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Characterization of intermetallic Fe–Mn–Si powders produced by casting and mechanical ball milling
Powder Technology 137 (2003) 139 – 147 www.elsevier.com/locate/powtec
Characterization of intermetallic Fe–Mn–Si powders produced by casting and mechanical ball milling Zongyin Zhang a,*, Rolf Sandstro¨m a, Karin Frisk b, Anders Salwe´n b a
Department of Materials Science and Engineering and Brinell Centre, Royal Institute of Technology, S-100 44 Stockholm, Sweden b Swedish Institute for Metals Research, Drottning Kristinas Va¨g 48, S-114 28 Stockholm, Sweden Received 7 November 2002; received in revised form 16 June 2003
Abstract Mechanical milling is a common method used to produce different powders. Milling time is one of the most important factors in the process, which affects characteristics such as particle size distribution and morphology. Four compositions of mechanically milled Fe – Mn – Si master alloy powders were investigated in the present paper. Milling times from 10 to 120 min were used. Particle size distribution and milling kinetics of Fe – Mn – Si powders were studied, and the parameters in breakage function have been determined. The results show that powder characteristics vary with the contents of silicon and manganese. During milling, the particle size initially decreases. At longer milling times, however, small particles agglomerate to larger particles (overmilling). The optimum milling time to get powders with very fine particle sizes is alloy-dependent. Apart from the agglomeration, the milling process of Fe – Mn – Si powders can be described by a classic batchgrinding equation based on the population balance model. D 2003 Elsevier B.V. All rights reserved. Keywords: Fe – Mn – Si powder; Particle size distribution; Modelling; Grinding kinetics; Breakage function
1. Introduction Manganese – silicon alloyed steels have been widely manufactured and used because of their good mechanical properties. Recently, Fe –Mn – Si alloys have been studied intensively since a shape memory effect in Fe – 30% Mn – 1% Si alloy was found in 1982 [1 –7]. Powder metallurgy has the advantage of smaller material consumption in comparison to conventional metallurgy. In the production of Fe –Mn – Si sintered steels, milled Fe – Mn – Si master alloy powder is added to iron powder, followed by pressing and sintering. The investigations of Mn – Si sintered steels have shown that Mn –Si sintered steels exhibit better mechanical properties than sintered iron [8– 10]. Transient liquid phase sintering of Fe –Mn – Si master alloy powder promotes a homogenization of alloying elements and accelerates densification. Generally, Fe –Mn –Si alloys are produced by melting and casting technique, and followed by hot rolling and heat treatment process to form products [2,4 – 6], or by a milling process to form powders [8 – 10]. Fe –Mn –Si master alloy powder produced using mechanical alloying has also been * Corresponding author. Tel.: +46-8-7906544; fax: +46-8-207681. E-mail address: [email protected] (Z. Zhang). 0032-5910/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2003.08.058
studied [11], and the results show that mechanically alloyed Fe – Mn – Si master alloy powder has a thermal stability similar to conventional powder. Mechanical milling is also used to make other alloy powders [12 – 16]. Mechanical alloying and milling are important processes: (i) to achieve powders with very fine particle size; (ii) to synthesize intermetallic compound powders, which have metastable structure and unique microstructure; and (iii) to make special alloys and compounds, which cannot be produced by conventional methods. Milling time is one of the most important factors for achieving the desired particle size of milled powders. Generally, the particle size of milled powders decreases with increasing milling time. However, long milling time results in agglomeration of small particles for some powders [17,18]. The kinetics of the milling process has been extensively studied and modelled [19 –25]. Most studies have dealt with the milling kinetics of oxides. However, only a few papers reported on milling kinetics of compounds. In the milling processes of ductile materials such as aluminium, copper, and brass [26], three stages occurred during milling, namely, flattening, abrasion, and breakage. Potapov and Campbell [27] reported that there are two breakage mechanisms in the milling of brittle solid particles, which are
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referred to as mechanisms I and II, depending on the crack orientation in the milled powder. In mechanism I, the cracks are oriented in the radial direction in the particles. The cracks in mechanism II appear after those in mechanism I and are perpendicular to them. The milling velocity also affects the mechanisms. Koch and Whittenberger [28] reviewed the mechanical milling of intermetallics and demonstrated that even in the milling of brittle intermetallics, extensive plastic deformation was observed. Lytle and Prisbrey [29] found that the phase constituents of materials also affect the milling process. The weaker phases, which are microstructurally heterogeneous, are ground rapidly, while the stronger phases are ground more slowly. In the present study, Fe –Mn –Si master alloy powders with different compositions were produced by casting and mechanical milling. The effects of milling time and the amounts of manganese and silicon on the particle size distribution of milled Fe – Mn – Si powders were studied. The milling mechanism and kinetics of Fe – Mn – Si master alloy powders were also investigated.
2. Experimental 2.1. The production of Fe – Mn – Si master alloy powders Four Fe – Mn – Si master alloys were produced by casting and ball milling, and denoted as M1, M2, M3, and M4 (see Table 1). Pure iron, Fe –75% Si ferrosilicon, and manganese were used as raw materials. Iron, ferrosilicon, and manganese were molten in an induction furnace under vacuum, and the ingots were cooled in argon. The melts were cast in a mould with 40 mm diameter. The ingots were crushed, passed through a 100-mesh sieve, and milled in a Fritsch planetary ball mill. n-Heptane (C7H16) was used as a milling medium. The weight ratio of ball to powder was 5:1. Milling times of 10, 30, 60, 90, and 120 min were used. The mill was rotated at 250 rpm. The powders were dried at 110 jC in vacuum after milling.
