IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 Modeling of the Effect of MgO and ZrO2 on Sintering of Alumina H. K.H.Al.Mayaly Departme nt of physics, College of Education I bnAl-Haitham, Unive rsity of Baghdad Recei ved in April 18 , 2010 Accepted in June 17, 2010 Abstract This research study ies the effect of M gO and ZrO2 as additives in sintering Al2O3 . The exp erimental results are modeled usin g ( L 2 _ r egression) technique , sintered density and grain size rate measurments were accounted by utilizing exp erimental r esults of undop ed , M gO dop ed and ZrO2 dop ed alumina imp regrated with sp herical lar ge p ores in final st age of sintering . The effect of each additive is inhibitian of the grain growt h and increasing the densification r ate which enhances t he kinietics of densification and the removal of large and sm all pores. Introduction Alumina ceramic (Al2O3) is a hard refractory ceramic, which has been used in high temp erature, st ructural and substrate app lications because of its good st rength and low thermal exp ansion cofficient . Nevertheless , like other mono lithic ceramics, Al2O3 is aptto suffer from low ductility and low fracture toughnees[I]. Dop ed samples were st udied fro the influence of varying the grain growt h rate of the alumina , M gO is a st rong solid-solution grain growt h inhibitor in high p urity alumina [2] , and ZrO2 when added in high enough concentrations, is an even st rong second-phase grain growt h inhibitor [3] . The intension of this st udy to was model mathematically the densification and grain size rate of dop ed Al2O3 sy st em using regression modeling technique utilizing M gO and ZrO2 as additives sep erately . IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 Theoretical background The p ores are calassified into two basic ty p es , there are the so-called matrix or first- generation p ore and the second ty p e, large so-called second-genertion p ores which originate from p articale agglomeration and p articale p acking irregularities within the p owder comp act [4] .The large pores are alway s more difficult to eleminate large voide for two basic reasons . First , simple kinietics dictates alonger time to fill a larger void by diffusion [5] , second a large p ore can be thermody namically st able depending on the value of dihedral and p ore size : grain size ratio (for a given dihedrol angle and pore size, there is a critical grain size above which the p ore is unst able and can sinter ),while below where it is st able and can not sinter. The models which are used in this st udy have asimp lifiying a ssump tions in order to p erform the calculations. 1) Pore shrinkage is controlled by lattice diffusion 2) The grain size is fixed at t he critical grain size which was taken to be 0.68 times the p ore size [6]. 3) The p ores are assummed to be sp herical with no thermody namic barrier for shrinkage [4,7]. The large-pore volume will st art to decrease (once the critical grain size is reached), the matrix grain growt h rate (dG/dt) can be given by [8] max 13.4 (1 ).....(1)b dG G MpG dt N G    Where N is the number of p ores surrounding each grain , M p is the average p ore mobility , G is the grain size , b  is the grain boundary energy , ε is the grain growt h rate factor and (G/Gm ax) is the ratio of average grain size over maximum grain size. The densification rate(dρ/dt) depends on the diffusion cofficient resp onsible for densification (Dlattice or D boundar y ) and the grain size [9]. / ...... ...( 2 ) nd CD G dt   where C is a constant and D is t he diffusion cofficient . The grain size exp onent, n, is 3 for lattice- diffusion controlled densification which is used in this st udy .