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1
S uc u al o de ing and magne ic p ope ies o a c-mel ed FeGa alloys
J.M. Bo ego, J.S. Blázquez, C.F. Conde and A. Conde
Depa amen o de Física de la Ma e ia Condensada, Ins i u o de Ciencia de
Ma e iales, C.S.I.C., Uni e sidad de Se illa, P.O. Box 1065, 41080 Se illa, Spain
S. Ro h
Leibniz Ins i u ü Me allische We ks o e, IFW D esden, Pos ach 270016,
D-01171 D esden, Ge many
Abs ac
X- ay di ac ion, Mössbaue spec ome y and magne ic p ope ies ha e been
pe o med on FeGa a c-mel ed bina y alloys in o de o s udy he composi ional
dependence o he s uc u al o de ing and magne ic p ope ies o hese alloys. The
a e age magne ic hype ine ield a 300 K dec eases wi h inc easing Ga con en as does
he a e age magne ic momen pe Fe a om and a linea dependence be ween bo h
quan i ies is ound o Ga con en up o 20 a . %. The subs i u ion o Fe by Ga a oms
inc eases he la ice pa ame e and causes a change in he o de o he c ys al s uc u e
ha has been modelled using a binomial dis ibu ion me hod. The e ec o Ga a oms as
nea neighbou s o Fe on he a e age magne ic hype ine ield is e alua ed.
Keywo ds: A-Magne ic in e me allics, B-Magne ic p ope ies, B-O de /diso de
ans o ma ions, F-Mössbaue spec oscopy
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2
1. In oduc ion
FeGa alloys ha e a ac ed g ea a en ion in he las ew yea s due o hei
supe io magne os ic i e p ope ies a low sa u a ion ield [1-4]. This quali y associa ed
wi h hei high mechanical s engh, good duc ili y, negligible magne ic hys e esis and
low cos [5] makes hese ma e ials e y p omising o senso and ac ua o applica ions.
Recen in es iga ions include he s udy o he in luence o he he mal his o y and
he s uc u al o de ing on hei magne os ic ion [6,7], he phase equilib ia and s abili y
o o de ed bcc phases in he Fe- ich po ion o he FeGa sys em [8] and he s uc u al
ans o ma ions in quenched FeGa alloys [9]. Mo eo e , ecen ly i was ound ha he
addi ion o Cu o Fe65.5C 4Mo4Ga4P12C5B5.5 amo phous alloy p oduces a nanoc ys alline
mic os uc u e consis en o FeGa nanoc ys als embedded in an amo phous ma ix [10].
These nanoc ys alline alloys a e in e es ing since hey would combine a la ge glass-
o ming abili y wi h good so magne ic p ope ies.
Howe e , a Mössbaue s udy o he FeGa alloy se ies is s ill missing. The
impo ance o his s udy is double. On one hand, s uc u e de e mina ion o FeGa alloys
by X- ay di ac ion is oublesome due o he simila i y in he a omic sca e ing ac o s
o Fe and Ga a oms which esul s in supe la ice e lec ions o e y low in ensi y. Fo
example, he in ensi y o he s onges supe la ice e lec ion associa ed wi h DO3 long-
ange o de is calcula ed o be only 0.6% o he s onges p ima y e lec ion. Mössbaue
spec ome y, as a sho ange o de sensi i e echnique, does allow dis inguishing
