Spa k plasma sin e ing in luence on mic os uc u e and mechanical
p ope ies o Ti:Ta/ca boni ide ce amic ma ix composi es
Jos´
e Manuel C´
o doba Gallego
Depa amen o de Química Ino g´
anica, Facul ad de Química, Uni e sidad de Se illa (US), C/T amon ana s/n, 41012 Se illa, Spain
ARTICLE INFO
Keywo ds:
Ce amic ma ix composi e
Spa k plasma sin e ing
Mic os uc u e
Mechanical p ope ies
ABSTRACT
A mechanically induced sel -sus aining eac ion was ca ied ou o syn hesize a Ti
0.9
Ta
0.1
C
0.5
N
0.5
/Co powde ed
ce me s, and hen hey we e sin e ed by spa k plasma sin e ing. Mic os uc u al pa ame e s e ec s s udied by
image analysis, and chemical composi ion (s udied by Rie eld analysis) on he mic oha dness, ha dening a e,
ac u e oughness, ans e se up u e s eng h, and Young’s modulus we e ela ed o he sin e ing condi ions.
The op imiza ion o he sin e ing condi ions (1150 ◦C, 30 MPa, and 8 min’ dwell ime) d o e o a homogeneous
mic os uc u e and ou s anding mechanical p ope ies. Also, he an alum was sugges ed o in luence he
in e acial ene gies o he sys em, yielding a s onge ha d phase skele on.
1. In oduc ion
Technically and comme cially, ce me s a e among he mos impo -
an composi e ma e ials due o hei excep ional ha dness and wea
esis ance. Because he cons i uen phases o i anium ca boni ide a e
excep ionally ha d and s able, he ce me s based on his ma e ial ha e
ex ao dina y esis ance o wea and c eep. They a e excellen op ions
o use as cu ing ools because o hese quali ies. Ca bides like TaC,
NbC, Mo
2
C, and WC, a e equen ly u ilized in milling applica ions and
in e up ed cu s o enhance cu ing pe o mance. These ca bides o m
solid-solu ion phases o mixed ca boni ides and exhibi ema kable ho
ha dness and he mal shock endu ance. [1–3].
The ha d componen o ce me s, called he mas e alloy, has a
composi ion ha de e mines bo h he p oduc ion condi ions and he
in ended applica ion’s echnical pe o mance, making i c ucial [4]. I is
widely accep ed in li e a u e [5–7] ha he o ma ion o ca boni ide
solid solu ions in e ms o e na y o qua e na y componen s uc u e is
gi en excellen pe o mance o ce me s syn hesized om he mix u e o
unalloyed ha d componen s wi h Co o Ni as binde . Ca boni ide solid
solu ions, which combine he ca bide and ni ide componen s in o a
single phase, ha e been ecommended as a way o enhance he cha -
ac e is ics o ce me s [8]. Based on Ti
y
M
T1-y
C
x
N
1-x
ca boni ides (M
T
=
Ta, Nb, Z , V) wi h a na ow size dis ibu ion and submic ome ic
cha ac e (250 nm), mechanically induced sel -sus aining eac ion
(MRS) has ecen ly been p oposed as a us wo hy and s aigh o wa d
me hod o p oducing high pu i y complex solid solu ion powde s
[9–12].
Con en ional ce amic ma e ial sin e ing me hods in ol e high
empe a u es. A high deg ee o sin e ing is achie ed by hea ing he
g een specimen o high empe a u es o p olonged pe iods in a ypical
sin e ing echnique. The sin e ed i em usually con ains la ge g ains as a
esul o hese un a o able condi ions, which eg e ably encou age
unwan ed ca bide g ain de elopmen in he p esence o me al liquids. As
a esul , he ool’s mechanical capabili ies a e educed. I is commonly
known ha a ine mic os uc u e esul s in be e mechanical quali ies
and a longe p oduc li espan.
Spa k plasma sin e ing (SPS), in compa ison o p essu eless sin e -
ing, is a no el sin e ing echnique ha applies p essu e and elec ic
cu en o he sample simul aneously [13–14]. A compa a i ely low
empe a u es (ap ox. 500 ◦C lowe han p essu eless sin e ing), and
as e hea ing a es (ap ox. 100 ◦C/min), i enables he apid consoli-
da ion o powde compac s o a high densi y. The SPS echnique has
shown p omising esul s in educing he sin e ing empe a u e while
simul aneously con olling g ain g ow h and seconda y phase o ma ion
[15–17]. I is unique o esea ching bulk nanoma e ials because o he
quick hea ing a e and po en ial o main ain he nanoscale du ing he
apid sin e ing cycle.