[5] In this st udy (reported in Ref [5]). Ultra-high-p urity α-alumina p owder for which the manufaturar claimed a(99.995%) p urity size of p owder was 0.45 μm and 97% of the p articles were less t han 1μm . IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 The following three comp ositions were chosen for this st udy (i) p ure alumina ; (ii) 250- p p m-M gO-dop ed alumina , and (iii) Al2O3 +10 Vol % ZrO2 . Large mono size p ores were introduced in to each comp osition by incorp orating latex sp heres (5.6 μm ) into the p owder mix before sintering .The ratio of the sp here volume / the sum of the sp here volume and the solid volume in each comp osition was (5%) .The p owder was cold-p ressed into p ellets of app roximately the same green density (47.5%) using a high-p urity alumina p unch and die set . The p ellets calcined at 1000 o c in air for 48 h , large p ores were p roduced after calcination as a result of burning out of the latex sp heres. The processing p rocedure for all comp osition was kept as consistent as p ossible to ensure similar initial microstructures . Sintering was conducted under flowing nitrogen gas in a furnace heated with graphite elements, the sp ecimens were heated at a constant rate of (60 o c/min) up to the sintering temp erature of 1620 o c (oxy gen p artial p ressure < 10 -11 atm <10 -6 p a ). Regression modeling technique The equation of L 2 _ regression which is used in this st udy can be exp ress as follows [10] 1 ( ) .. . .. . . .. . (3 ) T T X A A A b   where A is the matrix , A T is the transp ose of matrix A , b is random abserv ation and X is the fixed p art of equation but unknown. The integral for m of the gr ain growt h rate equation (1) [4]. max 13.4 ln ln (1 ) ..........(4) t t t p b G G G M Y t N G      � � and the integral form of densification rate equation (2) ( 1 ) .. .. .. .( 5 ) (1 ) n t t t C D G t n       � � Aft er simp lifing the integr al exp ression for equation (4) and (5) we get a suitable form of equation (3) that can be adop ted to L 2 _ regression . 1 1 m a x ln (1 ) ........(6 )t t G G z t Y G    � IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 (1 ) 2 2........(7) n t t Z G t Y    � Where Z1 is the grian size rate p arameter and equals t o 13.4 [ ]p bM Y N  ,Z2 if the densification rate parameter and equals to [CD / (1-n)] , Y1 is the grain size rate coff icient and equals to [ 1 m a x l n (1 )t o G G z t G   ] and Y2 is densification rate cofficient and equals to [ 1 2 n t oP Z G t  ] The grain size and d ensity value were measured using model of L 2 _ Regression (see-Ref II) Results and Disussion Figs . (1) and (2) showed the effect of M gO and ZrO2 dop ed alumina which have a large ( � 5 μm ) model sp herical pores on the density date as a function of time at 1629oc . As can be seen that both M gO and ZrO2 increased the desification rate of Al2O3 . ZrO2 had more effective in enhanced densification rate than M gO . The calculatedion by model sintered densites of sample with ZrO2 addition was ranged between [ 92 and 97.9% ] and for samples with M gO addition was ranged between [ 91 and 97.2 % ] . The ZrO2-dop ed samples did reach a slightly higher density than the M gO-dop ed samples , however , this does imp ly that a fraction of the p ores were indeed thermody namically unst able and cabable to shrink . Such pores would be able to shrink at a faster rate than those in the M gO – dop ed samp les due to smaller grain size and associated fast er kinetics. Fig. (3) and Fig. (4) are showed the grain size versus t ime date for M gO-dop ed , and ZrO2- dop ed aluminas which imregnated with large ( � 5 µm ) model sp herical p ores at 1620 oc . M gO and ZrO2 were very effective in inhibiting grain growt h in the sy st em (ZrO2 more so than M gO), t he grain sizes for undop ed and M gO-dop ed samples well beyond the critical grain size and the large p ores do not readily disapp er even when thermodynamics is p ermitt ing . The degree of grain growt h inhibition was fast er with t he ZrO2-dop ed samp les , where the small grain size of these samp les showed that not all the p ores were necessarily thermody namically unst able for any reasonble lenght of sinterin g time. In Table (1) we can see the grain size rate p arameter of doping samples increases , this can be exp lained in terms of t he number of pores which increase with dop ing and this may naturally decreases densification rate parameters . IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 Table (2) lists t he grain size rate cofficient and densification rate cofficient , t he doping lowers both