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Mechanism of the precipitation of the spinel from MgO-Al2O3 solid solutions
J. Phys.
Chenz. Solids
Pergsmon
MECHANISM
Press 1965. Vol. 26, pp. 1293-1297.
OF FROM
THE
Printed in Great Britain.
PRECIPITATION
MgO-A1203
OF
SOLID
V. S. STUBICAN
and
THE
SPINEL
SOLUTIONS
RUSTUM
ROY
Department of Ceramic Technology and Materials Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania (Received
13 October
1964; in revised form 8 February
1965)
Abstract-The recently reported c-ystalline solubility of Ala01 in MgO was confirmed. Unit cell dimensions and densities were measured independently and the existence of a predominant cationvacancy model established for these crystalline solutions. The precipitation of the spine1 was effected in the air at 1350” and 1100°C and studied by quantitative X-ray diffraction. The precipitation is a diffusion controlled process and the equation y = l-exp[-(t/T)n] fits the experimental results for y = 0.05 -0.95. The exponent IZwas found to be very close to 3/2, suggesting that under the experimental conditions the growing particles were approximately spheroidal. Electron probe investigations showed that the preferred sites for the nucleation and the precipitation of spine1 were the grain boundaries and intergranular voids.
1. INTRODUCTION
importance of the study of precipitation phenomena was recognized in the field of metals several decades ago, where the most widely studied precipitation process is that which occurs during the age hardening of alloys. Almost all fundamental knowledge concerning precipitation phenomena in solids has been obtained by studying metal systems.(l) The only analogous technology in oxide systems is the precipitation of Al203 in spine1 jewel bearings and it is in this very oxide system that SAALFELDand JAGODZINSKI@)have studied the mechanism of the exsolution of A1203 from the spine1 crystalline solution. Recently ALPER et aZ.(s) have reported considerable solubility of A1203 in MgO at very high temperatures. The crystalline solutions obtained at high temperatures could be retained metastably at room temperature by fast quenching. It is obvious that, due to the charge difference between Mgs+ and Al3+, such crystalline solutions must contain very high concentrations of point defects. The purpose of this investigation was to characterize the point defects present in the MgO-Al203 THE
crystalline solutions, by using precise cell dimensions and density measurements, and then to study the rate of the precipitation of the spine1 from crystalline solutions containing increasing numbers of point defects. Finally, it was hoped to obtain some insight into the mechanism of the precipitation.
2. EXPERIMENTAL
PROCEDURES
The solid solutions of alumina in magnesium oxide were prepared in an induction furnace designed to allow very fast quenching of the specimens in water.(s) The flow of 6 liters of nitrogen per min was maintained through the induction furnace to maintain a neutral atmosphere. The specimens were heated in the form of pellets on the top of a magnesia rod. To avoid direct contact of the material investigated with the magnesia rod, 2-3 pellets were placed on top of the rod and only the highest was used for the determination of the densities, precise unit cell measurements and precipitation experiments. The pellets were prereacted at 1500°C to avoid MgO evaporation and 1293
1294
V.
S.
STUBICAN
then heated, usually for 15-20 min, in the temperature range 1800-2000°C. Temperature measurements were made with a calibrated Leeds & Northrup optical pyrometer. No emissivity corrections were applied because the cavity of the furnace used approximated fairly well to the black body conditions. The unit cell dimensions of the solid solutions phases were determined by using a Norelco diffractometer by plotting cell dimensions calculated from the high angle peaks, versus sins8 of the peaks and extrapolating to 90%‘. The densities of the solid solutions were determined by the sink-float technique in Tl malonateTl formate solutions,@) using pellets compacted under pressures near 40,000 atm.* The densities of a few specimens were determined by using a picnometer and degassing in vacuum under toluene. At least three determinations were made for each composition. The precision of the first method was + 0.5% and the second + 0.1%. The deviation of the obtained results from the arithmetical mean values was less than 0.5%. The exsolution experiments were performed in the air in a furnace with Pt-10% Rh winding, where temperature control was better than &2”C. The amounts of the exsolved spine1 were determined by the X-ray diffraction method using counting techniques. Standards for the calibration curve were prepared by mechanically mixing different amounts of spine1 and magnesium oxide. From the ratios of the number of counts for the (400) diffraction peaks of the spine1 and magnesium oxide, the calibration curve was obtained. Due to the relatively small amount of the spine1 present in the exsolved specimens, the accuracy of the data was estimated to be only f 10%. A sample containing 3.5 mol% AlsOa was used in the electron probe study. A pellet heated at 1900°C in the induction furnace and quenched in air was reheated at 1350°C for 3 hr. After the heat treatment the pellet was mounted and polished. A thin layer of carbon was then deposited on the surface. The distribution of the aluminum and magnesium ions in the specimen could be observed when an X-ray image was obtained with the * The unpublished results from this laboratory have shown that under such pressures the theoretical densities of the ionic compounds were approached within @ 5 y0 in a few min.
