DETERMINTAION of SINTERING MECHANISM and GRAIN GROWTH KINETICS of Mgo-DOPED Al2o3

JTM

DETERMINTAION OF SINTERING MECHANISM AND GRAIN GROWTH KINETICS OF MgO-DOPED Al2O3

oleh : Muhammad Akbar Rhamdhani *, Syoni Soepriyanto**, Aditianto Ramelan *, A. Barliansyah ***

Sari

MgO dalam bentuk larutan padat dapat tersegregasi di sepanjang batas butir keramik Al2O3. Ini akan menurunkan mobilitas batas butir dan juga menghambat pertumbuhan butir. Artikel ini membahas tentang penentuan mekanisme sintering dan kinetika pertumbuhan butir Al2O3 yang didoping oleh MgO yang disinter pada 1773K. Model penyusutan linear digunakan untuk menentukan mekanisme sintering. Besar butir rata-rata dari sampel ditentukan dari data difraksi sinar-x dengan menggunakan metode fluktuasi statistic. Hasil menunjukkan bahwa mekanisme sintering untuk sampel dengan 0.1wt% dan 0.3 wt% MgO didominasi oleh difusi permukaan, dan untuk sampel dengan 0.5 wt% dan 1.0 wt% MgO didominasi oleh difusi batas butir. Besar butir rata-rata untuk sampel Al2O3 yang disinter selama 2 jam adalah 21.1μm. Untuk waktu sintering yang sama, doping MgO sebanyak 0.1 wt% sampai 1.0 wt% menurunkan besar butir rata-rata menjadi masing-masing 12 sampai 10μm.

Kata kunci : MgO-doped Al2O3, model penyusutan linear, metode fluktuasi statistik, sintering, pertumbuhan butir

Abstract

MgO in the form of a solid solution can segregate along the Al2O3 ceramic grain boundary. This will lower the grain boundary mobility and also inhibit the grain growth. This article describes the determination of the sintering mechanism and grain growth kinetics of MgO-doped Al2O3 sintered at 1773K. A linear shrinkage model was used for determining the sintering mechanism. Average grain size of ceramic samples was determined from their x-ray diffraction data, by implementing the statistical fluctuation method (SFM). The results showed that the sintering mechanism for samples with 0.1 wt% and 0.3 wt% MgO was dominated by surface diffusion, while for 0.5 wt% and 1.0 wt% MgO dominated by grain boundary diffusion. The average grain size for pure Al2O3 sample, sintered for 2 hours, was 21.1μm. For the same sintering time, MgO doping of 0.1 wt% to 1.0 wt% reduced the average grain size down to 12 to 10μm, respectively.

Keywords : MgO-doped Al2O3, linear shrinkage model, statistical fluctuation method, sintering, grain growth

* Materials Engineering Study Program, Department of Mechanical Engineering, Institute of Technology Bandung. Ganesha 10, Bandung, Indonesia, Ph/Fax (62) 22 2508144 contact e-mail: [email protected] ** Department of Mining Engineering, Institute of Technology Bandung *** Department of Chemistry, Institute of Technology Bandung

I. INTRODUCTION wt%) allows Al2O3 ceramics to be sintered to its theoretical density and its translucent state. MgO Since the work of Coble (1961), MgO-doped is also known to eliminate discontinuous grain Al2O3 has been the subject of numerous growth, suppress pore-grain boundary separation investigations. A small addition of MgO (∼0.25 and decrease the average grain growth rate