Table 1 Characteristics of Fe – Mn – Si master alloy powders Sample ID
Mn (wt.%)
Si (wt.%)
Phase constituent (S)
Liquidus (jC)
Solidus (jC)
M1
35
14
1170
1090
M2
35
20
(Fe,Mn)3Si, (Fe,Mn)5Si3 – S, (Fe,Mn)9Si2 – S (Fe,Mn)3Si, (Fe,Mn)5Si3, (Fe,Mn)9Si2 – S (Fe,Mn)3Si, (Fe,Mn)5Si3, (Fe,Mn)9Si2 – S (Fe,Mn)3Si, (Fe,Mn)5Si3 – S, (Fe,Mn)9Si2 – S
1225
1115
M3
M4
45
60
20
14
S—a small amount of the phase in the powder.
1215
1125
1110
1085
2.2. Characteristics of Fe – Mn – Si master alloy powders Liquidus and solidus temperatures of the Fe – Mn – Si master alloy powders were evaluated by differential thermal analysis. Phase constituents of the Fe – Mn – Si master alloy powders were analysed by X-ray diffraction. M1 powder mainly contains (Fe,Mn)3Si, and M2, M3, and M4 contain mainly (Fe,Mn)3Si and (Fe,Mn)5Si3. All four master alloys contain a small amount of (Fe,Mn)9Si2. The composition, phase constituents, and liquidus and solidus temperatures of the Fe– Mn –Si powders are shown in Table 1. The particle size distribution was determined in a SYMPATEC analyser. A scanning electron microscope (SEM) was used to observe the particle morphology.
3. Modelling of milled kinetics The undersize distribution function of milled powder for time-continuous and size-continuous state satisfies the equation [30,31]: Z xm B2 Fðx; tÞ BFðx; tÞ BBðc; xÞ BFðc; tÞ ¼ SðxÞ þ SðcÞ dc BxBt Bx Bx Bc x ð1Þ where F(x,t) is the weight fraction of materials finer than size x after grinding, c is the particle size to be broken, S(x) is the selection function (the breakage rate constant for size x), B(c,x) is the breakage function (i.e., the particle size distribution produced from the initial particle size c), and t is the milling time. Reid [30] gave an analytical solution to Eq. (1) for a special case whenS(c)BB(c,x)/Bx takes on a constant value K (a grinding rate constant) with assumptions presented in Eqs. (2) and (3): SðxÞ ¼ Kx
ð2Þ
Bðc; xÞ ¼ x=c
ð3Þ
Eq. (2) expresses that the selection function S(x) only depends on the particle size x and is proportional to the particle size (i.e., larger particles are easy to break). Eq. (3) expresses that the breakage function depends on the final particle size x as well as on initial particle size c. Larger initial particle size leads to smaller breakage function. Eq. (1) can be expressed as Eq. (4) after integration of Eqs. (2) and (3). B2 Fðx; tÞ BFðx; tÞ ¼ SðxÞ þ K½Fðxm ; tÞ Fðx; tÞ BxBt Bx
ð4Þ
In Eq. (4), the first term shows that large particles are broken into small particles, and that the breakdown is faster the larger the particles are. The second term indicates that more smaller particles than larger particles are created, which should obviously be the case.
Z. Zhang et al. / Powder Technology 137 (2003) 139–147
The solution to Eq. (1) can be expressed as: Rðx; tÞ ¼ Rðx; 0ÞexpðKxtÞ
ð5Þ
where R(x,0) is the initial oversize distribution function, R(x,t) is the oversize distribution function of particles after grinding a time t, and R(x,t) = 1 F(x,t). Nakajima and Tanaka [32] used instead the relationships shown in Eqs. (6) and (7): SðxÞ ¼ Kxn Bðc; xÞ ¼
m x c
ð6Þ ð7Þ
although it is more difficult to demonstrate. The following analytical solutions to Eq. (1) can be obtained: Rðx; tÞcRðx; 0Þexp t ðlKxn tÞm b Rðx; tÞ ¼ Rðx; 0Þexp t Kxn tb
ð8Þ for m ¼ n
ð9Þ
where l and m are constants. l and m can be determined by from a plot where lm and m are given as a function of m/n [33]. Eq. (8) can be rewritten as follows [34]: Rðx; tÞ ln ln ¼ mlnðlKtÞ þ nmlnðxÞ ð10Þ Rðx; 0Þ and mln(lKt) can be expressed as: mlnðlKtÞ ¼ mlnðlKÞ þ mlnðtÞ
where n and m are constants. The variation of the breakage rate and particle size distribution with the particle size will depend on the values of n and m, which are decided by the characteristics of materials and mills. Eq. (4) has a similar form for the case where m = n and m,n>1. Thus, the same interpretation as for m = n = 1 can be used, with the difference between the small and larger particles further enhanced. When m p n, the interpretation is approximately the same,
141
ð11Þ
4. Results and discussion 4.1. Particle size distribution Scanning electron micrographs of the M1 original powder and the powders milled for 30, 60, and 120 min are
Fig. 1. Scanning electron micrographs of the M1 powder: (a) before milling; (b) after milling for 30 min; (c) after milling for 60 min; and (d) after milling for 120 min.
