Science o Sin e ing, 48 (2016) 317-324
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doi: 10.2298/SOS1603317P
UDK 546.62; 546.831; 622.785; .001.572
A P ac ical App oach o he Calcula ion o he Ac i a ion
Ene gy o he Sin e ing
Pouchly Vacla *), H uby Jan, Maca Ka el
CEITEC BUT, B no Uni e si y o Technology, Technicka 10, 616 00 B no, Czech
Republic
Abs ac :
Newly de eloped so wa e o calcula ion o ac i a ion ene gy (Qs in he ollowing) o
sin e ing using he Wang and Raj model is p esen ed. To demons a e he p ac ical po en ial
o he so wa e and o e alua e he beha iou o he Qs du ing he sin e ing p ocess, alumina
and cubic zi conia ce amic compac s we e p epa ed om nanome ic powde s. The esul s
ob ained wi h bo h ma e ials a e in ag eemen wi h p e iously published da a calcula ed by
di e en app oaches. In he in e al o in e es ( ela i e densi ies om 60 % o almos 100 %
o heo e ical densi y), bo h ma e ials show simila beha iou . Th ee dis inc egions can be
seen: he ini ial cons an alues o Qs 868 kJ/mol and 762 kJ/mol o alumina and cubic
zi conia, espec i ely; a egion con aining linea d op o Qs and he inal egion o cons an
Qs alues 625 kJ/mol and 645 kJ/mol o alumina and cubic zi conia, espec i ely.
Keywo ds: Sin e ing, Ac i a ion ene gy, Alumina, Zi conia.
1. In oduc ion
The ce amic p ocessing s a s om he syn hesis o ce amic powde and g een body
o ma ion. The compac ed g een body is usually po ous and agile. To ob ain desi ed
unc ional p ope ies, he sin e ing s ep has o be in oduced [1]. Du ing he sin e ing p ocess,
he g een body is hea ed a empe a u es app oaching mel ing. This allows po es o sh ink and
disappea , which leads o densi ica ion. The sin e ing p ocess is di ided in o h ee s ages [2].
Du ing he ini ial s age, he su ace o he pa icles is smoo hed and he e is an ini ia ion o he
neck o ma ion [3]. Du ing he in e media e s age, he necks g ow quickly and high o e all
sh inkage o he g een body occu s. The po osi y apidly dec eases and g ain bounda ies a e
o med. When he densi y eaches i s c i ical alue, he po es a e no longe in e connec ed and
he g een body en e s he inal s age o sin e ing. The po es a e now closed, hus hei
sh inkage a e is slow and e en mo e di icul . The inal sin e ing s age is usually connec ed
wi h apid g ain g ow h, as a way o disappea ance o s able po es [4].
To desc ibe he non-equilib ium he modynamics and kine ics o sin e ing, he
knowledge o he ac i a ion ene gy o all con ibu ing mechanisms is essen ial. Howe e , i is
di icul o expe imen ally measu e he ac i a ion ene gy o sin e ing (Qs in he ollowing) o
each sin e ing mechanism sepa a ely. Fo una ely, he Qs o he whole sin e ing p ocess can
be e alua ed. Two pa icula models, among o he s, caugh a en ion o scien is s in ecen
yea s such as Mas e Sin e ing Cu e model (MSC in he ollowing) [5] and he Wang and
Raj model [6]. Few yea s ago, we de eloped he so wa e o e alua ion o he Qs by he MSC
model [7]. Since he publica ion o he MSC so wa e, he ce amic socie y has showed in e es
*) Co esponding au ho : acla .pouchl[email p o ec ed]
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318
in such applica ions, so we would like o con ibu e u he in his opic. The aim o his pape
is o p esen so wa e o calcula ion o he Qs using he Wang and Raj model. Wi h he help
o newly de eloped so wa e, we can easily e alua e he Qs in wide densi y ange. To show
he scien i ic impac o his enginee ing app oach, we p esen calcula ions o Qs o wo
common ma e ials, pu e alumina and cubic zi conia. The new da a would help o unde s and
he sin e ing p ocess o hese ma e ials e en u he .