be ween o de ed and diso de ed a omic s uc u es. Fo nanoc ys alline alloys and due o
he complexi y o hei magne ic hype ine s uc u e, he cha ac e iza ion o he
hype ine pa ame e s o FeGa c ys als becomes an essen ial in o ma ion.
In he p esen wo k, a c-mel ed polyc ys alline Fe100-yGay (y=5, 10, 20 and 25)
alloys we e p epa ed in o de o s udy a ia ions in he a omic sho ange o de a oom
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3
empe a u e wi h subs i u ion o Fe by Ga. A local model based on a binomial
dis ibu ion me hod [11] was used in o de o co ela e he magne ic hype ine
pa ame e s wi h he s uc u al o de ing o hese alloys. The in luence o Ga subs i u ion
o Fe on he la ice pa ame e , sa u a ion magne iza ion, magne ic momen and Cu ie
empe a u e o hese alloys is also epo ed. The in e es o his s udy is ocused in
demons a ing ha Mössbaue echnique is able o supply de ailed quan i a i e da a o
he s uc u al o de ing o such sys ems as Fe-Ga bina y alloy whe e con en ional X- ay
di ac ion echniques can no esol e an o de ed s uc u e due o he simila i y be ween
he sca e ing ac o s o i s cons i uen s.
2. Expe imen al
Fe100-yGay (y = 5, 10, 20 and 25 a . %) alloys we e p epa ed by a c-mel ing om
pu e Fe (99.95%) and Ga (99.999%) in an Edmund-Bühle high acuum a c-mel ing
sys em. The a c-mel ed bo oms (~2 cm diame e and ~0.8 mm hick) we e emel ed
se e al imes o ge homogeneous samples.
X- ay di ac ion (XRD) pa e ns we e eco ded a oom empe a u e using a
B ucke AXS D8-Ad ance di ac ome e wi h Cu K adia ion on slices ~100 m hick
cu om he bulk samples.
Fo he momagne ic (TMG) expe imen s, he magne ic ield o a small magne
(20 mT) was applied o he sample and he empe a u e a ia ion o he magne ic o ce
was eco ded in a he mobalance (Pe kin-Elme TGA-7) as an appa en weigh change
o he sample. The Cu ie empe a u e, TC, was de e mined om low ield magne iza ion
cu es, by he “kink poin ” me hod.
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The sa u a ion magne iza ion, Ms, was measu ed on samples ~5 mg a oom
empe a u e wi h a Lakesho e 7407 ib a ing sample magne ome e (VSM), using a
maximum applied ield o 15 kOe.
Mössbaue spec a on he same samples s udied by XRD we e aken a 300 K in a
ansmission geome y using a 57Co(Rh) sou ce, wi h he -beam pe pendicula o he
ibbon plane. The alues o he hype ine pa ame e s we e e ined using NORMOS [12]
and MOSFIT p og ams [13]. The isome shi alues a e quo ed ela i e o -Fe a 300
K.
3. Resul s
3.1 X- ay di ac ion
X- ay di ac og ams o as-cas samples show ha he subs i u ion o Fe by Ga
shi s he posi ion o di ac ion lines co esponding o bcc phase o pu e -Fe o
smalle alues o 2. Figu e 1a shows, as an example, he XRD pa e n o Fe75Ga25
alloy. The inc ease o he la ice pa ame e , a, caused by Ga addi ion can be exp essed
by (Fig. 1b):
ya )1(00020.0)2(2869.0


