ma e ials
A icle
Villa i E ec a Low S ain in Magne oac i e Ma e ials
G aciela Riesgo 1, Lau a Elbaile 2, Ja ie Ca izo 2, Rosa io Díaz C espo 2, Ma íaÁngeles Ga cía3,
Yadi To es 4,* and José Ángel Ga cía2
1Cen o de Segu idad Ma í ima In eg al Jo ellanos, Camín del Cen o de Sal amen o n 279,
33393 Gijón, Spain; g aciela g@cen ojo ellanos.es
2Depa amen o de Física, Uni e sidad de O iedo, c/Cal o So elo s/n, 33007 O iedo, Spain;
[email p o ec ed] (L.E.); [email p o ec ed] (J.C.); [email p o ec ed] (R.D.C.); [email p o ec ed] (J.Á.G.)
3Depa amen o de Ciencia de los Ma e iales, Uni e sidad de O iedo, c/Independencia n 13,
33004 O iedo, Spain; [email p o ec ed]
4Depa amen o de Ingenie ía y Ciencia de los Ma e iales y el T anspo e, Uni e sidad de Se illa,
41011 Se illa, Spain
*Co espondence: [email p o ec ed]; Tel.: +34-954482279
Recei ed: 25 Ap il 2020; Accep ed: 26 May 2020; Published: 29 May 2020


Abs ac :
Magne ic composi es o so magne ic FeGa pa icles embedded in a silicone ma ix ha e
been syn hesized. The Villa i e ec has been s udied depending on he size and concen a ion o
he pa icles and on he magne ic s a e o he composi e. The esul s indica e a dec ease in he Villa i
e ec when he concen a ion o he magne ic pa icles inc eases. These esul s sugges a ela ionship
be ween he Villa i e ec and he mechanical p ope ies o he composi es. The Young’s modulus
o he composi es has been ob ained by mic oinden a ion and hei alues ela ed o he in ensi y
and slope o he Villa i signals. The esul s a e explained on he basis ha he educ ion in he c oss
sec ion o he composi e when submi ed o s ess is he main o igin o he a ia ion o he magne ic
lux in he Villa i e ec in his kind o composi e. I has also been ob ained ha he magne ic s a e o
he composi e plays an impo an ole in he Villa i signal. When he magne iza ion o he composi e
is g ea e , he magne ic lux ac oss he composi e is g ea e oo and, so, he same educ ion in he c oss
sec ion o igina es a g ea e Villa i signal.
Keywo ds: magne os ic i e composi es; Villa i e ec ; magne oac i e ma e ials; so magne ic ma e ial
1. In oduc ion
Magne oac i e composi es a e sma ma e ials whose p ope ies depend on he applied magne ic
ield. In hese ma e ials, he mechanical p ope ies o an elas ome ma ix a e combined wi h
he magne ic p ope ies o he ille pa icles and so, he ype, concen a ion and alignmen o he ille
pa icles a ec he p ope ies o he composi e. Due o he dipole-dipole in e ac ion o he magne ic
pa icles, he applica ion o an ex e nal magne ic ield p oduces an inc ease in he Young’s modulus o
he ma e ial which is known as magne o heological e ec . In his way, a ma e ial wi h a magne ically
unable Young’s modulus is ob ained. These ma e ials ha e high magne os ic ion which depends
on he pe cen age o e omagne ic ma e ial [
1
] and he a angemen o he pa icles in he ma ix.
Fo iso opic magne o heological elas ome s, an ex ension along he applied magne ic ield was
ound [2], while a comp ession was ob ained in aniso opic ones [3].
These composi es used o be made wi h i on pa icles o nano o mic o sizes dispe sed in a silicon
polyme ma ix [
4
–
7
]; howe e , ecen ly o he ma ices: polyme s, polyes e , ubbe s, he moplas ic
elas ome s, e c. and pa icles: e i es (o ba ium, cobal , i on and s on ium), alloys o FeAl, and FaGa,
e c., a e being used [8–12].
Ma e ials 2020,13, 2472; doi:10.3390/ma13112472 www.mdpi.com/jou nal/ma e ials
Ma e ials 2020,13, 2472 2 o 15
Fi s ly, hese ma e ials we e de eloped and s udied only as magne o heological elas ome s due
o he dependence o hei mechanical p ope ies on he applied magne ic ield [
13
,
14
]. In his sense,
nowadays he e is in ense esea ch in composi es o med by an elas ome ma ix and ha d magne ic
ma e ials [
15
–
17
]. These ma e ials ha e p ope ies simila o hose made wi h ma e ials wi h so
magne ic p ope ies, bu wi hou he need o apply a magne ic ield. In addi ion, when he ha d
magne ic pa icles a e aligned du ing he manu ac u e p ocess a lexible magne is ob ained.
