Master Sintering Surface – A Practical Approach to Its Construction and Utilization for Spark Plasma Sintering Prediction

Science o Sin e ing, 44 (2012) 169-175 ________________________________________________________________________ _____________________________ *) Co esponding au ho : [email p o ec ed] DOI:10.2298/SOS1202169P UDK 622.785:531.3 Mas e Sin e ing Su ace – A P ac ical App oach o I s Cons uc ion and U iliza ion o Spa k Plasma Sin e ing P edic ion V. Pouchly1*), K. Maca1,2, Y. Xiong3, J.Z. Shen3 1Depa men o Ce amics and Polyme s, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, Technicka 2896/2, 616 69 B no, Czech Republic 2 CEITEC BUT, B no Uni e si y o Technology, Technicka 3058/2 616 69 B no, Czech Republic 3Depa men o Ma e ials and En i onmen al Chemis y, A henius Labo a o y, S ockholm Uni e si y, S-106 91 S ockholm, Sweden Abs ac : The sin e ing is a complex he mally ac i a ed p ocess, hus any p edic ion o sin e ing beha iou is e y welcome no only o indus ial pu poses. P esen ed pape shows he possibili y o densi ica ion p edic ion based on concep o Mas e Sin e ing Su ace (MSS) o p essu e assis ed Spa k Plasma Sin e ing (SPS). Use iendly so wa e o e alua ion o he MSS is p esen ed. The concep was used o densi ica ion p edic ion o alumina ce amics sin e ed by SPS. Keywo ds: Spa k Plasma Sin e ing, Mas e Sin e ing Su ace, Sin e ing kine ics, Alumina 1. In oduc ion The sin e ing o ce amics always leads o educ ion o sample size. The sin e ing sh inkage in con en ional ma e ials is ypically be ween 12 and 25% o he ela i e leng h o sample, hus i is easy o measu e i [1]. Th ee a iables can be simul aneously eco ded in a high- empe a u e dila ome e : ime, empe a u e and leng h o he sample. The change o sample leng h i sel consis s o sum o he ollowing changes: empe a u e expansion o he sample [2], phase ans o ma ions [3] and sin e ing sh inkage [4]. I sin e ing sh inkage can be sepa a ed, hen i is possible o ecalcula e he sin e ing sh inkage o a densi ica ion cu e. Such ecalcula ion is desc ibed in ou p e ious pape [5]. Once he densi ica ion cu e is c ea ed, one can simply ollow he hea ing p o ile and s op sin e ing a a equi ed densi y. This can be bene icial o easy inding he empe a u e o i s s ep o Two-S ep Sin e ing [6, 7] o he empe a u e necessa y o closed po osi y o pos -HIPing [8]. The p oblem occu s, when he di e en hea ing a e, sin e ing empe a u e o dwell ime is desi able. This p oblem can be o e come ia Mas e Sin e ing Cu e (MSC) concep . The MSC was de i ed by Su and Johnson in 1996 [9] om simpli ied sin e ing model published by Hansen and co-wo ke s [10]: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛Γ + Γ Ω =− 43 G D G D kTLd dL bb δ γ , (1) V. Pouchly e al. /Science o Sin e ing, 44 (2012) 169-175 ___________________________________________________________________________ 170 whe e L is he sample leng h, is he ime, γ is he su ace ene gy, Ω is he a omic olume, k is he Bol zmann cons an , T is he absolu e empe a u e, G is he mean g ain size, D is he coe icien o olume di usion, Db is he coe icien o g ain bounda y di usion, δ is he hickness o g ain bounda y and Γ ep esen s geome ic ac o s as he d i ing o ce in sin e ing. I a single di usion mechanism is esponsible o densi ica ion and, a he same ime, he mic os uc u e is unc ion only o sample densi y (so i is independen o he mal his o y), we can ea ange Eq. (1) o Eq. (2): d RT Q T d G D k n∫∫ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛−= ΓΩ 0 0 exp 1 )(3 ))(( 0 ρ ρρ ρ δγ ρ ρ , (2) whe e Q is he appa en ac i a ion ene gy o sin e ing p ocess, R is he gas cons an and ρ is densi y. I he igh side o his equa ion is deno ed as Θ , he ela ionship be ween ρ and Θ is en i led as MSC [9]. The usual cons uc ion o MSC is ca ied ou ia ew cons an hea ing a e expe imen s ollowed by op imiza ion o ac i a ion ene gy alue o achie e bes o e lap among indi idual ρ = ( Θ) unc ions [11]. I such ac i a ion ene gy is ound, ρ = ( Θ) unc ions o all expe imen s become one (mas e ) cu e [12].The ob ained MSC oge he wi h Eq.