The Wang and Raj model
The model o Wang and Raj is based on a model o Young and Cu le [8, 9]. They
combined he model o sh inkage du ing sin e ing wi h a he modynamic backg ound, o ind
he Qs. Thei model is based on a densi ica ion a e acco ding o Eq. 1:
n
RTQ
G
T
e
A
d
d)(
/
ρρ
−
= (1)
whe e,
R
VC
A
3/2
γ
= (2)
C is a cons an , V is mola olume and (
ρ
) is a unc ion only o a densi y. The densi ica ion
a e can be also w i en as:
d
dT
dT
d
d
d
ρρ
= (3)
Combining and loga i hm o Eq. 1 and 3, Eq. 4 will be ob ained:
()
GnA
RT
Q
d
dT
dT
d
Tslnln)(lnln −++−=
⎟
⎠
⎞
⎜
⎝
⎛
ρ
ρ
. (4)
When a plo o he le -hand side o he Eq. 4 is plo ed agains 1/T, he slope o he line
de e mines he Qs. This calcula ion is alid only i no g ain g ow h occu s. Un o una ely, he
g ain size cons an ly inc eases du ing he sin e ing p ocess [2]. Ne e heless, when he g ain
size e alua ed o one speci ic ela i e densi y is no dependen on hea ing schedule, he
equa ion s ill can be sol ed [10].
To p ac ically calcula e he Qs, a leas h ee dila ome y measu emen s a di e en
hea ing a es a e ecommended. Fi s ly, exac densi y alue is chosen and he densi ica ion
a e is calcula ed o all hea ing a es used. Then assump ion o no g ain g ow h, o ha he
g ain size a he speci ic ela i e densi y is no dependen on he hea ing schedule [10] is
made. Now, he le side o Eq. 4 a he speci ic ela i e densi y o all hea ing a es is
calcula ed. When he le hand side o Eq. 4 is plo ed agains 1/T, a poin belonging o each
hea ing a e used is ob ained. I all p esump ions a e alid, hese poin s lay on a line which
slope de e mines he Qs.
WaR So wa e
Calcula ion o Qs by he Wang and Raj model o s a is ically signi ican amoun o
samples, ma e ials o densi ies could be ime consuming. The e o e, we de eloped a so wa e
applica ion, which dec eases he p ocessing ime. The unc ional diag am o he so wa e is
shown in Fig. 1. The so wa e s a s wi h he impo o da a in he CSV o ma , which con ain
eco ds o ime, empe a u e and ela i e densi y o e e y sample. To ob ain eliable esul s,
he minimum o h ee measu emen s using di e en hea ing a es a e equi ed. The
applica ion hen calcula es Qs o each de ined ela i e densi y and plo s he calcula ed esul s.
P. Vacla e al./Science o Sin e ing, 48 (2016) 317-324
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319
Fig. 1. P ocessing scheme o he p esen ed so wa e.
Fig. 2. So wa e in e ace wi h plo ed esul s o densi ica ion a e and Qs.
P. Vacla e al. /Science o Sin e ing, 48 (2016) 317-324
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320
Va ious pa ame e s o calcula ion can be changed o sui e wide ange o inpu da a.
The use can de ine he ange o da a, om which he i s de i a ion o Eq. 4 is calcula ed, o
ob ain he desi ed smoo hness o he cu e. Addi ionally, h ee linea i ing me hods can be
selec ed: leas squa e, leas absolu e esidual and bisqua e. All hese pa ame e s can be
changed a any ime and he esul s a e ecalcula ed in he eal ime. I any e o s in he inpu
da a a e de ec ed, he so wa e au oma ically no i ies he use . The use hen can easily selec
o omi da a causing he e o s. The calcula ed esul s a e plo ed in eal ime and can be
di ec ly expo ed o xls o cs ile. The sc eensho om so wa e in e ace wi h calcula ed
esul s is p esen ed in Fig. 2. The so wa e is eely a ailable ia email eques o he au ho s.