This s udy looked in o how he SPS se ings a ec ed he sin e ing o
powde s wi h submic ome ic g ain sizes, Ti
0,9
Ta
0,1
C
0,5
N
0,5
/Co, ha
we e p oduced ia MSR. The esul ing ce me s’ mic os uc u e and
mechanical cha ac e is ics (ha dness, ac u e oughness, ans e se
up u e s eng h (TRS), and Young’s modulus) we e assessed and con-
as ed wi h hose o he compa able cemen ed ca bides and o dina y
ce me s.
E-mail add ess: [email p o ec ed].
Con en s lis s a ailable a ScienceDi ec
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h ps://doi.o g/10.1016/j.ij mhm.2025.107094
Recei ed 4 Janua y 2025; Recei ed in e ised o m 29 Janua y 2025; Accep ed 12 Feb ua y 2025
In e na ional Jou nal o Re ac o y Me als and Ha d Ma e ials 128 (2025) 107094
A ailable online 13 Feb ua y 2025
0263-4368/© 2025 The Au ho . Published by Else ie L d. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
2. Ma e ials and me hods
The Ti
0.9
Ta
0.1
C
0.5
N
0.5
solid solu ion was syn hesized by MRS, and he
desc ip ion o he syn hesis p ocedu e and cha ac e iza ion (XRD, SEM,
TEM, and image analysis) o he as-syn hesized powde s pe o med in a
p e ious esea ch [12].
The ob ained powde s we e sin e ed using SPS-1050-CE (D . Sin e ,
Japan) a 1150 ◦C unde di e en holding imes and p essu es (see
Table 1). X- ay di ac ion diag ams and Scanning Elec on Mic oscopy
images o ce me s polished su aces we e ob ained using simila pa-
ame e s as desc ibed in [18] The la ice pa ame e s, phase olume
ac ion, and ce amic s oichiome y we e de e mined om he XRD di-
ag am using he Rie eld analysis by he use o he Fullp o [19] com-
pu e p og am.
The Vicke s es was ca ied ou in a Mic oha dness FM-700 (Fu u e-
Tech. Co p) wi h a load o 49 mN, 196 mN, and 981 mN and dwell ime
anging om 5 s o 90 s a oom empe a u e. Se e al mic o-
inden a ions (12 imes) a di e en loca ions we e aken on he pol-
ished ce me o e e y un. The s a ed alue was ound om he a e age
o he measu ed alues (
σ
= ±5 %). The ac u e oughness (KIC) was
measu ed by using h ee inden a ion me hods unde an inden a ion load
o 1 kg and hey we e desc ibed below.
The pieces o lexu al es s we e cu om he spa k plasma sin e ed
cylinde s and buil in o ingo s wi h ba shapes (dimensions o 3×4×25
mm). The oom empe a u e (RT) lexu al s eng h was ca ied ou in a
h ee-poin bending a angemen , using a c osshead speed o 0.5 mm/
min and span o 20 mm (AGS-X 10kN Se ies Dual Column Elec ome-
chanical Tes F ame, Shimadzu, Japan). All samples we e g ound o
dimensions using esin-bound diamond g inding wheels and su ace
g inde s o achie e dimensional accu acy as well as good su ace
inishing.
The image analysis was ca ied ou by using he Image P o-Plus 6.0
so wa e and mic os uc u al pa ame e s we e ob ained as desc ibed in
C´
o doba e al. [20].
3. Resul s and discussion
3.1. Composi ional analysis
The phase composi ion o he sin e ed bodies was in es iga ed by
XRD analysis as shown in Fig. 1. The XRD pa e ns show he peaks
cha ac e is ic o he ce amic phase (•) and he me allic binde phases
consis ing o he in e me allics (*) Ti
x
Ta
1-x
Co
2
[Fd3m] and (○) Ti
x
Ta
1-
x
Co [Pm3m] p oduced du ing he high- empe a u e sin e ing. Table 2
desc ibes he quan i ica ion o he phases obse ed in he XRD pa e ns,
he la ice pa ame e s, he cohe en di ac ion domains, and he co -
esponding ce amic composi ion ob ained om Rie eld analysis.