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Fig. 2. Particle size distributions of the M1 powder milled for different times.
shown in Fig. 1. The particle shape of the powders before and after milling was angular. The particle size of the original powder significantly decreases after milling. The particle size distributions of M1 and M3 milled for different times are shown in Figs. 2 and 3. Ninety percent of the particles have a size less than 42 Am in M1 powder milled for 10 min, and a size less than 29 Am in M3 powder milled for the same time. The particle size distribution curves move significantly to the left with increasing milling time up to 30 min, which means that the particle size of the powders initially decreases quickly and an effective milling of
powders occurs in this period. When longer milling times were used, a different behaviour was observed in the M1 and M3 powders. The particle size decreases slightly in the M1 powder. About the same particle size distribution curve was obtained in M1 powders milled for 60, 90, and 120 min in the size range up to 30 Am, and this also occurs in M3 powder milled for 30 and 60 min. When milling time increases from 60 to 90 min in the M3 powder, the particle size distribution curve moves to the right. The shape of the particle size distribution curve of powder milled for 90 min deviates from the normal shape due to the agglomeration of
Fig. 3. Particle size distributions of the M3 powder milled for different times.
Z. Zhang et al. / Powder Technology 137 (2003) 139–147
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Fig. 4. Particle size distributions of the M2 and M4 powders milled for 10 and 90 min.
small particles. Comparing the particle size distribution of M3 powder milled for 90 min with that of powder milled for 30 min, it was found that powder milled for 90 min had a much larger amount of coarser particles than that milled for 30 min. During the milling process, small particles adhere together to form big particles, which leads a decrease in the number of smaller particles and an increase in the number of larger particles. The four Fe –Mn –Si master alloy powders show different behaviours during milling due to varying silicon and manganese contents, which results from the different characteristics of the powders. The particle size distributions of M2 and M4 milled for 10 and 90 min are shown in Fig. 4. Comparing the four powders, the order from large to small mean particle size of the powders milled for 10 min is M1, M4, M2, and M3, while that of the powders milled for 90 min is M4, M1, M3, and M2. Phase identification showed that the M1 and M4 powders mainly contain the (Fe,Mn)3Si phase, and the M2 and M3 powders contain a mixture of (Fe,Mn)3Si and (Fe,Mn)5Si3. Silicon has a larger solid-solution-strengthening effect than manganese in steel [35], which may be the reason why the M2 and M3 powders are more brittle than the M1 and M4 powders and are easier to break. This can be seen for the M1 and M3 powders in the following way. The M1 and M3 powders have about the same initial size distributions (see Figs. 2 and 3). However, after 10 and 30 min of milling times, the M3 powders have a finer size distribution than the M1 powders. The specific surface area of milled powders initially increased from 58 to 86 m2/kg for the M1 powder and from 130 to 160 m2/kg for the M3 powder when the milling time increased from 10 to 30 min. The specific surface areas
hardly change after milling for 60 –90 min. Generally, the specific surface area of powders is a function of the particle size of milled powders without agglomeration. The surface area increases with decreasing particle size. However, in the agglomerated powders, the surface area and particle size change individually. For example, the specific surface areas of M3 powders milled for 30, 60, and 90 min are almost the same, but the particle size distributions showed large differences. Many different factors affect the characteristics of milled powders, such as the amount of original powder, the ratio of ball to powder, ball size, energy efficiency, etc. [17,19,20,34,36]. Alloy composition and the phase constituents also affect milled powder properties. For example, the M1 alloy cannot be milled as fine as the M4 alloy even
Fig. 5. The particle size change of milled powders as a function of milling time; the three regions I, II, and III are explained in the text.
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Fig. 6. Variation of logarithm of R(x,t)/R(x,0) for different milling times with particle size for the M1 powder; R(x,t) is the oversize distribution function.
after a very long time. Hard materials such as oxides and soft metals and compounds show different milling behaviours. Agglomeration occurs in some materials for long time milling [17,18], while it does not take place in brittle materials [34]. The particle size change as a function of milling time is schematically given in Fig. 5. The particle size decreases quickly with increasing milling time when milling has just started (stage I). When a certain milling time is reached, which may be called the critical time, two alternative behaviours are observed. Either the particle size decreases slowly with increasing milling time (stage II), or agglomeration takes place (stage III). In the latter case, the particle size increases with increasing milling time after the critical time. Agglomerated particles of the M3 alloy are obtained after 90 min of milling. The critical time is very important for reasons of productivity, production cost, etc. The
Fig. 7. Same as Fig. 6 for M3 powder.