and RUSTUM
ROY
X-ray detector set for aluminum respectively. 3. RESULTS
AND
and magnesium
DISCUSSION
In Fig. 1, the part of the phase diagram for the system MgO-AlsOa as determined by Alper et al. is shown. According to these authors, the eutectic between MgO and MgAls04 is at 45 weight y0 MgO and at 1995 & 15°C and there is a relatively large field of crystalline solid solution of Al203 in MgO. Figure 2 shows our measurements of the unit cell dimensions of the crystalline solutions and that they decrease as the amount of the aluminum ions in the solution increases. Furthermore, it is evident from Fig. 2 that the limit of the solubility of AlsOs in MgO at 1880 k 15°C is 4.3 mol O/aAlsO3 (10.2 weight %) which result is in good agreement with the quoted phase diagram (Fig. 1). Figure 3 shows the comparison between the expected densities computed by assuming a cation vacancy model and the arithmetical mean values of the experimentally determined densities. The agreement is very good if the results are adjusted for the difference obtained for the pure MgO, between the superpressure compacted MgO and the known density of MgO. The increase in the experimentally determined densities beyond 4.3 mol y. Also3 in Fig. 3 is due to the presence of spine1 in the specimens. The rate of the precipitation of the spine1 from the periclase solid solutions was studied for the specimen obtained at 1950+ 15°C. The reaction was carried out isothermally at 1350” and 1100°C. The results obtained at 1350°C are shown in Fig. 4. The interesting features of these results are: the increasing rate of precipitation with increasing amounts of aluminum ions in the solid solution and the lack of any induction period. There is no doubt that the precipitation of spine1 comprises formation of nuclei and the growth of nuclei. For the analysis of the results obtained one may assume that all nuclei form at t = 0 (no induction period). Thus it suffices to focus attention on the growth stage of the phenomenon where the precipitation proceeds by the growth of a fixed number of nuclei. Furthermore, one may assume initially that the rate of growth is determined by the rate of diffusion, and that the diffusion coefficient of the slowest diffusing ion is independent of the concentration. Following the
M~C~NISM
OF PRECIPITATION
OF TNE
SPINEL
FROM
&&O-AI&r
SOLID
SOLUTIONS
1295
FIG. 2. The unit cell dimensions of the crystaIline solid solutions of A1203 in MgO. Specimens prepared at 188OklS”C.
of JOHNSON and MEHL,@) \NERT,(@ ZENER,(~) the rate of the growth of particles which grow in a matrix without mutual interference, may be written
treatment
z
=fM
andf(t) is same function of time, This rate will be lessened by mutual interference of growing particles. According to JOHNSONand MEEIL@) the impkgement allowance is estimated by multiplying the overall rate of precipitation by (1 --y), thus
(1)
where y is the fraction of the spine1 precipitated
1296
2
I
3
4
Mel % Al 0 23
FIG. 3. The arithmetical mean values of the measured densities compared with densities calculated for cation vacancy model for crystalline solutions of Ala03 in MgO. Specimens prepared at 188O”k 15°C.
Solving equation (2) gives
t y = 1 -exp[
-
I
f(t) dr]
(3)
0
The explicit form of this equation is y=l-exp
-
It was found by ZENER(~) that the value of the exponent n in the equation (4) is 3/2 for the spherical particles growing by a diffusion controlled process and 5/2 for disc shaped particles. The precipitation of spine1 is evidently a diffusion controlled process as can be seen from Fig. 5.