As shown in Table 2, he Ti/Ta a io was somewha cons an
ega dless o he sin e ing condi ions used. Howe e , he C/N a io o
(Ti, Ta)(C, N) dec eased when he sin e ing condi ions we e s onge (C/
N a io; SPS1, 1.50, SPS2, 1.38; SPS3, 0.92; SPS4, 0.75). This ca bon loss
was a ibu ed o he ca bon dissolu ion inc easing in he binde phase.
The mos signi ican change in he binde phase con en (Table 2) is
obse ed in sample SPS4, when a p essu e o 60 MPa was used. Because
he powde con aine o he SPS is no sealed, he e was some loss o he
binde du ing he p ocess, and a smalle amoun was obse ed and
quan i ied by he composi ional analysis in compa ison wi h he o he
samples. This ac was co obo a ed by he p esence o solidi ied d op-
le s a he ou side o he con aine .
In Fig. 2 a e shown cha ac e is ic sample SEM images sin e ed unde
Table 1
Summa y o spa k plasma sin e ing condi ions.
Sample Nominal Composi ion Weigh [g] Sin e ing Pa ame e s
1
Ti
0.90
Ta
0.10
C
0.5
N
0.5
+20 %Co
4 1150 ◦C 30 MPa 120 s
2 12 1150 ◦C 30 MPa 120 s
3 12 1150 ◦C 30 MPa 480 s
4 12 1150 ◦C 60 MPa 120 s
Fig. 1. XRD pa e ns o he sin e ed ce me s by SPS. (•) Ti
x
Ta
1-x
C
y
N
1-y
[Fm3m],
(*) Ti
x
Ta
1-x
Co
2
[Fd3m], (○) Ti
x
Ta
1-x
Co [Pm3m].
Table 2
Composi ion, la ice pa ame e , cohe en di ac ion domain o he ce amic phase, and desc ip ion o e e y binde phase ound by Rie eld analysis. Fo e e y phase
he % ol. is included. The las column illus a es he goodness o i ness o e e y analysis ca ied ou .
Ce amic Phase Binde Phase
Sample Ce amic Composi ion a (Å) D [nm] % ol. Ce am Co
2
Ti(Ta) [Fd3m] [%] CoTi(Ta) [Pm3m] [%]
χ
2
SPS1 Ti
0.90
Ta
0.10
C
0.60
N
0.40
43,162 33 78,7 15,7 5,6 1,8
SPS2 Ti
0.86
Ta
0.14
C
0.58
N
0.42
43,184 67 75,2 19,0 5,8 2,2
SPS3 Ti
0.91
Ta
0.09
C
0.48
N
0.52
43,157 74 77,1 18,0 4,8 3,0
SPS4 Ti
0.92
Ta
0.08
C
0.43
N
0.57
43,170 52 86,5 11,0 2,5 2,7
Fig. 2. SEM images showing he cha ac e is ic mic os uc u e o he sin-
e ed powde s.
J.M. C´
o doba Gallego
In e na ional Jou nal o Re ac o y Me als and Ha d Ma e ials 128 (2025) 107094
2
di e en condi ions. Da a ob ained om he image analysis a e p e-
sen ed in Table 3. Quan i ica ion o he phases p esen ed on he sin e ed
samples h ough image analysis ga e esul s consis en wi h hose ob-
ained by he XRD esul s by Rie eld analysis. All he samples p esen ed
a highly dense (densi ica ion o ~98 % ±2 %, om image analysis, i e
images a simila scale we e analyzed) and uni o m mic os uc u e.
Al hough ea ly milling p oduc s con ained ypical pa icle agg ega es,
no anomalous de elopmen o g ains was de ec ed. This indica es ha
he sin e ing be ween agg ega es and ine pa icles was p e en ed by he
spa k plasma sin e ing.
Mos o he mic ome ic pa icles obse ed in samples SPS1 and SPS4
displayed a ypical co e- im mic os uc u e p o iding e idence o g ain
g ow h by dissolu ion-p ecipi a ion p ocesses despi e he low empe a-
u e and he sho esidence ime a he maximum sin e ing empe a-
u e. In con as , he co e- im mic os uc u e app ecia ed in samples
SPS2 and SPS3 is ba ely isible.