Fig. 8. Normalized oversize and particle size relationship of milled M1 powder after 10, 30, 60, and 90 min (model according to Eq. (8)).
shorter the critical time is, the easier it is to get fine particles. 4.2. Milling kinetics of Fe –Mn – Si master alloy powders The milling kinetics of materials is normally described by batch-grinding equations, and several forms and solutions have been used in different conditions [19,23 – 25,34]. Milling kinetics is also dependent on the materials to be broken. Firstly, the milling kinetics of Fe –Mn –Si master alloy powders has been examined by using Eq. (5). For a given milling time, the logarithm of ratio R(x,t) to R(x,0) should vary linearly with particle size according Eq. (5). Variation of [ln(R(x,t)/R(x,0))]/t with particle size for milled M1 and M3 powders milled for different times is shown in Figs. 6 and 7. There is no linear relationship between value of [ln(R(x,t)/R(x,0))]/t and particle size x. This shows that
Fig. 9. Same as Fig. 8 for M3 powder for 10, 30, and 60 min.
Z. Zhang et al. / Powder Technology 137 (2003) 139–147 Table 2 Breakage parameters of the M1 and M3 powders Alloy
nm
m
n
m/na
m
l
K (lm) n/h
M1 M3
1.7 1.2
0.39 0.37
4.4 3.2
0.2 0.2
0.88 0.64
5.6 5.6
5.7 10 7 2.4 10 4
a
Extrapolation used when determining the value.
the breakage rates of the milled M1 and M3 powders do not fit Eq. (5). The milling kinetics of Fe –Mn –Si master alloy powders was also studied by using Eq. (8). The change of ln[ ln(R(x,t)/R(x,0))] with ln(x) in Eq. (10) for M1 and M3 powders milled for different times is shown in Figs. 8 and 9. It is indicated that there is an approximately linear relationship between the cumulative oversize functions and the logarithmic scale of particle size in two powders, which indicate that the milling process for M1 and M3 can be described well using Eq. (8) [i.e., the parameters of grinding kinetics Eq. (8) obtained by the linear regression analysis can be used to reproduce the particle size distribution of the products]. The constants n, m, and lK in Eq. (10) have been derived by fitting to the data. Values of lm and m/n can be obtained from a plot of lm and m versus m/n [33]. Breakage parameters of the M1 and M3 milled powders are shown in Table 2. In the milling process of both powders, n value is larger than 1. From Eq. (6), the selection function exponentially decreases with decreasing particle size. Larger particles are broken much faster than smaller particles. The M1 and M3 powders have the same values of m and l, and different values of K, n, and m,
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which leads to different breakage rate constants. The breakage rate constant K of the M3 powder is 400 times as high as that of the M1 powder. It means that for the same time, the milled M3 powder has much finer particles than the M1 powder. In other words, shorter time is needed for the M3 powder to get a certain particle size than for the M1 powder, as pointed out above. The time dependence of R(x,t)/R(x,0) for the M1 and M3 powders has been calculated from Eq. (8) using the parameters in Table 2. The time dependence of experimental data is compared with calculated results in Figs. 10 and 11. It is illustrated that the kinetics of the grinding process of Fe –Mn – Si master alloy powders can be described by classic batch-grinding equations based on the population balance model until agglomeration of particles sets in. The good agreement between experimental data and modelled results confirms that Eq. (8) can be used to predict the particle size distribution of the milled Fe – Mn – Si compound powders at different times. Comparing the Fe – Mn – Si master alloy powders with that of alumina, diamond, and quartz [34], the breakage rate constant of alumina, diamond, and quartz is around a few thousands of times higher than that of the Fe – Mn – Si master alloy powders. Alumina, diamond, and quartz could consequently be ground to much finer particle size. Fe – Mn –Si master alloy powders are tougher than alumina, diamond, and quartz powders, and agglomeration will occur in Fe – Mn – Si master alloy powders milled at longer times. Hence, it is difficult for Fe –Mn –Si master alloy powders to form very fine particles. The breakage rate constant is affected by many factors such as ball size, mill speed, size
Fig. 10. Comparison of experimental and simulating results in milled M1 powder for normalized oversize distribution; points are experimental data, and lines are model results according to Eq. (8).
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Fig. 11. Same as Fig. 10 for M3 powder.
and charge weight of feed materials, and liquid volume [19,34].
from the Swedish Foundation for Strategic Research, Sweden, is gratefully acknowledged. The authors would like to thank Ms. Inger Persson (Ho¨gana¨s, Sweden) for her help with the evaluation of powder properties.
5. Conclusions 1. Fine Fe– Mn –Si master alloy powders can be produced by mechanical ball milling from as-cast Fe – Mn – Si ingot. The mean particle size of the powders varies between 5 and 15 Am and depends on the compositions of Fe– Mn – Si master alloys. 2. Comparing the four alloys, 20% Si alloys are easier to crush and mill into fine powder compared to the 14% Si alloys. The effect of silicon content on the particle size distribution of milled Fe – Mn – Si master alloy powders is much more significant than that of manganese content. A finer final particle size can be obtained in the alloy powders with higher silicon compositions. 3. The particle size of milled powders decreases strongly after milling for 10 and 30 min. Agglomeration of small particles into large particles takes place in the alloy powders milled for longer times. In the agglomerated powders, there are more large particles compared to the powders without agglomeration. The optimum milling time of the Fe– Mn – Si master alloy powders seems to be around 60 min. 4. The milling process can be successfully described by classic batch-grinding equations based on the population balance model up to the start of the agglomeration.
