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Computational study on grain growth in cemented carbides
International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40 www.elsevier.com/locate/ijrmhm
Computational study on grain growth in cemented carbides J. Kishino a b
a,*
, H. Nomura b, S.-G. Shin b, H. Matsubara b, T. Tanase
a
Mitsubishi Materials Corp, 1511 Furumagi, Ishige, Yuuki-gun, Ibaraki 300-2795, Japan Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Aichi 456-8587, Japan Received 20 September 2001; accepted 5 October 2001
Abstract Micro-grained cemented carbides are widely applied to the tools such as solid endmills and micro-drills. The knowledge on grain growth of carbides is very important for manufacturing micro-grained cemented carbides. In the present study, continuous and discontinuous grain growth in such cemented carbides is investigated using the Monte Carlo computer simulation technique. The Ostwald ripening process (solution/re-precipitation) and the grain boundary migration process are assumed in the simulation as grain growth mechanism. The effects of liquid phase fraction, grain boundary energy and an implanted coarse grain are examined. The results of these simulations qualitatively agree with experimental ones and suggest that distribution of liquid phase and WC/WC grain boundary energy as well as contamination by coarse grain are important factors controlling discontinuous grain growth in cemented carbides. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Cemented carbides; Simulation; Grain growth; WC; Grain boundary
1. Introduction In the last decade, a lot of attention has been paid to micro-grained cemented carbides as a material for sharp edged tools such as endmills and micro-drills. Tungsten carbide grains grow during liquid phase sintering and the grain size strongly affects the mechanical properties of the alloy. Therefore control of microstructure is very important to produce highly qualified carbide tools. The grain growth process in cemented carbides can be characterized by continuous and discontinuous ones. Continuous grain growth is recognized as a uniform growth of the individual grains. Discontinuous grain growth is known as an undesired formation of isolated coarse WC grains which grow faster and larger than the surrounding grains. In the production of micro-grained cemented carbides, controlling both continuous and discontinuous grain growth in the microstructure has to be taken into account. Especially, the isolated coarse grains deteriorates the performance of the material. One of the effective methods for controlling grain growth is doping grain growth inhibitors, such as VC and Cr3 C2 [1–3].
*
Corresponding author. Tel.: +81-297-42-7092; fax: +81-297-427094. E-mail address: [email protected] (J. Kishino).
The grain growth in liquid phase sintered materials, which is generally understood as a solution/re-precipitation process called Ostwald ripening, has often been studied from a theoretical point of view [4–9]. Most of studies assume that carbide grains are completely surrounded by a liquid phase. These classical theories of Ostwald ripening are not sufficient to explain the grain growth mechanism in cemented carbides [10–14], especially in the case of low binder content which is popular for industrial applications. Because in that case WC grains are not completely surrounded by a binder phase, but contact with neighboring grains. Simulation techniques seem useful to examine the effects of both solid/ liquid and solid/solid interface on grain growth behavior. In the present study, the Monte Carlo computer simulation technique is utilized to investigate continuous and discontinuous grain growth mechanisms in cemented carbides. Because grain growth simulation using the Monte Carlo method is considered to be useful for understanding the grain growth behavior in complicated systems [15–17]. In addition to the simulations, experiments on microstructures of WC–Co and WC–VC–Co systems are performed. Comparing the simulations to the experimental results, the grain growth mechanism is discussed with special focus on the presence of WC/WC grain boundaries.
0263-4368/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 1 ) 0 0 0 6 8 - 3
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2. Simulation method The grain growth simulation was carried out on the basis of the Potts model using the Monte Carlo method [18,19]. The temperature term in the Boltzman equation is set at zero. A two-dimensional lattice comprised of solid (WC) cell and liquid (Co binder phase) cell was used to simulate the microstructure of cemented carbides. The lattice size was 200 200 cells. The number of crystal orientations of solid particles, Q, was fixed at 64. Two kinds of mass transfer were assumed in the simulation algorithm. If a solid cell is selected in the array, the mass transfer proceeds through grain boundaries in the solid owing to the same way as the Potts model. If a liquid cell is selected, the mass transfer
through the liquid phase is designed in the algorithm as follows. The selected liquid cell changes to a solid cell with an arbitrary number of Q and the energy change ðDG1Þ is calculated, then the solid cell undergoes a random walk until it hits another solid cell without back steps in a liquid phase. The hit solid cell is changed to a liquid cell and the energy change ðDG2Þ is calculated again. If the total energy change is less than zero ðDG1 þ DG2 < 0Þ, the trial is successful; otherwise the trial is canceled. When a solid cell neighboring at least one liquid cell is selected, the same manner as above is carried out though the phase change is opposite. If a liquid cell neighboring only a liquid cell, the trial is canceled. This procedure is repeated for several hundred Monte Carlo steps (MCS). Refer to the reports [17] for the details.
Fig. 1. Simulated microstructure evolution for fl ¼ 10%, csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9 as a function of Monte Carlo steps: (a) 0; (b) 200; (c) 500; and (d) 1000 MCS.