The sample SPS1 showed he highes a e age ce amic pa icle size
(Ø =2.56
μ
m), while he samples SPS2, SPS3, and SPS4 we e lowe , and
in c escendo om SPS2 o SPS4 (Ø =1.10, 1.95 and 2.28
μ
m, espec-
i ely). I is common o use an op ical py ome e ocused on he ou e
su ace o he die o measu e and con ol he empe a u e du ing SPS
expe imen s. This isn’ good enough o high hea ing a es, whe e he
SPS p ocess’s iabili y is one o i s mos e iden bene i s. I migh be
su icien o e y slow hea ing a es whe e he mal equilib ium can be
eached. Mo eo e , because hea ing is esis i e, bo h he sample’s and
he die’s conduc i i ies a ec he empe a u es inside and ou side he
sample. The e is a no iceable empe a u e di e ence be ween he sam-
ples when a low-conduc i e ma e ial is u ilized (in his example, a
composi e made o ce amic and in e me allic phases) [21]. Due o he
inc emen in mass on he samples om SPS1 o he es , he dis ance o
be a eled by he cu en is inc eased, and he e o e he esis i i y o
he sample ( esis i i y quan i ies how s ongly he ma e ial opposes he
low o elec ic cu en and i is a unc ion o he dis ance oamed). So,
he jump om 4 g (SPS1) o 12 g (SPS2, 3, and 4) inc eased he em-
pe a u e g adien , he e o e he empe a u e eached inside sample
SPS1 is highe han in he o he ones, and his e ec is shown in he
coa sening o he SPS1 ce amic g ains espec he o he samples. Also,
he o ma ion o a clea co e- im mic os uc u e in sample SPS1 (Fig. 2
(a)) co obo a ed he inside highe empe a u e eached. To o m a co e-
im mic os uc u e, a liquid phase sin e ing has o be eached du ing he
p ocess, and he e o e highe sin e ing empe a u es a e needed.
When a simila weigh was used (samples SPS2, 3, and 4) and simila
empe a u e inside he sample can be supposed, he g ain coa sening
was due o an enhancemen o he elemen di usion du ing he sin e ing
because o he inc emen in he sin e ing ime (SPS3) and p essu e
(SPS4).
Simila beha io was obse ed in e ms o con igui y and mean ee
pa h. Sample SPS1 showed he highes con igui y and lowes mean ee
pa h alues o he se o samples s udied, while samples SPS2, 3, and 4
showed an inc emen in he con igui y om SPS2(0.25) <SPS3(0.28) <
SPS4(0.32) and a dec ease in he mean ee pa h om SPS2(1.32) >
SPS3(1.27) >SPS4(1.20). As abo e, he coa sening o he g ains due o
he highe empe a u e in sample SPS1 inc eased he con ac be ween
he ce amic pa icles and he e o e he inc ease in he con igui y and he
educ ion o he mean ee pa h.
3.2. Mechanical p ope ies
In Table 3 is showed he ha dness, he ac u e oughness, he
ans e se up u e s eng h and he young’s modulus o he samples
s udied. Fig. 3 depic s SEM mic og aphs showing inden a ions c ea ed
on he su ace o he in es iga ed objec , as well as c acks eme ging om
hem, unde 1 kg o ce. Ha dness alues we e compu ed using he di-
mensions o he imp ession c ea ed on he su ace o he specimens, and
he alues epo ed in Table 3 a e he a e age o wel e uns.
The SPS4 sample showed he highes ha dness (16.0 GPa) while he
es o he samples p esen ed a mic oha dness o abou ~14 GPa. This
can be explained by he loss o binde du ing he sin e ing p ocedu e
which made he p ope combina ion o ce amic pa icle size and con-
igui y o each he highes mic oha dness in sample SPS4.
Mic oinden a ions a di e en loads (49 mN, 196 mN, and 981 mN)
we e pe o med a se e al ime uns o es ablish he s eng hening o he
ma e ial by wo k ha dening, and esul s a e p esen ed in Fig. 4. As a
esul o disloca ion mo emen s and disloca ion gene a ion wi hin he
ma e ial’s c ys al s uc u e, i is e iden ha he mic oha dness in-
c eases wi h un ime. This esis ance o disloca ion- o ma ion shows up
as a esis ance o plas ic de o ma ion, which accoun s o he obse ed
Table 3
Vicke s ha dness, con igui y and a e age ee pa hway, wi h he a e age ce amic pa icle size, ce amic olume, binde olume and po ous olume ha we e ex ac ed
om he image analysis o he selec ed samples.