Acknowledgements The funding support from the Swedish National Board for Technical Development (NUTEK), Sweden, as well as
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Characterization of intermetallic Fe–Mn–Si powders produced by casting and mechanical ball milling Zongyin Zhang a,*, Rolf Sandstro¨m a, Karin Frisk b, Anders Salwe´n b a
Department of Materials Science and Engineering and Brinell Centre, Royal Institute of Technology, S-100 44 Stockholm, Sweden b Swedish Institute for Metals Research, Drottning Kristinas Va¨g 48, S-114 28 Stockholm, Sweden Received 7 November 2002; received in revised form 16 June 2003
Abstract Mechanical milling is a common method used to produce different powders. Milling time is one of the most important factors in the process, which affects characteristics such as particle size distribution and morphology. Four compositions of mechanically milled Fe – Mn – Si master alloy powders were investigated in the present paper. Milling times from 10 to 120 min were used. Particle size distribution and milling kinetics of Fe – Mn – Si powders were studied, and the parameters in breakage function have been determined. The results show that powder characteristics vary with the contents of silicon and manganese. During milling, the particle size initially decreases. At longer milling times, however, small particles agglomerate to larger particles (overmilling). The optimum milling time to get powders with very fine particle sizes is alloy-dependent. Apart from the agglomeration, the milling process of Fe – Mn – Si powders can be described by a classic batchgrinding equation based on the population balance model. D 2003 Elsevier B.V. All rights reserved. Keywords: Fe – Mn – Si powder; Particle size distribution; Modelling; Grinding kinetics; Breakage function
1. Introduction Manganese – silicon alloyed steels have been widely manufactured and used because of their good mechanical properties. Recently, Fe –Mn – Si alloys have been studied intensively since a shape memory effect in Fe – 30% Mn – 1% Si alloy was found in 1982 [1 –7]. Powder metallurgy has the advantage of smaller material consumption in comparison to conventional metallurgy. In the production of Fe –Mn – Si sintered steels, milled Fe – Mn – Si master alloy powder is added to iron powder, followed by pressing and sintering. The investigations of Mn – Si sintered steels have shown that Mn –Si sintered steels exhibit better mechanical properties than sintered iron [8– 10]. Transient liquid phase sintering of Fe –Mn – Si master alloy powder promotes a homogenization of alloying elements and accelerates densification. Generally, Fe –Mn –Si alloys are produced by melting and casting technique, and followed by hot rolling and heat treatment process to form products [2,4 – 6], or by a milling process to form powders [8 – 10]. Fe –Mn –Si master alloy powder produced using mechanical alloying has also been * Corresponding author. Tel.: +46-8-7906544; fax: +46-8-207681. E-mail address: [email protected] (Z. Zhang). 0032-5910/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2003.08.058
studied [11], and the results show that mechanically alloyed Fe – Mn – Si master alloy powder has a thermal stability similar to conventional powder. Mechanical milling is also used to make other alloy powders [12 – 16]. Mechanical alloying and milling are important processes: (i) to achieve powders with very fine particle size; (ii) to synthesize intermetallic compound powders, which have metastable structure and unique microstructure; and (iii) to make special alloys and compounds, which cannot be produced by conventional methods. Milling time is one of the most important factors for achieving the desired particle size of milled powders. Generally, the particle size of milled powders decreases with increasing milling time. However, long milling time results in agglomeration of small particles for some powders [17,18]. The kinetics of the milling process has been extensively studied and modelled [19 –25]. Most studies have dealt with the milling kinetics of oxides. However, only a few papers reported on milling kinetics of compounds. In the milling processes of ductile materials such as aluminium, copper, and brass [26], three stages occurred during milling, namely, flattening, abrasion, and breakage. Potapov and Campbell [27] reported that there are two breakage mechanisms in the milling of brittle solid particles, which are
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referred to as mechanisms I and II, depending on the crack orientation in the milled powder. In mechanism I, the cracks are oriented in the radial direction in the particles. The cracks in mechanism II appear after those in mechanism I and are perpendicular to them. The milling velocity also affects the mechanisms. Koch and Whittenberger [28] reviewed the mechanical milling of intermetallics and demonstrated that even in the milling of brittle intermetallics, extensive plastic deformation was observed. Lytle and Prisbrey [29] found that the phase constituents of materials also affect the milling process. The weaker phases, which are microstructurally heterogeneous, are ground rapidly, while the stronger phases are ground more slowly. In the present study, Fe –Mn –Si master alloy powders with different compositions were produced by casting and mechanical milling. The effects of milling time and the amounts of manganese and silicon on the particle size distribution of milled Fe – Mn – Si powders were studied. The milling mechanism and kinetics of Fe – Mn – Si master alloy powders were also investigated.
2. Experimental 2.1. The production of Fe – Mn – Si master alloy powders Four Fe – Mn – Si master alloys were produced by casting and ball milling, and denoted as M1, M2, M3, and M4 (see Table 1). Pure iron, Fe –75% Si ferrosilicon, and manganese were used as raw materials. Iron, ferrosilicon, and manganese were molten in an induction furnace under vacuum, and the ingots were cooled in argon. The melts were cast in a mould with 40 mm diameter. The ingots were crushed, passed through a 100-mesh sieve, and milled in a Fritsch planetary ball mill. n-Heptane (C7H16) was used as a milling medium. The weight ratio of ball to powder was 5:1. Milling times of 10, 30, 60, 90, and 120 min were used. The mill was rotated at 250 rpm. The powders were dried at 110 jC in vacuum after milling.