J. Kishino et al. / International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40
The predominant parameters in the present simulation are the interface energy between a solid cell and liquid cell ðcsl Þ, grain boundary energy between solid cells ðcss Þ, which can be set low or high, and the liquid content (fl).
3. Materials and experimental procedures WC–Co and WC–VC–Co alloys were produced by powder metallurgical technique. WC and VC powders with an average particle size of about 1:5 lm and Co powder of 1:2 lm were used as starting powders. The content of Co was varied from 10 to 40 in volume percent. The atomic ratio of V=ðV þ CoÞ for WC–VC–Co alloy was fixed at 0.04. The carbon content of all alloys was in the higher side of the two phase region. The
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powders were ball-milled in ethanol for 48 h, dried in vacuum, sieved and then pressed. Green compacts of the mixed powders were sintered at 1673 K for 1 h in vacuum. Microstructures of these alloys were observed by scanning electron microscopy (SEM:S-800, HITACHI) and field emission typed high resolution transmission electron microscopy (FE-TEM:HF2000, HITACHI) equipped with energy dispersive X-ray spectrometer (EDS). The TEM specimens were prepared by the following procedure: spherical rods (3 mm in diameter) were cut into about 0.5 mm thick discs, mechanically ground to the thickness of about 0.1 mm, thinned to the thickness of about 0.05 mm by dimpling (Gatan Precision Dimple Grinder) and finally ion-milled (Gatan Duomill) using Ar ions. Nano probe EDS quantitative analysis was performed in the spot mode to accurately investigate grain boundary structure. The electron probe
Fig. 2. Simulated microstructures for csl ¼ 0:4, css1 ¼ 1:1, and css2 ¼ 0:9 at 1000 MCS as a function of liquid fraction: (a) 5%; (b) 10%; (c) 20%; and (d) 40%.
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was set to be 1 nm in diameter and was positioned onto WC/WC grain boundary.
4. Result and discussion 4.1. Grain growth in an un-doped system The simulation parameters are selected referring to the previous reports [17]. Fig. 1 is a series of simulated microstructures for fl ¼ 10%, csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9 as a function of Monte Carlo steps, where css1 and css2 are higher and lower solid/solid grain boundary energy, respectively. Two kinds of grain boundary energy are set to give reality to the grain boundary character. The values of csl , css1 and css2 are relative energy, which are chosen for grain growth modeling that the energy ratios, csl =css1 and csl =css2 , are below 0.5. This means that the
dihedral angle h is zero, because WC–Co cemented carbides are known to have high wettability [11]. On the other hand, the two types of mass transfer mechanism for grain growth are employed. One is a solution/re-precipitation mechanism through the liquid phase. The other is the mass transfer across the solid/ solid grain boundary. In Fig. 1, the solid phase and the liquid phase are represented by gray and black areas, respectively. The difference in darkness of gray area for the solid phase corresponds to the different grain orientation. Fig. 2 shows a series of simulated microstructures for csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9 at 1000 MCS as a function of liquid fraction. It is clear that the microstructure is strongly influenced by the liquid phase content. At 5% liquid phase content, the microstructure is relatively homogeneous. In contrast, at 10% liquid phase content, several preferentially grown grains are
Fig. 3. Microstructures of WC–(10–40) vol% Co sintered at 1673 K: (a) 10%; (b) 20%; (c) 30%; and (d) 40%.
J. Kishino et al. / International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40
observed, and a discontinuous microstructure is formed. In these cases, these are both solid/solid and solid/liquid interfaces. When a liquid phase with thickness of one cell exists between two solid particles, coalescence of particles easily takes place if their grain orientations are the same. At more than 20% liquid phase content, the microstructure is homogeneous, and the liquid phase perfectly surrounds the solid grains. These results would indicate that the grain growth at lower liquid phase content occurs through two types of mass transfer mechanisms, i.e. through solid/liquid interfaces and solid/solid grain boundaries. At higher liquid phase content, mass transfer via solid/liquid interfaces plays a major role in grain growth. Fig. 3 shows SEM images of the microstructures of WC–(10–40) vol% Co alloys. The contiguity of WC grains decrease with binder content, not reaching zero
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even at 40% Co content. In the alloy with 20% binder content, the microstructure is inhomogeneous. In contrast, the discontinuous grain growth is not observed in the alloys with 10% Co and more than 30% Co contents. These microstructures resemble the simulated grain growth behavior in Fig. 2, though the change in contiguity and the binder content which yields the discontinuous grain growth are different. These differences are considered to be caused by two dimension of the simulation. From these simulation and experimental results, the mechanism of discontinuous grain growth is proposed as follows. In the lower cobalt content, even if the dihedral angle h is zero, some grain boundaries of particles are not wetted. The co-existence of the wetted and unwetted grain boundaries plays an important role in the grain growth behavior. At the wetted grain boundary, the growth is pronounced by the effect of Ostwald
Fig. 4. Simulated microstructures with an implanted coarse grain as a function of Monte Carlo steps for fl ¼ 10%, csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9: (a) 0; (b) 200; (c) 500; and (d) 1000 MCS.
