ACTIVATION ENERGIES FOR SINTERING AND GRAIN GROWTH IN SINTERED MAGNESITES

Transcription

1 ACTIVATION ENERGIES FOR SINTERING AND GRAIN GROWTH IN SINTERED MAGNESITES

2 149 ACTIVATION ENERGY FOR SINTERING AND GRAIN GROWTH PROCESSES IN SINTERED NATURAL MAGNESITE WITH AND WITHOUT TITANIA 9.1 INTRODUCTION : Sintering of oxides can be considered as a process of densification, the principal motivation of which is the reduced surface free energy. Activated sintering is restricted by definition to those processes which lowers the activation energy barrier for the rate controlling transport step. The explanation of activated sintering include diffusional Cl, 23, solution precipitation C33 and electronic configuration model C43. In order for micros true tural changes or chemical reactions to take place in condensed phases, it is essential that atoms be able to move about in the crystalline or non-crystalline solids. There are a number of possible mechanisms by which an atom can move from one position to another in a crystalline structure. If the energy of an atom in a stable position is considered as it moves from one lattice site to another by a diffusion jump, it is imperative that there be an intermediate position of higher energy than the stable position. If this was not so, no driving force would be required to change the position of the atom and it would not be classed as an atom in a stable position. The magnitude of energy which must be supplied in order to overcome this energy barrier is called the activation energy for the process E51 as shown in figure 9.1. Vacancies and interstitials play an important role in atomic diffusion providing unstable position for the atom to reside /borrow energy /store energy.. Neighbouring atoms can move into a vacancy. After one such move, the new vacancy can receive another atom and the process is continued, and the net result is homogenization.

3 Energy Figure 9.1 : Schematic diagram of forward and backward reactions.

4 151 Sintering of MgO occurs in three stages s (a) Rearrangement of MgO crystallite structure with rapid (b) (c) reduction in surface area and MgO grains. A process controlled by surface diffusion and evaporation-condensation without change of specific volume of pores and shrinkage of MgO grains. A process controlled by volume and grain boundary diffusion with considerable shrinkage of aggregates. From the study of microstructural analysis it was evident from the study that titania had a very significant effect on the grain size. Titania was also likely to have a strong influence on the cationic diffusion rate. Charge neutrality condition requires an Mg vacancy be created for addition of each Ti4+ ion in MgO lattice. There are a number of possible activation energies for mass transport processes depending upon the specific associated defects which are generally responsible for ionic diffusion processes. The values range from about loo to 600 kj/mole for the same material with only slight differences in the chemical composition or the processing conditions. A definitive interpretation of the processes involved is difficult because of this wide range of observed experimental values C61. Although the diffusion coefficient in the sintering process is exponentially dependent upon temperature, the activation energy is made up of two parts C71, the energy for creation of the vacancy and the energy for vacancy movement In this study, it was anticipated that the measurement of activation energy would throw light on the possible role of additives in the grain growth during sintering of natural Indian magnesites. 9.2 ACTIVATION ENERGY FOR INITIAL STAGE SINTERING IN SINTERED MAGNESITE WITH TITANIA : The kinetics of sintering is usually studied by observing the time dependance of neck growth between the spherical

5 particles and/or shrinkage of the powder compact. Sintering mechanisms are identified by comparing the observed kinetics with those predicted by various theoretical models based on different mass transport mechanisms. Various workers, CB-123 have proposed different models based on different assumptions. The results can be summarised by a general equation of the form Sn = kt, where S = x/a or At_/L0l n and k are constants. The value of n depends mainly on transport mechanism operative during the sintering process. Experimentally the values of n are determined from the plots of logarithm shrinkage *A vs. logarithm time. The experimentally obtained shrinkage values for the initial period of sintering of five minutes under isothermal conditions between 1300 and 1450 C are listed in table 9.1. The plot of shrinkage % vs. time for Salem magnesite with 0.2 wt% titaniais shown in figure 9.2. Up to- 5% of shrinkage is plotted in this figure VALUES SOAKING OF SHRINKAGE AT DIFFERENT table 9.1 % (100 X AL/LC) TEMPERATURE OBTAINED UP TO 5 MINUTES OF TIME (min) (C) (C) (C) <C> (C) The calculated values of n reveal that they range

