2024 Volume 65 Issue 10 Pages 1224-1233
Liquid phase sintering behavior of metal-glass system is experimentally and numerically analyzed. From the experimental observation, glass wets metal surfaces and assists the metal particles rearrangement, which is very important for annihilating pores. From the experiment, the amount of glass influences not only on the porosity but also on the grain growth behavior significantly. The sintering behavior is well reproduced by computational study by using Monte Carlo method with experimentally obtained surface energies of metal-glass system. The numerical study suggests that the frequency factor of Ostwald should be smaller than that of solid grain growth in this metal-glass powder system. Finally, this study suggests that spatial distribution is very important for grain growth. Although glass prevents the metal particle contact, the glass assists the metal particles rearrangement that contributes to metal grain growth.
This Paper was Originally Published in J. Jpn. Soc. Powder Powder Metallurgy 69 (2022) 239–248.
The metal-glass composites are widely employed in the industrial use by powder metallurgy such as metal electrode of electric parts that composed of dielectric materials. The densification of metal electrode is performed at lower sintering temperature compared to ceramics in order to avoid the reduction of sintered ceramics [1], where the ceramics are sintered in in advance. For this reason, copper or silver is used, since their sintering temperature is relatively lower compared to ceramics. The glass powder in these metal electrodes is liquefied at sintering temperature [2, 3]. This makes sintering temperature of metal-glass system decrease compared to the original pure metals [1]. The sintering of metal-glass system has been treated as the sintering in liquid (namely, liquid phase sintering) [4–6], but some studies do not clearly state as liquid phase sintering [1, 7]. In addition, the grain growth behavior by the solution-precipitation (Ostwald ripening) has been reported in condition of large glass fraction [8, 9], whereas the Ostwald is ruled out in case of low glass fraction [6]. Furthermore, the dependence of sintering behavior of the metal-glass system on materials of metal or glass, their composition and sintering temperatures, makes it impossible to control the sintering behavior precisely only by experiment. From these backgrounds, coupled analysis by experiment and numerical simulation is promising.
The sintering simulation methods (principles) are categorized into micro to macro-scales. The Molecular Dynamics Method [10] and Phase Field Method [11] in micro-scale are not always suitable because of the computational demanding and difficulty to incorporate difficult physics of complex systems. On the contrary, the macro-scale finite element method [12] for sintering deformation analysis lacks the resolution of microstructure analysis. Compared to these methods, the Monte Carlo (MC) method in micro scale do not explicitly incorporate characteristics of materials in quantitative, whereas it makes relatively easy to handle different physics in the complex system simultaneously. It also contributes to reduce computational demand. Recently, MC simulation for liquid-phase sintering is reported by Matsumoto and Matsubara et al. [13]. This MC simulation method is expected to be applied to the designing of industrial process or the development of new materials. Simultaneously, this MC simulation seems useful for the analysis of liquid sintering of metal-glass system focused in this study, however, the powder metallurgy of glass-liquid system has not been studied by MC simulation.
In this study, firstly, the densification behavior of metal-glass system is experimentally investigated. Furthermore, the grain growth behavior of the copper or silver containing relatively small amount of glass system is experimentally observed, where the grain growth behavior of metals in such small amount of glass has not been reported in detail. Through this study, the simulation microstructure by MC for metal-glass system is shown to be reasonable compared to that experimental liquid phase sintering. Finally, dominant mechanism of grain growth of metal-glass system in this study material is attributed to solid diffusion between the solid grain boundaries rather than Ostwald ripening. The contribution of metal particle rearrangement to the increment of solid grain boundaries is also shown by this study.
Table 1 shows the materials (symbols and compositions) and the sintering temperature. Copper or silver particles with an average diameter of 3.0 µm were used for metal. ZnO·B2O3·SiO2 powder with a median particle diameter of 1.5 µm with softening temperature 589°C was used for glass. For copper-glass system, the volume fraction of glass used were 0, 7.0, 13.0 and 19.0% and were designated as CuG-0E, CuG-7E, CuG-13E and CuG-19E, respectively. Each of these mixed powders were dry ground in a mortar. Next, cylinder shape green compaction was made by compressing 0.70 g of mixed powder to axial direction using a 12.0 mm diameter mold. Each green compaction was then sintered at 600, 650 and 750°C for 3 hours in 0.1% hydrogen/99.9% nitrogen atmosphere to obtain sintered body. The same procedures were used for silver-glass system, except the sintering temperature was 585, 700 and 750°C. The glass volume fraction 0–19.0% were designated as AgG-0E, AgG-7E, AgG-13E and AgG-19E, respectively.