148 Journal JTM Vol. XII No. 3/2005 (Johnson and Coble, 1978; Franken and Gehring, growth and linear shrinkage can be obtained as 1981; Burke and Prochazka, 1981; Berry and follows: Harmer, 1986; Kingery et al., 1997). 2 ΔLx1 ⎛⎞ = ⎜⎟ .….……. (2) Using secondary ion mass spectrometry (SIMS) LAo 4 ⎝⎠ imaging, Soni et al. (1995) had shown that Mg is segregated along the Al2O3 grain boundaries thus By combining Equations (1) and (2), the suppressing grain growth. The presence of following is obtained, MgAl2O4 as a second phase also contributes to the p suppression of grain growth as it acts as a pinning ⎛⎞ΔL t 2 ⎜⎟= ZT() ………… (3) agent. L Aq ⎝⎠o The key to achieve a pore-free microstructure where p and q are exponent parameters, ΔL is the (translucency) is the prevention of pore-grain linear shrinkage, and Lo is the initial length. The boundary separation. In a single phase solid state values of p, q, and Z(T) for each transport sintering, maximum densification occurs when mechanism are also summarized in Table 1. pores located at grain boundaries are removed by lattice or grain boundary diffusion processes. In the absence of magnesia, pores become entrapped 1.2. Statistical Fluctuation Model (SFM) within the alumina grains as abnormal grain growth takes place during sintering (Handwerker X-ray diffraction technique can be used for et al., 1989). Once residual pores become trapped determining the average grain size of a material. within the grain, they are impossible to be Scherrer (Cullity, 1978) developed an expression removed in a reasonable firing time since the for measuring average grain size which is based lattice transport required is extremely slow. This on line broadening of x-ray diffraction pattern prohibits further densification. peaks. His equation, however, is accurate only for materials with average grain size smaller than The current study focuses on the determination of 1μm. For grain sizes or particles larger than 1 μm, the dominant sintering mechanism and the grain Warren (1960) developed the statistical growth kinetics of MgO-doped Al2O3. The linear fluctuation method. The principle of the model is shrinkage model is used to determine the sintering as follows: in ideal cases of a material with fine mechanism and the grain growth kinetics are grain sizes, the change of orientation and material investigated by measuring the average grain size position relative to the diffractometer does not from x-ray diffraction patterns and by change the total area under the peak in the implementing the statistical fluctuation method diffraction pattern. Conversely, for bigger grain (SFM) developed by Warren (1960). sizes where fewer grains contribute to the peak, the area under the peak will vary depending on the orientation and material position. The SFM 1.1. Two Dimensional Linear Shrinkage Model technique for measuring average grain size was developed based on this variation of the area From previous studies (Swandajani, 1994; under the peak of the pattern. Soepriyanto et al., 1995; Lumanauw, 1996), the neck growth between grains for each transport The mathematical formulation of the approach is mechanism during sintering can be generalized written as follows: 2 into the following mathematical equation: 3jAYYΩ−γ ⎡ ⎤ 3 o ⎣ ⎦ D = ………… (4) n 2 ⎛⎞x t 2πμ2 ⎡⎤Y ….……... (1) ⎣⎦ ⎜⎟= BT() m ⎝⎠AA where D is the average diameter of the grain (assuming a spherical shape), j is the multiplicity where n and m are the exponent parameters, t is factor for a particular plane, μ is the linear the time of sintering, x is the neck radius, and A is absorption coefficient, Y is the total counts, and the sphere radius. Each transport mechanism has Y is the average counts of a peak intensity for a different values of n, m, and B(T) as summarized particular plane. Ao is the beam slit area and Ω is in Table 1. By approximating the value of ρ with the space angle and can be calculated using the 2 x /4A and ΔL with ρ, a relationship between neck following equation:

Journal JTM Vol. XII No. 3/2005 149 ωl a high-temperature horizontal-tube resistant .………… (5) =Ω 2 furnace in air atmosphere. Doping concentrations R sin4 θ of 0.1 wt%, 0.3 wt%, 0.5 wt% and 1.0 wt% of where ω and l are the width and the length of the MgO and sintering times of 1, 2, and 3 hours were receiving slit, R is the radius of the diffractometer, used as the experimental parameters for this study. and θ is the Bragg diffraction angle. All the geometrical parameters and the configuration of Linear shrinkage of the fired ceramics was the diffractometer are shown in Figure 1. The measured using vernier-calipers and micrometers. detailed derivation of the statistical fluctuation The density measurements were conducted using equations has been described elsewhere (Warren, a water-immersion technique. The linear 1960; Rhamdhani, 2000; Di Nunzio and shrinkage model was used to determine the Abbruzzese, 1992; Ginting et al., 1997). sintering mechanism. The investigation of the

grain growth kinetics was carried out by The feasibility of this technique had been measuring the average grain size from x-ray analyzed by many investigators and acceptable diffraction data by implementing the SFM. error measurements were obtained, i.e. 10-30%.