[nm] (1)
whe e y is he Ga con en (a . %) o he alloy. Addi ional weak e lec ions due o he
possible occu ence o DO3 o de ing o he s uc u e a e no de ec ed. In ac , as i was
said abo e, he simila i y be ween he a omic sca e ing ac o s o Fe and Ga makes his
de ec ion di icul , unlike o FeSi alloys.
3.2 Magne ic p ope ies
The sa u a ion magne iza ion, MS, a 300 K, shows a linea dependence wi h he
Ga con en , y, up o 20 a . % Ga (see Fig. 2a.), ha can be exp essed by:
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5
yM S)5(0.3)6(223  [emu/g] (2)
The a e age magne ic momen pe Fe a om, <

Fe>, dec eases as he Fe con en
dec eases (Fig. 2b). A linea dependence o <

Fe> wi h y is obse ed o Ga con en up
o 20 %, ha can be gi en by:
y
Fe )3(004.0)3(24.2 

[

B] (3)
The di e en beha iou o MS and <

Fe> below and abo e y = 20 a . % sugges s a
change in he s uc u al o de ing o he bina y alloy.
The Cu ie empe a u e, TC, o he a c-mel ed alloys dec eases mono onously wi h
he Ga con en o he alloy as can be obse ed in Fig. 2c.
3.3 Mössbaue spec ome y
Fig. 3 shows Mössbaue spec a o he s udied alloys eco ded a oom
empe a u e. The hype ine s uc u e is s ongly dependen on Ga con en . Fo
y ≤ 20 a . % a six line pa e n is obse ed, wi h inc easing line wid hs as he Ga con en
o he alloy inc eases. The Mössbaue spec um co esponding o Fe75Ga25 alloy is
quali a i ely di e en o hose o alloys wi h lowe Ga con en , exhibi ing addi ional
and sha pe lines ha sugges some s uc u al change.
The i ing o he spec a was i s ied using se e al independen sex e s wi h
ee wid h bu only he spec um co esponding o he alloy wi h 5 a .% Ga could be
sa is ac o ily i ed using his model. Nei he he spec um o he 25 a .% Ga could be
clea ly decomposed in o wo componen s wi h p opo ions 3:1, as could be expec ed o
a s oichiome ic Fe3Ga wi h a DO3 s uc u e.
The bes i ing o he spec a was a ained using a disc e e magne ic hype ine
ield dis ibu ion (HFD) wi h a linea co ela ion be ween he magne ic hype ine ield
and he isome shi o he componen s o he dis ibu ion in o de o ep oduce he

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6
asymme ical shape o he spec a [14]. The quad upola spli ing was a e aged o ze o.
The ob ained HFDs a e shown in Fig. 3 ( igh hand side).
HFDs co esponding o y = 5 and 10 a . % Ga ange om 25 o 36 T and show no
signi ican di e ences: only a small shi o he maximum om 32 T o 31.5 T and a
small inc ease in he wid h o he dis ibu ion om 3.5 T o 4.6 T ( o a Gaussian
i ing) wi h inc easing Ga con en . Fo y = 20 a . % Ga alloy, he HFD co esponds o a
much b oade six-line pa e n spec um and anges om 18 o 36 T wi h a main
maximum a 30.5 T and a shoulde a 21.5 T. The magne ic hype ine ield dis ibu ion
o Fe75Ga25 alloy, ha anges om 16 o 36 T, consis s o wo clea maxima, labelled as
“a” and “b” in Fig. 3, cen ed a 20 T and 30.5 T and wi h ac ion a eas o 0.54 and
0.46, espec i ely. Fo a co ec i ing o he spec um i was necessa y o add a numbe
o componen s wi h magne ic hype ine ields anging om 1.5 o 16 T (~ 4 % o he
o al Fe a oms).
The a e age magne ic hype ine ield a 300 K dec eases wi h inc easing Ga
con en (Fig. 4a) as does he a e age magne ic momen pe Fe a om, and a linea
dependence be ween hese wo quan i ies is ound o Ga con en  20 a . % (Fig. 4c).
The dec ease o <Bh > wi h y, o y up o 20 a . %, can be exp essed by a linea
ela ion:
yBh )2(23.0)3(1.33  [T] (4)
The alue o <Bh > a y = 0 a . % o Ga is in ag eemen wi h he expec ed alue o
Bh o pu e -Fe phase a oom empe a u e, 33.0 T. Fo compa ison, Fig.4a also shows
he composi ional dependence o <Bh > o FeAl [15] and FeSi [16] alloys. A
discon inuous jump a 20 a .% me alloid is encoun e ed o FeGa and FeAl alloys, bu
his jump is no so clea o FeSi alloys.
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7
The a e age isome shi (Fig. 4b) inc eases linea ly wi h Ga con en up o
20 a .% Ga ollowing he ela ion:
yIS )5(0070.0)5(003.0




[mm/s] (5)
The angle , de ined by he di ec ion o he magne ic hype ine ield and he
p opaga ion di ec ion o he  ays, can be ob ained om he in ensi ies o he second
and he hi d abso p ion lines o he spec a. Fo he p esen alloys, a alue o a ound
55 º e eals he absence o ex u e o magne ic momen s o all alloys.
4. Local o de modelling
Using a binomial dis ibu ion, he p obabili y, Pnm, o a bcc en i onmen wi h n
Ga a oms as nea neighbou s (NN), in he i s shell, and m Ga a oms as nex nea
neighbou s (NNN), in he second shell is gi en by he exp ession:
8 6
( ) ( ) ( ) ( )
n m n m
NN NNN NN NNN
nm Ga Ga Fe Fe
P M x x x x
 