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The sintered specimen at each temperature was polished to half height. The polished face was observed by SEM and porosity (pores) was obtained from the SEM photograph. While particle shape is obtained from the SEM photograph, their crystal grain cannot be obtained. Validation study needs crystal grain observation since crystal orientation is taken into consideration in the simulation algorithm. Therefore, in this study, the polished face was cut to be 20 µm width and 15 µm depth, perpendicular to the polished face with FIB (Focused Ion Beam), then SIM (Scanning Ion Microscope) [14] images were obtained to contrast the cross section with the crystal grain. The electric current density of the SIM was set lower than that of FIB so that bare cross section would not be damaged. The secondary electron image was obtained using Ga ion sources. Then, the relative crystal grain size of the SIM photographs was visually compared by eyes.
2.2 Simulation method (1) ModelIn this study, random walk is performed from each calculation cell. The microstructural evolution is progressed in direction to reduce the total energy of the system, where the success or failure of each trial is judged from the energy change of the whole system caused by the exchange of the cells. For detail, see literature by Matsumoto et al. [13]. For the solid grain growth trial, when randomly selected and their neighbor cells are both solid and have different crystal orientation Q, the crystal orientation of the one exchange to meet another. As a result, grain growth is performed. For the solid phase sintering, random walk is performed in solid parts starting from a pore cell. When the random walked pore cell hits the solid grain boundary, the pore is annihilated. Simultaneously, the starting pore is exchanged to solid phase, while solid cell at the outermost surface in calculation region is exchanged to pore. The wetting of the solid phase is expressed with an algorithm [13] that exchanging the liquid or pore itself cell who’s neighbor is solid. The rearrangement of particle by liquid is expressed with an algorithm [13] that shifts whole related particle rather than one cell. The solution-precipitation is expressed with an algorithm [13] that makes the solid diffuse in the liquid part and precipitates on another solid (Ostwald ripening).
(2) ConditionsSimulation conditions are shown in Table 2. The calculation region is 100 × 100 × 100 cells. The surface 5 pore cells of the calculation region for each direction is assigned as pore, in order to express outer space of the specimen. Internal 65 × 65 × 65 cells of the calculation region is used for the evaluation of the solid grain size and the relative density. The contiguity (Css) between the solid phase is calculated by Css = 2Nss/(2Nss + Nsl), where Nss and Nsl represent the number of solid grain boundaries and solid-liquid interfaces, respectively. The glass fractions by volume are 0, 7.0, 13.0 and 19.0% for copper-glass system. These four conditions are designated as CuG-0S, CuG-7S, CuG-13S and CuG-19S, respectively. Similarly, these glass fraction conditions for silver-glass system are designated as AgG-0S, AgG-7S, AgG-13S and AgG-19S, respectively. Each discrete cells are assigned to solid or liquid or pore phase. Each solid cell is assigned a natural number between 1 and 64 which represents the crystal orientation (Q). The cell at the different phase interface, excess energies (γ) are inputted, where γSL, γSV, γLV and γGB are interface of solid-liquid, solid-pore, liquid-pore and solids with different Q, respectively. The average grain size 4.7 cells and porosity 53.1% are used as initial microstructure. The initial simulation microstructures are prepared to have same cell configuration between different glass fraction conditions by numerically converting a part of solid cell to glass cell.
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Next, surface energy and frequency factors are described. First, the surface energies are explained below. The holding temperatures of initial 0–3000 and later half of 3001–6000 Monte Carlo Steps (referred to as MCS) for copper system are 650 and 750°C, respectively. In case of liquid phase sintering, energy balance is given as as γSV = γSL + γLV cos θ, where γSV, γLV, γSL and θ are interface energies between solid-gas, liquid-gas, solid-liquid and contact angle, respectively. Therefore, when γSV = 1.2, γLV = 1.1 and γSL = 0.4 are assigned, the experimentally observed dihedral angle (25°) of glass on surface of copper specimen as described later is given. In addition, solid boundary is expressed as γGB = 2γSL cos(ϕ/2) by using interface energies of boundary γGB, solid-liquid γSL and dihedral angle ϕ. Therefore, in case γGB > 2γSL condition, the solid grain boundaries are easily wetted. In this study, from the experimentally observed microstructure described later, γGB = 1.0 and γSL = 0.4 are inputted to satisfy γGB > 2γSL, so that liquid relatively penetrates the solid grain boundary with ease. On the other hand, the holding temperatures of initial 0–3000 and later half of 3001–6000 MCS for silver system are 585 and 750°C, respectively. At initial half of 0–3000 MCS who’s temperature is below the glass softening point, glass is non active solid in this simulation, where interface energy is not assigned to glass. In contrary, at later half of 3001–6000 MCS, the interface energy is assigned to glass to satisfy the experimentally observed contact angle (25°) as described later.