Nowadays, he magne oac i e ma e ials a e applied in di e en echnical applica ions such as
magne ic dumping [
18
], ac ua o s [
19
], in he ehicle indus y as dynamic ib a ion abso be s [
20
],
and sensing [
21
]. These ma e ials ha e also been used in di e en biomedical applica ions: in pe is al ic
de ices like mic opumps [
22
], in d ug deli e y o con ol he ime and amoun o d ug deli e y om
a ese oi [
23
], in hype he mia due o he possibili y o induc ing hea in a magne ic elas ome by
an al e na ing magne ic ield [
24
] and o p oduce a i icial muscles due o hei mechanical p ope ies
and he equency a which he s ain d ops o hal o his ampli ude [25].
The la ge magne os ic ion in hese ma e ials makes hem o g ea in e es o use in ac ua o s and
senso s [
26
,
27
]. In ecen yea s, he ene gy ha es ing is eme ging as an al e na i e o con en ional
ba e ies. The con e sion o mechanical ene gy in o elec ical ene gy is ob ained by he Villa i
e ec [
28
,
29
]. This e ec is one o he many magne omechanical e ec s [
30
], and i is ela ed di ec ly o
he change o he magne ic pe meabili y o he ma e ial due o he magne ic aniso opy induced by
s ess. The e is a g ea deal o li e a u e on his subjec in he ’classical’ bulk so magne ic ma e ials,
such as amo phous and e i es [
31
–
34
]. Howe e , al hough he magne os ic ion in composi es is
well s udied [
7
,
35
], he e a e ew wo ks abou he Villa i e ec [
36
–
39
]. In a monoli hic ma e ial,
he magne os ic ion and he Villa i e ec a e closely linked because he Villa i e ec is due only o
a magne ic e ec ; howe e , in magne o elas ome s ma e ials he e is ano he con ibu ion, due o
he mechanical p ope ies o he ma ix [40,41].
In addi ion, some s udies heo e ical [
42
] and expe imen al [
43
] ela ed o he e ec o
he applica ion o uni o m magne ic ields on he beha io o e ogels a e epo ed in he li e a u e.
I was ound ha he spa ial dis ibu ion o he magne ic pa icles plays an essen ial ole
in he magne ode o ma ion e ec . In he wo k ca ied ou by Zuba e e al. [
42
], indica ed ha
an inc ease in he pa icle concen a ion in he composi e can quali a i ely change he ype o
magne ode o ma ion. Fo i s pa , in he wo k o Sa ono e al. [
44
], he beha io o magne ic
ma e ials o manu ac u e biosenso s used in biomedical applica ions is s udied. The de elopmen o
e ogels (FG) wi h mic on sized magne ic pa icles o magne i e and s on ium hexa e i e is e y
a ac i e as hey mimic he li ing issue. In his con ex , Elhajja e al. [
45
], p esen ed a summa y o
he esea ch conduc ed in he las wo decades, ela ed o he ad ances in magne os ic i e polyme
composi es (MPCs) and hei applica ions. Howe e , hese a e being limi ed by he complexi y o his
p oblem a nume ous le els. In his con ex , he ime, s ain ampli ude, equency, magne ic ield,
shea a e, and empe a u e a e expec ed o in luence he o ces o de ing he pa icles and ha e no
ye been s udied sys ema ically. Fu he mo e, a uni ied unde s anding o he in e ac ion be ween
he elec omagne ic beha io , mechanical loads and he mal condi ions is also needed. On he o he
hand, he in e nal c acking o in e ace deg ada ion may lead o educed cyclic magne os ic ion as
he s ain ans e be ween pa icles and ma ix wi hin he composi e is s ongly educed. Finally,
he di icul y in conduc ing ep esen a i e expe imen s is limi ing he abili y o de elop ad anced
modeling app oaches.
Recen ly, some o he au ho s [
46
] ha e ound ha in Fe75Ga25/silicone composi es he Villa i
e ec is due o he change o he c oss sec ion o he sample when i is submi ed o a ensile s ess and
a model has been de eloped whose p edic ions i e y well wi h he expe imen al esul s. The o igin
o his e ec is comple ely di e en om ha o he classical Villa i e ec which, as i was men ioned
p e iously, is due o he change o he magne ic pe meabili y o he ma e ial; so his new e ec could
be be e named “s ain-Villa i e ec ” o a oid any con usion wi h he classical Villa i e ec .
Ma e ials 2020,13, 2472 3 o 15
In his wo k i has also been ob ained ha in composi es submi ed o a magne ic ield o 1 T
a e manu ac u ed a good signal o he Villa i e ec is ob ained wi hou he necessi y o applying
a magne ic ield o he sample du ing he measu ing p ocess. This esul inc eases he in e es in using
hese ma e ials in s ain and o ce senso s because he use o a p ima y coil is sa ed.
All hese esul s b ing ou he ela ionship be ween he Villa i e ec and he mechanical p ope ies
o he composi es. In o de o u he hese esul s, in his a icle a s udy o he Villa i e ec
in Fe81Ga19/silicone composi es in unc ion o he concen a ion and size o he so magne ic pa icles
has been de eloped. The Villa i e ec has also been s udied in unc ion o he magne ic s a e o
he sample. The esul s ein o ce he idea o he change o he c oss sec ion o he composi e as
he o igin o he Villa i signal in his kind o ma e ial.