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ripening and, if the binder layer is thin, coalescence of grains. On the other hand, at the unwetted grain boundary, the growth is restricted by grain boundary migration. In other words, the localization of cobalt liquid phase could contribute to the discontinuous grain growth. Next, the effect of coarse grains on discontinuous microstructures was examined in the simulation. Some articles report that coarse WC particles in a green compact act as seeds for rapid grain growth [10]. Then, in a matrix with 10% fl was implanted a single solid grain with a diameter 18 times greater than the average of the matrix solid grains. At the same time, the implanted coarse grain is set to be surrounded by a liquid binder phase with thickness of 2 cells, and the energy condition of the simulation is the same as that of Fig. 1. Fig. 4 is a series of simulated microstructures as a function of Monte Carlo steps. As shown in Fig. 4, the
discontinuous grain growth occurs in the matrix similar to Fig. 1. Besides the implanted grain grows faster than the matrix grains through solution/re-precipitation and coalescence with neighboring grains. This result, which agrees with the result of the previous report [10], suggests that the presence of coarse grains in a fine grained matrix can be a reason for discontinuous growth in addition to the factors such as fl and css . Therefore, the contamination by coarse grains must be avoided in the manufacturing process of fine grained cemented carbides, especially with low cobalt content.
4.2. Grain growth in an inhibitor doped system A simulation for an inhibitor doped system is tried. In the previous study, Shin and Matsubara [14] reported
Fig. 5. Simulated microstructures for grain growth with fl ¼ 10%, csl ¼ 0:4, css1 ¼ 0:7 and css2 ¼ 0:6 as a function of Monte Carlo steps, assuming an inhibitor doped system: (a) 0; (b) 200; (c) 500; and (d) 1000 MCS.
J. Kishino et al. / International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40
that the contiguity of WC in VC doped WC–Co alloys was higher than that in non-doped alloys, which suggests that the wettability in VC doped alloy is reduced. Therefore, the values of grain boundary energy were chosen to give csl =css1 and csl =css2 to be above 0.5. Simulation results for grain growth with fl ¼ 10%, csl ¼ 0:4, css1 ¼ 0:7 and css2 ¼ 0:6 as a function of Monte Carlo steps is shown in Fig. 5. Fig. 6 indicates a series of simulated microstructures at 1000 MCS for the same energy condition as in Fig. 5 as a function of liquid content. These microstructures are quite different from the abovesimulated microstructures for the non-doped system (Figs. 1 and 2). The liquid phase exists in isolated pockets between interconnecting solid particles. Most of grains are only partly wetted by a liquid phase even in 40% liquid content. No discontinuous grain growth is expressed and the grain size slightly increase with liquid content.
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Fig. 7 shows the experimental microstructures of VC doped WC–Co alloys. Regardless of binder content, the continuous grain growth of WC particles is observed. In the low binder alloy, the addition of VC effectively restricts the grain growth. However, the effects diminish with increase in binder content. This grain growth behavior is similar to the simulated result. This might indicate that the addition of VC decreases grain boundary energy, css , and then WC grains have high contiguity as reported [14]. In such a case, the growth rate of WC grains is considered to be mainly controlled by the grain boundary migration. 4.3. Observation of WC/WC grain boundary In the previous sections, both simulation and experimental results suggest that the existence of WC/WC grain
Fig. 6. Simulated microstructures for csl ¼ 0:4; css1 ¼ 0:7 and css2 ¼ 0:6 at 1000 MCS as a function of liquid content: (a) 10%; (b) 20%; (c) 30%; and (d) 40%.
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Fig. 7. Microstructures of VC doped WC–(10–40) vol% Co sintered at 1673 K: (a) 10%; (b) 20%; (c) 30%; and (d) 40%.
boundary has a remarkably strong influence on the mechanism of discontinuous grain growth and grain growth inhibition. However, in spite of many previous studies on the grain boundaries of cemented carbides, there are a lot of controversial discussions concerning the grain boundary structure. Some TEM studies confirmed the existence in contiguous grain boundaries free from a cobalt phase [21–23]. On the contrary, Egami et al. and Sharma et al. [24,25] have reported that a cobalt phase layer is present between WC grains. Therefore, in the present study, the grain boundary structure was in detail investigated by TEM–EDS in order to clarify whether the contiguous grain boundaries are present or not. Fig. 8 shows the lattice image of a WC/WC grain boundary in a WC–VC–10 vol% Co alloy. According to the coincidence site lattice (CSL) theory, this grain boundary is identified as a R2 coincidence boundary. In
this image, no other phase is observed at the grain boundary. However, as shown in Fig. 9, EDS analysis of the grain boundary detects cobalt and vanadium element only at the grain boundary. Figs. 8 and 9 indicate that this type of WC/WC grain boundary is contiguous at atomic level where Co and V atoms co-segregate. The grain boundary structure in a non-doped WC–Co alloy is also analyzed. The TEM and EDS results, which are not shown in the present paper, indicate that the cobalt also segregates at the contiguous WC/WC grain boundary. Therefore, it is considered that cobalt segregation is not so effective as vanadium for grain growth inhibition according to the results in Fig. 3 and many investigations [10,14,20]. The grain boundary segregation of, above all, vanadium atoms could decrease the grain boundary energy and wettability of boundaries, and then both continuous and discontinuous grain growth is
J. Kishino et al. / International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40
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Fig. 8. High resolution electron micrograph of a WC/WC grain boundary in a VC doped WC–Co alloy. Left-side crystal is aligned with its h0 0 0 1i axis parallel to the electron beam, and right-side crystal h1 2 1 0i axis.