7
L”
I
where n is a constant independent of the concentration and temperature, and’ 7 L” is the characteristic time for the precipitation. I.00
040
-“O I
0.60 x 040
1350
“C
0.20
4
8
I2 TIME
16 20 IHOURS)
24
28
FIG. 4. The fractional precipitation y as a function time at 1350°C. Specimens prepared at 1950 + 15°C.
FIG. 5. Comparison of the results in Fig. 4 with equation (4).
Equation (4) fits the experimental results very well for y = 0.05-0.95. The values for the exponent n are very close to 3/Z (Fig. 6) suggesting that, under the experimental conditions, the growing particles
MECHANISM
OF PRECIPITATION
OF THE
SPINEL
are spheroidal. A sample containing 46 mol y0 AlsOs was used for the precipitation studies at 1100°C. The equation (4) fits well the obtained results at this temperature and the value of n was found to be 1.48.
I
Ix
io-4
Ix
io-5
I
I
I
T iii
z
-I@
t
FIG. 6. l/7 (7, the characteristic time for precipitation) as a function of the number of Ala+ ions (or cation vacancies) in the solid solution.
The interpretation of the constant 7 in the equation (4) is rather more difficult. MORIN and REISS@)gave the following expression for the rate of the growth of an isolated spherical particle growing by diffusion of the same species.
c-c, -=
exp{[-&N(G)-
c8)~]1y2q3k39
co-c, = exp( - ats/s)
(5)
Where c is the amount of the solute precipitated, Co the starting concentration of solute, C, the saturation concentration of the solute, N is the number of particles, ~1is the increment of volume due to the diffusant, D diffusion coeffiecint.
FROM
MgO-AhO
SOLID
SOLUTIONS
1297
By comparing equations (4) and (5) one can conclude that, at certain temperature, T is a function of the rate of diffusion, the degree of supersaturation, and the number of nuclei present. The increase in 11~ on Fig. 7 is then probably due to the increase in the degree of saturation, the number of nuclei present at t = 0, and the increase in mobility of the ions caused by the increase in the number of cation vacancies. It is interesting to note that l/~ becomes very high indeed for specimens which have compositions exactly on the boundary line dividing the field of the spinell,,) from the field of the spinelc,,) + MgO (Figs. 7 and 1). Figures 7 and 8 show the spatial distribution of the precipitated spine1 found in the electron probe study. There are preferred reaction and precipitation on the grain boundaries and intragranular voids which are thus favorable sites for nucleation. A similar phenomenon was previously found by STUBICAN~~~VIECHNICKI(~)in manyoxide systems. It is surprising that in such a case the kinetics would fit a ‘spheroidal’ growth model. However, the material for the growth of the spine1 particles may be supplied by diffusion via the grain boundaries as well as through the bulk of the grains. The apparently continuous precipitate on the grain boundaries is probably formed by the aggregation of the ‘spheroidal’ particles. Acknowledgement-This work was supported by the United States Air Force, Office of Scientific Research under Contract No. AF 4G(628)-957. REFERENCES 1. NEWKIRK J. B., in Precipitation from Solid Scluticns, edited by MEHL R. F., published by ASTM, pp. 6-149 (1959). 2. SAALFELDH. and JAGODZINSKIH., Z. Krist. 109,87 (1957). 3. ALPER A. M.. MCNALLY R. N.. RIBBE P. H. and DOMAN R. ‘C., J. Amer. Ceram. Sot., 45, 263 (1962). 4. SULLIVAN J. O., U.S. Bur. Mines, Tech. Paper No. 381 (1926). 5. JOHNSON W. A. and MEHL R. F., Trans. AIME, 135,416 (1939). 6. WERTC. A.; J. Appl. Phys. 20,943 (1949). 7. ZENER C., J. Appl. Phys. 20,950 (1949). 8. MORIN F. J. and REISS H., J. Phys. and Chem. Solids 3, 196 (1957). 9. STUBICANV. S. and VIECHNICKID., to be published in J. Appl. Phys.