The technique was successfully implemented in measuring the average grain size of KCl (Warren,

1960), 0.01wt%C-steel (Rhamdhani, 2000) and III. RESULTS AND DISCUSSION Zircalloy (Ginting et al., 1997). However, to the authors’ knowledge there has not been any work 3.1. Sintering Mechanism to evaluate this method for measuring grain size of ceramic sample. The effect of MgO doping on the linear shrinkage

and the bulk density is shown in Figure 3. To

some extent, the greater the amount of MgO II. EXPERIMENTAL PROCEDURE added, the greater the linear shrinkage and as a

result, the density is greater as well. In the range Alumina ceramic samples were prepared from of experimental parameters and conditions pure Al O (99.9%) and MgO (99.9%) powders 2 3 studied, the theoretical density of alumina ceramic obtained from Merck. Calcinations of Al O at 2 3 could not be achieved. Longer sintering time, 1373 K were conducted to transform any phases higher sintering temperature, as well as more present in the powders into the alpha phase, i.e. controlled atmosphere are required for complete γ ,,θκ→ α. X-ray diffraction analyses were densification. conducted to confirm this transformation. The effect of MgO doping to densification can be By sieving, the mean particle size of the starting easily understood. In the sintering process, both alumina powder was determined to be 55 μm. densification and grain growth are in a This value, however, represents a mean competition. The densification process is limited agglomerated-particle size. Figure 2(a) shows a if mass transport occurs for grain growth. In the scanning electron microscope image of the same way, the grain growth is limited if mass agglomerated particles. Upon calcinations and transport occurs for densification. Since the milling, the agglomerates ruptured and the mean presence of MgO in Al2O3 reduces the grain size reduced to a value of 3 μm. This was growth, the mass transport is mainly for considered to be the better representation of the densification. Therefore, to some extent, denser true mean particle size. Figure 2(b) shows an ceramics can be expected for higher MgO SEM image of the powder after calcinations and dopings. The effect of sintering time on linear milling. The detailed information about particle shrinkage and bulk density is also shown in size distribution is described elsewhere Figure 3. The largest linear shrinkage and bulk (Rhamdhani, 2000). density, with respect to MgO dopings, was obtained for a sintering time of 3 hours. Longer Proper amounts of MgO were added to Al2O3 and sintering time allows further diffusion of matters, wet-milled using an ethanol-medium. The thus better densification. suspension was dried while being milled continuously. After further drying, the doped The sintering mechanism was determined using powders were cold-pressed into a disk at 30,000 N the linear shrinkage model. Equation (3) can be (195 MPa). Sintering was conducted at 1773 K in rearranged to obtain the following relation:

150 Journal JTM Vol. XII No. 3/2005 coarsening in which the neck growth between ΔLZT()1/ p 2 particles lowers the specific surface area and no ⎛⎞ material shrinkage occurs (Barsoum, 1997). log=+ log⎜⎟q logt ……... (6) LApo ⎝⎠ However, the experimental results showed that the samples with MgO doping concentrations of 0.1 From the experimental data, a plot between log wt% and 0.3 wt% also experience shrinkage. This suggests that other mechanisms that lead to ΔL/Lo and log t can be developed. The slope, which is equal to 2/p, should have a value of densification such as lattice or grain boundary 0.333 for a grain boundary mechanism and 0.4 for diffusion were also at play. Although the sintering a volume diffusion mechanism (Table I). The was dominated by surface diffusion, it does not experimental data are plotted in Figure 4. It can be necessary mean that it was the sole mechanism. seen that for 0.5 wt% and 1.0 wt% MgO The dominant mechanism for samples with MgO concentrations, the slopes are 0.316 and 0.321, doping concentrations of 0.5 wt% and 1.0 wt% respectively. These corresponds to values of p = were found to be through grain boundary 6.32 and p = 6.23. Thus, it can be concluded that diffusion where significant material shrinkage the mechanism for sintering of samples with MgO occurs. doping concentration 0.5 – 1.0 wt% is dominated by grain boundary diffusion ( p ≅ 6 ). 3.2. Grain Growth MgO doping of the amount 0.1 wt% and 0.3 wt% give slopes of 0.241 and 0.288. These results were The grain growth kinetics of the MgO-doped not expected as they deviate from the expected Al2O3 samples were investigated by measuring values of 0.333 or 0.4. The linear shrinkage model the average grain size of the sintering product of could not be used for determining the sintering the different experimental parameters. As mechanism. Therefore, the neck growth model mentioned earlier in the text, the average grain was used for samples with MgO doping size of the samples was determined from x-ray concentrations of 0.1 wt% and 0.3 wt%. By using diffraction data by using the SFM method Equation (2), the values of neck growth x/A that developed by Warren (1960). corresponds to each value of ΔL/Lo, were calculated. A similar procedure was then used, i.e. The calculation results of the average grain size plotting the values of log x/A versus log t, and the were plotted against MgO doping concentration results are shown in Figure 5. for sintering time of 1, 2, and 3 hours, as depicted in Figure 6. It can be seen from the graph that the The slopes, which are equal to 1/n, were average grain size of the ceramics decreases with calculated to be 0.1399 and 0.1401 for ceramics increasing concentration of MgO doping. The with MgO concentrations of 0.1 wt% and 0.3 average grain size of a sample with 100% Al2O3 wt%, respectively. These correspond to values of sample, sintered for 2 hours, was 21.1μm. For the n = 7.15 and n = 7.13. These values of n are close same sintering time (2 hours), MgO doping of 0.1 to 7 and from Table 1 it can be seen that this wt% to 1.0 wt% reduced the average grain size relates to a surface diffusion mechanism. It can down to 12 to 10μm, respectively. then be concluded that the mechanism for sintering of samples with MgO doping The kinetics of the grain growth can be generally concentrations of 0.1 and 0.3 wt% is dominated described in the following general form (Fortes, by surface diffusion. 1992):

