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Aggregate and necking force in Mn–Zn ferrite
Materials Letters 57 (2003) 1467 – 1470 www.elsevier.com/locate/matlet
Aggregate and necking force in Mn–Zn ferrite Hyo Soon Shin a, Suk Kee Lee b, Byung Kyo Lee a,* a
Department of Inorganic Materials Engineering, Kyungpook National University, Taegu, 702-701, South Korea b Department of Polymer Science, Kyungpook National University, Taegu, 702-701, South Korea Received 3 June 2002; accepted 15 July 2002
Abstract An experimental technique is proposed for evaluating the strength of aggregates during powder compaction. The technique is based on the interpretation of compaction pressure vs. green density. A Rumpf’s equation was correlated with the equation suggested by Duckworth. Neck strength between primary particles, H=(r0pa2e Bp)/((1 p)K) in manganese zinc ferrite aggregate is thought to be 4.05 10 5 N, with reference value of r0. Manganese zinc ferrite decomposed from the precipitates of alcoholic dehydration was fractured at 300 MPa of the compaction pressure. From this, H was calculated as 5.03 10 5 N. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Aggregate; Neck strength; Mn – Zn ferrite; Alcoholic dehydration; Agglomerate; Porosity
1. Introduction In general, ceramic powders are known to intrinsically contain agglomerates. Agglomerates can be classified as being either hard or soft. Hard agglomerates that is to say aggregate are partially sintered or consisting of cemented groups of particles where as soft agglomerates are groups held together by van der Waals forces and can be broken apart with surfactants [1]. Agglomeration is important since it can affect the flow properties of the powders, green and fired density of bodies. Perhaps, more importantly, it has been reported that hard agglomerates may cause lower density in otherwise dense ceramic bodies [2]. Many powders used in fabricating ceramic bodies are prepared by precipitation or by solid-state reaction *
Corresponding author. Tel.: +82-53-950-5633; fax: +82-53950-5645. E-mail address: [email protected] (B.K. Lee).
method. Calcination almost always results in the formation of porous aggregates. The strength of these aggregates significantly affects the powders’ subsequent response to processing as well as the microstructure and properties of the bodies. Milling is normally used in ceramic processing to break down porous aggregates, and the milling condition required depends on the aggregate strength. In spite of the recognized importance of aggregate strength and porosity, no quantitative technique is available for measuring these powder characteristics [3]. Niesz et al. [3] assumed that the semilogarithmic pressure – density relationship observed during the compaction of granulated powders was analogous to that which exists between mechanical strength and porosity. It is also assumed that the pressure at the break point between linear potions of the curve was a measure of the strength of the granules. After testing agglomerated alumina powders, it was concluded that compaction data could also show the presence of
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 1 0 3 5 - 2
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H.S. Shin et al. / Materials Letters 57 (2003) 1467–1470
agglomerates in an unagglomerated powder. Rumpf [4] reported that the load corresponding to the break point may be taken as a measure of the strength of the agglomerates and that the strength for each contact points was related to the agglomerate strength. In this study, an experimental technique has been proposed for evaluating the strength of the aggregates in powder. The technique was based on the interpretation of compaction data plotted as compaction pressure vs. green density. In the process, the equation used by Rumpf was related to the equation used by Duckworth.
is constant (about 0.5) and K is calculated to be 6 from p [9]. When a and rf are measured, H can be calculated. At fracture, Eq. (1) is: rf ¼ r0 eBp Introducing Eq. (3) into Eq. (2) yields: r0 eBp ¼
Ryshkewitch [5] showed that the compression strength was related to porosity in the sintered alumina and zirconia. The logarithm of compression strength and porosity was a linear reaction. At discussion of Ryshkewitch’s paper, Duckworth [6] showed that compression strength is:
ð4Þ
and H¼
2. Neck strength of aggregate
ð1 pÞKH pa2
ð3Þ
r0 pa2 eBp pa2 rf ¼ ð1 pÞK ð1 pÞK
ð5Þ
In Eq. (5), H could be calculated if each of the values were introduced, however the strength of the nonporous body had to be given from a reference. With r0 = 8000 N/mm2 in ferrite [10] and a = 0.4 Am, H would theoretically be 4.05 10 5 N. Therefore, it is necessary to compare rf given by hydraulic pressing.
