IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (1) 2011 Modeling of the Effect of MgO and ZrO2 on Sintering of Alumina H. K.H.Al.Mayaly Department of physics, College of Education IbnAl-Haitham, University of Baghdad Received in April 18 , 2010 Accepted in June 17, 2010 Abstract This research studyies the effect of MgO and ZrO2 as additives in sintering Al2O3 . The experimental results are modeled using ( L2 _ regression) technique , sintered density and grain size rate measurments were accounted by utilizing experimental results of undoped , MgO doped and ZrO2 doped alumina impregrated with spherical large pores in final stage of sintering . The effect of each additive is inhibitian of the grain growth and increasing the densification rate which enhances the kinietics of densification and the removal of large and small pores. Introduction Alumina ceramic (Al2O3) is a hard refractory ceramic, which has been used in high temperature, structural and substrate applications because of its good strength and low thermal expansion cofficient . Nevertheless , like other mono lithic ceramics, Al2O3 is aptto suffer from low ductility and low fracture toughnees[I]. Doped samples were studied fro the influence of varying the grain growth rate of the alumina , MgO is a strong solid-solution grain growth inhibitor in high purity alumina [2] , and ZrO2 when added in high enough concentrations, is an even strong second-phase grain growth inhibitor [3] . The intension of this study to was model mathematically the densification and grain size rate of doped Al2O3 system using regression modeling technique utilizing MgO and ZrO2 as additives seperately. IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (1) 2011 Theoretical background The pores are calassified into two basic types , there are the so-called matrix or first- generation pore and the second type, large so-called second-genertion pores which originate from particale agglomeration and particale packing irregularities within the powder compact [4] .The large pores are always 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 pore can be thermodynamically stable depending on the value of dihedral and pore size : grain size ratio (for a given dihedrol angle and pore size, there is a critical grain size above which the pore is unstable and can sinter ),while below where it is stable and can not sinter. The models which are used in this study have asimplifiying a ssumptions in order to perform the calculations. 1) Pore shrinkage is controlled by lattice diffusion 2) The grain size is fixed at the critical grain size which was taken to be 0.68 times the pore size [6]. 3) The pores are assummed to be spherical with no thermodynamic barrier for shrinkage [4,7]. The large-pore volume will start to decrease (once the critical grain size is reached), the matrix grain growth 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 pores surrounding each grain , Mp is the average pore mobility , G is the grain size , b is the grain boundary energy , ε is the grain growth rate factor and (G/Gmax) is the ratio of average grain size over maximum grain size. The densification rate(dρ/dt) depends on the diffusion cofficient responsible for densification (Dlattice or D boundary) and the grain size [9]. / ...... ...( 2 )nd C D G d t   where C is a constant and D is the diffusion cofficient . The grain size exponent, n, is 3 for lattice- diffusion controlled densification which is used in this study .[5] In this study (reported in Ref [5]). Ultra-high-purity α-alumina powder for which the manufaturar claimed a(99.995%) purity size of powder was 0.45 μm and 97% of the particles were less than 1μm . IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (1) 2011 The following three compositions were chosen for this study (i) pure alumina ; (ii) 250- ppm-MgO-doped alumina , and (iii) Al2O3 +10 Vol % ZrO2 . Large mono size pores were introduced in to each composition by incorporating latex spheres (5.6 μm) into the powder mix before sintering .The ratio of the sphere volume / the sum of the sphere volume and the solid volume in each composition was (5%) .The powder was cold-pressed into pellets of approximately the same green density (47.5%) using a high-purity alumina punch and die set . The pellets calcined at 1000o c in air for 48 h , large pores were produced after calcination as a result of burning out of the latex spheres. The processing procedure for all composition was kept as consistent as possible to ensure similar initial microstructures . Sintering was conducted under flowing nitrogen gas in a furnace heated with graphite elements, the specimens were heated at a constant rate of (60oc/min) up to the sintering temperature of 1620oc (oxygen partial pressure < 10-11 atm <10-6 pa ). Regression modeling technique The equation of L2_ regression which is used in this study can be express as follows [10] 1 ( ) .. . .. . . .. .(3 ) T T X A A A b   where A is the matrix , AT is the transpose of matrix A , b is random abservation and X is the fixed part of equation but unknown. The integral form of the grain growth 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        � � After simplifing the integral expression for equation (4) and (5) we get a suitable form of equation (3) that can be adopted to L2_ regression . 1 1 max ln (1 ) ........(6 )t t G G z t Y G    � IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (1) 2011 (1 ) 2 2........