2. Ma e ials and Me hods
Composi es wi h CeysMs-Tech silicone ma ix and Fe-Ga magne ic pa icles ein o cemen ha e
been manu ac u ed. Fe-Ga pa icles ha e been chosen as a magne ic ille because hey exhibi ela i ely
high magne os ic ion.
In o de o ob ain Fe-Ga pa icles high pu i y (99.9%) Fe and Ga me als we e used as aw ma e ials
and i s manu ac u e has been ca ied ou in wo s eps.
Fi s , alloys ingo s o Fe81Ga19 we e p epa ed by induc ion mel ing unde acuum a mosphe e.
F om hese ingo s, ibbons o abou 2 mm wide and 60
µ
m hick we e p oduced by plana low cas ing
in acuum a mosphe e wi h a oll speed o 17.5 m/s.
Secondly, 25 g o manually c opped ibbons o Fe81Ga19 we e milled unde acuum a mosphe e
using a plane a y ball mill (Re sch, PM 100 model, TENCAM, Changsha, China). A 500 mL 1.2080 ool
s eel ja wi h 20 empe ed s eel balls o 10 mm in diame e we e used as a milled con aine , se ing a ball
o powde a io o 40:1 wi h a o a ional speed o 400 pm. To educe u he powde con amina ion, no
lub ica ion o p ocess con ol agen s we e added. The milling p ocess las ed 2 h and i was in e up ed
e e y 20 min o dissipa e he accumula ed hea . In o de o ace he e olu ion on he pa icle size,
du ing each milling in e up ion, pa icles we e sie ed using A STM E-11/95 sie es o ming 4 di e en
g oups o pa icle sizes: unde 50
µ
m, 150–180
µ
m, 180–250
µ
m, and abo e 250
µ
m. Each g oup we e
weigh ed and ca e ully e u ned o he ja o es a he milling; his p ocedu e was epea ed un il
he 2 h o milling was eached.
Once he me allic ein o cemen s had been sie ed and classi ied in di e en size dis ibu ion anges,
wo ypes o polyme ma ix composi es ma e ials we e manu ac u ed: 1) using di e en ein o cemen
con en s and pa icles size <50
µ
m, and 2) a ying he size dis ibu ions, lea ing cons an he Fe81Ga19
pa icles con en (60 w .%). Table 1shows Fe81Ga19/Silicone composi e ma e ials analyzed in his
wo k. In all cases he mix u e o he me al ein o cemen s and he silicone ma ix (Silicone Ceys
Ms-Tech, L’Hospi ale de Llob ega , Spain) a e ca e ully mixed o 5 min, using a s i e ba a oom
empe a u e, gua an eeing a good homogeniza ion o he dis ibu ion o he powde s and a oiding
deg ada ion o he polyme ic ma e ial. Nex , he mix u e was pu in o a cylind ical-shaped mold wi h
a heigh o 50 mm, a diame e o 5 mm in he cen al pa and 8 mm a he ends, o ob ain he samples
o he measu emen o he Villa i e ec , and in o a mold in he shape o a ec angula p ism wi h
a heigh o 50 mm and 25 mm
2
o c oss sec ion o manu ac u e he samples o he measu emen o
Young’s modulus.
Ma e ials 2020,13, 2472 4 o 15
Table 1. Pa ame e s o manu ac u ed composi es.
Pa icles Size (µm) Weigh F ac ion (w .%)
In luence o ein o cemen con en
<50
45
65
75
In luence o pa icles size
150–180
60
180–250
>250
Finally, he samples we e cu ed o 36 h wi hou applying any magne ic ield (iso opic composi es).
A e manu ac u ing, he iso opic composi es we e subjec ed o an applied magne ic ield o 1 T
in he longi udinal di ec ion o he sample magne izing i in his di ec ion. A pic u e o he inal shape
o he composi es is shown in Figu e 1.
Ma e ials 2020, 13, x FOR PEER REVIEW 4 o 16
Table 1. Pa ame e s o manu ac u ed composi es.
Pa icles Size
(µm)
Weigh F ac ion
(w .%)
In luence o ein o cemen con en <50
45
65
75
In luence o pa icles size
150–180
60
180–250
>250
Figu e 1. Pic u e o he composi es: Cylind ical o Villa i measu emen s and ec angula p ims o
measu emen s o mic oinden a ion.
The mechanical p ope ies o he composi es we e ca ied ou by means o he Young's modulus
measu emen . The Young's modulus o he samples was measu ed by mic oinden a ion (P-h) cu es.
The measu emen s o mic oinden a ion we e pe o med in a Mic o es machine (MTR3/50-50/NI)
using a Vicke s inden e . The de ails o he me hod ollowed ha e been shown elsewhe e [47].