Image Analysis Mechanical P ope ies
Con igui y
(C)
Mean ee
pa h (
μ
m)
Ce amic
Pa icle Size
(
μ
m)
Ce amic
Volume (%
ol)
Binde
Volume (%
ol)
Po ous
Volume (%
ol)
Sample H
(1.0)
[GPa]
K
ic
[MPam
1/
2
]*
T ans e se Rup u e
S eng h [MPa]
Young’s
Modulus
[GPa]
0,36 1,09 2,56 80 19 1 SPS114,1 6,2/5,4/
5,0 130,6 139,7
0,25 1,32 1,10 78 21 1 SPS214,4 8,5/8,0/
7,9 448,6 324,1
0,28 1,27 1,95 80 19 1 SPS314,6 7,4/7,0/
7,1 546,0 402,7
0,32 1,20 2,28 85 14 1 SPS416,0 6,7/5,1/
6,0 522,3 318,4
*
Re , [22,23], [24,25].
Fig. 3. Cha ac e is ic SEM mic og aphs o mic oinden a ion ma ks ca ied ou
on polished su ace o he sin e ed samples.
J.M. C´
o doba Gallego
In e na ional Jou nal o Re ac o y Me als and Ha d Ma e ials 128 (2025) 107094
3
s eng hening. F om he slope o he lineal i ing o he da a, he
ha dening o he ma e ial as a unc ion o ime is p esen ed o e e y
s udied sample o e e y load in Fig. 5. A highe load lowe ha dening
a e was obse ed. A highe load, he a ea unde he inden a ion ip is
bigge and he numbe o disloca ions, which con ibu es o he
s eng hening, pe uni a ea was lowe han when low load was used.
F ac u e oughness has been e alua ed o each sample using Eqs.
(1)–(3). The esul s ob ained a e shown in Table 3, whe e sligh di e -
ences in he calcula ed K
ic
can be seen depending on he exp ession used.
(She y e al.) [22,23]
KIC(P) = 0,0319×(P
a×
∑l
√)(1)
(Shube e al) [24]
KIC(S) = 0,0028×
H ×P×∑l
√(2)
(E ans and Cha les e al.) [25]
KIC(EC) = 0,16×H ×
a
√
(c
a)
3
/
2
(3)
whe e K
ic
[M Pa m
1/2
], P: load [N], l: c ack leng h: [mm], H
: ha dness
[N/mm
2
], a: hal -diagonal [mm] and c: c ack+hal diagonal [mm]. I
should be no ed a his poin ha he equa ion o Schube e al. [24] was
de i ed om ha o She y e al. [22,23], and can be deduced by
adjus ing he uni s and expe imen al pa ame e s. E en so, in ou case i
was used as a way o in oducing di e en expe imen al pa ame e s in o
an equa ion o ob ain K
IC,
and be able o compa e he da a ob ained wi h
di e en expe imen al c i e ia. Finally, in his way, o K
IC
compa ison,
while he E ans and Cha les equa ion, which was o med in he p e ious
decade, was p oduced o ma e ials in gene al, he She y and Shube
equa ions we e cons uc ed o composi e ma e ials, such as cemen ed
ca bides (WC-Co), simila o he ma e ial p esen ed in his wo k.
The a e age K
ic
alues ob ained om he equa ions used can be
summa ized as; SPS1, 5.6; SPS2, 8.1; SPS3, 7.1 and SPS4, 5.9. These
alues a e closely ela ed o he a e age g ain size and he mean ee
pa h. The smalle he g ain size o highe he mean ee pa h is, he
g ea e he ac u e oughness. The olume pe cen age o g ain bo de s
o in e aces g ows signi ican ly wi h dec easing g ain size o inc easing
mean ee pa h. In ma e ials such as in e me allic compounds and ce-
amics, which a e usually ex emely s ong bu e y b i le, educing he
g ain size o inc easing he mean ee pa h inc emen p omo es duc ili y
by inc easing he p obabili y o g ain bounda y sliding. Pe o mance
gains and a la ge p ocessing ad an age a e p o ided by his.
The TRS and Young’s modulus de e mined a oom empe a u e o
he s udied samples a e p esen ed in Table 3. A cons an sin e ing
empe a u e, he oughe is he sin e ing condi ions (highe ime o
highe applied p essu e), he g ea e is he TRS. Samples SPS3 and SPS4
showed he highes combina ion o TRS and Young’s modulus in com-
pa ison wi h samples SPS1 and SPS2, showing he sample SPS1 he
lowes alues o all s udied samples.