(2) can be used o p edic ion o densi ica ion cu e o any hea ing schedule o he same ce amic g een body [13]. An and Han [14] accommoda ed MSC o p essu e-assis ed sin e ing by in oducing ano he independen a iable – p essu e; hey cons uc ed so-called Mas e Sin e ing Su ace (MSS). The applied p essu e gene ally shi s he densi ica ion cu e o lowe empe a u es. This imp o ed model enables also densi ica ion p edic ion wi h a ia ions in: hea ing a e, sin e ing empe a u e, dwell ime and p essu e. The calcula ions, which lead o MSS cons uc ion, a e complica ed and ime-consuming. To b idge his p oblem we de eloped simple and use - iendly so wa e o MSS cons uc ion. The Spa k Plasma Sin e ing (SPS) is e y p omising echnique o sin e ing o ce amics, me als, composi es e c. In SPS he pulsed DC powde is combined wi h an applied p essu e o he pu pose o enhance sin e ing p ocess. Pulsed Joule hea p o ides he ad an age o apid empe a u e inc ease (up o se e al hund ed °C/min) and possibili y o elec o- mig a ion o elec o-plas ici y [15]. I he sample is no conduc i e (as alumina in his pape ) he passing cu en hea s he die and ma e ial is hea ed due o con ec ion o hea . The SPS can usually eco d he mo ion o p essing am du ing he sin e ing p ocess. The SPS hus can wo k as a simple high empe a u e and p essu e dila ome e , which allows cons uc ion o MSS om SPS expe imen s. The main goal o his pape is o desc ibe he easy way o cons uc ion o MSS and o show i s u iliza ion o SPS desc ip ion and p edic ion in case o alumina ce amics. So wa e o calcula ions o MSS The so wa e can impo (in he xls, asc o x o ma ) up o 10 di e en densi ica ion cu es wi h di e en hea ing a es, sin e ing empe a u es, dwells, and p essu e alues. Then he dependence o Mean Pe pendicula Cu e Dis ance (MPCD) [16] o Mean Residual Squa es (MRS) is used o ind he op imal ac i a ion ene gy and o de elop he MSS o used ce amic ma e ial (see Fig. 1). Wi h his MSS, he so wa e can p edic densi ica ion beha iou o gi en sample o any empe a u e-p essu e sin e ing p o ile. The expo o MSS calcula ions is possible in xls, asc, o x o ma . All he s eps can be done au oma ically o manually. The so wa e is a ailable o esea ch communi y o ee and can be eques ed ia email o au ho s. V.Pouchly e al./Science o Sin e ing, 44 (2012) 169-175 ___________________________________________________________________________ 171 Fig. 1. P in sc een om he so wa e a) Indi idual ρ = ( Θ) unc ions, b) Es ablishing o op imal ac i a ion ene gy 2. Expe imen al To e i y p esen ed concep o MSS, he SPS expe imen s wi h alumina powde AKP 30 (Sumi omo Chemical Ame ica Inc. New Yo k, median pa icle size 300 nm) we e pe o med. Sin e ing as well as shaping was p o ided in SPS D . Sin e 2050 (Sumi omo Coal Mining Co., Japan) appa a us. The 2.3g o powde was loaded in o a g aphi e die wi h inne diame e o 12 mm. The ou e su ace o he die was co e ed by g aphi e blanke wi h a b) a) V. Pouchly e al. /Science o Sin e ing, 44 (2012) 169-175 ___________________________________________________________________________ 172 hickness o ~7 mm o