In o de o s udy he in luence o he elas ic and magne ic p ope ies o composi es on hei
Villa i esponse, he measu emen s ha e been ca ied ou in di e en s eps, as shown in Figu e 2.
Figu e 2. Scheme o Villa i measu emen s.
The classical induc ion me hod was used o ob ain he emnan magne iza ion o he composi es
a e being submi ed o an applied magne ic ield o 1 T. The measu emen s we e ob ained by means
5 mm
Figu e 1.
Pic u e o he composi es: Cylind ical o Villa i measu emen s and ec angula p ims o
measu emen s o mic oinden a ion.
The mechanical p ope ies o he composi es we e ca ied ou by means o he Young’s modulus
measu emen . The Young’s modulus o he samples was measu ed by mic oinden a ion (P-h) cu es.
The measu emen s o mic oinden a ion we e pe o med in a Mic o es machine (MTR3/50-50/NI) using
a Vicke s inden e . The de ails o he me hod ollowed ha e been shown elsewhe e [47].
In o de o s udy he in luence o he elas ic and magne ic p ope ies o composi es on hei Villa i
esponse, he measu emen s ha e been ca ied ou in di e en s eps, as shown in Figu e 2.
Ma e ials 2020, 13, x FOR PEER REVIEW 4 o 16
Table 1. Pa ame e s o manu ac u ed composi es.
Pa icles Size
(µm)
Weigh F ac ion
(w .%)
In luence o ein o cemen con en <50
45
65
75
In luence o pa icles size
150–180
60
180–250
>250
Figu e 1. Pic u e o he composi es: Cylind ical o Villa i measu emen s and ec angula p ims o
measu emen s o mic oinden a ion.
The mechanical p ope ies o he composi es we e ca ied ou by means o he Young's modulus
measu emen . The Young's modulus o he samples was measu ed by mic oinden a ion (P-h) cu es.
The measu emen s o mic oinden a ion we e pe o med in a Mic o es machine (MTR3/50-50/NI)
using a Vicke s inden e . The de ails o he me hod ollowed ha e been shown elsewhe e [47].
In o de o s udy he in luence o he elas ic and magne ic p ope ies o composi es on hei
Villa i esponse, he measu emen s ha e been ca ied ou in di e en s eps, as shown in Figu e 2.
Figu e 2. Scheme o Villa i measu emen s.
The classical induc ion me hod was used o ob ain he emnan magne iza ion o he composi es
a e being submi ed o an applied magne ic ield o 1 T. The measu emen s we e ob ained by means
5 mm
Figu e 2. Scheme o Villa i measu emen s.
The classical induc ion me hod was used o ob ain he emnan magne iza ion o he composi es
a e being submi ed o an applied magne ic ield o 1 T. The measu emen s we e ob ained by means o
a luxme e in eg a o (Magne -Physik EF 4, Köln, Ge many) connec ed o a pickup coil ha su ounds
Ma e ials 2020,13, 2472 5 o 15
he composi e. This coil o 7 mm inne diame e consis s o 20,000 u ns o coppe wi e o 0.05 mm
diame e . The magne ic cha ac e iza ion o he Fe81Ga19 pa icles was ca ied ou a oom empe a u e
using a ib a ing sample magne ome e (EV9–VSM 2.2 T, Mic oSense, Edinbu gh, UK).
The expe imen al sys em o measu e he Villa i e ec has been shown elsewhe e [
46
], and basically
consis s o a di ec powe supply which p o ides an elec ical cu en o a p ima y coil o magne ize
he sample and a pick up coil ha su ounds he sample. The Villa i signal is ob ained by means o
a luxme e connec ed o he pickup coil ha su ounds he sample, which is also connec ed o ano he
iden ical seconda y winding in se ies opposi ion. The pickup p o ides a signal p opo ional o B,
and he seconda y winding p o ides a signal p opo ional o
µ0
Ha. The e o e, he luxme e p o ides
a signal p opo ional o M. The ensile s ess was applied o he sample adding di e en weigh s o
a holde ixed o one end o he sample while he o he was a ached o a ixed jaw. The scheme o
he expe imen al se up is shown in Figu e 3.
Ma e ials 2020, 13, x FOR PEER REVIEW 5 o 16
o a luxme e in eg a o (Magne -Physik EF 4, Köln, Ge many) connec ed o a pickup coil ha
su ounds he composi e. This coil o 7 mm inne diame e consis s o 20,000 u ns o coppe wi e o
0.05 mm diame e . The magne ic cha ac e iza ion o he Fe81Ga19 pa icles was ca ied ou a oom
empe a u e using a ib a ing sample magne ome e (EV9–VSM 2.2 T, Mic oSense, Edinbu gh, UK).