       
        (6)
whe e )(NN
U
xand )(NNN
U
xa e he concen a ion o U a oms (Ga o Fe) in he se o 8 NN
a oms o he i s shell and in he se o 6 NNN a oms o he second shell, espec i ely,
ha su ounds he cen al Fe a om. The mul iplici y, M, can be calcula ed as:
!)!6(
!6
!)!8(
!8
mmnn
M



(7)
Howe e , he composi ion o he neighbou hood o he Fe a oms mus be s ongly
a ec ed, no only by he global composi ion, bu also by he o de ing o he c ys alline
s uc u e. In a ully diso de ed A2 s uc u e, he Ga and Fe posi ions a e
indis inguishable and hei dis ibu ion would be andom. The e o e, he a omic
composi ion o he i s and second shells is he same, xFe and xGa, o Fe and Ga a oms,
espec i ely. Howe e , i is impo an o no e ha using Mössbaue spec ome y (MS),
om he 15 a oms (one cen al su ounded by 8 as NN and 6 as NNN) which a e p obed
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8
and o m he clus e uni , he cen al one is o ced o be a Fe a om. The e o e, he
p obabili ies o inding a Fe a om o a Ga a om in he neighbou hood o he p obe a e
modi ied wi h espec o he global composi ion (Fe100-yGay, wi h xFe = (100-y)/100,
xGa = y/100). In ac , he a e age numbe o Fe a oms in a g oup o 15 is 15xFe and he
a e age numbe o Ga a oms is 15xGa. Taking in o accoun ha he cen al p obe is a Fe
a om, he a e age numbe o Fe a oms in he 8 NN plus 6 NNN will be 15xFe-1 and,
hus, he co ec ed Fe concen a ion, 14/)115(  Fe
co
Fe xx , in he NN plus NNN
en i onmen is dec eased wi h espec o he global alue, and he co ec ed Ga
concen a ion,
15 /14
co
Ga Ga
x x, is enhanced wi h espec o i s global concen a ion in
he alloy.
In he case o o de ed s uc u es, he posi ions o Ga and Fe a oms in he
elemen a y cell a e dis inguishable. Fo a pe ec o de ed DO3 s uc u e, only possible
o an alloy composi ion o Fe75Ga25, a Ga a om is always su ounded by 8 Fe a oms as
NN and 6 Fe a oms as NNN, bu o Fe a oms, wo di e en si es a e p esen ; namely,
1/3 o he Fe a oms ha e 8 Fe a oms as NN and 6 Ga a oms as NNN (D si e) and 2/3
ha e 4 Fe and 4 Ga a oms as NN and 6 Fe a oms as NNN (A si e). (Table 1).
Fo alloy composi ions Fe100-yGay wi h y < 25 a . %, he e is no possibili y o a
pe ec o de ed s uc u e as he numbe o Fe a oms is in excess and he numbe o Ga
a oms is less han he needed. The e o e, we assume a “maximum o de ed” s uc u e in
which Ga a oms will be always loca ed in hei co ec si es and he Ga si es which can
no be occupied by Ga a oms will be illed wi h he exceeding Fe a oms. Thus,
“maximum o de ed” s uc u e implies ha a Fe si e will ne e be occupied by a Ga
a om bu some Ga si es will be occupied by Fe a oms, esul ing h ee di e en si es o
Fe (Table 1): A and D si es, which a e co ec Fe si es, and Ga si es occupied by Fe
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9
a oms. The dis ibu ion o he 100-y Fe a oms will be as ollows: 50 will be in A si es,
25 in D si es and 25-y Fe a oms will be subs i u ing Ga a oms.
Each Fe a om in an A si e in a pe ec o de ed DO3 s uc u e has 4 Ga a oms as
NN bu o a Ga con en lowe han 25 a . %, a Fe a om in an A si e could ha e 4, 3, 2, 1
o 0 Ga a oms as NN. Analogously, he possible con igu a ions o a Fe a om in a D si e
anges om 6 o 0 Ga a oms as NNN. Finally, a Fe a om in a “Ga a om-si e” will
always ha e 0 Ga a oms as NN and 0 Ga a oms as NNN (Table 1).
Taking in o accoun he p e ious conside a ions o ob ain he concen a ion o Fe
and Ga a oms in he NN and NNN se s o a oms, he p obabili ies o he di e en
con igu a ions can be calcula ed using equa ion (6). The esul s o diso de ed and
o de ed s uc u es a e shown in igu es 5 and 6, espec i ely.
5. Discussion
(a) Alloys wi h low Ga con en (10 a . %)
Assuming he e ec o he Ga a oms on he magne ic hype ine ield o be
p opo ional o he numbe o Ga a oms in he i s shell, n, and he numbe o Ga a oms
in he second shell, m, he a e age magne ic hype ine ield can be exp essed by:



