis ing mic os uc u e a he e y ea ly s ages o nanoc ys-
alliza ion. A i s app oxima ion would be o conside ins an-
aneous nuclea ion egime, i.e., he numbe o nanoc ys als
emains cons an du ing he nanoc ys alliza ion. A e his, i
is easy o ob ain he alue o N
o each alloy: 0.01 and
0.00016 nm−3 o he Cu-HT and HT alloys, espec i ely,
which yields X⬃65% o a alue o Do 5 and 20 nm,
espec i ely. The alue o mcan be ob ained as he numbe
o a oms in he nanoc ys al imes i s a omic magne ic mo-
men , which can be es ima ed as 2.2
B. The bcc uni cell
con ains wo a oms in a olume equal o a3, whe e a
=0.28625 nm is he la ice pa ame e ,10 he e o e,
m共D兲= 2.2
B2
a3
D3
6.共2兲
A his poin , magne iza ion can be ob ained as a unc-
ion o he g ain size using Eq. 共1兲, whe e N
would cha ac-
e ize he mic os uc u e o each pa icula case. The nex
s ep will be o ela e he g ain size D o he empe a u e. This
can be done using he known kine ic pa ame e s o hese
alloys11,12 and he A ami equa ion. Al hough his equa ion is
alid o iso he mal egimes, we a e only in e es ed in a e y
small empe a u e ange, jus a e he onse o c ys alliza-
ion. The e o e, kine ic pa ame e s will be used in he ol-
lowing wi hou conside ing hei he mal dependence.
The A ami equa ion es ablishes a ela ionship be ween
he ac ion o he p ocess, X*, and he ime, ,
X*=1−exp关−共K 兲n兴,共3兲
whe e Kis he equency ac o and nis he A ami expo-
nen . The A ami exponen is app oxima ely 1 and is inde-
penden o he empe a u e a he ea ly s ages o
nanoc ys alliza ion.12 K ollows an A henius- ype depen-
dence wi h he empe a u e,
K=K0exp共−Q/kBT兲,共4兲
whe e K0is a cons an and Qis an ac i a ion ene gy. F om
he kine ic esul s, K0⬃1013 s−1 and Q⬃2.4 eV.12 In he aim
o simpli ying he calcula ions and aking in o accoun ha
we a e in e es ed in a e y small empe a u e ange, he he -
mal dependence o Khas been neglec ed and a alue o
⬃0.0004 s−1 共a T=725 K兲has been used. X*=X/0.65 o
bo h he s udied alloys, hus X*=1 a he end o he nanoc-
ys alliza ion. F om =共T−TX兲/

, and aking in o accoun
共2兲and 共3兲,
T=TX−

Kln
冉
1− 1
0.65N
6D3
冊
,共5兲
whe e TXis 710 K o he Cu-HT alloy and 730 K o he
HT alloy, and

=5 K/min, he same alue as used in he
VSM expe imen s.
Conside ing a sensi i i y o he VSM de ice o
0.1 memu, he de ec ion limi o he magne iza ion will be
abou 0.1 mT in he case o he s udied samples 共sample
mass ⬃8 mg, densi y ⬃7.8 g/cm3兲. Figu e 3 shows he e -
ec o he applied ield on he de ec ed c ys alliza ion onse
as is expec ed unde he assump ions indica ed abo e; ex-
pe imen al alues om Fig. 2 a e also included. I can be
seen ha he obse ed beha io is quali a i ely ep oduced.
An impo an e ec o he applied magne ic ield is ound o
FIG. 2. Magne iza ion M共T兲cu es o Fe60Co18Nb6B16−yCuy共y=0,1兲al-
loys a a hea ing a e o ⬃5 K/min egis e ed in he ib a ing-sample mag-
ne ome e 共VSM兲a he ea ly s ages o nanoc ys alliza ion using di e en
applied ields.
044308-3 Blázquez
e al.
J. Appl. Phys. 97, 044308 共2005兲
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he Cu-HT sample 共wi h a much lowe g ain size han HT兲:
he de ec ion limi o 0.2 T is o e come a a empe a u e
18 K lowe han o 0.002 T. Howe e , o he HT sample
his di e ence is smalle han 2 K. In e ms o c ys alline
olume ac ion, o he HT sample he de ec ion limi would
be o e come o X⬍2% e en o he lowes applied ield
共0.002 T兲. Howe e , in he case o he Cu-HT alloy a B
=0.002 T, he de ec ion limi would be o e come only o
X⬎15%, which could explain why he appa en onse o
c ys alliza ion is de ec ed in his case e en la e han using
DSC 共Table I兲.
Al hough s ong assump ions we e made o model he M
signal, he ends obse ed expe imen ally a e desc ibed wi h
a ai ly good quali a i e ag eemen . I mus be aken in o
accoun ha he app oxima ions used abo e lose hei alid-
i y as he di e ence in empe a u e be ween he de ec ed on-
se s becomes la ge : he iso he mal kine ic pa ame e s will
be modi ied and, a a high c ys alline olume ac ion, supe -
pa amagne ic pa icles will in e ac .13 These e ec s could ex-
plain he o e es ima ed modeled alue o he c ys alliza ion
onse o he Cu-HT alloy a 0.002 T wi h espec o he
expe imen al alue. As he ange o empe a u es is ex-
ended, he empe a u e dependence o Kshould be aken
in o accoun . On he o he hand, as he c ys alline olume
ac ion inc eases, he in e ac ion among he pa icles will
modi y he magne ic esponse o he sys em om he simple
Lange in unc ion used in his wo k. Ne e heless, he ob-
se ed end is success ully desc ibed.
V. CONCLUSIONS
In conclusion, o a compa ison o calo ime ic and mag-
ne ic echniques as ools o de ec ing he c ys alliza ion on-
se , i has o be aken in o accoun ha he sensi i i y o he
la e can be dependen , in some cases, on he applied mag-
ne ic ield. The gene ally accep ed idea ha magne ic ech-
niques ha e a highe sensi i i y han he calo ime ic ones is
no necessa ily ue in p esence o a e y ine mic os uc u e,
which can p oduce a supe pa amagne ic beha io .
ACKNOWLEDGMENTS
This wo k was suppo ed by he CICYT o he Spanish
Go e nmen and EU FEDER 共P ojec MAT 2001-3175兲, and
he PAI o he Regional Go e nmen o Andalucía. One o
he au ho s 共J.S.B.兲acknowledges a esea ch con ac o ha
egional go e nmen .
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FIG. 3. Expe imen al TX
mag ob ained by ib a ing-sample magno eme e
共VSM兲measu emen s 共solid symbols兲and esul s o he modelliza ion 共hol-
low symbols兲o Fe60Co18Nb6B16−yCuy共y=0,1兲alloys as nonin e ac ing
monodispe sed supe pa amagne ic pa icles 共nume ical densi ies N
=0.01
and 0.00016 nm−3 and c ys alliza ion onse empe a u e TX=710 and 730 K
o he alloys wi h and wi hou Cu, espec i ely兲. The expe imen al symbols
a e joined by lines as a guide o he eye.
044308-4 Blázquez
e al.
J. Appl. Phys. 97, 044308 共2005兲
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