2. Expe imen al
2.1. Ma e ials
Alumina and cubic zi conia comme cial g ade ce amic powde s we e used. De ailed
in o ma ion abou hese powde s a e gi en in Table I. Pa icle size (DBET) was ob ained om
speci ic su ace a ea using he ni ogen abso p ion me hod (BET me hod, ChemBe 3000,
Quan ach ome, USA). The heo e ical densi ies (ρ h) used o he calcula ion o he DBET and
calcula ion o he ela i e densi ies a e ρ h TAI = 3.99 g/cm3 and ρ h Z8Y = 5.99 g/cm3.
Tab. I De ailed in o ma ion abou powde s used.
Powde P oduce G ade Abb e ia ion DBET [nm]
Al2O3Taimei Chemicals, Japan TM-DAR TAI 100
Z O2 (+8 mol% Y2O3) Tosoh Co po a ion, Japan TZ-8Y Z8Y 70*
*da a p o ided by manu ac u e
2.2. P epa a ion o ce amic g een bodies
Powde s we e shaped in o discs o 30 mm in diame e and 5 mm in heigh by cold
isos a ic p essing (Au ocla e Enginee ing, Inc., USA). P essing was done a he p essu e o
300 MPa o 5 min. Samples we e hen p e-sin e ed a 800 °C/1 h. In o de o use he samples
in he dila ome e , 4 mm x 4 mm x 15 mm p isms we e cu om each sample.
2.3. Sin e ing
Sin e ing o he samples was ca ied ou using he high empe a u e dila ome e
(L70/1700, Linseis, Ge many). Fou di e en hea ing a es 2, 5, 10 and 20 °C/min we e used
o calcula e he Qs. The ela i e sh inkage cu es we e con e ed o densi ica ion cu es by
me hodology desc ibed in he li e a u e [7, 11]. The pa ame e s o he sin e ing a e p esen ed
in he Table 2. A e he sin e ing, ela i e densi ies o he samples we e measu ed using he
A chimedes me hod in acco dance wi h he EN623-2.
2.4. Calcula ion o ac i a ion ene gies o sin e ing
The calcula ion o Qs by he Wang and Raj model was ealized by so wa e desc ibed
in chap e “WaR So wa e” om dila ome y measu emen s using ou hea ing a es o 2, 5,
10 and 20 °C/min.
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3. Resul s and discussion
3.1. Densi ica ion cu es
The densi ica ion cu es, calcula ed om dila ome y measu emen s, a e p esen ed in
Fig. 3. The hea ing schedules o all samples and hei ela i e densi ies a e sin e ing a e
p esen ed in Table II. All samples eached ela i e densi y highe han 99.5 % T. D.
5 °C/min
Tempe a u e [°C]
800 1000 1200 1400
Rela i e densi y [% .d]
40
50
60
70
80
90
100
TAI
Z8Y
Fig. 3. Densi ica ion cu es a 5 °C/min.
Tab. II Sin e ing pa ame e s and inal densi ies o samples.
Ma e ial Hea ing a e
[°C/min] Sin e ing emp. / dwell
[°C/min] ρ el
[% .d.]