It was estimated that the error measurement of DDKnn− =⋅t ..………... (7) data in Figures 4 and 5 is 30% maximum. The R2 o values of the lines in Figures 4 and 5 were ranging or for D <<< D, from 0.78 to 0.99. o

n The results of the investigation of the dominant DK= ⋅t …………... (8) sintering mechanism in this study are summarized in Table 2. For samples with MgO doping where Do is the initial average-grain-diameter, n is concentrations of 0.1 wt% and 0.3 wt%, the the grain growth exponent and K is the grain dominant sintering mechanism is through surface growth constant which includes the grain diffusion. Theoretically, a sintering mechanism boundary mobility term (Mgb) and the grain through surface diffusion will only cause a boundary energy term (γgb).

Journal JTM Vol. XII No. 3/2005 151 The value of n may vary due to, for example, segregation at the grain boundaries and second, uneven grain boundary mobility caused by the pinning of the grain boundaries by fine second- presence of inhibitors. A grain growth exponent n particles of spinel MgAl2O4. The solute drag = 2 (i.e. parabolic growth law) was predicted by mechanism is operating below the solubility limit. the simple theory of Burke and Turnbull (1952) Grain growth can be also inhibited by the and is often considered as an ideal value for n. presence of pores, inclusions and solute impurities Experimental values of n usually deviates from n (Kingery et al., 1997). These inhibitors act as = 2. In most cases, n is larger than 2. It was also pinning agents that constrain the movement of the observed that experimental grain growth grain boundary. The shape of curvature also plays exponents obtained from Equations (7) and (8) a role in this grain boundary behavior. A sharp may change with time as steady state conditions curvature can drag these inhibitors while a are not prevalent during growth (Fortes, 1992). shallow curvature can not.