the grain growth model of cemented carbides. Further refinements are needed: three-dimensional grain growth, grain growth during densification, effect of carbon content on grain growth, etc.
5. Conclusion
Fig. 9. EDS analysis of the WC/WC grain boundary in Fig. 8.
considered to be inhibited by low mobility of the vanadium segregated grain boundary. The present simulation model appears qualitatively to reproduce some features of experimentally observed grain growth behavior in cemented carbides. There are, however, many unquantified variables and kinetics in
The computer simulation based on the Monte Carlo method was performed in order to investigate continuous and discontinuous grain growth in cemented carbides. The Ostwald ripening process (solution/ re-precipitation) and the grain boundary migration process were assumed in the simulation as grain growth mechanism. The effects of liquid phase content, an implanted coarse grain and grain boundary energy are examined. The results obtained were qualitatively agreed with experimental results. The results of these simulations suggest that distribution of liquid phase and grain boundary energy balance as well as contamination by coarse grains are important factors controlling discontinuous grain
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growth in a WC–Co system. In a VC doped WC–Co system, in particular, grain boundary energy was considered to be a significant factor for grain growth inhibition. The grain boundary segregation of V, which was revealed by TEM–EDS analysis, could affect the energy, resulting in low mobility of the WC/WC grain boundary and leading to remarkable grain growth inhibition. References [1] Suzuki H, Fuke Y, Hayashi K. J Jpn Soc Powder Powder Metall 1972;19:106. [2] Hayashi K, Fuke Y, Suzuki H. J Jpn Soc Powder Powder Metall 1972;19:67. [3] Bock A, Schubert WD, Lux B. Powder Met Int 1992;24:20. [4] Greenwood GW. Acta Metall 1956;4:243. [5] Lifshitz IM, Slyozov VV. J Phys Chem Solids 1961;19:35. [6] Wagner C. Z Electrochem 1961;65:581. [7] Sarian S, Weart HW. J Appl Phys 1966;37:1675. [8] Ardell AJ. Acta Metall 1972;20:61. [9] Voorhees PW, Glicksman ME. Metall Trans A 1984;15:1081. [10] Exner HE. In: Viswanadham RF, Rowcliffe DJ, Gurland J, editors. Science of Hard Materials. New York: Plenum Press; 1983. p. 233.
[11] Warren R, Waldron MB. Powder Metall 1972;15:166. [12] Almond EA, Roebuck B. Int J Ref Met Hard Mater 1987;6:137. [13] Matsubara H, Shin SG, Sakuma T. Trans Jpn Inst Met 1991;32:951. [14] Shin SG, Matsubara. In: German RM, Messing GL, Cornwell RG, editors. Sintering Technology. New York: Marcel Dekker; 1996, p. 157. [15] Tajika M, Matsubara H, Rafaniello W. J Ceram Soc Jpn 1997;105:928. [16] Okamoto Y, Hirosaki N, Matsubara H. J Ceram Soc Jpn 1999;107:109. [17] Matsubara H, Brook RJ. In: Koumoto K, Sheppard LM, Matsubara H, editors. Ceramic Transactions, vol. 71. Westerville, OH, USA: American Ceramics Society; 1996, p. 403. [18] Anderson MP, Srolovitz DJ, Grest GS, Sahni PS. Acta Metall 1984;32:783. [19] Grest GS, Srolovitz DJ, Anderson MP. Acta Metall 1985;33:509. [20] Schubert WD, Bock A, Lux B. Int J Ref Met Hard Mater 1995;13:281. [21] Suzuki T, Shibuki K, Ikuhara Y. Philos Mag Lett 1995;71:289. [22] Jayaram V, Sinclair R. J Am Ceram Soc 1983;66:137. [23] Vicens J, Benjdir M, Nouet G, Dubon A, Laval JY. J Mater Sci 1994;29:987. [24] Egami A, Ehira M, Machida M. In: Bildstein H, Eck R, editors. Proceedings of the 13th International Plansee Seminar, vol. 3. Reutte: Plansee AG; 1993. p. 639. [25] Sharma NK, Ward ID, Fraser HL, Williams WS. J Am Ceram Soc 1980;63:194.