Chenz. Solids
Pergsmon
MECHANISM
Press 1965. Vol. 26, pp. 1293-1297.
OF FROM
THE
Printed in Great Britain.
PRECIPITATION
MgO-A1203
OF
SOLID
V. S. STUBICAN
and
THE
SPINEL
SOLUTIONS
RUSTUM
ROY
Department of Ceramic Technology and Materials Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania (Received
13 October
1964; in revised form 8 February
1965)
Abstract-The recently reported c-ystalline solubility of Ala01 in MgO was confirmed. Unit cell dimensions and densities were measured independently and the existence of a predominant cationvacancy model established for these crystalline solutions. The precipitation of the spine1 was effected in the air at 1350” and 1100°C and studied by quantitative X-ray diffraction. The precipitation is a diffusion controlled process and the equation y = l-exp[-(t/T)n] fits the experimental results for y = 0.05 -0.95. The exponent IZwas found to be very close to 3/2, suggesting that under the experimental conditions the growing particles were approximately spheroidal. Electron probe investigations showed that the preferred sites for the nucleation and the precipitation of spine1 were the grain boundaries and intergranular voids.
1. INTRODUCTION
importance of the study of precipitation phenomena was recognized in the field of metals several decades ago, where the most widely studied precipitation process is that which occurs during the age hardening of alloys. Almost all fundamental knowledge concerning precipitation phenomena in solids has been obtained by studying metal systems.(l) The only analogous technology in oxide systems is the precipitation of Al203 in spine1 jewel bearings and it is in this very oxide system that SAALFELDand JAGODZINSKI@)have studied the mechanism of the exsolution of A1203 from the spine1 crystalline solution. Recently ALPER et aZ.(s) have reported considerable solubility of A1203 in MgO at very high temperatures. The crystalline solutions obtained at high temperatures could be retained metastably at room temperature by fast quenching. It is obvious that, due to the charge difference between Mgs+ and Al3+, such crystalline solutions must contain very high concentrations of point defects. The purpose of this investigation was to characterize the point defects present in the MgO-Al203 THE
crystalline solutions, by using precise cell dimensions and density measurements, and then to study the rate of the precipitation of the spine1 from crystalline solutions containing increasing numbers of point defects. Finally, it was hoped to obtain some insight into the mechanism of the precipitation.
2. EXPERIMENTAL
PROCEDURES
The solid solutions of alumina in magnesium oxide were prepared in an induction furnace designed to allow very fast quenching of the specimens in water.(s) The flow of 6 liters of nitrogen per min was maintained through the induction furnace to maintain a neutral atmosphere. The specimens were heated in the form of pellets on the top of a magnesia rod. To avoid direct contact of the material investigated with the magnesia rod, 2-3 pellets were placed on top of the rod and only the highest was used for the determination of the densities, precise unit cell measurements and precipitation experiments. The pellets were prereacted at 1500°C to avoid MgO evaporation and 1293
1294
V.
S.
STUBICAN
then heated, usually for 15-20 min, in the temperature range 1800-2000°C. Temperature measurements were made with a calibrated Leeds & Northrup optical pyrometer. No emissivity corrections were applied because the cavity of the furnace used approximated fairly well to the black body conditions. The unit cell dimensions of the solid solutions phases were determined by using a Norelco diffractometer by plotting cell dimensions calculated from the high angle peaks, versus sins8 of the peaks and extrapolating to 90%‘. The densities of the solid solutions were determined by the sink-float technique in Tl malonateTl formate solutions,@) using pellets compacted under pressures near 40,000 atm.* The densities of a few specimens were determined by using a picnometer and degassing in vacuum under toluene. At least three determinations were made for each composition. The precision of the first method was + 0.5% and the second + 0.1%. The deviation of the obtained results from the arithmetical mean values was less than 0.5%. The exsolution experiments were performed in the air in a furnace with Pt-10% Rh winding, where temperature control was better than &2”C. The amounts of the exsolved spine1 were determined by the X-ray diffraction method using counting techniques. Standards for the calibration curve were prepared by mechanically mixing different amounts of spine1 and magnesium oxide. From the ratios of the number of counts for the (400) diffraction peaks of the spine1 and magnesium oxide, the calibration curve was obtained. Due to the relatively small amount of the spine1 present in the exsolved specimens, the accuracy of the data was estimated to be only f 10%. A sample containing 3.5 mol% AlsOa was used in the electron probe study. A pellet heated at 1900°C in the induction furnace and quenched in air was reheated at 1350°C for 3 hr. After the heat treatment the pellet was mounted and polished. A thin layer of carbon was then deposited on the surface. The distribution of the aluminum and magnesium ions in the specimen could be observed when an X-ray image was obtained with the * The unpublished results from this laboratory have shown that under such pressures the theoretical densities of the ionic compounds were approached within @ 5 y0 in a few min.