mn
nm
mn
nmh mPqnPB
,,
33
[T] (8)
whe e q and a e he educ ion o Bh pe Ga a om in he i s and he second shell,
espec i ely. The linea i y be ween he educ ion o Bh and he numbe o Ga a oms as
NN (o NNN) yielding o q (o ) is no a s ong hypo hesis o low Ga con aining alloys
(expec ed o be in a diso de ed s uc u e) as he mos p obable con igu a ions a e hose
o 0, 1 o 2 Ga a oms as NN o NNN (Fig. 5). Fo ully diso de ed sys ems, he
ela ionships be ween bo h Pnmn and Pnmm wi h y a e linea (Fig. 7). The e o e, om
equa ions (4) and (8) i is possible o ob ain:
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16
[15] D.S. Schmool, E. A aujo, M.M. Amado, M. Aleg ia Feio, D. Ma ín Rod íguez,
J.S. Ga i aonandia and F. Plazaola, J. Magn. Mag. Ma e . 272-276 (2004) 1342.
[16] M.B. S ea ns, Phys. Re . 129 (1963) 1136.
[17] G. Inden and W. Pi sch, Z. Me allkde, 62 (1971) 627.

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17
Table 1. De ini ion o he di e en Fe si es in a pe ec o de ed DO3 s uc u e and in a
“maximum o de ed” s uc u e o Fe100-yGay alloys.
S uc u e Si e
NN Fe
a oms
NN Ga
a oms
(n)
NNN Fe
a oms
NNN Ga
a oms
(m)
Pe ec
o de ed DO3
y=25 a .%
Fe a om in
D si e 8 0 0 6
Fe a om in
A si e 4 4 6 0
Ga a om
si e 8 0 6 0
“Maximum
o de ed”
y<25 a . %
Fe a om in
D si e 8 0  6  6
Fe a om in
A si e 4  4 6 0
Fe a om
in a Ga a om
si e
8 0 6 0
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Figu e cap ions
FIG. 1. (a) XRD pa e n co esponding o Fe75Ga25 alloy and (b) la ice pa ame e , a, o
he bcc phase o FeGa alloys as a unc ion o he Ga con en o he alloy.
FIG.2. (a) Composi ional dependence o he sa u a ion magne iza ion, MS; (b) a e age
magne ic momen pe Fe a om, <

Fe>, a 300 K and (c) Cu ie empe a u e, TC, o
Fe100-yGay alloys.
FIG. 3. T ansmission Mössbaue spec a a 300 K and hei co esponding i ing (solid
line) and magne ic hype ine ield dis ibu ions o Fe100-yGay alloys.
FIG. 4. (a) Composi ional dependence o he a e age magne ic hype ine ield, <Bh >;
(b) a e age isome shi , <IS>, o FeGa alloys. Fo compa ison, i is also shown he
composi ional dependence o <Bh > o FeAl [12] and FeSi [13] bina y alloys on (a). (c)
A e age magne ic hype ine ield, <Bh >, as a unc ion o he a e age magne ic momen
pe Fe a om, <