The ema kable inc emen in TRS and Young’s modulus om sample
SPS1 o samples SPS2, SPS3, and SPS4 can be explained in e ms o
con igui y and mean ee pa h. The highe he mean ee pa h and lowe
Fig. 4. Mic oha dness e sus ime o he inden a ion un showing he inc emen in he mic oha dness o he sample by wo king ha dening.
Fig. 5. Ha dening a e (GPa/s) e sus inden a ion load.
J.M. C´
o doba Gallego
In e na ional Jou nal o Re ac o y Me als and Ha d Ma e ials 128 (2025) 107094
4
he con igui y is, he g ea e he TRS and Young’s modulus a e [26,27].
The combina ion o alues o ce amic pa icle size, con igui y and mean
ee pa h made o he sample SPS3 is he bes ma ch o ha e he highes
TRS alue.
Cha ac e is ics SEM image o a ac u e su ace o sample SPS3 is
p esen ed in Fig. 6. In Fig. 6(a), a seconda y elec ons image shows he
opog aphy o he ac u e su ace, and in Fig. 6(b), a backsca e ing
elec on image shows he phase dis ibu ion associa ed wi h he
di e en con as s. The ac u e su ace obse ed o s udied ce me s
showed mainly a ypical ans-g anula ac u e. This kind o ac u e
mechanism showed he high adhesion be ween he ce amic phase and
he in e me allic phase. I is sugges ed ha an alum p esence in lu-
enced he in e acial ene gies o he sys em, yielding a s onge ha d
phase sca olding.
The ce me ac u e su aces become ine and he a io o in e -
g anula ac u e inc eases o some ex en wi h he inc easing o ine
ce amic g ins con en (Fig. 6, igh op). I is e iden ha he me al
binde is s ill co e ing he g ains on he ac u e su ace, displaying
dimples.
The ollowing desc ibes he oughening mechanisms: he p esence o
co eless g ains (samples SPS2 and SPS3) can be hough o be ad an-
ageous o he ce me s’ oughness. I is simple o p omo e mo e ac u e
o ma ion a he in e ace be ween he co e and im since he bonding
o ce he e is weake han ha o he homogeneous g ain (samples SPS1
and SPS4). I implies ha highe ac u e oughness is achie ed by
ce me s wi h a single phase and no co e/ im in e ac ion [28,29].
In compa ison wi h o he epo s [30] whe e an alum p esence
wo sens he mechanical p ope ies, he spa k plasma sin e ing ech-
nique has p o en o o m an adequa e en i onmen o he ob aining o
sin e ed bodies wi h ou s anding mechanical p ope ies.
4. Conclusions
The e ec s o SPS pa ame e s on mic os uc u e and mechanical
p ope ies o Ti
0.9
Ta
0.1
C
0.5
N
0.5
/Co-based ce me s we e in es iga ed and
he conclusions ob ained in his s udy can be summa ized as ollows:
(i) Highly densi ied p oduc s we e ob ained independen ly o he
condi ions used.
(ii) The bes combina ion o mechanical p ope ies and homogeneous
mic os uc u e was ob ained when sin e ing ime was held o 8
min a 30 MPa and 1150 ◦C.
(iii) Ha dening a e was quan i ied as a unc ion o he mic oha dness
e sus un ime.
Conside ing he simplici y o he composi ions, hese ce me s
showed g ea po en ial o u u e applica ions. The p esence o an alum
is hough o ha e a posi i e e ec on he g ain and/o phase bo de s. I
is p oposed ha an alum a ec s he sys em’s in e acial ene gies,
esul ing in he p oduc ion o an in e me allic binde and a s onge ha d
phase skele on.
CRediT au ho ship con ibu ion s a emen
Jos´
e Manuel C´
o doba Gallego: W i ing – e iew & edi ing, W i ing
– o iginal d a , Visualiza ion, Valida ion, Supe ision, So wa e, Re-
sou ces, P ojec adminis a ion, Me hodology, In es iga ion, Fo mal
analysis, Da a cu a ion, Concep ualiza ion.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial
in e es s o pe sonal ela ionships ha could ha e appea ed o in luence
he wo k epo ed in his pape .
Acknowledgmen s
I would like o hank An onia Gallego C´
a denas and Jos´
e F ancisco
C´
o doba Sosa o hei unwa e ing s eng h and suppo , o always
pushing me o mo e o wa d e en in he mos di icul and haza dous
si ua ions.
Da a a ailabili y
No da a was used o he esea ch desc ibed in he a icle.
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