The expe imen al sys em o measu e he Villa i e ec has been shown elsewhe e [46], and
basically consis s o a di ec powe supply which p o ides an elec ical cu en o a p ima y coil o
magne ize he sample and a pick up coil ha su ounds he sample. The Villa i signal is ob ained by
means o a luxme e connec ed o he pickup coil ha su ounds he sample, which is also connec ed
o ano he iden ical seconda y winding in se ies opposi ion. The pickup p o ides a signal
p opo ional o B, and he seconda y winding p o ides a signal p opo ional o µ0Ha. The e o e, he
luxme e p o ides a signal p opo ional o M. The ensile s ess was applied o he sample adding
di e en weigh s o a holde ixed o one end o he sample while he o he was a ached o a ixed
jaw. The scheme o he expe imen al se up is shown in Figu e 3.
Figu e 3. Expe imen al se up o measu ing he Villa i e ec .
Fi e measu emen s in loading/unloading cycles o he Villa i e ec we e pe o med o ensu e
he epea abili y o he esul s. In he ange o he measu emen s pe o med in ou wo k he e is a
good epea abili y o he esul s and no hys e esis e ec ha e been obse ed. On he o he hand, a
good linea i y is ob ained in all he measu emen s. The lack o hys e esis and he linea i y o he
signal make his kind o ma e ial e y p omising o use in senso echnology, because hese wo
cha ac e is ics a e undamen al in he signal used in his ield.
The measu emen s ha e been pe o med un il a de o ma ion o abou 10% because highe
s esses p oduce de ec s in he subjec ion pa s o he samples.
3. Resul s and Discussion
The hys e esis loops and he magne ic p ope ies o he di e en Fe81Ga19 magne ic pa icles
used in his wo k a e shown in Figu e 4 and Table 2.
Figu e 3. Expe imen al se up o measu ing he Villa i e ec .
Fi e measu emen s in loading/unloading cycles o he Villa i e ec we e pe o med o ensu e
he epea abili y o he esul s. In he ange o he measu emen s pe o med in ou wo k he e is a good
epea abili y o he esul s and no hys e esis e ec ha e been obse ed. On he o he hand, a good
linea i y is ob ained in all he measu emen s. The lack o hys e esis and he linea i y o he signal make
his kind o ma e ial e y p omising o use in senso echnology, because hese wo cha ac e is ics a e
undamen al in he signal used in his ield.
The measu emen s ha e been pe o med un il a de o ma ion o abou 10% because highe s esses
p oduce de ec s in he subjec ion pa s o he samples.
3. Resul s and Discussion
The hys e esis loops and he magne ic p ope ies o he di e en Fe81Ga19 magne ic pa icles
used in his wo k a e shown in Figu e 4and Table 2.
Ma e ials 2020, 13, x FOR PEER REVIEW 6 o 16
Figu e 4.
Hys e esis loops o he magne ic pa icles. The inse shows he enla gemen o he cen al
pa o he loops.
Table 2. Magne ic p ope ies o he pa icles in unc ion o he size.
Size o he Pa icles (µm) Hc (Oe) M (emu/g) Ms (emu/g)
<50 52 ± 1 9 ± 1 183 ± 1
150–180 32 ± 1 6 ± 1 183 ± 1
180–250 58 ± 1 13 ± 1 182 ± 1
>250 33 ± 1 10 ± 1 184 ± 1
Al hough he esul s shown in Table 2 do no p esen a clea co ela ion be ween he size o he
mic opa icles and he alue o he coe ci e ield, in all cases he so magne ic beha io o hese
pa icles is con i med.
Figu e 5 shows he images o he composi es make wi h he di e en sizes o pa icles used. The
pho og aphs show a ce ain dispe sion in shape and size o he pa icles. The images also show a
andom dis ibu ion o he pa icles in all he composi es, and he e o e he shape aniso opy due o
he non- ounded pa icles would be a e aged, esul ing in he iso opic composi es. No agg ega es
a e obse ed ha could con ibu e o an inc ease in he coe ci e ield o he composi es [48]. The
di e en dis ibu ion o sizes obse ed would explain he beha io o he coe ci e ield.
Figu e 4.
Hys e esis loops o he magne ic pa icles. The inse shows he enla gemen o he cen al
pa o he loops.

Ma e ials 2020,13, 2472 6 o 15
Table 2. Magne ic p ope ies o he pa icles in unc ion o he size.
Size o he Pa icles (µm) Hc (Oe) M (emu/g) Ms (emu/g)
<50 52 ±1 9 ±1 183 ±1
150–180 32 ±1 6 ±1 183 ±1
180–250 58 ±1 13 ±1 182 ±1
>250 33 ±1 10 ±1 184 ±1
Al hough he esul s shown in Table 2do no p esen a clea co ela ion be ween he size o
he mic opa icles and he alue o he coe ci e ield, in all cases he so magne ic beha io o hese
pa icles is con i med.
Figu e 5shows he images o he composi es make wi h he di e en sizes o pa icles used.