and RUSTUM
ROY
X-ray detector set for aluminum respectively. 3. RESULTS
AND
and magnesium
DISCUSSION
In Fig. 1, the part of the phase diagram for the system MgO-AlsOa as determined by Alper et al. is shown. According to these authors, the eutectic between MgO and MgAls04 is at 45 weight y0 MgO and at 1995 & 15°C and there is a relatively large field of crystalline solid solution of Al203 in MgO. Figure 2 shows our measurements of the unit cell dimensions of the crystalline solutions and that they decrease as the amount of the aluminum ions in the solution increases. Furthermore, it is evident from Fig. 2 that the limit of the solubility of AlsOs in MgO at 1880 k 15°C is 4.3 mol O/aAlsO3 (10.2 weight %) which result is in good agreement with the quoted phase diagram (Fig. 1). Figure 3 shows the comparison between the expected densities computed by assuming a cation vacancy model and the arithmetical mean values of the experimentally determined densities. The agreement is very good if the results are adjusted for the difference obtained for the pure MgO, between the superpressure compacted MgO and the known density of MgO. The increase in the experimentally determined densities beyond 4.3 mol y. Also3 in Fig. 3 is due to the presence of spine1 in the specimens. The rate of the precipitation of the spine1 from the periclase solid solutions was studied for the specimen obtained at 1950+ 15°C. The reaction was carried out isothermally at 1350” and 1100°C. The results obtained at 1350°C are shown in Fig. 4. The interesting features of these results are: the increasing rate of precipitation with increasing amounts of aluminum ions in the solid solution and the lack of any induction period. There is no doubt that the precipitation of spine1 comprises formation of nuclei and the growth of nuclei. For the analysis of the results obtained one may assume that all nuclei form at t = 0 (no induction period). Thus it suffices to focus attention on the growth stage of the phenomenon where the precipitation proceeds by the growth of a fixed number of nuclei. Furthermore, one may assume initially that the rate of growth is determined by the rate of diffusion, and that the diffusion coefficient of the slowest diffusing ion is independent of the concentration. Following the
M~C~NISM
OF PRECIPITATION
OF TNE
SPINEL
FROM
&&O-AI&r
SOLID
SOLUTIONS
1295
FIG. 2. The unit cell dimensions of the crystaIline solid solutions of A1203 in MgO. Specimens prepared at 188OklS”C.
of JOHNSON and MEHL,@) \NERT,(@ ZENER,(~) the rate of the growth of particles which grow in a matrix without mutual interference, may be written
treatment
z
=fM
andf(t) is same function of time, This rate will be lessened by mutual interference of growing particles. According to JOHNSONand MEEIL@) the impkgement allowance is estimated by multiplying the overall rate of precipitation by (1 --y), thus
(1)
where y is the fraction of the spine1 precipitated
1296
2
I
3
4
Mel % Al 0 23
FIG. 3. The arithmetical mean values of the measured densities compared with densities calculated for cation vacancy model for crystalline solutions of Ala03 in MgO. Specimens prepared at 188O”k 15°C.
Solving equation (2) gives
t y = 1 -exp[
-
I
f(t) dr]
(3)
0
The explicit form of this equation is y=l-exp
-
It was found by ZENER(~) that the value of the exponent n in the equation (4) is 3/2 for the spherical particles growing by a diffusion controlled process and 5/2 for disc shaped particles. The precipitation of spine1 is evidently a diffusion controlled process as can be seen from Fig. 5.