Computational study on grain growth in cemented carbides J. Kishino a b
a,*
, H. Nomura b, S.-G. Shin b, H. Matsubara b, T. Tanase
a
Mitsubishi Materials Corp, 1511 Furumagi, Ishige, Yuuki-gun, Ibaraki 300-2795, Japan Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Aichi 456-8587, Japan Received 20 September 2001; accepted 5 October 2001
Abstract Micro-grained cemented carbides are widely applied to the tools such as solid endmills and micro-drills. The knowledge on grain growth of carbides is very important for manufacturing micro-grained cemented carbides. In the present study, continuous and discontinuous grain growth in such cemented carbides is investigated using the Monte Carlo computer simulation technique. The Ostwald ripening process (solution/re-precipitation) and the grain boundary migration process are assumed in the simulation as grain growth mechanism. The effects of liquid phase fraction, grain boundary energy and an implanted coarse grain are examined. The results of these simulations qualitatively agree with experimental ones and suggest that distribution of liquid phase and WC/WC grain boundary energy as well as contamination by coarse grain are important factors controlling discontinuous grain growth in cemented carbides. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Cemented carbides; Simulation; Grain growth; WC; Grain boundary
1. Introduction In the last decade, a lot of attention has been paid to micro-grained cemented carbides as a material for sharp edged tools such as endmills and micro-drills. Tungsten carbide grains grow during liquid phase sintering and the grain size strongly affects the mechanical properties of the alloy. Therefore control of microstructure is very important to produce highly qualified carbide tools. The grain growth process in cemented carbides can be characterized by continuous and discontinuous ones. Continuous grain growth is recognized as a uniform growth of the individual grains. Discontinuous grain growth is known as an undesired formation of isolated coarse WC grains which grow faster and larger than the surrounding grains. In the production of micro-grained cemented carbides, controlling both continuous and discontinuous grain growth in the microstructure has to be taken into account. Especially, the isolated coarse grains deteriorates the performance of the material. One of the effective methods for controlling grain growth is doping grain growth inhibitors, such as VC and Cr3 C2 [1–3].
*
Corresponding author. Tel.: +81-297-42-7092; fax: +81-297-427094. E-mail address: [email protected] (J. Kishino).
The grain growth in liquid phase sintered materials, which is generally understood as a solution/re-precipitation process called Ostwald ripening, has often been studied from a theoretical point of view [4–9]. Most of studies assume that carbide grains are completely surrounded by a liquid phase. These classical theories of Ostwald ripening are not sufficient to explain the grain growth mechanism in cemented carbides [10–14], especially in the case of low binder content which is popular for industrial applications. Because in that case WC grains are not completely surrounded by a binder phase, but contact with neighboring grains. Simulation techniques seem useful to examine the effects of both solid/ liquid and solid/solid interface on grain growth behavior. In the present study, the Monte Carlo computer simulation technique is utilized to investigate continuous and discontinuous grain growth mechanisms in cemented carbides. Because grain growth simulation using the Monte Carlo method is considered to be useful for understanding the grain growth behavior in complicated systems [15–17]. In addition to the simulations, experiments on microstructures of WC–Co and WC–VC–Co systems are performed. Comparing the simulations to the experimental results, the grain growth mechanism is discussed with special focus on the presence of WC/WC grain boundaries.
0263-4368/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 1 ) 0 0 0 6 8 - 3
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J. Kishino et al. / International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40
2. Simulation method The grain growth simulation was carried out on the basis of the Potts model using the Monte Carlo method [18,19]. The temperature term in the Boltzman equation is set at zero. A two-dimensional lattice comprised of solid (WC) cell and liquid (Co binder phase) cell was used to simulate the microstructure of cemented carbides. The lattice size was 200 200 cells. The number of crystal orientations of solid particles, Q, was fixed at 64. Two kinds of mass transfer were assumed in the simulation algorithm. If a solid cell is selected in the array, the mass transfer proceeds through grain boundaries in the solid owing to the same way as the Potts model. If a liquid cell is selected, the mass transfer
through the liquid phase is designed in the algorithm as follows. The selected liquid cell changes to a solid cell with an arbitrary number of Q and the energy change ðDG1Þ is calculated, then the solid cell undergoes a random walk until it hits another solid cell without back steps in a liquid phase. The hit solid cell is changed to a liquid cell and the energy change ðDG2Þ is calculated again. If the total energy change is less than zero ðDG1 þ DG2 < 0Þ, the trial is successful; otherwise the trial is canceled. When a solid cell neighboring at least one liquid cell is selected, the same manner as above is carried out though the phase change is opposite. If a liquid cell neighboring only a liquid cell, the trial is canceled. This procedure is repeated for several hundred Monte Carlo steps (MCS). Refer to the reports [17] for the details.
Fig. 1. Simulated microstructure evolution for fl ¼ 10%, csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9 as a function of Monte Carlo steps: (a) 0; (b) 200; (c) 500; and (d) 1000 MCS.
