A Practical Approach for the Calculation of the Activation Energy of the Sintering

Science o Sin e ing, 48 (2016) 317-324 ________________________________________________________________________ _____________________________ 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] P. Vacla e al. /Science o Sin e ing, 48 (2016) 317-324 ___________________________________________________________________________ 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 ___________________________________________________________________________ 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 ___________________________________________________________________________ 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. P. Vacla e al./Science o Sin e ing, 48 (2016) 317-324 ___________________________________________________________________________ 321 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 ___________________________________________________________________________ 322 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 1. Ge man, R. M., Sin e ing Theo y and P ac ice. 1996: John Wiley and Sons Inc. 2. Mayo, M. J., P ocessing o nanoc ys alline ce amics om ul a ine pa icles. In e ina ional Ma e ials Re iews, 1996. 41(3): p. 85-115. P. Vacla e al./Science o Sin e ing, 48 (2016) 317-324 ___________________________________________________________________________ 323 3. Akash, A. and M. J. 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A., e al., Z -96 di usion in polyc ys alline scandia s abilized zi conia. Jou nal o he Eu opean Ce amic Socie y, 2005. 25(9): p. 1591-1595. 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 ___________________________________________________________________________ 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 a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons — A ibu ion 4.0 In e na ional license (h ps://c ea i ecommons.o g/licenses/by/4.0/).