Next, frequency factor is described. The frequency factors for solid grain growth, pore sink at the grain boundary, Ostwald ripening, rearrangement of solid particle by liquid and liquid phase wetting to solid are given by FGG, FSink, FOST, Fra, Flhd and Fphd, respectively. The absolute value of these frequency factors are between 0–1. When the frequency factor of solid grain growth (FGG) is higher than that of pore sink (Fsink), pore remains at solid grain boundary with lenticular shape in literature study [15]. The experimentally observed microstructure of zero glass fraction condition in this study, the pores were observed at triple junction rather than solid grain boundaries as described later. Therefore, higher pore sink frequency (Fsink) compared to solid grain growth factor (FGG) is inputted. These frequency factors (Fsink, FGG) of zero liquid fraction are inputted to these frequency factors of liquid containing conditions, where absolute values are same even if glass fractions are different. The frequency factor of solid particle rearrangement by liquid phase (Fra) is empirically determined. The frequency factor of Ostwald ripening (FOST) is used as the simulation parameter study, in order to numerically take solution-precipitation phenomenon into consideration, where FOST = 0.01 or 10 times large value (FOST = 0.1) are used. The frequency of liquid phase wetting (Flhd and Fphd) are followed the values in Matsumoto et al. [13].
Figure 1 shows the SEM photograph of glass power placed on the sintered copper specimen at 650°C, where the copper specimen was sintered in advance before glass powder placed on their surface. The observation temperature is ambient. The liquefied glass wets the surface of sintered copper specimen surface. The contact angle measured by the θ/2 method was 25°. Figure 2 shows the SEM microstructures of green and sintered specimen for copper-glass system. The porosities of the green measured from the SEM photographs were almost same between four different glass fractions, where absolute values are 53.0, 53.9, 53.5 and 53.7%, respectively (Figs. 2(a)–(d)). At 600°C, the grain sizes of copper are almost same to that ambient (Fig. 2(e)), while liquefied glass wets the copper particle surface (Figs. 2(f)–(h)). At 650°C, neck growth is observed for copper (Fig. 2(i)). At this temperature, the liquefied glass penetrates the interface of solid grain boundaries, then the porosities are decreased in proportion to glass fraction (porosities at 650°C are 27.8, 25.4, 23.7 and 20.4%, respectively, shown in Table 3). At 750°C, copper particle relaxes their shape (rounded interface, gap shrinkage). This makes the configuration of pores discontinuous. The densification is progressed in proportion of glass fractions (the porosities are 17.2, 8.1, 5.1 and 4.5%, respectively).
SEM image of 650°C-fired glass on sintered Cu.
SEM images of experimental CuG-0E-19E. White: Cu, Dark gray: Glass, Black: Pore. (a) CuG-0E green, (b) CuG-7E green, (c) CuG-13E green, (d) CuG-19E green, (e) CuG-0E 600°C, (f) CuG-7E 600°C, (g) CuG-13E 600°C, (h) CuG-19E 600°C, (i) CuG-0E 650°C, (j) CuG-7E 650°C, (k) CuG-13E 650°C, (l) CuG-19E 650°C, (m) CuG-7E 750°C, (n) CuG-7E 750°C, (o) CuG-13E 750°C, (p) CuG-19E 750°C.
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Figure 3 shows the SIM microstructures of green and sintered specimen for copper-glass system. The copper particles are polycrystal as shown in the microstructure of green (Fig. 3(a)). At 650°C, the larger grain size compared to green is visually seen (Figs. 3(b)–(e)). This suggests the solid diffusion between grains in one particle and diffusion between inter-particles by sintering. The grain sizes are almost same when visually comparing the microstructures between different glass fraction conditions. At 750°C, the grain growth is progressed further (Figs. 3(f)–(i)). This suggests that the relaxation of the solid particle shape may contribute to the solid diffusion. Similarly to 650°C, at sintering temperature 750°C, the grain sizes have visually almost no difference between these different glass fraction conditions.