3. Experimental procedure r ¼ r0 eBp
ð1Þ
where r and r0 are the strengths of a porous and a nonporous body, B is the gradient at the plot of lnr vs. p, and p is the porosity expressed as a fraction [7]. Niesz et al. [3] introduced Eq. (1) in the experiment of uniaxial pressing of an aggregate, and reported that his results agreed with Eq. (1). He explained that an aggregate is a particle composed of grains held together by neck areas formed by diffusion. On the other hand, Rumpf [4] defined the strength of an aggregate as follows: rf ¼
ð1 pÞKH pa2
ð2Þ
where rf is the fracture strength, p is the porosity, K is the coordination number of a primary particle, H is the neck strength between primary particles, and a is the diameter of primary particle. Pampuch and Haberko [7] explained that porosity of an aggregate was related to cold pressing pressure from Rumpf’s equation. In a precipitation method, Shin and Lee [8] calculated the porosity of an aggregate and proposed that it is constant, because primary particles in the aggregate are packed randomly, and the aggregate is formed by necking in initial sintering. Therefore, in Eq. (2), p
In this study, manganese zinc ferrite powder, synthesized by an alcoholic dehydration method, was used. This is a kind of a coprecipitation method showing the narrow size distribution of primary particles. Spherical aggregates, composed of spherical primary particles, were produced [11]. The starting materials were Mn3O4, ZnO and ferric citrate. The amounts of each oxide were measured, mixed with 60 wt.% aqueous citric acid, and heated to obtain a clear solution. In the later experiment, Mn3O4 and ZnO were dissolved in 85 wt.% formic acid and boiled to achieve a clear solution. Ferric citrate was separately dissolved in deionized water and boiled. Ammonium hydroxide (14.8 N NH4OH) was added to achieve a clear solution. The as-prepared citrate or formate solutions were mixed and sprayed into a 12fold volume of reagent grade ethyl alcohol. Obtained Mn – Zn – Fe – citrate – formate complex salts were washed with ethyl alcohol, filtered, and then dried at 110 jC. A two-step calcination process was adopted; after an initial calcination at 400 jC in air for 4 h for the decomposition of citric and formic radicals, the second calcination was carried out at 900 jC for 20 min in nitrogen atmosphere for the formation of the ferrite phase.
H.S. Shin et al. / Materials Letters 57 (2003) 1467–1470
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A portion of the calcined powders was ball milled for 20 min and the non-ball-milled portion was used as aggregate. Powders were pressed into pellets, before being pressed at 0 – 650 MPa isostatically. Green densities of pellets were measured by a dimensional method. Centrifugal particle size analyzer measured particle size distribution. A scanning electron microscopy was used to observe the morphology of the calcined powders and green bodies.
4. Results and discussion Fig. 1 shows SEM photograph of (a) the reground powders, while (b) is that of the spherical aggregate particles which contain necks between the primary particle. Because the aggregate particles and reground powders were synthesized by the solution technique, the primary particle size is uniform, as shown in the
Fig. 1. SEM photographs of (a) reground fine powders and (b) aggregates.
Fig. 2. Green density of aggregated powders as a function of compression pressure.
figure. As these figure are similar to the aggregate model, the powder in Fig. 1a is suitable to measure the neck strength. Neck is the solid bridge, which was formed during heating of precipitated powders. In this figure, primary particle size could be taken as approximately 0.4 Am. It was also shown that the sizes of some aggregates are higher than 1 Am. In the case of nonballmilled powders, aggregated powder (>1 Am) has a large fraction, while in reground powders, aggregated powder has a small fraction. Fig. 2 shows green densities with variation in compression pressure. An increase in the green density was continuous until 200 MPa. From 200 to 300 MPa, the green density did not increase drastically from 300 MPa, the increase continues. This can be accounted for the fact that green density increases under 200 MPa due to the rearrangement of the aggregates, and green density increases again over 300 MPa, due to fracture of the aggregates. Therefore, fracture strength of the aggregate can be taken as 300 MPa. This fracture phenomenon of the aggregate is continuous to 400 MPa, but because fractured powders exist between aggregates, green density increases more gradually from 400 MPa. Fig. 3 shows SEM photographs of aggregates of fractured green bodies with variation in pressure. In (a), aggregates are neither fractured nor arranged and in (b), aggregates are not fractured but arranged and large pores were found to disappear. In the case of (c), some aggregates are fractured and others surrounded by fractured powders are not fractured. In (d), aggre-
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Fig. 3. Fracture morphology of aggregated Mn – Zn ferrite green compacts with variation of pressure; (a) 100, (b) 250, (c) 450, and (d) 600 MPa.
gates are almost fractured or being fractured. These results are in agreement with those of Fig. 2. Therefore, it can be concluded that fracture pressure of aggregates is approximately 300 MPa experimentally. Introducing this result into Eq. (5), neck strength, H is 5.03 10 5 N when a is 0.4 Am (in Fig. 1) and p is approximately 0.5 by Shin’s article [8]. The value of H, obtained by an experiment, does not differ greatly from the theoretical value of 4.05 10 5 N. The slight difference is thought to be caused by errors of rf in the experiment and of constant in Eq. (5). For the reground manganese zinc ferrite with variation in pressure, an increase of green density is continuous until saturated above 600 MPa. Green density at 600 MPa is 0.62 and higher than that of Fig. 2. The reason is because the increase in packing density was due to the primary particle from the fracture of the aggregate.