J. Kishino et al. / International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40
The predominant parameters in the present simulation are the interface energy between a solid cell and liquid cell ðcsl Þ, grain boundary energy between solid cells ðcss Þ, which can be set low or high, and the liquid content (fl).
3. Materials and experimental procedures WC–Co and WC–VC–Co alloys were produced by powder metallurgical technique. WC and VC powders with an average particle size of about 1:5 lm and Co powder of 1:2 lm were used as starting powders. The content of Co was varied from 10 to 40 in volume percent. The atomic ratio of V=ðV þ CoÞ for WC–VC–Co alloy was fixed at 0.04. The carbon content of all alloys was in the higher side of the two phase region. The
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powders were ball-milled in ethanol for 48 h, dried in vacuum, sieved and then pressed. Green compacts of the mixed powders were sintered at 1673 K for 1 h in vacuum. Microstructures of these alloys were observed by scanning electron microscopy (SEM:S-800, HITACHI) and field emission typed high resolution transmission electron microscopy (FE-TEM:HF2000, HITACHI) equipped with energy dispersive X-ray spectrometer (EDS). The TEM specimens were prepared by the following procedure: spherical rods (3 mm in diameter) were cut into about 0.5 mm thick discs, mechanically ground to the thickness of about 0.1 mm, thinned to the thickness of about 0.05 mm by dimpling (Gatan Precision Dimple Grinder) and finally ion-milled (Gatan Duomill) using Ar ions. Nano probe EDS quantitative analysis was performed in the spot mode to accurately investigate grain boundary structure. The electron probe
Fig. 2. Simulated microstructures for csl ¼ 0:4, css1 ¼ 1:1, and css2 ¼ 0:9 at 1000 MCS as a function of liquid fraction: (a) 5%; (b) 10%; (c) 20%; and (d) 40%.
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was set to be 1 nm in diameter and was positioned onto WC/WC grain boundary.
4. Result and discussion 4.1. Grain growth in an un-doped system The simulation parameters are selected referring to the previous reports [17]. Fig. 1 is a series of simulated microstructures for fl ¼ 10%, csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9 as a function of Monte Carlo steps, where css1 and css2 are higher and lower solid/solid grain boundary energy, respectively. Two kinds of grain boundary energy are set to give reality to the grain boundary character. The values of csl , css1 and css2 are relative energy, which are chosen for grain growth modeling that the energy ratios, csl =css1 and csl =css2 , are below 0.5. This means that the
dihedral angle h is zero, because WC–Co cemented carbides are known to have high wettability [11]. On the other hand, the two types of mass transfer mechanism for grain growth are employed. One is a solution/re-precipitation mechanism through the liquid phase. The other is the mass transfer across the solid/ solid grain boundary. In Fig. 1, the solid phase and the liquid phase are represented by gray and black areas, respectively. The difference in darkness of gray area for the solid phase corresponds to the different grain orientation. Fig. 2 shows a series of simulated microstructures for csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9 at 1000 MCS as a function of liquid fraction. It is clear that the microstructure is strongly influenced by the liquid phase content. At 5% liquid phase content, the microstructure is relatively homogeneous. In contrast, at 10% liquid phase content, several preferentially grown grains are
Fig. 3. Microstructures of WC–(10–40) vol% Co sintered at 1673 K: (a) 10%; (b) 20%; (c) 30%; and (d) 40%.
J. Kishino et al. / International Journal of Refractory Metals & Hard Materials 20 (2002) 31–40
observed, and a discontinuous microstructure is formed. In these cases, these are both solid/solid and solid/liquid interfaces. When a liquid phase with thickness of one cell exists between two solid particles, coalescence of particles easily takes place if their grain orientations are the same. At more than 20% liquid phase content, the microstructure is homogeneous, and the liquid phase perfectly surrounds the solid grains. These results would indicate that the grain growth at lower liquid phase content occurs through two types of mass transfer mechanisms, i.e. through solid/liquid interfaces and solid/solid grain boundaries. At higher liquid phase content, mass transfer via solid/liquid interfaces plays a major role in grain growth. Fig. 3 shows SEM images of the microstructures of WC–(10–40) vol% Co alloys. The contiguity of WC grains decrease with binder content, not reaching zero
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even at 40% Co content. In the alloy with 20% binder content, the microstructure is inhomogeneous. In contrast, the discontinuous grain growth is not observed in the alloys with 10% Co and more than 30% Co contents. These microstructures resemble the simulated grain growth behavior in Fig. 2, though the change in contiguity and the binder content which yields the discontinuous grain growth are different. These differences are considered to be caused by two dimension of the simulation. From these simulation and experimental results, the mechanism of discontinuous grain growth is proposed as follows. In the lower cobalt content, even if the dihedral angle h is zero, some grain boundaries of particles are not wetted. The co-existence of the wetted and unwetted grain boundaries plays an important role in the grain growth behavior. At the wetted grain boundary, the growth is pronounced by the effect of Ostwald
Fig. 4. Simulated microstructures with an implanted coarse grain as a function of Monte Carlo steps for fl ¼ 10%, csl ¼ 0:4, css1 ¼ 1:1 and css2 ¼ 0:9: (a) 0; (b) 200; (c) 500; and (d) 1000 MCS.