SIM images of experimental CuG-0E-19E. (a) CuG-0E green, (b) CuG-0E 650°C, (c) CuG-7E 650°C, (d) CuG-13E 650°C, (e) CuG-19E 650°C, (f) CuG-0E 1E 750°C, (g) CuG-7E 750°C, (h) CuG-13E 750°C, (i) CuG-19E 750°C.
Figure 4 shows the SEM photograph of glass power placed on the sintered silver specimen at 650°C, where the silver specimen was sintered in advance before glass powder placed on their surface. The observation temperature is ambient. The liquefied glass wets the surface of sintered silver specimen surface. The contact angle measured by the θ/2 method was 25°. Figure 5 shows the SEM microstructures of green and sintered specimen for silver-glass system. The porosities of the green measured from the SEM photographs were almost same between four different glass fractions, where absolute values are 51.9, 53.7, 52.9 and 53.2%, respectively (Figs. 5(a)–(d)). At 585°C, the neighboring particles get closer by grain growth (Fig. 5(e)). By getting close the silver particles, the total area of solid particles in the SEM observation area is significantly increased, as a results, densified microstructures are observed. On the contrary, absolute value of the porosities are large in proportion to the glass fractions at 585°C, which is just below the glass softening point (Figs. 5(f)–(h)) (the porosities are 34.4, 37.0, 38.5 and 42.1, respectively, as shown in Table 4). At 700°C, the neck growth of silver particles is progressed further (Fig. 5(i)). At this temperature for glass containing conditions, the silver particles significantly relax their shape, and their surfaces are covered by wet glass (Figs. 5(j)–(l)). At 750°C, the relaxation of the silver particle is also seen for zero glass fraction condition (Fig. 5(m)). At this temperature, densified microstructures are observed with aggregated and locally distributed pore configurations (the porosities are 18.4, 5.9, 3.9 and 3.7%, respectively, as shown in Table 4).
SEM image of 650°C-fired glass on sintered Ag.
SEM images of experimental AgG-0E-19E. White: Ag, Dark gray: Glass, Black: Pore. (a) AgG-0E green, (b) AgG-7E green, (c) AgG-13E green, (d) AgG-19E green, (e) AgG-0E 585°C, (f) AgG-7E 585°C, (g) AgG-13E 585°C, (h) AgG-19E 585°C, (i) AgG-0E 700°C, (j) AgG-7E 700°C, (k) AgG-13E 700°C, (l) AgG-19E 700°C, (m) AgG-0E 750°C, (n) AgG-7E 750°C, (o) AgG-13E 750°C, (p) AgG-19E 750°C.
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Figure 6 shows the SIM microstructures of green and sintered specimen for silver-glass system. The silver particles are polycrystal as shown in the microstructure of green (Fig. 6(a)). At 585°C of zero glass fraction condition, some silver particles are monocrystals (Fig. 6(b)). At this temperature, the grain sizes are almost same when visually comparing the microstructures between the three different glass fraction conditions (Figs. 6(c)–(e)). In contrary, at 750°C, larger grains are observed for glass containing condition compared to that zero glass condition AgG-0E (Figs. 6(f)–(i)).
SIM images of experimental AgG-0E-19E. (a) AgG-0E green, (b) AgG-0E 585°C, (c) AgG-7E 585°C, (d) AgG-13E 585°C, (e) AgG-19E 585°C, (f) AgG-0E 750°C, (g) AgG-7E 750°C, (h) AgG-13E 750°C, (i) AgG-19E 750°C.
Figure 7 shows simulation microstructure evolution for copper system. The initial microstructures were prepared to have same cell configuration between four different compositions by numerically converting a part of solid cell to glass cell as shown in Figs. 7(a)–(d). When visually comparing the microstructures of holding temperature 650°C (3000 MCS) condition, the total pore area of CuG-0S is decreased compared to the initial, where CuG-0S has no-liquid (Fig. 7(e)). On the other hand, when glass liquid is included, wetting of solid surface and interface are visually observed. As a result, smaller pore area of these conditions are observed compared to CuG-0S at 650°C (Figs. 7(f)–(h)). When visually comparing the microstructure of holding temperature 750°C (6000 MCS) condition, further evolution of copper grain growth and pore area reduction are observed. Then, similarly to 650°C, when liquid glass is included, smaller pore area are visually observed compared to CuG-0S (Fig. 7(j)–(l)). These simulation results are qualitatively in good agreement with experimental microstructure (Fig. 2). The contiguity (Css) and the number of solid contact (Nss) measured during the sintering simulation for copper system are plotted in Fig. 8. Smaller contiguity Css is obtained in condition glass liquid fraction is large (Fig. 8(a)). The number of solid contact (Nss) is increased in proportion to MCS for all simulation cases. These simulation results are qualitatively agreement to visual information from Fig. 7.