5. Conclusion (1) H is related to r0 from Duckworth’s and Rumpf’s equations. The equation is H=(r0pa2e Bp)/ ((1 p)K), and H is 4.05 10 5 N in manganese
zinc ferrite powder synthesized by an alcoholic dehydration method. (2) Manganese zinc ferrite aggregates were fractured at 300 MPa. Introducing this value into Rumpf’s equation, H was calculated 5.03 10 5 N. References [1] F.F. Lange, J. Am. Ceram. Soc. 67 (1984) 83. [2] D.W. Johnson Jr., D.J. Nitti, L. Berrin, Am. Ceram. Soc. Bull. 51 (1972) 896. [3] D.E. Niesz, R.B. Bennett, M.J. Snyder, Am. Ceram. Soc. Bull. 51 (1972) 677. [4] H. Rumpf, Chem. Ing. Technol. 30 (1958) 144. [5] E. Ryshkewitch, J. Am. Ceram. Soc. 36 (1953) 65. [6] W. Duckworth, J. Am. Ceram. Soc. 36 (1953) 68. [7] R. Pampuch, K. Haberko, in: P. Vincenzini (Ed.), Ceramic Powders: Agglomerates in Ceramic Micropowders and Their Behaviour on Cold Pressing and Sintering, Elsevier, Amsterdam, Netherlands, 1983. [8] H.S. Shin, B.K. Lee, J. Mater. Sci. 32 (1997) 4803. [9] F.N. Rhines, in: G.Y. Onoda Jr., L.L. Hench (Eds.), Ceramic Processing before Firing: Dynamic Particle Stacking, Wiley, USA, 1978. [10] A. Goldman, Modern Ferrite Technology, Van Nostrard Reinhold, New York, 1990. [11] P. Sainamthip, V.R.W. Amarakoon, J. Am. Ceram. Soc. 71 (1988) 644.
Aggregate and necking force in Mn–Zn ferrite Hyo Soon Shin a, Suk Kee Lee b, Byung Kyo Lee a,* a
Department of Inorganic Materials Engineering, Kyungpook National University, Taegu, 702-701, South Korea b Department of Polymer Science, Kyungpook National University, Taegu, 702-701, South Korea Received 3 June 2002; accepted 15 July 2002
Abstract An experimental technique is proposed for evaluating the strength of aggregates during powder compaction. The technique is based on the interpretation of compaction pressure vs. green density. A Rumpf’s equation was correlated with the equation suggested by Duckworth. Neck strength between primary particles, H=(r0pa2e Bp)/((1 p)K) in manganese zinc ferrite aggregate is thought to be 4.05 10 5 N, with reference value of r0. Manganese zinc ferrite decomposed from the precipitates of alcoholic dehydration was fractured at 300 MPa of the compaction pressure. From this, H was calculated as 5.03 10 5 N. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Aggregate; Neck strength; Mn – Zn ferrite; Alcoholic dehydration; Agglomerate; Porosity
1. Introduction In general, ceramic powders are known to intrinsically contain agglomerates. Agglomerates can be classified as being either hard or soft. Hard agglomerates that is to say aggregate are partially sintered or consisting of cemented groups of particles where as soft agglomerates are groups held together by van der Waals forces and can be broken apart with surfactants [1]. Agglomeration is important since it can affect the flow properties of the powders, green and fired density of bodies. Perhaps, more importantly, it has been reported that hard agglomerates may cause lower density in otherwise dense ceramic bodies [2]. Many powders used in fabricating ceramic bodies are prepared by precipitation or by solid-state reaction *
Corresponding author. Tel.: +82-53-950-5633; fax: +82-53950-5645. E-mail address: [email protected] (B.K. Lee).