s / n *
[% .d. / –]
2 1500 / 0 99.67 0.07 / 12
5 1500 / 0 99.63 0.10 / 09
10 1500 / 0 99.59 0.10 / 09
TAI
20 1500 / 0 99.59 0.14 / 12
2 1500 / 0 99.62 0.06 / 09
5 1500 / 0 99.54 0.05 / 09
10 1500 / 10 99.63 0.04 / 09
Z8Y
20 1500 / 60 99.72 0.10 / 09
* whe e s = s anda d de ia ion and n = numbe o measu emen s
3.2. The Wang and Raj model
Fig. 4 shows he Qs calcula ed in acco dance wi h he model o Wang and Raj. Bo h
ma e ials exhibi he same end in he linea dec ease o Qs du ing sin e ing. Such dec ease o
Qs was al eady obse ed by o he au ho s [10, 12]. Addi ionally, bo h TAI and Z8Y show
cons an Qs in he high and low densi y egion. This beha iou we al eady epo ed o doped
and undoped alumina in ou ecen s udies [13]. The e alua ed nominal alues o Qs o TAI
we e 868 kJ/mol and 625 kJ/mol in he high and low densi y egion espec i ely. The Z8Y
sample exhibi s dec ease o Qs om 762 kJ/mol o 645 kJ/mol.

P. Vacla e al. /Science o Sin e ing, 48 (2016) 317-324
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TAI
Rela i e densi y [% . d.]
60 70 80 90 100
Q
s
[kJ/mol]
600
650
700
750
800
850
900
Z8Y
Rela i e densi y [% . d.]
60 70 80 90 100
Q
s
[kJ/mol]
620
640
660
680
700
720
740
760
780
800
Fig. 4. Ac i a ion ene gies calcula ed by he Wang and Raj model.
The summa y o Qs alues and mean alues o low/high densi y egions a e p esen ed
in Table III. Compa ison o hese esul s wi h ano he app oach o calcula ion, he p e iously
published MSC da a [14], as well as da a published by o he au ho s [12, 14-17] a e included
as well.
Tab. III Compa ison o esul s o ac i a ion ene gy calcula ions by Wang and Raj model wi h
MSC da a and o he au ho s.
Ma e ial Wang and Raj
[kJ/mol] MSC [kJ/mol] O he au ho s
60 – 70 % 90 – 95 % 60 – 93 % 93 – 99 %
TAI 868 625 770 570
679/278 [16],
739 [18]
Z8Y 762 645 750 460
233 [19],
460/309 [20],
730/580 [12]
4. Conclusion
Newly de eloped so wa e o ime e icien calcula ion o Qs by Wang and Raj
model was in oduced. Bo h expe imen al ma e ials exhibi he same change o Qs du ing
sin e ing. The Qs dec eases du ing he sin e ing by mo e han 200 kJ/mol in case o alumina
ce amics and mo e han 100 kJ/mol in case o cubic zi conia ce amics. These esul s a e in
ag eemen wi h p e iously published Qs alues calcula ed by bo h Wang and Raj model and
MSC model.
Acknowledgemen
The esea ch has been inancially suppo ed by he Minis y o Educa ion, You h and
Spo s o he Czech Republic unde he p ojec CEITEC 2020 (LQ1601).
5. Re e ences
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3. Akash, A. and M. J. Mayo, Po e g ow h du ing ini ial-s age sin e ing. Jou nal o he
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Садржај: Презентован је нови софтвер за рачунање енергије активације синтеровања
коришћењем модела Ванга и Раџа. Алумина и кубични цирконијум су припремљени из
нанометарских прахова, да би се показао практични потенцијал софтвера и да би се
видело понашање енергије активације током синтеровања. Добијени резултати су у
P. Vacla e al. /Science o Sin e ing, 48 (2016) 317-324
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324
сагласности са претходно објављеним резултатима рачунатим по другим моделима.
У посматраном интервалу (релативна густина 60 % до скоро 100 % теоријске
густине), оба материјала показују слично понашање. Уочена су три региона: почетне
вредности од 868 kJ/mol и 762 kJ/mol за алумину и цирконијум, тим редом; део са
линеарним падом вредности енергије активације и финални део са вредностима од 625
kJ/mol и 645 kJ/mol за алуминијум и цирконијум, тим редом.
Кључне речи: синтеровање, енергија активације, алумина, цирконијум
© 2016 Au ho s. Published by he In e na ional Ins i u e o he Science o Sin e ing. This
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