the densification and gr ain size rate cofficient resp ectively where the dop ent p articals may form barriers along the diffusion p ath and reduce the densification Conclusion The modeling technique shows that the calculated results using L 2 _Regression technique agr ees with exp erimental results, and M gO-dop ed alumina imp ragnated with lar ge pores have effective in inhibitin g grain growt h rate and increases the densification rate , while the effect of ZrO2 dop ed alumina was fast er than M gO , Z rO2 dop ed samp les have more effective in enhanced densification and inhibition the grain growt h rate. Re ferences 1. Nanchou,S. ;Hwalu,H. Fwulii ,D. and Huang, J.L. (2009), Proc essing and physical p rop erties of Al2O3/alumina alloy comp osites. Ceramics International 35: 7-12 2. Bennison ,S.J. and Harmer, M .p . (1985),Grain growt h kinetics alumina in the absence of aliquid p hase.J.Am.Ceram.Soc.68(1) :22-24. 3. lan ge ,F.F. and Hirlin ger, M .M . (1984),Hindrance of grain growt h in Al2O3 by ZrO2 inclusions . J.Am.Ceram. Soc.67(3) :68-164. 4. Zhao ,J. and Harmer ,M .P. (1988),Effect of p ore dist ribution on microst ucture development. I, matrix p ores.J.Am.Ceram. Soc. 71(2):20-113. 5. Zhao ,J. and Harmer ,M .P. (1988),Effect of p ore dist ribution on microst ructure development. II, First and second gener ation p ores . J .Am.Ceram.Soc,71(7) :39-530. 6. Kingery, W.D. and Francois ,B. (1967), Sintering of Cry st alline Oxides.I.Int eractions between grain boundaries and pores,(98-471) in sintering and retated phenomena,Edited by G.C.Ky czy nski,N.A.Hooton,and G.F.Gibbon,Gordon Breach,Newy ork. 7. Coble ,R.L. (1961),Sintering cryst alline solids I.Int ermediate and final st age diffusion models,J.App l.p hy s(32): 92-787. 8. Brook ,R.J. (1976),Cont rolled grain growt h in ceramic sy st ems .(64-331).intreatise on materials science and technolo gy , 9.Edited by F.F.Y.wong academic p ress.Newy ork. 9. Berry ,K.A. and Harmer ,M .P. (1986),Effect of M gO solute on microstructure development in Al2O3 .J.Am.ceram.Soc.69(2): 49-143. 10. Robert.J.Vander bei (2001), Linear programming.Foundations and extensions,second edition ,Copy right C. 11. M aly aly ,H.K. (2005),Analysis t he three st age of sintering usin g lin ear p rogrammin g. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 Table (1):Grain size and densification rate paramete rs in three case , undoped, MgO- doped an d ZrO2-do ped alumi na impregte d with large model pores Undop ed M gO-dop ed ZrO2-dop ed Grain size rate p arameter (Z1) 90.583 93.964 94.651 Desification rate p arameter (Z2) 1.574 1.102 0.578 Table (2): Grain size and densification rate cofficient in three case , undoped , MgO-doped and ZrO2 –doped alumi na i mpregnated with l arge model pores Undop ed M gO-dop ed ZrO2-dop ed Grain size rate cofficient (Y1) 0.00559 0.00511 0.00238 Densification rate cofficient (Y2) 4.397 0.6562 0.0604 IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 Fig (1) Density data of undope d a nd MgO dope d a lumina s impregnated w ith large pores a s a function of time 90 92 94 96 98 100 0 100 200 300 400 500 600 700 Time (min) D e n s it y (g m /m ^ 3 ) undoped exp undoped cal MgO doped ex p MgO doped ca l Fig(2) Densi ty data of undoped an d ZrO2 doped al umi nas i mpregnated with la rge pores as a function of time 90 92 94 96 98 100 0 100 200 300 400 500 600 700 Time (min) d e n s it y ( g m /m ^ 3 ) undoped exp undoped c al ZrO2 doping exp ZrO2 doping c al IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (1) 2011 2011) 1( 24المجلد مجلة ابن الهیثم للعلوم الصرفة والتطبیقیة في تلبید االلومینا ZrO2و MgOثیر نموذج تأأ حنان كاظم حسون جامعة بغداد ،ابن الھیثم –كلیة التربیة ،قسم الفیزیاء 2010نیسان 18استلم البحث في 2010حزیران 17قبل البحث في -:الخالصة ،L2-Regressionبأستخدام تقنیة نمذجت النتائج التجریبیة تم.في تلبید االلومینا ZrO2,MgOتأثیر اضافة درس والمطعمة ب MgOالمطعمة ب ،بأستخدام نتائج تجریبیة لأللومینا غیر مطعمة معدل كثافة التلبید والحجم الحبیبي حسب و ZrO2 و منع النمو الحبیبي وزیادة ه ان تأثیر نوعي التطعیم.عملیة التلبید بالفجوات الكبیرة في المرحلة النهائیة من والمشبعة .حركیات التكاثف وحركة الفجوات الكبیرة والصغیرة زیادةمعدل التكاثف حیث