Fe>, a 300 K.
FIG. 5. P obabili ies, Pnm, o a Fe si e o ha e n Ga a oms as NN, in he i s shell, and m
Ga a oms as NNN, in he second shell o a ully diso de ed A2 s uc u e, calcula ed
using equa ion (6), o he di e en s udied alloys.
FIG. 6. P obabili ies, Pnm, o a Fe si e o ha e n Ga a oms as NN, in he i s shell, and m
Ga a oms as NNN, in he second shell o a “maximum o de ed” DO3 s uc u e,
calcula ed using equa ion (6), o he di e en s udied alloys.
FIG. 7. Summa o ies o he p oduc s Pnm

n and Pnm

m, as a unc ion o he Ga con en
o Fe100-yGay alloys.
FIG. 8. <Bh > dependence on he a e age numbe o Ga a oms as nea neighbou s, <n>,
o bo h ully diso de ed and “maximum o de ed” s uc u es. The expe imen al Bh
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19
alues co esponding o maxima “a” and “b” o he HFD o Fe75Ga25 alloy a e also
shown.
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20
FIGURE 1
20 40 60 80 100
0 5 10 15 20 25
2.86
2.88
2.90
2.92
(a)
(220)
(211)
(200)
In ensi y (a.u.)
2 The a (º)
(110)
(b)
a (A)
Ga con en (a .%)
o
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21
FIGURE 2
0 5 10 15 20 25
700
800
900
1000
1100
0 5 10 15 20 25
120
160
200
240
0 5 10 15 20 25
1.8
2.0
2.2
Ga con en (a . %)
(c)
(b)
T
c
(K)
(a)
M
s
(emu/g)
<
Fe
> (
B
)

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22
FIGURE 3
0
10
20
0
10
20
30
0
10
-8 -4 0 4 8 0 10 20 30 40
0
10
20
P(B
h
)
x=20
x=10
x=5
x=25
(mm/s)
Rela i e ansmission
b
Bh (T)
a
In e me allics. Vol. 15. Núm. 2. 2007. Pag. 193-200
h p://dx.doi.o g/10.1016/j.in e me .2006.05.007
23
FIGURE 4
0 5 10 15 20 25
0.00
0.06
0.12
0.18
0.24
0 5 10 15 20 25
24
28
32
2.3 2.2 2.1 2.0 1.9 1.8
24
28
32
<IS> (mm/s)
Ga con en (a . %)
(b)
(a)
FeGa
FeAl
FeSi
<B
h
> (T)
(c)
<B
h
> (T)
<Fe> (B)
In e me allics. Vol. 15. Núm. 2. 2007. Pag. 193-200
h p://dx.doi.o g/10.1016/j.in e me .2006.05.007
24
FIGURE 5
0
2
4
6
8
0.00
0.05
0.10
0
2
4
6
Fe80Ga20 diso de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)
0
2
4
6
8
0.0
0.1
0.2
0
2
4
6
Fe90Ga10 diso de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)
0
2
4
6
8
0.0
0.2
0.4
0
2
4
6
Fe95Ga5 diso de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)
0
2
4
6
8
0.00
0.05
0.10
0
2
4
6
Fe75Ga25 diso de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)
In e me allics. Vol. 15. Núm. 2. 2007. Pag. 193-200
h p://dx.doi.o g/10.1016/j.in e me .2006.05.007
25
FIGURE 6
0
2
4
6
8
0.0
0.2
0.4
0
2
4
6
Fe95Ga5 o de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)
0
2
4
6
8
0.0
0.1
0.2
0
2
4
6
Fe80Ga20 o de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)
0
2
4
6
8
0.0
0.1
0.2
0
2
4
6
Fe90Ga10 o de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)
0
2
4
6
8
0.0
0.3
0.6
0
2
4
6
Fe75Ga25 o de ed
P obabili y
Ga a oms in 2nd shell (NNN)
Ga a oms in 1s shell (NN)