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ripening and, if the binder layer is thin, coalescence of grains. On the other hand, at the unwetted grain boundary, the growth is restricted by grain boundary migration. In other words, the localization of cobalt liquid phase could contribute to the discontinuous grain growth. Next, the effect of coarse grains on discontinuous microstructures was examined in the simulation. Some articles report that coarse WC particles in a green compact act as seeds for rapid grain growth [10]. Then, in a matrix with 10% fl was implanted a single solid grain with a diameter 18 times greater than the average of the matrix solid grains. At the same time, the implanted coarse grain is set to be surrounded by a liquid binder phase with thickness of 2 cells, and the energy condition of the simulation is the same as that of Fig. 1. Fig. 4 is a series of simulated microstructures as a function of Monte Carlo steps. As shown in Fig. 4, the
discontinuous grain growth occurs in the matrix similar to Fig. 1. Besides the implanted grain grows faster than the matrix grains through solution/re-precipitation and coalescence with neighboring grains. This result, which agrees with the result of the previous report [10], suggests that the presence of coarse grains in a fine grained matrix can be a reason for discontinuous growth in addition to the factors such as fl and css . Therefore, the contamination by coarse grains must be avoided in the manufacturing process of fine grained cemented carbides, especially with low cobalt content.
4.2. Grain growth in an inhibitor doped system A simulation for an inhibitor doped system is tried. In the previous study, Shin and Matsubara [14] reported
Fig. 5. Simulated microstructures for grain growth with fl ¼ 10%, csl ¼ 0:4, css1 ¼ 0:7 and css2 ¼ 0:6 as a function of Monte Carlo steps, assuming an inhibitor doped system: (a) 0; (b) 200; (c) 500; and (d) 1000 MCS.
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that the contiguity of WC in VC doped WC–Co alloys was higher than that in non-doped alloys, which suggests that the wettability in VC doped alloy is reduced. Therefore, the values of grain boundary energy were chosen to give csl =css1 and csl =css2 to be above 0.5. Simulation results for grain growth with fl ¼ 10%, csl ¼ 0:4, css1 ¼ 0:7 and css2 ¼ 0:6 as a function of Monte Carlo steps is shown in Fig. 5. Fig. 6 indicates a series of simulated microstructures at 1000 MCS for the same energy condition as in Fig. 5 as a function of liquid content. These microstructures are quite different from the abovesimulated microstructures for the non-doped system (Figs. 1 and 2). The liquid phase exists in isolated pockets between interconnecting solid particles. Most of grains are only partly wetted by a liquid phase even in 40% liquid content. No discontinuous grain growth is expressed and the grain size slightly increase with liquid content.
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Fig. 7 shows the experimental microstructures of VC doped WC–Co alloys. Regardless of binder content, the continuous grain growth of WC particles is observed. In the low binder alloy, the addition of VC effectively restricts the grain growth. However, the effects diminish with increase in binder content. This grain growth behavior is similar to the simulated result. This might indicate that the addition of VC decreases grain boundary energy, css , and then WC grains have high contiguity as reported [14]. In such a case, the growth rate of WC grains is considered to be mainly controlled by the grain boundary migration. 4.3. Observation of WC/WC grain boundary In the previous sections, both simulation and experimental results suggest that the existence of WC/WC grain
Fig. 6. Simulated microstructures for csl ¼ 0:4; css1 ¼ 0:7 and css2 ¼ 0:6 at 1000 MCS as a function of liquid content: (a) 10%; (b) 20%; (c) 30%; and (d) 40%.
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Fig. 7. Microstructures of VC doped WC–(10–40) vol% Co sintered at 1673 K: (a) 10%; (b) 20%; (c) 30%; and (d) 40%.
boundary has a remarkably strong influence on the mechanism of discontinuous grain growth and grain growth inhibition. However, in spite of many previous studies on the grain boundaries of cemented carbides, there are a lot of controversial discussions concerning the grain boundary structure. Some TEM studies confirmed the existence in contiguous grain boundaries free from a cobalt phase [21–23]. On the contrary, Egami et al. and Sharma et al. [24,25] have reported that a cobalt phase layer is present between WC grains. Therefore, in the present study, the grain boundary structure was in detail investigated by TEM–EDS in order to clarify whether the contiguous grain boundaries are present or not. Fig. 8 shows the lattice image of a WC/WC grain boundary in a WC–VC–10 vol% Co alloy. According to the coincidence site lattice (CSL) theory, this grain boundary is identified as a R2 coincidence boundary. In
this image, no other phase is observed at the grain boundary. However, as shown in Fig. 9, EDS analysis of the grain boundary detects cobalt and vanadium element only at the grain boundary. Figs. 8 and 9 indicate that this type of WC/WC grain boundary is contiguous at atomic level where Co and V atoms co-segregate. The grain boundary structure in a non-doped WC–Co alloy is also analyzed. The TEM and EDS results, which are not shown in the present paper, indicate that the cobalt also segregates at the contiguous WC/WC grain boundary. Therefore, it is considered that cobalt segregation is not so effective as vanadium for grain growth inhibition according to the results in Fig. 3 and many investigations [10,14,20]. The grain boundary segregation of, above all, vanadium atoms could decrease the grain boundary energy and wettability of boundaries, and then both continuous and discontinuous grain growth is
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Fig. 8. High resolution electron micrograph of a WC/WC grain boundary in a VC doped WC–Co alloy. Left-side crystal is aligned with its h0 0 0 1i axis parallel to the electron beam, and right-side crystal h1 2 1 0i axis.