In this study, the grain growth exponents (n) and In the ceramic samples studied, at least two grain growth constants (K) were determined. inhibitors acted as pinning agents, i.e. pore and n n Graphs of log (D -Do ) with different values of n second phase particles. Since we were dealing were plotted versus log t for each MgO-doped with initial and intermediate stages of sintering, Al2O3 composition. These are shown in Figure 7. the presence of large amount of pores was For example, the experimental data for 0.1 wt% expected. The second phase particles, in this case MgO with n values of 2, 3, and 4 were plotted in MgAl2O4, were also likely to form and be present Figure 7(a). The correct value of the grain growth during sintering and grain growth since the constant (n) will give the experimental data line a amount of MgO added was above its solubility slope of one. For samples with 0.1 wt% MgO, the limit. Solubility limit of MgO in Al2O3 was slope equal to one was acquired by inserting the reported to be a few hundred ppm, i.e. ~500 ppm value of n = 2.85. Thus it can be concluded that (Chiang et al., 1997). the grain growth constant for this composition is equal to 2.85. The same procedure was used to The morphology of the fracture of the ceramic determine the value of n for the other samples. samples was observed using scanning electron For samples with 0.3 wt%, 0.5 wt% and 1.0 wt% microscopy. Figure 9 shows the SEM image of MgO, the grain growth constants were determined fracture morphology of the 0.1 wt% MgO sample to be 2.20, 1.85, and 1.55, respectively. These sintered for 1 hour. The images revealed that the values are in agreement with the literature, i.e. for average grain size of the ceramic is smaller than metals and ceramics they range between 2 to 4, the value determined from x-ray diffraction data with a mean value of 2.6 (Barsoum, 1997). using the statistical fluctuation method. It seemed that the SFM method picked up the average size The value of the grain growth constant (K) can of collections of grains. The average sizes of these subsequently be determined after the value of n collections of grains were consistent with the n n for each system is obtained. Plots of log(D -Do ) experimental data on Figure 6. versus log t for each system with its correct value of n were constructed and shown in Figure 8. Figure 9 also shows the complexity of the Slope of these lines are 1. The value of K for each microstructure of the ceramic samples during system was obtained by determining the value of initial and intermediate stage of sintering. This n n log(D -Do ) at log t = 0. This value corresponds to particular sample experience both densification the value of log K. The results are shown in Table and also grain coarsening. This is in agreement 3. The value of K represents how fast the grain with the results from Baik and Ik Bae (1994) boundary moves, i.e. a higher value of K means a which found that MgO addition increases the higher value of grain boundary mobility (Mgb), coarsening kinetics although also promotes therefore grain growth proceeds faster. The results densification. for both the grain growth constants and the exponents are shown in Table 3. It can be seen that the increase amount of MgO doping lowers IV. CONCLUDING REMARKS both the grain growth exponent and the constant. Sintering mechanism and grain growth kinetics of The mechanism by which MgO reduces the MgO-doped Al2O3 were studied. The linear boundary mobility in Al2O3 is still the subject of shrinkage model was found to be useful. It was some discussions. Two major mechanisms had found that the dominant mechanism for the been proposed: first, solute drag due to Mg sintering was through surface diffusion for MgO

152 Journal JTM Vol. XII No. 3/2005 doping concentrations of 0.1 wt% and 0.3 wt% ρ = radius of curvature of the neck area and grain boundary diffusion for MgO doping θ = Bragg diffraction angle concentrations of 0.5 wt% and 1.0 wt% MgO. The application of the linear shrinkage model was extended for determining sintering mechanisms ACKNOWLEDGEMENTS other than those that resulted in densification, i.e. surface diffusion. This involved a back- The authors wish to thank Dr. M. Laniwati at Chemical calculation of neck growth values from each of Engineering Department-ITB; Mr. I. Ginting, Mr. the linear shrinkage values. Djoko and Mr. Dani at BATAN. The authors also The statistical fluctuation method was used to acknowledge the technical assistance from Mr. W. determine the average grain size of the ceramic Wawan in the Physical Metallurgy and Ceramic Lab, sample. However, it seemed that the average size Dept. of Mining Engineering-ITB; Mr. T. Koco and Mr. of collections of grains was picked up instead of A. Genaatmadja in the Metallurgy Lab, Materials the average size of the actual grain. As with many Engineering Study Program-ITB. published papers, this is clearly not the final word and more works should be done, by ourselves or REFERENCES others. It is expected that this work, with all the limitations, will stimulate a level of discussion 1. Baik, S. and Ik Bae, S., 1994, J. Am. Ceram. from which a clear explanation will emerge. Soc., vol. 77 (10), pp. 2499-504.

2. Barsoum, M., 1997, Fundamentals of

Ceramics, McGraw Hill, New NOMENCLATURE York.