method. Calcination almost always results in the formation of porous aggregates. The strength of these aggregates significantly affects the powders’ subsequent response to processing as well as the microstructure and properties of the bodies. Milling is normally used in ceramic processing to break down porous aggregates, and the milling condition required depends on the aggregate strength. In spite of the recognized importance of aggregate strength and porosity, no quantitative technique is available for measuring these powder characteristics [3]. Niesz et al. [3] assumed that the semilogarithmic pressure – density relationship observed during the compaction of granulated powders was analogous to that which exists between mechanical strength and porosity. It is also assumed that the pressure at the break point between linear potions of the curve was a measure of the strength of the granules. After testing agglomerated alumina powders, it was concluded that compaction data could also show the presence of
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 1 0 3 5 - 2
1468
H.S. Shin et al. / Materials Letters 57 (2003) 1467–1470
agglomerates in an unagglomerated powder. Rumpf [4] reported that the load corresponding to the break point may be taken as a measure of the strength of the agglomerates and that the strength for each contact points was related to the agglomerate strength. In this study, an experimental technique has been proposed for evaluating the strength of the aggregates in powder. The technique was based on the interpretation of compaction data plotted as compaction pressure vs. green density. In the process, the equation used by Rumpf was related to the equation used by Duckworth.
is constant (about 0.5) and K is calculated to be 6 from p [9]. When a and rf are measured, H can be calculated. At fracture, Eq. (1) is: rf ¼ r0 eBp Introducing Eq. (3) into Eq. (2) yields: r0 eBp ¼
Ryshkewitch [5] showed that the compression strength was related to porosity in the sintered alumina and zirconia. The logarithm of compression strength and porosity was a linear reaction. At discussion of Ryshkewitch’s paper, Duckworth [6] showed that compression strength is:
ð4Þ
and H¼
2. Neck strength of aggregate
ð1 pÞKH pa2
ð3Þ
r0 pa2 eBp pa2 rf ¼ ð1 pÞK ð1 pÞK
ð5Þ
In Eq. (5), H could be calculated if each of the values were introduced, however the strength of the nonporous body had to be given from a reference. With r0 = 8000 N/mm2 in ferrite [10] and a = 0.4 Am, H would theoretically be 4.05 10 5 N. Therefore, it is necessary to compare rf given by hydraulic pressing.
3. Experimental procedure r ¼ r0 eBp
ð1Þ
where r and r0 are the strengths of a porous and a nonporous body, B is the gradient at the plot of lnr vs. p, and p is the porosity expressed as a fraction [7]. Niesz et al. [3] introduced Eq. (1) in the experiment of uniaxial pressing of an aggregate, and reported that his results agreed with Eq. (1). He explained that an aggregate is a particle composed of grains held together by neck areas formed by diffusion. On the other hand, Rumpf [4] defined the strength of an aggregate as follows: rf ¼
ð1 pÞKH pa2
ð2Þ
where rf is the fracture strength, p is the porosity, K is the coordination number of a primary particle, H is the neck strength between primary particles, and a is the diameter of primary particle. Pampuch and Haberko [7] explained that porosity of an aggregate was related to cold pressing pressure from Rumpf’s equation. In a precipitation method, Shin and Lee [8] calculated the porosity of an aggregate and proposed that it is constant, because primary particles in the aggregate are packed randomly, and the aggregate is formed by necking in initial sintering. Therefore, in Eq. (2), p
In this study, manganese zinc ferrite powder, synthesized by an alcoholic dehydration method, was used. This is a kind of a coprecipitation method showing the narrow size distribution of primary particles. Spherical aggregates, composed of spherical primary particles, were produced [11]. The starting materials were Mn3O4, ZnO and ferric citrate. The amounts of each oxide were measured, mixed with 60 wt.% aqueous citric acid, and heated to obtain a clear solution. In the later experiment, Mn3O4 and ZnO were dissolved in 85 wt.% formic acid and boiled to achieve a clear solution. Ferric citrate was separately dissolved in deionized water and boiled. Ammonium hydroxide (14.8 N NH4OH) was added to achieve a clear solution. The as-prepared citrate or formate solutions were mixed and sprayed into a 12fold volume of reagent grade ethyl alcohol. Obtained Mn – Zn – Fe – citrate – formate complex salts were washed with ethyl alcohol, filtered, and then dried at 110 jC. A two-step calcination process was adopted; after an initial calcination at 400 jC in air for 4 h for the decomposition of citric and formic radicals, the second calcination was carried out at 900 jC for 20 min in nitrogen atmosphere for the formation of the ferrite phase.
H.S. Shin et al. / Materials Letters 57 (2003) 1467–1470
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A portion of the calcined powders was ball milled for 20 min and the non-ball-milled portion was used as aggregate. Powders were pressed into pellets, before being pressed at 0 – 650 MPa isostatically. Green densities of pellets were measured by a dimensional method. Centrifugal particle size analyzer measured particle size distribution. A scanning electron microscopy was used to observe the morphology of the calcined powders and green bodies.