7
L”
I
where n is a constant independent of the concentration and temperature, and’ 7 L” is the characteristic time for the precipitation. I.00
040
-“O I
0.60 x 040
1350
“C
0.20
4
8
I2 TIME
16 20 IHOURS)
24
28
FIG. 4. The fractional precipitation y as a function time at 1350°C. Specimens prepared at 1950 + 15°C.
FIG. 5. Comparison of the results in Fig. 4 with equation (4).
Equation (4) fits the experimental results very well for y = 0.05-0.95. The values for the exponent n are very close to 3/Z (Fig. 6) suggesting that, under the experimental conditions, the growing particles
MECHANISM
OF PRECIPITATION
OF THE
SPINEL
are spheroidal. A sample containing 46 mol y0 AlsOs was used for the precipitation studies at 1100°C. The equation (4) fits well the obtained results at this temperature and the value of n was found to be 1.48.
I
Ix
io-4
Ix
io-5
I
I
I
T iii
z
-I@
t
FIG. 6. l/7 (7, the characteristic time for precipitation) as a function of the number of Ala+ ions (or cation vacancies) in the solid solution.
The interpretation of the constant 7 in the equation (4) is rather more difficult. MORIN and REISS@)gave the following expression for the rate of the growth of an isolated spherical particle growing by diffusion of the same species.
c-c, -=
exp{[-&N(G)-
c8)~]1y2q3k39
co-c, = exp( - ats/s)
(5)
Where c is the amount of the solute precipitated, Co the starting concentration of solute, C, the saturation concentration of the solute, N is the number of particles, ~1is the increment of volume due to the diffusant, D diffusion coeffiecint.
FROM
MgO-AhO
SOLID
SOLUTIONS
1297
By comparing equations (4) and (5) one can conclude that, at certain temperature, T is a function of the rate of diffusion, the degree of supersaturation, and the number of nuclei present. The increase in 11~ on Fig. 7 is then probably due to the increase in the degree of saturation, the number of nuclei present at t = 0, and the increase in mobility of the ions caused by the increase in the number of cation vacancies. It is interesting to note that l/~ becomes very high indeed for specimens which have compositions exactly on the boundary line dividing the field of the spinell,,) from the field of the spinelc,,) + MgO (Figs. 7 and 1). Figures 7 and 8 show the spatial distribution of the precipitated spine1 found in the electron probe study. There are preferred reaction and precipitation on the grain boundaries and intragranular voids which are thus favorable sites for nucleation. A similar phenomenon was previously found by STUBICAN~~~VIECHNICKI(~)in manyoxide systems. It is surprising that in such a case the kinetics would fit a ‘spheroidal’ growth model. However, the material for the growth of the spine1 particles may be supplied by diffusion via the grain boundaries as well as through the bulk of the grains. The apparently continuous precipitate on the grain boundaries is probably formed by the aggregation of the ‘spheroidal’ particles. Acknowledgement-This work was supported by the United States Air Force, Office of Scientific Research under Contract No. AF 4G(628)-957. REFERENCES 1. NEWKIRK J. B., in Precipitation from Solid Scluticns, edited by MEHL R. F., published by ASTM, pp. 6-149 (1959). 2. SAALFELDH. and JAGODZINSKIH., Z. Krist. 109,87 (1957). 3. ALPER A. M.. MCNALLY R. N.. RIBBE P. H. and DOMAN R. ‘C., J. Amer. Ceram. Sot., 45, 263 (1962). 4. SULLIVAN J. O., U.S. Bur. Mines, Tech. Paper No. 381 (1926). 5. JOHNSON W. A. and MEHL R. F., Trans. AIME, 135,416 (1939). 6. WERTC. A.; J. Appl. Phys. 20,943 (1949). 7. ZENER C., J. Appl. Phys. 20,950 (1949). 8. MORIN F. J. and REISS H., J. Phys. and Chem. Solids 3, 196 (1957). 9. STUBICANV. S. and VIECHNICKID., to be published in J. Appl. Phys.