3. Berry, K.A. and Harmer, M.P., 1986, J. Am. A = sphere radius Ceram. Soc, vol. 69 (2), pp. 143-9. Ao = beam slit area = ω.l 4. Burke, J.E. and Prochazka, S., 1981, Proc. of th ao = lattice constant 5 Int. Conf. on Sintering, D = average grain diameter September 7-10, Portoroz- Db = grain boundary diffusivity Yugoslavia. Ds = surface diffusivity 5. Burke, J.E. and Turnbull, D., 1952, Prog. Dv = lattice diffusivity Metal Phys., vol. 3, pp. 220. j = multiplicity factor 6. Chiang, Y-M., Birnie III, D.P. and Kingery, K = grain growth constant W.D., 1997, Physical Ceramics, Principles for Ceramic Science and k = Boltzmann’s constant Engineering, John Wiley and Sons, ΔL = shrinkage New York. Lo = initial length 7. Coble, R.L., 1961, J. Appl. Phys., vol. 32 (5), Mgb = grain boundary mobility pp. 787-99. m, n, p, q = exponent parameters 8. Cullity, B.D., 1978, Elements of X-Ray m = mass of the evaporating gas molecules Diffraction, 2nd Ed., Addison- n = grain growth exponent Wesley Publ. Co. Inc. New York. 9. Di Nunzio, P.E. and Abbruzzese, G., 1992, Po = pressure R = gas constant Mat. Sci. Forum, Vol. 94-96, Trans R = radius of diffractometer Tech Publ., Switzerland, pp. 467- 74. t = time 10. Fortes, M.A., 1992, Mat. Sci. Forum, Vol. 94- T = temperature, K 96, Trans Tech Publ., Switzerland, x = neck radius pp. 319-24. Y = total counts 11. Franken, P.E.C. and Gehring, A.P., 1981, J. of Y = average counts Mater. Sci., vol. 16, pp. 384-8. α = evaporation coefficient 12. Ginting, I., Tanto, I. and Encey, T., 1997, δ = grain boundary width Proc. Seminar Sains and Teknologi b Nuklir, PPTN-BATAN Bandung, γ = grain boundary/surface energy March 19-20. γ = correction for preferred orientation 13. Handwerker, C.A., Morris, P.A. and Coble, μ = linear absorption coefficient R.L., 1989, J. Am. Ceram. Soc., vol. Ω = space angle = ε.φ 72 (1), pp. 130-6.

Journal JTM Vol. XII No. 3/2005 153 14. Johnson, W.C. and Coble, R.L., 1978, J. Am. 17. Soepriyanto, S., Lumanauw, D. and Ceram. Soc., vol. 61 (12), pp. 110- Swandajani, J., 1995, J. Tek. 4. Mineral, vol. II (2), pp. 49-63. 15. Lumanauw, D., 1996, Pemodelan Sintering 18. Soni, K., Thompson, A.M., Harmer, M.P., Multipartikel Untuk Tahap Awal, Williams, D.B., Chabala, J.M. and Antara dan Akhir, B.Eng. Thesis, Levi-Setti, R., 1995, Appl. Phys. Dept. Mining Engineering, ITB. Letter, vol. 66 (21), pp. 2795-7. 16. Rhamdhani, M.A., 2000, Penentuan 19. Swandajani, J., 1994, Analisa Sintering Tahap Mekanisme Sintering dan Kinetika Awal Dengan Simulasi Komputer, Pertumbuhan Butir Keramik Al2O3 B.Eng. Thesis, Dept. Mining yang Didoping MgO, B.Eng. Engineering, ITB. Thesis, Materials Engineering 20. Warren, B.E., 1960, J. Appl. Phys., vol. 31 Program Study, ITB. (12), pp. 2237-9.

Table 1 - Neck growth and linear shrinkage model (Soepriyanto et al., 1995) Neck growth model Mechanisms n m B(T) 4αγπmP3/2 Evaporation and Condensation 3 2 o ()RT3/2 A 2 2 32Daγ 3 Lattice diffusion along surface 5 3 vo kT 56Daγ 4 Surface diffusion 7 4 s o kT 32Daδγ 3 Grain boundary diffusion 6 4 bb o kT Lattice diffusion along grain 32Daγ 3 5 3 vo boundary kT Linear shrinkage model Mechanisms p q Z(T) 32Daγ 3 Grain boundary diffusion 6 8 vo kT Lattice diffusion along grain Daγ 3 5 6 vo boundary kT

Table 2 - Dominant sintering mechanism in the systems studied Dominant sintering Exponent-parameter MgO doping mechanism value 0.1 wt% Surface diffusion p 6 0.3 wt% Surface diffusion p 6 0.5 wt% Grain boundary diffusion n 7 1.0 wt% Grain boundary diffusion n 7 Table 3 - The grain growth exponents (n) and constants (K) in the systems studied Grain growth Grain growth constant MgO doping exponents (n) (K, μmn/s) 0.1 wt% 2.85 0.179680 0.3 wt% 2.20 0.029121 0.5 wt% 1.85 0.009579

154 Journal JTM Vol. XII No. 3/2005 1.0 wt% 1.55 0.004756

Figure 1 – Geometrical parameters (left) and configuration of the diffractometer used in the experiments (right) from Ginting et al. (1997).

(a) (b) Figure 2 – Scanning electron microscope images of: (a) alumina powder as is (470X), (b) alumina powder after calcinations and milling (8000X).