6 153 between 1.0 and 0.7, with the average value being 0.8. It has been pointed out by Johnson, that n varies depending on the relative importance of grain boundary and volume diffusion in the material transport. During the first stage, when the viscous flow of the ' liquid is the rate determining process in sintering within a liquid secondary phase, shrinkage would be proportional to a power of time slightly greater than unity C141. Singu C151 has shown that the slope is increased by concurrent surface diffusion and decreased by vapour transport. It is interesting to note that log shrinkage against log time for each sample at different temperature are linear though not completely parallel. For each composition, the n values decreases with increasing temperature signifying a change in the relative contribution of the two mechanisms at different temperatures. Here, the first stage is characterised by increase in grain size and density of the compact, whereas, in the second stage, a more rapid grain growth occur ed C163. Attempts have also been made to determine the sintering mechanism by analysing the data on the isothermal sintering. For this purpose the value of exponent n was determined from log log plots of % linear shrinkage against time using the equation suggested by Johnson C171. The plots are based on the equation : Sn = kt (9.4) where, k is a temperature dependant constant, AL/L0 is the relative linear shrinkage, t is the time and n is an exponent whose value varies with the mechanism of material transport. or, n log S = log k + log t-- (9.5) or, log S = 1/n log k + 1/n log t at t = 1, log t = 0, therefore, log S = 1/n log k (9.6) Again, k = k0 e* Q/RT> (9.7)

7 154 log k = log k0 - Q/2.303.RT (9.7) or, log S = 1/n log k0-1/n (Q/2.303 R T) (9.8) The value of n was obtained from reciprocal slopes of log S vs. log t given in figure 94- and table 9.1. Arrhenius plot of log k against reciprocal absolute temperature (1/T) for natural Salem magnesite is shown in figure 9.3. Slopes from these plots give Q/2.303 R from which Q, the activation energy for sintering is calculated. Plotting log k vs. 1/T the slope becomes, -m = Q/2.303 R (9.9) Q = R (-m) 104 Cal/mole (9.10) Q = X X 4.2 X (-m) X lo4 J/mole (9.11) TABLE 9.2 RATE CONSTANT AND ACTIVATION ENERGY FOR INITIAL SINTERING IN SALEM MAGNESITE WITH TITANIA 1/T X 104 K"1 log k slope (m) Activation Energy kj/mole The activation energy for sintering in MgO generally varies between 399 and 367 k J/mole C181, in which the lower value corresponds to the tracer diffusion of Mg in pure MgO. The activation energy of MgO with titania 119,201 varies between k J/mole where the lower value corresponds to the oxygen diffusion in the periclase crystal. The value of activation energy of MgO with iron oxide is generally found to be about 394 kj/mole E213. In the present case the value of the activation

8 155 SHRINKAG E^) o o c <D i Figure 9.2 : Log-log plots of shrinkage (90) vs time In sintered Salem Magnesite with 0.2 wt% tltannla addition. Figure 9.3 : Arrhenius plot of -log K against reciprocal absolute temperature (1/T) for sintered Salem Magnesite with 0.2 wt% tltanla.

9 156 energy for sintering lies within this range. Very rapid initial sintering rate found in this case was due to the presence of liquid which contributes to sintering when impurities are present. Sintering and shrinkage in general can be expressed in terms of the action of capillary farces. In general there is a tendency towards spheroidisation of the particles during sintering and this may contribute appreciably to the observed shrinkage of compacts where the grains are initially of irregular shape. In the actual compacts, particle size distribution, particle shape and irregularity of packing would all play a part in determining the form of shrinkage curves and would influence the nature of sintering C CALCULATION OF ACTIVATION ENERSY FOR BRAIN GROWTH IN SINTERED NATURAL MAGNESITE WITH AND WITHOUT TITANIA : In the previous chapter, it was observed that when the grain boundary velocity depends on the boundary curvature, isothermal grain growth theoretically obeys the relation Glfn Gton = k (tf - to) (8.1) and for Gto «Gtf and to = 0, Glfn = k.tf (8.2) Expressing k, the rate constant as where, k = ko exp C-Qq/RTI (9.6) Qa is the activation energy for grain growth process and R and T have their usual meaning and combining (8.2) and (9.6), or, Glfn = ktf * k0.tf. exp C Qa/RT1 (9.12) In CGlfn/tf3 = In kd + C-Q0/RT3 Rewriting, log (Glfn/tf) = log k0 - Qo/2.303 RT (9.13) A linear plot of log (Glfn/tf) Vs 1/T provided the activation energy -Qo where the slope m = R