The pho og aphs show a ce ain dispe sion in shape and size o he pa icles. The images also show
a andom dis ibu ion o he pa icles in all he composi es, and he e o e he shape aniso opy due o
he non- ounded pa icles would be a e aged, esul ing in he iso opic composi es. No agg ega es a e
obse ed ha could con ibu e o an inc ease in he coe ci e ield o he composi es [
48
]. The di e en
dis ibu ion o sizes obse ed would explain he beha io o he coe ci e ield.
Ma e ials 2020, 13, x FOR PEER REVIEW 7 o 16
(a) (b)
(c) (d)
Figu e 5. Op ical mic og aphs showings mic os uc u e o Fe81Ga19/silicone composi es wi h
pa icles size: (a) <50 µm and con en o 45 w .%; (b) 150–180 µm; (c) 180–250 µm; (d) > 250 µm and
con en o 60 w .%.
3.1. In luence o he Con en o Rein o cemen
To s udy he in luence o he ein o cemen con en in he Villa i e ec in his kind o composi e,
he concen a ions o 45, 65 and 75 w .% o pa icles wi h size <50 µm ha e been used. The Villa i
signal has been measu ed in as-manu ac u ed samples and in samples submi ed o a magne ic ield
o 1 T a e cu ed as indica ed in Figu e 2 in he second and ou h s eps. In hese s eps a bias magne ic
ield o 2 mT has been applied o he measu emen s o he Villa i e ec . In he las s ep i was no
necessa y o apply he bias ield o ob ain a Villa i signal due o he emnan magne iza ion o he
composi es. The esul s ob ained in he second and ou h s eps o he p ocedu e a e shown in Figu e
6.
Figu e 5.
Op ical mic og aphs showings mic os uc u e o Fe81Ga19/silicone composi es wi h pa icles
size: (
a
)<50
µ
m and con en o 45 w .%; (
b
) 150–180
µ
m; (
c
) 180–250
µ
m; (
d
)>250
µ
m and con en o
60 w .%.
Ma e ials 2020,13, 2472 7 o 15
3.1. In luence o he Con en o Rein o cemen
To s udy he in luence o he ein o cemen con en in he Villa i e ec in his kind o composi e,
he concen a ions o 45, 65 and 75 w .% o pa icles wi h size <50
µ
m ha e been used. The Villa i signal
has been measu ed in as-manu ac u ed samples and in samples submi ed o a magne ic ield o 1 T
a e cu ed as indica ed in Figu e 2in he second and ou h s eps. In hese s eps a bias magne ic ield
o 2 mT has been applied o he measu emen s o he Villa i e ec . In he las s ep i was no necessa y
o apply he bias ield o ob ain a Villa i signal due o he emnan magne iza ion o he composi es.
The esul s ob ained in he second and ou h s eps o he p ocedu e a e shown in Figu e 6.
Ma e ials 2020, 13, x FOR PEER REVIEW 8 o 16
(a) (b)
Figu e 6. Villa i e ec in unc ion o he ille concen a ion: (a) As-manu ac u ed samples; (b) a e
being submi ed o a magne ic ield o 1 T, second and ou h s eps o he p ocedu e, espec i ely.
Figu e 6a shows ew di e ences be ween he Villa i signals ob ained o he di e en
manu ac u ed composi es. A e being submi ed o he magne ic ield o 1 T, in Figu e 6b i can be
obse ed a d ama ic inc ease in he Villa i signal co esponding o he composi es o 45 w .% and 65
w .%, while o he 75 w .% a sligh di e ence is obse ed.
These esul s sugges ha he ini ial magne iza ion o he composi es a e being subjec ed o he
magne ic ield o 1 T a ec s hei Villa i esponse. The applied magne ic ield p oduces an alignmen
o he magne iza ion o he pa icles esul ing in a ne magne iza ion o he composi e ma e ial ha
inc eases wi h inc easing concen a ion o he pa icles, so he Villa i signal should inc ease wi h he
concen a ion o he ille s. Howe e , as can be seen, he esul s show an opposi e beha io ; when he
ille concen a ion inc eases, he Villa i e ec dec eases. This is because in his kind o composi e
he e is an impo an con ibu ion o he Villa i signal due o he educ ion in he magne ic lux linked
o he educ ion in he c oss sec ion o he composi es when submi ed o a s ess [46]. In his way,
he inc ease in he ein o cemen con en p oduces a high igidi y o he composi e ha educes he
Villa i e ec because he e is a smalle educ ion in he su ace o he composi e wi h he s ess. This
in e p e a ion also explain he inc ease in he Villa i signal in he samples submi ed o he ield o 1
T because, in his case, he magne iza ion o he composi e is highe , so an equal educ ion in he
c oss sec ion o he sample will p oduce a g ea dec ease in he magne ic lux h ough i . To highligh
he esul s Figu e 7 shows he signals o he Villa i e ec measu ed in unc ion o he di e en s eps
o he p ocedu e.