Simulation images of CuG-0S-19S. (a) CuG-0S green, (b) CuG-7S green, (c) CuG-13S green, (d) CuG-19S green, (e) CuG-0S 650°C, (f) CuG-7S 650°C, (g) CuG-13S 650°C, (h) CuG-19S 650°C, (i) CuG-0S 750°C, (j) CuG-7S 750°C, (k) CuG-13S 750°C, (l) CuG-19S 750°C.
Contiguity (Css) and number of solid-solid interfaces (Nss) of simulation CuG-0S-19S for holding(sintering) at 650°C and 750°C. (a) Css, (b) Nss.
Next, porosity and grain growth behavior are compared between the simulation cases. The porosity measured during the sintering simulation for copper system are plotted in Fig. 9. Two figures are arranged side by side, where holding temperatures of left and right figures are 650°C (0–3000 MCS) and 750°C (3001–6000 MCS), respectively. The higher amount of glass liquid resulting in lower amount of porosity for all MCS stages. The lower amount of porosity observed in liquid containing condition is explained by pore annihilation routes, where pores annihilate by pore sink at solid grain boundary and solid particle rearrangement motion caused by liquid. Hence, it is supposed that glass liquid fraction contributes to densification. Simulation and experimental porosities are shown in Table 3. The simulation and experimental porosities are qualitatively in good agreement for 650 and 750°C conditions. The average grain size measured during the sintering simulation for copper system are plotted in Fig. 10. The simulation grain growth behaviors between different amount of liquid fractions include zero are almost same. This result is qualitatively in good agreement with experiment.
Porosities of simulation CuG-0S-19S for holding(sintering) at 650°C and 750°C.
Grain size of simulation CuG-0S-19S for holding(sintering) at 650°C and 750°C.
The average grain size vs. relative density relationship for copper system is plotted in Fig. 11(a). This figure is drawn by integrating the relationships of porosity vs. MCS in Fig. 9 and grain size vs. MCS in Fig. 10. The expression of this figure makes it possible to compare average grain size between different composition at same relative density [16]. This figure suggests that the large amount of liquid phase at initial results in slower grain growth evolution, when comparing at same relative density. At the final stage of 750°C condition, larger relative density is obtained in proportion to liquid fraction, whereas resulting grain sizes are almost same between these four conditions. This average grain size vs. relative density relationship is also simulated by inputting 10 times large Ostwald ripening frequency (Fost = 0.10) as shown in Fig. 11(b). Contrary to Fig. 11(a), the grain growth increment as a function of relative density between four cases are almost same, whereas larger grain size of glass containing three conditions are obtained compared to that of no-glass condition.
Relative density-grain size of simulation CuG-0S-19S. (a) Fost = 0.01, (a) Fost = 0.1.
Figure 12 shows the simulation microstructure evolution. The initial microstructures were prepared in same procedure to copper system. When visually comparing the microstructures of holding temperature 585°C condition, grain growth and densification behaviors are observed in reverse proportion to glass fraction (Fig. 12(e)–(h)). As a result, no glass containing condition AgG-0S shows largest microstructural evolution at this holding temperature. On the contrary, at 750°C, liquid glass containing three conditions show lower amount of porosities than AgG-0S, which glass fraction is zero. At this temperature, pores are aggregated and unevenly distributed. This pore aggregation is explained from the viewpoint of total energy reduction, where pore aggregation contributes to the reduction of pore surface area compared to isolated pore configuration. These simulation microstructural features are qualitatively in good agreement with that experiment (Fig. 4). The contiguity (Css) and the number of solid contact (Nss) measured during the sintering simulation for silver system are plotted in Fig. 13. The amount of glass at the initial configuration result in the small amount of contiguity due to the increment of solid-liquid interfaces (Fig. 13(a)). The number of solid contact (Nss) is significantly increased at holding temperature 750°C compared to 585°C for liquid containing three cases. These simulation results are qualitatively agreement to visual information from Fig. 12.
Simulation images of AgG-0S-19S. (a) AgG-0S green, (b) AgG-7S green, (c) AgG-13S green, (d) AgG-19S green, (e) AgG-0S 585°C, (f) AgG-7S 585°C, (g) AgG-13S 585°C, (h) AgG-19S 585°C, (i) AgG-0S 750°C, (j) AgG-7S 750°C, (k) AgG-13S 750°C, (l) AgG-19S 750°C.