10 157 or, Activation Energy, Qq = X X 4.2 X (-m) X 10*J/mole------(9.14) figures 9.4 a and b show the effect of temperature on grain growth and activation energies for grain growth as determined from Arrhenius plots of log(gtf3/t) versus reciprocal absolute temperature based on Equation (9.14). Here the kinetic exponent, n was assumed to be 3 following Nicholson C193 as given in table 9.3 and gave the activation energies shown in table 9.4. The data is within the range of previously published activation energies for MgO grain growth during sintering as given in table 9.3. However, linear fits of the experimental data suggested an average, kinetic exponent, n, close to 3.5 for Salem magnesite and 4 for Almora magnesite. table 9.5 lists the negative slopes of Salem and Almora magnesite as obtained from the Arrhenius plots shown in figure 9.5 a and b using this experimental fit data. The activation energies were calculated from this data and are listed in table 9.5 as the experimental results. table 9.3 REPORTED KINETIC EXPONENTS AND ACTIVATION ENERGY FOR GRAIN GROWTH IN MAGNESIA s Kinetic Q Material Authors ref. exponent kj/mole Pure MgO Spriggs et al C Pure MgO Daniels et al C MgO + lwt% Ti02 Nicholson Q MgO + lwt*/, Fe203 Nicholson C Pure MgO Varela ,6 345 Pure MgO Gupta C183

11 158 1/7 x 1CT1 (K 1) ALMORA MAGNESITE /r x io'1 (k-1) Figure 9.4 : Arrhenius plots of log (G3/t) versus 1/T where G Is the average grain diameter, t is the time and T is absolute temperature for sintered natural magnesite with 0.5 wt% Ti*3^ addition, fired at 1700 C with two hours soaking. (a) Salem (b) Almora

12 159 1/T X 10"* (k-1) ALMORA MAGNESfTE o tn J9 1/T X 10^ (k'1) Figure 9.5 : Arrhenius plots of log (Gn/t) versus 1/T where G is average grain diameter, t Is the time and T is the absolute temperature for sintered natural magnesites wth 0 to 0.5 wt% TiC>2 at 1700 C with two hours soaking. (a) Salem (b) Almora n = 3.5 n = 4

13 160 TABLE 9.4 SLOPES OF ARRHENIUS PLOTS OF S3/t VERSUS 1/T AND ACTIVATION ENERGIES OF SALEM AND ALMORA SINTERED COMPACTS WITH AND WITHOUT TITANIA (ASSUMING A KINETIC EXPONENT, n, OF 3). Salem Magnesite SO* SI 52 S3 S4 Slope m Act. Energy kj/mole Almora Magnesite AO A1 A2 A3 A4 Slope m Act. Energy kj/mole * for sample codes. see TABLE 3.1A, chapter 3.0. TABLE 9.5 SLOPES OF ARRHENIUS PLOTS OF Gn/t VERSUS 1/T AND ACTIVATION ENERGIES OF SALEM AND ALMORA SINTERED COMPACTS WITH AND WITHOUT TITANIA WITH KINETIC EXPONENT, (n =3.5 AND 4.0 FOR SALEM AND ALMORA MAGNESITES) Salem Magnesite SO* SI S2 S3 S4 Slope m Act. Energy kj/mole Almora Magnesite AO A1 A2 A3 A4 Slope m Act. Energy kj/mole * for sample codes. see TABLE 3.1A, chapter 3.0 The study magnesites follows the reveals law Gn * that grain growth in natural kt at a given temperature both in

14 162 phase increases the activation energy of formation and the heat of solubility of crystal phase into the fluid C291. MgO has a closed packed rock salt structure and will not ordinarily tolerate interstitial cation or anion. This vacancy concentration can be enhanced by impurities of valence different from the host ions. It is also believed that the presence of a grain boundary glassy phase can decrease the apparent grain boundary energy and increase the diffusion distance across the boundary C30,313. In Almora magnesite, the activation energies, obtained were 341 kj/mole and kj/mole as given in table 9.4. The lower activation energy for compacts of Almora magnesite with Ti02 may be indicative of a surface diffusion mechanism because the activation energy for surface diffusion mechanism is expected to be smaller than the grain boundary diffusion C323. Here, it is anticipated that surface diffusion occurs by a surface vacancy mechanism. In Almora magnesites, some Ti ions compete for the Fe sites which are in solid solution with periclase. Even so, some Ti ions go into the bond also for which faster grain growth occurs in additive cases as explained but the effect is less than similar samples based on Salem magnesite. The competition between Ti and Fe for Mg sites does not permit full exploitation of Ti02 action in the Almora magnesite causing a limit of grain growth. Yet, there is definite benefit in grain size through titania addition. It is anticipated that ilmenite would be an effective source of Ti02 for such systems. It is hypothesised that the expected new mechanism in Salem magnesite for higher activation energy is one of grain growth in the presence of a reactive liquid which is not in equilibrium with the main phase, in which reaction induced grain growth impediment is the rate controlling step. The reactive secondary phase generally situated at the grain junctions involving a dissolving reaction from the secondary