Table 1 Characteristics of Fe – Mn – Si master alloy powders Sample ID
Mn (wt.%)
Si (wt.%)
Phase constituent (S)
Liquidus (jC)
Solidus (jC)
M1
35
14
1170
1090
M2
35
20
(Fe,Mn)3Si, (Fe,Mn)5Si3 – S, (Fe,Mn)9Si2 – S (Fe,Mn)3Si, (Fe,Mn)5Si3, (Fe,Mn)9Si2 – S (Fe,Mn)3Si, (Fe,Mn)5Si3, (Fe,Mn)9Si2 – S (Fe,Mn)3Si, (Fe,Mn)5Si3 – S, (Fe,Mn)9Si2 – S
1225
1115
M3
M4
45
60
20
14
S—a small amount of the phase in the powder.
1215
1125
1110
1085
2.2. Characteristics of Fe – Mn – Si master alloy powders Liquidus and solidus temperatures of the Fe – Mn – Si master alloy powders were evaluated by differential thermal analysis. Phase constituents of the Fe – Mn – Si master alloy powders were analysed by X-ray diffraction. M1 powder mainly contains (Fe,Mn)3Si, and M2, M3, and M4 contain mainly (Fe,Mn)3Si and (Fe,Mn)5Si3. All four master alloys contain a small amount of (Fe,Mn)9Si2. The composition, phase constituents, and liquidus and solidus temperatures of the Fe– Mn –Si powders are shown in Table 1. The particle size distribution was determined in a SYMPATEC analyser. A scanning electron microscope (SEM) was used to observe the particle morphology.
3. Modelling of milled kinetics The undersize distribution function of milled powder for time-continuous and size-continuous state satisfies the equation [30,31]: Z xm B2 Fðx; tÞ BFðx; tÞ BBðc; xÞ BFðc; tÞ ¼ SðxÞ þ SðcÞ dc BxBt Bx Bx Bc x ð1Þ where F(x,t) is the weight fraction of materials finer than size x after grinding, c is the particle size to be broken, S(x) is the selection function (the breakage rate constant for size x), B(c,x) is the breakage function (i.e., the particle size distribution produced from the initial particle size c), and t is the milling time. Reid [30] gave an analytical solution to Eq. (1) for a special case whenS(c)BB(c,x)/Bx takes on a constant value K (a grinding rate constant) with assumptions presented in Eqs. (2) and (3): SðxÞ ¼ Kx
ð2Þ
Bðc; xÞ ¼ x=c
ð3Þ
Eq. (2) expresses that the selection function S(x) only depends on the particle size x and is proportional to the particle size (i.e., larger particles are easy to break). Eq. (3) expresses that the breakage function depends on the final particle size x as well as on initial particle size c. Larger initial particle size leads to smaller breakage function. Eq. (1) can be expressed as Eq. (4) after integration of Eqs. (2) and (3). B2 Fðx; tÞ BFðx; tÞ ¼ SðxÞ þ K½Fðxm ; tÞ Fðx; tÞ BxBt Bx
ð4Þ
In Eq. (4), the first term shows that large particles are broken into small particles, and that the breakdown is faster the larger the particles are. The second term indicates that more smaller particles than larger particles are created, which should obviously be the case.
Z. Zhang et al. / Powder Technology 137 (2003) 139–147
The solution to Eq. (1) can be expressed as: Rðx; tÞ ¼ Rðx; 0ÞexpðKxtÞ
ð5Þ
where R(x,0) is the initial oversize distribution function, R(x,t) is the oversize distribution function of particles after grinding a time t, and R(x,t) = 1 F(x,t). Nakajima and Tanaka [32] used instead the relationships shown in Eqs. (6) and (7): SðxÞ ¼ Kxn Bðc; xÞ ¼
m x c
ð6Þ ð7Þ
although it is more difficult to demonstrate. The following analytical solutions to Eq. (1) can be obtained: Rðx; tÞcRðx; 0Þexp t ðlKxn tÞm b Rðx; tÞ ¼ Rðx; 0Þexp t Kxn tb
ð8Þ for m ¼ n
ð9Þ
where l and m are constants. l and m can be determined by from a plot where lm and m are given as a function of m/n [33]. Eq. (8) can be rewritten as follows [34]: Rðx; tÞ ln ln ¼ mlnðlKtÞ þ nmlnðxÞ ð10Þ Rðx; 0Þ and mln(lKt) can be expressed as: mlnðlKtÞ ¼ mlnðlKÞ þ mlnðtÞ
where n and m are constants. The variation of the breakage rate and particle size distribution with the particle size will depend on the values of n and m, which are decided by the characteristics of materials and mills. Eq. (4) has a similar form for the case where m = n and m,n>1. Thus, the same interpretation as for m = n = 1 can be used, with the difference between the small and larger particles further enhanced. When m p n, the interpretation is approximately the same,
141
ð11Þ
4. Results and discussion 4.1. Particle size distribution Scanning electron micrographs of the M1 original powder and the powders milled for 30, 60, and 120 min are
Fig. 1. Scanning electron micrographs of the M1 powder: (a) before milling; (b) after milling for 30 min; (c) after milling for 60 min; and (d) after milling for 120 min.