0.16 2.78 3h 0.15 2.73 )

3h 3 0.14 2.68 2h 0.13

0.12 2h 2.63 0.11 2.58 1h

Linear Shrinkage 0.1 1h Bulk De ns it2.53 y ( g/cm 0.09

0.08 2.48 00.51 00.51 MgO addition (wt%) MgO addition (wt%)

(a) (b) Figure 3 – The effect of MgO doping on the linear shrinkage (a) and the bulk density (b) for sintering time of 1, 2, and 3 hours

Journal JTM Vol. XII No. 3/2005 155

Figure 4 – The changes of linear shrinkage for various MgO doping concentration with various sintering time (in log scale)

Figure 5 – The changes in neck growth with various sintering time (in log scale)

3h 14 m) μ 12 2h 10 Grain Size ( 8 1h

6 00.51 MgO addition (wt%)

Figure 6 – The effect of MgO doping on the average grain size of Al2O3 ceramic.

156 Journal JTM Vol. XII No. 3/2005

(a) (b)

Figure 7 – Determination of grain growth exponents (n); additional line on each graph with slope=1 was also drawn. The correct value of n will give the experimental-data line a slope of one, (a) 2.85 for 0.1 wt% MgO, (b) 2.20 for 0.3 wt% MgO, (c) 1.85 for 0.5 wt% MgO, and (d) 1.57 for 1.0 wt% MgO.

n n Figure 8 – Plots of log (D -Do ) vs log t for each system with its correct grain growth constant.

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(a) (b) Figure 9 – Scanning electron microscope images of fracture surface of 0.5 wt% MgO-doped alumina sintered for 1 hour (a) at 7131 X magnification, and (b) at 14262 X magnification.

2 Appendix 3jAΩ−γ ⎡ Y Y ⎤ 3 o ⎣ ⎦ D = 2 2 ⎡⎤ Example of average grain size calculation 2πμ ⎣⎦Y using the SFM: 3⋅⋅ 12 0.4608 ⋅ 1.112 ⋅ 10−−34 ⋅ 3.132 ⋅ 10 D3 = 5369 D = 1.024.10-3 cm = 10.24μm

Table A – X-ray diffraction data for (113) plane

Y1 Y1 Y2 Y2 Y3 Y3 2 θ o o o (0 ) corr. (45 ) corr. (90 ) corr. 43.41 78 0 86 8 94 16 43.44 99 21 96 18 114 36 43.47 135 57 121 43 145 67 43.50 200 122 239 161 226 148 43.53 322 244 328 250 414 336 43.56 535 457 532 454 673 595 43.59 934 856 850 772 1132 1054 43.62 1291 1213 1304 1226 1578 1500 Experimental set up 43.65 1668 1590 1720 1642 1870 1792 43.68 2088 2010 2120 2042 2216 2138 Sample 0.1 wt%MgO-Al2O3 43.71 2490 2412 2412 2334 2417 2339 X-ray target: Cu (λ=1.54) 43.74 2748 2670 2656 2578 2299 2221 Alumina rhombohedral plane (113) 43.77 2484 2406 2456 2378 2125 2047 o o 43.80 2021 1943 1991 1913 1798 1720 Range 2θ = 43.41 -44.04 43.83 1607 1529 1619 1541 1458 1380 2 Ao = 0.4608cm 43.86 1334 1256 1243 1165 1006 928 43.89 984 906 961 883 736 658 j = 12 (multiplicity of plane 113), γ =1 43.92 571 493 568 490 489 411 μ Al2O3 (linear absorption coefficient) = 43.95 324 246 306 228 287 209 -1 2 -1 43.98 170 92 185 107 160 82 272cm , 2π μ = 5369cm 44.01 129 51 112 34 121 43 o o 3 divergence slit, 1 receiving slit 44.04 89 11 92 14 80 2 w = 0.25cm, l = 1.49cm, R = 15cm Total counts 20585 20281 19722 Ω = wl/4R2sinθ =1.112x10-3 Position (o) Y Y2 From Table A, Y = 20196, Y 2 =408006157, 0 20585 423742225 2 45 20281 411318961 and ⎣⎦⎡⎤Y =407878416, 90 19722 388957284 408006157 = 222 20196 = Y 2 ()YY−− Y Y −4 Y Thus, 22==⋅3.132 10 YY 407878416 = 2 []Y

158 Journal JTM Vol. XII No. 3/2005