15 163 phase into the main phase. The transport of the dissolving component from the multiple grain junctions to the bulk of crystal which is assumed to be faster diffusion process and slow bulk diffusion from the grain boundary to the centre of the crystals. The result of this transport mechanism is that during the total dissolving time, the grain boundary concentration is continuously enlarged, while the concentration in the bulk of the crystals slowly increases. The lowering in free enthalpy is assumed to be much larger for the chemical (dissolving) reaction than for grain growth C333. The general classification of grain growth impediment characteristics are shown in table 9.6. table 9.6 GRAIN GROWTH CHARACTERISTICS DUE TO IMPEDING MECHANISMS IN THE PRESENCE OF STABLE SECONDARY LIQUID 1333 GRAIN GROWTH IMPEDING MECHANISM: PORE DRAG AND PRECIPITATE DRAG STABLE LIQUID SECONDARY PHASE AT (A) ONLY ON THE MULTIPLE GRAIN JUNCTIONS <B) ENVELOPING THE GRAINS EFFECT DN GRAIN GROWTH -Drag strongly reduced High probability of abnormal grain growth -Drag eliminated -Ostwald ripening GRAIN GROWTH IMPEDING STABLE LIQUID SECONDARY PHASE AT (A) ONLY ON THE MULTIPLE GRAIN JUNCTION (B) ENVELOPING THE GRAINS MECHANISM : IMPURITY DRAG EFFECT ON GRAIN GROWTH -Drag hardly influenced -Drag remains in a modified way Retarded Ostwald ripening

16 164 In the present case when the grain growth occurs the average grain size increases which implies that the average distance for the slow bulk diffusion is increased and the contribution of the fast grain boundary diffusion to the transport of the dissolving component is lowered. Therefore, when the dissolving reaction is not yet finished it will be retarded by grain growth. It is based on the fact that the gain in free enthalpy for a chemical (dissolving) reaction is much larger than for grain growth C333. Upon increasing the titania concentration from 0.05 to 0.5 wt.% Ti02 the differential increase in grain growth gradually decreases indicating that there is limit of solubility of Ti02 in the system of cryptocrystalline Salem magnesite with silica impurity beyond which further addition of TiQ2 does not give additional improvement in grain growth. The testimony of this fact lies in the identical values of activation energy of 607 kj/mole obtained in S3 and S4 samples with 0.2 and 0.5 wt % Ti02 addition with respect to the original ft magnesite. The higher TiOz content in S4 results in a considerably larger grain size, from 88 pm in S3 for 1700 C/2 hr condition to 123 ium in S4 under the same conditions. It is believed that the larger amount of mineraliser promotes the content of reactive liquid and the grain growth is enhanced. However, the primary mechanism of grain growth in Salem magnesite with between 0.2 and 0.5 wt % Ti02 remains one of reaction induced grain growth impediment with an activation energy of about 607 kj/mole as shown in figure 9.6. Interestingly, an identical value of 610 kj/mole was obtained by Nicholson C193 as given in table 9.3 for 1 wt % Fe203 in pure MgO though the value for 1 wt M Ti02 was only 435 kj/mole. It should be noted that S4 contains nearly 1 wt % Ti02 with reference to MgO. The possible reason for the difference in values obtained by Nicholson C191 and this study lies in the purity of MgO used.

17 165 * Salem, n = 3.5 ACTIVATION ENERGY (k J /m o le ) * Salem, n ) TiTANIA ADDED (wt* w r t MAGNESfTE) Almarq.n Almora,n 4 3 Figure 9.6 : Plot of activation energy for grain growth as a function of titanla addition in sintered natural Indian magnesites.

18 166 It may be concluded that the same hypothesised mechanism of reaction induced grain growth impediment in the presence of a reactive liquid was responsible for the high activation energy observed in this study and by Nicholson C193 compared to that in pure MgO observed by others as given in table ,19,23,24,253. Therefore, the presence of sufficient impurities in fine crystallite MgO (cryptocrystalline Salem or pure MgO) leads to different mechanism of grain growth. On the other hand, the marginal changes in activation energy in impure crystalline Almora magnesite when compared to pure MgO or to the relative quantity of impurities leads to the conclusion that surface diffusion leading to grain growth controlled by impurity drag is, probably, the most significant mode of enhancing grain growth due to impurity addition in these crystalline natural magnesites. The higher activation energy of Salem magnesite in presence of Ti02 can be attributed either to the enthalpy for defect formation or to the presence of a a modified liquid phase which decrease the rate of material transfer at the interface. In presence of the liquid phase diffusion path is increased. Again the process of solution, diffusion through a liquid film and precipitation is usually slower than a jump across a boundary.

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