(7)n t t Z G t Y    � Where Z1 is the grian size rate parameter and equals to 13.4 [ ]p bM Y N  ,Z2 if the densification rate parameter and equals to [CD / (1-n)] , Y1 is the grain size rate cofficient 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 density value were measured using model of L 2_ Regression (see-Ref II) Results and Disussion Figs . (1) and (2) showed the effect of MgO and ZrO2 doped alumina which have a large ( � 5 μm ) model spherical pores on the density date as a function of time at 1629 o c . As can be seen that both MgO and ZrO2 increased the desification rate of Al2O3 . ZrO2 had more effective in enhanced densification rate than MgO . The calculatedion by model sintered densites of sample with ZrO2 addition was ranged between [ 92 and 97.9% ] and for samples with MgO addition was ranged between [ 91 and 97.2 % ] . The ZrO2-doped samples did reach a slightly higher density than the MgO-doped samples , however , this does imply that a fraction of the pores were indeed thermodynamically unstable and cabable to shrink . Such pores would be able to shrink at a faster rate than those in the MgO – doped samples due to smaller grain size and associated faster kinetics. Fig. (3) and Fig. (4) are showed the grain size versus time date for MgO-doped , and ZrO2- doped aluminas which imregnated with large ( � 5 µm ) model spherical pores at 1620 oc . MgO and ZrO2 were very effective in inhibiting grain growth in the system (ZrO2 more so than MgO), the grain sizes for undoped and MgO-doped samples well beyond the critical grain size and the large pores do not readily disapper even when thermodynamics is permitting . The degree of grain growth inhibition was faster with the ZrO2-doped samples , where the small grain size of these samples showed that not all the pores were necessarily thermodynamically unstable for any reasonble lenght of sintering time. In Table (1) we can see the grain size rate parameter of doping samples increases , this can be explained in terms of the number of pores which increase with doping and this may naturally decreases densification rate parameters . IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (1) 2011 Table (2) lists the grain size rate cofficient and densification rate cofficient , the doping lowers both the densification and grain size rate cofficient respectively where the dopent particals may form barriers along the diffusion path and reduce the densification Conclusion The modeling technique shows that the calculated results using L 2 _Regression technique agrees with experimental results, and MgO-doped alumina impragnated with large pores have effective in inhibiting grain growth rate and increases the densification rate , while the effect of ZrO2 doped alumina was faster than MgO , ZrO2 doped samples have more effective in enhanced densification and inhibition the grain growth rate. References 1. Nanchou,S. ;Hwalu,H. Fwulii ,D. and Huang, J.L. (2009), Processing and physical properties of Al2O3/alumina alloy composites. Ceramics International 35: 7-12 2. Bennison ,S.J. and Harmer, M.p. (1985),Grain growth kinetics alumina in the absence of aliquid phase.J.Am.Ceram.Soc.68(1) :22-24. 3. lange ,F.F. and Hirlinger, M.M. (1984),Hindrance of grain growth in Al2O3 by ZrO2 inclusions . J.Am.Ceram.Soc.67(3):68-164. 4. Zhao ,J. and Harmer ,M.P. (1988),Effect of pore distribution on microstucture development. I, matrix pores.J.Am.Ceram.Soc. 71(2):20-113. 5. Zhao ,J. and Harmer ,M.P. (1988),Effect of pore distribution on microstructure development. II, First and second generation pores . J .Am.Ceram.Soc,71(7) :39-530. 6. Kingery, W.D. and Francois ,B. (1967),Sintering of Crystalline Oxides.I.Interactions between grain boundaries and pores,(98-471) in sintering and retated phenomena,Edited by G.C.Kyczynski,N.A.Hooton,and G.F.Gibbon,Gordon Breach,Newyork. 7. Coble ,R.L. (1961),Sintering crystalline solids I.Intermediate and final stage diffusion models,J.Appl.phys(32): 92-787. 8. Brook ,R.J. (1976),Controlled grain growth in ceramic systems .(64-331).intreatise on materials science and technology, 9.Edited by F.F.Y.wong academic press.Newyork. 9. Berry ,K.A. and Harmer ,M.P. (1986),Effect of MgO 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. Malyaly ,H.K. (2005),Analysis the three stage of sintering using linear programming. IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (1) 2011 Table (1):Grain size and densification rate parameters in three case , undoped, MgO- doped and ZrO2-doped alumina impregted with large model pores Undoped MgO-doped ZrO2-doped Grain size rate parameter (Z1) 90.583 93.964 94.651 Desification rate parameter (Z2) 1.574 1.102 0.578 Table (2): Grain size and densification rate cofficient in three case , undoped , MgO-doped and ZrO2 –doped alumina impregnated with large model pores Undoped MgO-doped ZrO2-doped 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. SCI. VOL.24 (1) 2011 Fig (1) Density data of undoped and MgO doped aluminas impregnated w ith large 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 si ty (g m /m ^ 3 ) undoped exp undoped cal MgO doped exp MgO doped cal Fig(2) Density data of undoped and ZrO2 doped al uminas impregnated with large 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 cal ZrO2 doping exp ZrO2 doping cal IBN AL- HAITHAM J. FOR PURE & APPL. SCI. 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