the grain growth model of cemented carbides. Further refinements are needed: three-dimensional grain growth, grain growth during densification, effect of carbon content on grain growth, etc.
5. Conclusion
Fig. 9. EDS analysis of the WC/WC grain boundary in Fig. 8.
considered to be inhibited by low mobility of the vanadium segregated grain boundary. The present simulation model appears qualitatively to reproduce some features of experimentally observed grain growth behavior in cemented carbides. There are, however, many unquantified variables and kinetics in
The computer simulation based on the Monte Carlo method was performed in order to investigate continuous and discontinuous grain growth in cemented carbides. The Ostwald ripening process (solution/ re-precipitation) and the grain boundary migration process were assumed in the simulation as grain growth mechanism. The effects of liquid phase content, an implanted coarse grain and grain boundary energy are examined. The results obtained were qualitatively agreed with experimental results. The results of these simulations suggest that distribution of liquid phase and grain boundary energy balance as well as contamination by coarse grains are important factors controlling discontinuous grain
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growth in a WC–Co system. In a VC doped WC–Co system, in particular, grain boundary energy was considered to be a significant factor for grain growth inhibition. The grain boundary segregation of V, which was revealed by TEM–EDS analysis, could affect the energy, resulting in low mobility of the WC/WC grain boundary and leading to remarkable grain growth inhibition. References [1] Suzuki H, Fuke Y, Hayashi K. J Jpn Soc Powder Powder Metall 1972;19:106. [2] Hayashi K, Fuke Y, Suzuki H. J Jpn Soc Powder Powder Metall 1972;19:67. [3] Bock A, Schubert WD, Lux B. Powder Met Int 1992;24:20. [4] Greenwood GW. Acta Metall 1956;4:243. [5] Lifshitz IM, Slyozov VV. J Phys Chem Solids 1961;19:35. [6] Wagner C. Z Electrochem 1961;65:581. [7] Sarian S, Weart HW. J Appl Phys 1966;37:1675. [8] Ardell AJ. Acta Metall 1972;20:61. [9] Voorhees PW, Glicksman ME. Metall Trans A 1984;15:1081. [10] Exner HE. In: Viswanadham RF, Rowcliffe DJ, Gurland J, editors. Science of Hard Materials. New York: Plenum Press; 1983. p. 233.
[11] Warren R, Waldron MB. Powder Metall 1972;15:166. [12] Almond EA, Roebuck B. Int J Ref Met Hard Mater 1987;6:137. [13] Matsubara H, Shin SG, Sakuma T. Trans Jpn Inst Met 1991;32:951. [14] Shin SG, Matsubara. In: German RM, Messing GL, Cornwell RG, editors. Sintering Technology. New York: Marcel Dekker; 1996, p. 157. [15] Tajika M, Matsubara H, Rafaniello W. J Ceram Soc Jpn 1997;105:928. [16] Okamoto Y, Hirosaki N, Matsubara H. J Ceram Soc Jpn 1999;107:109. [17] Matsubara H, Brook RJ. In: Koumoto K, Sheppard LM, Matsubara H, editors. Ceramic Transactions, vol. 71. Westerville, OH, USA: American Ceramics Society; 1996, p. 403. [18] Anderson MP, Srolovitz DJ, Grest GS, Sahni PS. Acta Metall 1984;32:783. [19] Grest GS, Srolovitz DJ, Anderson MP. Acta Metall 1985;33:509. [20] Schubert WD, Bock A, Lux B. Int J Ref Met Hard Mater 1995;13:281. [21] Suzuki T, Shibuki K, Ikuhara Y. Philos Mag Lett 1995;71:289. [22] Jayaram V, Sinclair R. J Am Ceram Soc 1983;66:137. [23] Vicens J, Benjdir M, Nouet G, Dubon A, Laval JY. J Mater Sci 1994;29:987. [24] Egami A, Ehira M, Machida M. In: Bildstein H, Eck R, editors. Proceedings of the 13th International Plansee Seminar, vol. 3. Reutte: Plansee AG; 1993. p. 639. [25] Sharma NK, Ward ID, Fraser HL, Williams WS. J Am Ceram Soc 1980;63:194.