minimize he hea loss and o imp o e empe a u e dis ibu ion du ing sin e ing. The empe a u e was measu ed using op ical py ome e ocused on a small hole d illed in o a su ace o a die. The p essu e was aised on i s inal alue du ing p ehea ing up o 600°C, and hen held cons an du ing whole sin e ing p ocess. The ini ial densi ies o samples o SPS we e measu ed geome ically wi h p ecision o ±2% o heo e ical densi y ( .d.). The MSS was cons uc ed om h ee independen MSCs. Fou hea ing a es 50, 100, 150 and 200 °C/min and p essu es o 20, 50 and 100MPa we e used o cons uc ion o indi idual MSCs. E e y indi idual MSC was c ea ed o a di e en alue o p essu e. MPCD was used o ind op imal ac i a ion ene gy. All MSCs we e han combined in o a MSS. Final ela i e densi ies we e de e mined on he basis o he A chimedes p inciple (EN 623-2) wi h dis illed wa e and using alumina .d. o 3.99g/cm3. 3. Resul s and discussion All o he hea ing schedules and eached inal densi ies a e summa ized in Tab. I. The lowes alue o inal densi y (97.08% .d.) had he sample 200/1400/20 (hea ing a e 200°C/min, inal empe a u e 1400°C wi hou dwell, applied p essu e o 20MPa) . This esul was expec ed acco ding o basic sin e ing heo y; ne e heless also small inal ela i e densi y would allow usage o he MSC concep . Tab. I Lis o all used hea ing schedules and ob ain densi ies Abb e ia ion Hea ing a e [°C/min] Ta ge empe a u e [°C] Holding ime [min] P essu e [MPa] Final densi y [% .d.] s/n [%/-] 50/1400/20 50 1400 0 20 99.22 0.06 100/1400/20 100 1400 0 20 98.46 0.03 150/1400/20 150 1500 0 20 98.90 0.04 200/1400/20 200 1400 0 20 97.08 0.02 50/1400/50 50 1400 0 50 99.61 0.04 100/1400/50 100 1400 0 50 99.49 0.02 150/1400/50 150 1500 0 50 99.56 0.03 200/1400/50 200 1400 0 50 99.24 0.02 50/1400/100 50 1400 0 100 99.80 0.03 100/1400/100 100 1400 0 100 99.77 0.03 150/1400/100 150 1500 0 100 99.60 0.03 200/1400/100 200 1400 0 100 99.52 0.02 120/1320/5/30 120 1320 5 30 99.29 0.03 No e: s is s anda d de ia ion, n is numbe o measu emen The samples sin e ed wi h a p essu e o 50 and 100MPa eached densi ies highe han 99% .d.. The Figs. 2a-c show he MSCs cons uc ed o cons an p essu es in he ange om 20 o 100MPa. All cons uc ed MSCs ha e a simila shape. Inc eased p essu e shi s MSC o lowe alue o Θ , which means highe ela i e densi ies a he same empe a u e. I can be seen in Fig. 2, ha all h ee MSCs we e success ully cons uc ed using he sin e ing ac i a ion ene gy o 600kJ/mol. The e is a wide ange o sin e ing ac i a ion ene gy (342-1064kJ/mol) epo ed in he li e a u e [17-19]. This is p obably caused by use o di e en ini ial powde , shaping echnology, sin e ing condi ions e c. The e o e he sin e ing ac i a ion ene gy es ablished om his non-iso he mal p ocess is no a ue ma e ial cha ac e is ic and we call i “appa en sin e ing ac i a ion ene gy”. Es ima ed ac i a ion ene gy in his wo k is in a good V.Pouchly e al./Science o Sin e ing, 44 (2012) 169-175 ___________________________________________________________________________ 173 ag eemen wi h Aminza e (608kJ/mol) [20] who also used a MSC concep . The combina ion o he MSCs wi h cons an p essu es o 20, 50 and 100MPa leading o MSS cons uc ion is shown in Fig. 3. The calcula ed su ace is smoo h wi hou any unexpec ed a e ac s. 20MPa log Θ -28 -26 -24 -22 -20 Rela i e Densi y [% .d.] 50 60 70 80 90 100 50/1400/20 100/1400/20 150/1500/20 200/1400/20 A e age EA 400 600 800 1000 MPCD 20 25 30 35 40 a) 50MPa log Θ -30 -28 -26 -24 -22 Rela i e Densi y [% .d.] 50 60 70 80 90 100 50/1400/50 100/1400/50 150/1500/50 200/1400/50 A e age EA 