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Fig. 2. Particle size distributions of the M1 powder milled for different times.
shown in Fig. 1. The particle shape of the powders before and after milling was angular. The particle size of the original powder significantly decreases after milling. The particle size distributions of M1 and M3 milled for different times are shown in Figs. 2 and 3. Ninety percent of the particles have a size less than 42 Am in M1 powder milled for 10 min, and a size less than 29 Am in M3 powder milled for the same time. The particle size distribution curves move significantly to the left with increasing milling time up to 30 min, which means that the particle size of the powders initially decreases quickly and an effective milling of
powders occurs in this period. When longer milling times were used, a different behaviour was observed in the M1 and M3 powders. The particle size decreases slightly in the M1 powder. About the same particle size distribution curve was obtained in M1 powders milled for 60, 90, and 120 min in the size range up to 30 Am, and this also occurs in M3 powder milled for 30 and 60 min. When milling time increases from 60 to 90 min in the M3 powder, the particle size distribution curve moves to the right. The shape of the particle size distribution curve of powder milled for 90 min deviates from the normal shape due to the agglomeration of
Fig. 3. Particle size distributions of the M3 powder milled for different times.
Z. Zhang et al. / Powder Technology 137 (2003) 139–147
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Fig. 4. Particle size distributions of the M2 and M4 powders milled for 10 and 90 min.
small particles. Comparing the particle size distribution of M3 powder milled for 90 min with that of powder milled for 30 min, it was found that powder milled for 90 min had a much larger amount of coarser particles than that milled for 30 min. During the milling process, small particles adhere together to form big particles, which leads a decrease in the number of smaller particles and an increase in the number of larger particles. The four Fe –Mn –Si master alloy powders show different behaviours during milling due to varying silicon and manganese contents, which results from the different characteristics of the powders. The particle size distributions of M2 and M4 milled for 10 and 90 min are shown in Fig. 4. Comparing the four powders, the order from large to small mean particle size of the powders milled for 10 min is M1, M4, M2, and M3, while that of the powders milled for 90 min is M4, M1, M3, and M2. Phase identification showed that the M1 and M4 powders mainly contain the (Fe,Mn)3Si phase, and the M2 and M3 powders contain a mixture of (Fe,Mn)3Si and (Fe,Mn)5Si3. Silicon has a larger solid-solution-strengthening effect than manganese in steel [35], which may be the reason why the M2 and M3 powders are more brittle than the M1 and M4 powders and are easier to break. This can be seen for the M1 and M3 powders in the following way. The M1 and M3 powders have about the same initial size distributions (see Figs. 2 and 3). However, after 10 and 30 min of milling times, the M3 powders have a finer size distribution than the M1 powders. The specific surface area of milled powders initially increased from 58 to 86 m2/kg for the M1 powder and from 130 to 160 m2/kg for the M3 powder when the milling time increased from 10 to 30 min. The specific surface areas
hardly change after milling for 60 –90 min. Generally, the specific surface area of powders is a function of the particle size of milled powders without agglomeration. The surface area increases with decreasing particle size. However, in the agglomerated powders, the surface area and particle size change individually. For example, the specific surface areas of M3 powders milled for 30, 60, and 90 min are almost the same, but the particle size distributions showed large differences. Many different factors affect the characteristics of milled powders, such as the amount of original powder, the ratio of ball to powder, ball size, energy efficiency, etc. [17,19,20,34,36]. Alloy composition and the phase constituents also affect milled powder properties. For example, the M1 alloy cannot be milled as fine as the M4 alloy even
Fig. 5. The particle size change of milled powders as a function of milling time; the three regions I, II, and III are explained in the text.
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Fig. 6. Variation of logarithm of R(x,t)/R(x,0) for different milling times with particle size for the M1 powder; R(x,t) is the oversize distribution function.
after a very long time. Hard materials such as oxides and soft metals and compounds show different milling behaviours. Agglomeration occurs in some materials for long time milling [17,18], while it does not take place in brittle materials [34]. The particle size change as a function of milling time is schematically given in Fig. 5. The particle size decreases quickly with increasing milling time when milling has just started (stage I). When a certain milling time is reached, which may be called the critical time, two alternative behaviours are observed. Either the particle size decreases slowly with increasing milling time (stage II), or agglomeration takes place (stage III). In the latter case, the particle size increases with increasing milling time after the critical time. Agglomerated particles of the M3 alloy are obtained after 90 min of milling. The critical time is very important for reasons of productivity, production cost, etc. The
Fig. 7. Same as Fig. 6 for M3 powder.