In gene al, ou esul s a e consis en wi h hose p esen ed by o he au ho s who ha e s udied
he beha io o e ogels. Filipcsei e al. [43], de ec ed a weak e ec o magne ode o ma ion o gels
con ained andomly dis ibu ed magne ic pa icles, as well as, no magne ode o ma ion and swelling
was obse ed o gels con aining aligned pa icles in he polyme ma ix wi h he applica ion o low
magne ic ields (300 mT). On he o he hand, Zuba e e al. [42], indica e ha i he pa icle
concen a ion is small and hey a e andomly dis ibu ed in he ma ix, he sample can de o m in he
magne ic ield di ec ion (depending on pa icles shape). While, a composi e wi h a high concen a ion
o he pa icles can only elonga e due o e ec o he pa icles spa ial disposi ion (sho anged o de ).
The e o e, o es ima e ampli ude o his magne ode o ma ion, one should conside bo h mechanical
(due o he local de o ma ions o he ma ix) and magne ic in e ac ions be ween he pa icles.
Figu e 6.
Villa i e ec in unc ion o he ille concen a ion: (
a
) As-manu ac u ed samples; (
b
) a e
being submi ed o a magne ic ield o 1 T, second and ou h s eps o he p ocedu e, espec i ely.
Figu e 6a shows ew di e ences be ween he Villa i signals ob ained o he di e en manu ac u ed
composi es. A e being submi ed o he magne ic ield o 1 T, in Figu e 6b i can be obse ed
a d ama ic inc ease in he Villa i signal co esponding o he composi es o 45 w .% and 65 w .%, while
o he 75 w .% a sligh di e ence is obse ed.
These esul s sugges ha he ini ial magne iza ion o he composi es a e being subjec ed o
he magne ic ield o 1 T a ec s hei Villa i esponse. The applied magne ic ield p oduces an alignmen
o he magne iza ion o he pa icles esul ing in a ne magne iza ion o he composi e ma e ial ha
inc eases wi h inc easing concen a ion o he pa icles, so he Villa i signal should inc ease wi h
he concen a ion o he ille s. Howe e , as can be seen, he esul s show an opposi e beha io ;
when he ille concen a ion inc eases, he Villa i e ec dec eases. This is because in his kind o
composi e he e is an impo an con ibu ion o he Villa i signal due o he educ ion in he magne ic
lux linked o he educ ion in he c oss sec ion o he composi es when submi ed o a s ess [
46
].
In his way, he inc ease in he ein o cemen con en p oduces a high igidi y o he composi e ha
educes he Villa i e ec because he e is a smalle educ ion in he su ace o he composi e wi h
he s ess. This in e p e a ion also explain he inc ease in he Villa i signal in he samples submi ed
o he ield o 1 T because, in his case, he magne iza ion o he composi e is highe , so an equal
educ ion in he c oss sec ion o he sample will p oduce a g ea dec ease in he magne ic lux h ough
i . To highligh he esul s Figu e 7shows he signals o he Villa i e ec measu ed in unc ion o
he di e en s eps o he p ocedu e.
Ma e ials 2020,13, 2472 8 o 15
Ma e ials 2020, 13, x FOR PEER REVIEW 9 o 16
(a) (b)
(c)
Figu e 7. Resul s o he Villa i e ec in he di e en s eps o he expe imen : (a) Composi es wi h 45
w .%; (b) composi es wi h 65 w .%; (c) composi es wi h 75 w .%.
Fu he mo e, di e en beha io can be obse ed in he Villa i signals measu ed in he second
and ou h s eps depending on he concen a ion o ein o cemen . The 45 w .% and 65 w .%
composi es show a conside able inc ease in he Villa i e ec when subjec ed o he 1 T magne ic ield.
Fo he 75 w .% composi e, he e a e sligh di e ences be ween ha submi ed o he 1 T magne ic
ield and he as-manu ac u ed one. These esul s ein o ce he idea o he ela ionship be ween he
Villa i signal and he elas ic p ope ies o he composi e.
Figu e 7 also shows ha hese composi es p esen a Villa i signal wi hou applying a bias ield
du ing he measu emen ( i h s ep).
To e i y he ela ionship be ween he Villa i e ec and he mechanical p ope ies, he Young´s
modulus o he composi es has been ob ained by mic oinden a ion (P-h cu es). In a p e ious wo k
[47], some o he au ho s ha e adap ed he Oli e and Pha [49–51] me hod o he kind o composi es
used in his wo k. In his me hod, he ha dness is ob ained om he loading-unloading cu es by he
exp ession:
=


(1)
whe e P
max
is he maximum load and A is he con ac a ea.
The e ec i e elas ic modulus E
e
was calcula ed by he exp ession:
Figu e 7.
Resul s o he Villa i e ec in he di e en s eps o he expe imen : (
a
) Composi es wi h
45 w .%; (b) composi es wi h 65 w .%; (c) composi es wi h 75 w .%.