4. Results and discussion Fig. 1 shows SEM photograph of (a) the reground powders, while (b) is that of the spherical aggregate particles which contain necks between the primary particle. Because the aggregate particles and reground powders were synthesized by the solution technique, the primary particle size is uniform, as shown in the
Fig. 1. SEM photographs of (a) reground fine powders and (b) aggregates.
Fig. 2. Green density of aggregated powders as a function of compression pressure.
figure. As these figure are similar to the aggregate model, the powder in Fig. 1a is suitable to measure the neck strength. Neck is the solid bridge, which was formed during heating of precipitated powders. In this figure, primary particle size could be taken as approximately 0.4 Am. It was also shown that the sizes of some aggregates are higher than 1 Am. In the case of nonballmilled powders, aggregated powder (>1 Am) has a large fraction, while in reground powders, aggregated powder has a small fraction. Fig. 2 shows green densities with variation in compression pressure. An increase in the green density was continuous until 200 MPa. From 200 to 300 MPa, the green density did not increase drastically from 300 MPa, the increase continues. This can be accounted for the fact that green density increases under 200 MPa due to the rearrangement of the aggregates, and green density increases again over 300 MPa, due to fracture of the aggregates. Therefore, fracture strength of the aggregate can be taken as 300 MPa. This fracture phenomenon of the aggregate is continuous to 400 MPa, but because fractured powders exist between aggregates, green density increases more gradually from 400 MPa. Fig. 3 shows SEM photographs of aggregates of fractured green bodies with variation in pressure. In (a), aggregates are neither fractured nor arranged and in (b), aggregates are not fractured but arranged and large pores were found to disappear. In the case of (c), some aggregates are fractured and others surrounded by fractured powders are not fractured. In (d), aggre-
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Fig. 3. Fracture morphology of aggregated Mn – Zn ferrite green compacts with variation of pressure; (a) 100, (b) 250, (c) 450, and (d) 600 MPa.
gates are almost fractured or being fractured. These results are in agreement with those of Fig. 2. Therefore, it can be concluded that fracture pressure of aggregates is approximately 300 MPa experimentally. Introducing this result into Eq. (5), neck strength, H is 5.03 10 5 N when a is 0.4 Am (in Fig. 1) and p is approximately 0.5 by Shin’s article [8]. The value of H, obtained by an experiment, does not differ greatly from the theoretical value of 4.05 10 5 N. The slight difference is thought to be caused by errors of rf in the experiment and of constant in Eq. (5). For the reground manganese zinc ferrite with variation in pressure, an increase of green density is continuous until saturated above 600 MPa. Green density at 600 MPa is 0.62 and higher than that of Fig. 2. The reason is because the increase in packing density was due to the primary particle from the fracture of the aggregate.
5. Conclusion (1) H is related to r0 from Duckworth’s and Rumpf’s equations. The equation is H=(r0pa2e Bp)/ ((1 p)K), and H is 4.05 10 5 N in manganese
zinc ferrite powder synthesized by an alcoholic dehydration method. (2) Manganese zinc ferrite aggregates were fractured at 300 MPa. Introducing this value into Rumpf’s equation, H was calculated 5.03 10 5 N. References [1] F.F. Lange, J. Am. Ceram. Soc. 67 (1984) 83. [2] D.W. Johnson Jr., D.J. Nitti, L. Berrin, Am. Ceram. Soc. Bull. 51 (1972) 896. [3] D.E. Niesz, R.B. Bennett, M.J. Snyder, Am. Ceram. Soc. Bull. 51 (1972) 677. [4] H. Rumpf, Chem. Ing. Technol. 30 (1958) 144. [5] E. Ryshkewitch, J. Am. Ceram. Soc. 36 (1953) 65. [6] W. Duckworth, J. Am. Ceram. Soc. 36 (1953) 68. [7] R. Pampuch, K. Haberko, in: P. Vincenzini (Ed.), Ceramic Powders: Agglomerates in Ceramic Micropowders and Their Behaviour on Cold Pressing and Sintering, Elsevier, Amsterdam, Netherlands, 1983. [8] H.S. Shin, B.K. Lee, J. Mater. Sci. 32 (1997) 4803. [9] F.N. Rhines, in: G.Y. Onoda Jr., L.L. Hench (Eds.), Ceramic Processing before Firing: Dynamic Particle Stacking, Wiley, USA, 1978. [10] A. Goldman, Modern Ferrite Technology, Van Nostrard Reinhold, New York, 1990. [11] P. Sainamthip, V.R.W. Amarakoon, J. Am. Ceram. Soc. 71 (1988) 644.