Fig. 8. Normalized oversize and particle size relationship of milled M1 powder after 10, 30, 60, and 90 min (model according to Eq. (8)).
shorter the critical time is, the easier it is to get fine particles. 4.2. Milling kinetics of Fe –Mn – Si master alloy powders The milling kinetics of materials is normally described by batch-grinding equations, and several forms and solutions have been used in different conditions [19,23 – 25,34]. Milling kinetics is also dependent on the materials to be broken. Firstly, the milling kinetics of Fe –Mn –Si master alloy powders has been examined by using Eq. (5). For a given milling time, the logarithm of ratio R(x,t) to R(x,0) should vary linearly with particle size according Eq. (5). Variation of [ln(R(x,t)/R(x,0))]/t with particle size for milled M1 and M3 powders milled for different times is shown in Figs. 6 and 7. There is no linear relationship between value of [ln(R(x,t)/R(x,0))]/t and particle size x. This shows that
Fig. 9. Same as Fig. 8 for M3 powder for 10, 30, and 60 min.
Z. Zhang et al. / Powder Technology 137 (2003) 139–147 Table 2 Breakage parameters of the M1 and M3 powders Alloy
nm
m
n
m/na
m
l
K (lm) n/h
M1 M3
1.7 1.2
0.39 0.37
4.4 3.2
0.2 0.2
0.88 0.64
5.6 5.6
5.7 10 7 2.4 10 4
a
Extrapolation used when determining the value.
the breakage rates of the milled M1 and M3 powders do not fit Eq. (5). The milling kinetics of Fe –Mn –Si master alloy powders was also studied by using Eq. (8). The change of ln[ ln(R(x,t)/R(x,0))] with ln(x) in Eq. (10) for M1 and M3 powders milled for different times is shown in Figs. 8 and 9. It is indicated that there is an approximately linear relationship between the cumulative oversize functions and the logarithmic scale of particle size in two powders, which indicate that the milling process for M1 and M3 can be described well using Eq. (8) [i.e., the parameters of grinding kinetics Eq. (8) obtained by the linear regression analysis can be used to reproduce the particle size distribution of the products]. The constants n, m, and lK in Eq. (10) have been derived by fitting to the data. Values of lm and m/n can be obtained from a plot of lm and m versus m/n [33]. Breakage parameters of the M1 and M3 milled powders are shown in Table 2. In the milling process of both powders, n value is larger than 1. From Eq. (6), the selection function exponentially decreases with decreasing particle size. Larger particles are broken much faster than smaller particles. The M1 and M3 powders have the same values of m and l, and different values of K, n, and m,
145
which leads to different breakage rate constants. The breakage rate constant K of the M3 powder is 400 times as high as that of the M1 powder. It means that for the same time, the milled M3 powder has much finer particles than the M1 powder. In other words, shorter time is needed for the M3 powder to get a certain particle size than for the M1 powder, as pointed out above. The time dependence of R(x,t)/R(x,0) for the M1 and M3 powders has been calculated from Eq. (8) using the parameters in Table 2. The time dependence of experimental data is compared with calculated results in Figs. 10 and 11. It is illustrated that the kinetics of the grinding process of Fe –Mn – Si master alloy powders can be described by classic batch-grinding equations based on the population balance model until agglomeration of particles sets in. The good agreement between experimental data and modelled results confirms that Eq. (8) can be used to predict the particle size distribution of the milled Fe – Mn – Si compound powders at different times. Comparing the Fe – Mn – Si master alloy powders with that of alumina, diamond, and quartz [34], the breakage rate constant of alumina, diamond, and quartz is around a few thousands of times higher than that of the Fe – Mn – Si master alloy powders. Alumina, diamond, and quartz could consequently be ground to much finer particle size. Fe – Mn –Si master alloy powders are tougher than alumina, diamond, and quartz powders, and agglomeration will occur in Fe – Mn – Si master alloy powders milled at longer times. Hence, it is difficult for Fe –Mn –Si master alloy powders to form very fine particles. The breakage rate constant is affected by many factors such as ball size, mill speed, size
Fig. 10. Comparison of experimental and simulating results in milled M1 powder for normalized oversize distribution; points are experimental data, and lines are model results according to Eq. (8).
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Fig. 11. Same as Fig. 10 for M3 powder.
and charge weight of feed materials, and liquid volume [19,34].
from the Swedish Foundation for Strategic Research, Sweden, is gratefully acknowledged. The authors would like to thank Ms. Inger Persson (Ho¨gana¨s, Sweden) for her help with the evaluation of powder properties.
5. Conclusions 1. Fine Fe– Mn –Si master alloy powders can be produced by mechanical ball milling from as-cast Fe – Mn – Si ingot. The mean particle size of the powders varies between 5 and 15 Am and depends on the compositions of Fe– Mn – Si master alloys. 2. Comparing the four alloys, 20% Si alloys are easier to crush and mill into fine powder compared to the 14% Si alloys. The effect of silicon content on the particle size distribution of milled Fe – Mn – Si master alloy powders is much more significant than that of manganese content. A finer final particle size can be obtained in the alloy powders with higher silicon compositions. 3. The particle size of milled powders decreases strongly after milling for 10 and 30 min. Agglomeration of small particles into large particles takes place in the alloy powders milled for longer times. In the agglomerated powders, there are more large particles compared to the powders without agglomeration. The optimum milling time of the Fe– Mn – Si master alloy powders seems to be around 60 min. 4. The milling process can be successfully described by classic batch-grinding equations based on the population balance model up to the start of the agglomeration.
Acknowledgements The funding support from the Swedish National Board for Technical Development (NUTEK), Sweden, as well as
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