In gene al, ou esul s a e consis en wi h hose p esen ed by o he au ho s who ha e s udied
he beha io o e ogels. Filipcsei e al. [
43
], de ec ed a weak e ec o magne ode o ma ion o gels
con ained andomly dis ibu ed magne ic pa icles, as well as, no magne ode o ma ion and swelling
was obse ed o gels con aining aligned pa icles in he polyme ma ix wi h he applica ion o low
magne ic ields (300 mT). On he o he hand, Zuba e e al. [
42
], indica e ha i he pa icle concen a ion
is small and hey a e andomly dis ibu ed in he ma ix, he sample can de o m in he magne ic ield
di ec ion (depending on pa icles shape). While, a composi e wi h a high concen a ion o he pa icles
can only elonga e due o e ec o he pa icles spa ial disposi ion (sho anged o de ). The e o e, o
es ima e ampli ude o his magne ode o ma ion, one should conside bo h mechanical (due o he local
de o ma ions o he ma ix) and magne ic in e ac ions be ween he pa icles.
Fu he mo e, di e en beha io can be obse ed in he Villa i signals measu ed in he second and
ou h s eps depending on he concen a ion o ein o cemen . The 45 w .% and 65 w .% composi es
show a conside able inc ease in he Villa i e ec when subjec ed o he 1 T magne ic ield. Fo he
75 w .% composi e, he e a e sligh di e ences be ween ha submi ed o he 1 T magne ic ield and
he as-manu ac u ed one. These esul s ein o ce he idea o he ela ionship be ween he Villa i signal
and he elas ic p ope ies o he composi e.
Figu e 7also shows ha hese composi es p esen a Villa i signal wi hou applying a bias ield
du ing he measu emen ( i h s ep).
To e i y he ela ionship be ween he Villa i e ec and he mechanical p ope ies, he Young’s
modulus o he composi es has been ob ained by mic oinden a ion (P-h cu es). In a p e ious wo k [
47
],
Ma e ials 2020,13, 2472 9 o 15
some o he au ho s ha e adap ed he Oli e and Pha [
49
–
51
] me hod o he kind o composi es
used in his wo k. In his me hod, he ha dness is ob ained om he loading-unloading cu es by
he exp ession:
H=Pmax
A(1)
whe e Pmax is he maximum load and Ais he con ac a ea.
The e ec i e elas ic modulus Ee was calcula ed by he exp ession:
Ee =S
β2
√π√A(2)
whe e Sis he slope o unloading P-h cu es and βis a co ec ion ac o dependen o he inden e .
Finally, he elas ic modulus was calcula ed om E
e
conside ing he elas ic modulus o he inden e
Ei, he Poisson’s a io o he inden e υiand ha o he silicone υ, by he exp ession:
E=1−υ2
1
Eee −(1−υ2
i)
Ei
(3)
In Figu e 8, he P-h loading and unloading cu es o he composi es illed wi h 45, 65 and 75 w .%
o magne ic pa icles a e shown.
Ma e ials 2020, 13, x FOR PEER REVIEW 10 o 16
 =
2
√

√

(2)
whe e S is he slope o unloading P-h cu es and β is a co ec ion ac o dependen o he inden e .
Finally, he elas ic modulus was calcula ed om E
e
conside ing he elas ic modulus o he
inden e E
i
, he Poisson´s a io o he inden e υ
i
and ha o he silicone υ, by he exp ession:
= 󰇛1−
󰇜
1
 −󰇛1−

󰇜

(3)
In Figu e 8, he P-h loading and unloading cu es o he composi es illed wi h 45, 65 and 75
w .% o magne ic pa icles a e shown.
Figu e 8. P-h cu es o he composi es wi h 45, 65 and 75 w .% o Fe81Ga19.
F om hese cu es he Young´s modulus shown in Table 3 a e ob ained.
Table 3. Young´s modulus o he composi es wi h 45, 65 and 75 w .% o Fe81Ga19.
Weigh F ac ion (w .%) Young’s Modulus (MPa)
45 1.77 ± 0.03
65 3.33 ± 0.03
75 6.37 ± 0.03
The Villa i signals o Figu e 6 ha e been adjus ed o a quad a ic unc ion in o de o compa e
he slopes ob ained om he adjus men s wi h he mechanical and magne ic p ope ies o he
composi es. In his way, Figu e 9 shows he slope o he adjus men o he Villa i signals, he Young´s
modulus and he ini ial magne ic lux o he samples in unc ion o he concen a ion o he pa icles
in he composi e.
Figu e 8. P-h cu es o he composi es wi h 45, 65 and 75 w .% o Fe81Ga19.
F om hese cu es he Young’s modulus shown in Table 3a e ob ained.
Table 3. Young’s modulus o he composi es wi h 45, 65 and 75 w .% o Fe81Ga19.
Weigh F ac ion (w .%) Young’s Modulus (MPa)
45 1.77 ±0.03
65 3.33 ±0.03
75 6.37 ±0.03
The Villa i signals o Figu e 6ha e been adjus ed o a quad a ic unc ion in o de o compa e
he slopes ob ained om he adjus men s wi h he mechanical and magne ic p ope ies o he composi es.