400 600 800 1000 MPCD 35 40 45 50 55 60 b) 100MPa log Θ -30 -28 -26 -24 -22 Rela i e Densi y [% .d.] 50 60 70 80 90 100 50/1400/100 100/1400/100 150/1500/100 200/1400/100 A e age EA 400 600 800 1000 MPCD 20 30 40 50 c) Fig. 2 The MSC o alumina o SPS p essu e o 20MPa and ac i a ion ene gy o 600kJ/mol (a), The MSC o alumina o SPS p essu e o 50MPa and ac i a ion ene gy o 600kJ/mol (b), The MSC o alumina o SPS p essu e o 100MPa and ac i a ion ene gy o 600kJ/mol (c) V. Pouchly e al. /Science o Sin e ing, 44 (2012) 169-175 ___________________________________________________________________________ 174 One o he bene i s o MSC and MSS is he possibili y o densi ica ion p edic ion o any hea ing and p essu e schedule. Fig. 4a and 4b compa e he densi ica ion beha iou o expe imen ally measu ed sample 120/1320/5/30 (hea ing a e 120°C/min, inal sin e ing empe a u e 1320°C o 5 minu es, applied p essu e 30 MPa) wi h densi ica ion p edic ion ia cons uc ed MSS (Fig. 3). Al hough he chosen sin e ing schedule a ied om p e ious expe imen s in hea ing a e, inal empe a u e, dwell ime and applied p essu e, he di e ence be ween he p edic ed and measu ed alues is in he ange o abou +/-0.2% .d. This esul s i s densi ica ion p ocess be e han i was published by An e al. [21], who changed only he hea ing a e and a p essu e, and hey ound de ia ion o 1%. Fig. 3. The MSS o alumina ce amic sin e ed in SPS Fig. 4. The o e lap be ween p edic ed and measu ed hea ing p o iles o sample 120/1320/5/30 (hea ing a e 120°C/min, inal sin e ing empe a u e 1320°C o 5 minu es, applied p essu e 30 MPa) 4. Conclusion I is shown in his s udy ha he Spa k Plasma Sin e ing can be desc ibed by Mas e Sin e ing Su ace concep . The MSS cons uc ion was demons a ed using alumina powde V.Pouchly e al./Science o Sin e ing, 44 (2012) 169-175 ___________________________________________________________________________ 175 wi h a pa icle size o 300nm, o which he sin e ing ac i a ion ene gy o 600kJ/mol was es ablished du ing SPS expe imen s. The calcula ions we e done by newly de eloped so wa e, which is also p esen ed in his pape . The alidi y o c ea ed MSS was e i ied by success ul p edic ion o alumina SPS kine ics. Acknowledgemen The au ho s g a e ully acknowledge he unding p o ided by he g an FSI-J-12-18, and B no Ph.D. Talen schola ship unded by he B no Ci y Municipali y. Re e ences 1. M. J. 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Maca, P ocessing and Applica ion o Ce amics, 3 (2009) 177. 14. K. An, M. K. Han, Ma. Sc.i Eng. a-S uc ., 391 (2005) 66. 15. R. Raj, M. Cologna, J. S. C. F ancis, J. Am. Ce am. Soc., 94 (2011) 1941. 16. V. Pouchly, K. Maca, Sci. Sin e ., 42 (2010) 25. 17. J. D. Wang, R. Raj, J. Am. Ce am. Soc., 74 (1991) 1959. 18. Z. He, J. Ma, Ce am. In ., 27 (2001) 261. 19. W. Q. Shao, S. O. Chen, D. Li, H. S. Cao, Y. C. Zhang, S. S. Zhang, Sci. Sin e ., 40 (2008) 251. 20. M. Aminza e, M. Mazahe i, F. Goles ani- a d, H. R. Rezaie, R. Ajeian, Ce am. In ., 37 (2011) 9. 21. K. J. An, H. J. Kim, M. K. Han, Ma e . T ans., 49 (2008) 1926. Садржај Обзиром да је синтеровање комплексан процес, свака предикција понашања материјала током синтеровања је добро дошла не само у индустријске сврхе. Овај рад показује могућност предвиђања процеса згушњавања базиран на концепту Мастер синтеринг површине (MСП) код синтеровања у плазми. Приказан је и софтвер за израцунавање МСП. Овај концепт је коришћен за предикцију процеса згушњавања алумине током синтеровања у плазми. Кључне речи: Плазма синтеровање, мастер синтеринг површина, кинетика синтеровања, алумина.