Contiguity (Css) and number of solid-solid interfaces (Nss) of simulation AgG-0S-19S for holding(sintering) at 585°C and 750°C. (a) Css, (b) Nss. Figure 12 Porosities of simulation AgG-0S-19S for holding(sintering) temperature of 585°C and 750°C.
Next, the change in porosity and grain size in these four cases are compared. The porosity measured during the sintering simulation for silver system are plotted in Fig. 14. Two figures are arranged side by side, where holding temperatures of left and right figures are 585°C (0–3000 MCS) and 750°C (3001–6000 MCS), respectively. In case of holding temperature 585°C, the glass retards the densification in proportion to their fraction. At this temperature 585°C (3000 MCS), AgG-0S, which does not include glass, shows smallest amount of porosity. On the contrary, at 750°C (6000 MCS), the porosity of liquid containing condition decreased significantly compared to AgG-0S with zero-liquid fraction. The amount of porosities between experiment and simulation are compared in Table 4. The amount of porosities between the experiment and simulation are in good agreement for the sintering temperatures of 585 and 750°C. The average grain size measured during the sintering simulation for silver system are plotted in Fig. 15. In case of holding temperature 585°C, the glass retards the silver grain growth in proportion to their fraction. On the contrary, at holding temperature 750°C, the grain size for liquid containing conditions is larger compared to AgG-0S of zero-liquid fraction.
Grain size of simulation AgG-0S-19S for holding(sintering) temperature of 585°C and 750°C.
Grain size of simulation AgG-0S-19S for holding(sintering) at 585°C and 750°C.
The average grain size vs. relative density relationship for silver system is plotted in Fig. 16(a). In this figure, the holding temperatures are 585 and 750°C initial and later half range, respectively, where the slope of the curves are changed at the temperature transition point. At initial half stage of 585°C condition, the smaller increment of relative density is obtained in proportion to glass fraction. On the other hand, at later half 750°C, the large amount of liquid phase at initial results in slower grain growth. At the final stage of 750°C condition, larger relative density and grain size are obtained compared to the no glass condition. Figure 16(b) shows the average grain size vs. relative density relationship simulated by inputting 10 times large Ostwald ripening frequency (Fost = 0.10). At holding temperature 585°C, The simulation grain sizes are almost same between 4 cases (6.4, 6.3, 6.3 and 6.4 cells, respectively). Contrary to Fig. 16(a), the grain growth increment as a function of relative density between four cases are almost same at holding temperature 750°C.
Relative density-grain size of simulation AgG-0S-19S. (a) Fost = 0.01, (b) Fost = 0.1.
The Ostwald ripening about metal-glass mixed powder system is discussed from the experimental and simulation results obtained in this study. In addition, the reason about the difference of the grain growth behavior between copper and silver containing glass is explained. These two considerations are described in order as follows.
The Ostwald ripening takes place by solution-reprecipitation progress. In such system, a strong dependence of the solid grain diameter on the metal-liquid composition has been reported [17]. On the other hand, in case of metal-glass system, focus is given on the densification behavior [1, 4–7]. There has been only a few studies about grain growth behavior for metal-glass system, furthermore, the amount of glass fraction for these studies are extremely large [8, 9]. Compared to these studies, the metal-glass system in this study, the experimentally observed grain diameters are almost same even if the amount of glass fractions are very different. This result lacks the evidence of the Ostwald ripening, who’s grain size differed significantly depending on the amount of liquid fraction. The shortcome of the evidence of the Ostwald ripening is thought to be attributed to the extremely small solubility of solid metal element in liquid glass phase (about 0.1 mol% [18]). Actually, in literature study, the element from metal solid has not been detected from glass phase in the polished metal-glass sintered specimen by SEM element mapping [6]. Similarly, the element from metal solid was not detected by the same evaluation method. From these experimental results in this study, it seems that the dominant grain growth mechanism is not the Ostwald ripening for materials used in this study.
Next, the Ostwald ripening about a metal-glass system is discussed from simulation results. As explained before, the reduction of the energy is obtained when liquid phase penetrating solid grain boundary, under the interface energies that are inputted in this study. Because of this wetted solid configuration, the Ostwald ripening caused by the solution-precipitation is well progressed in the simulation when high frequency factor about the Ostwald trial is applied (Figs. 11(b) and 16(b)), even if solid diffusion between neighboring solid grain boundary cannot be obtained. Since the number of Ostwald trial is increased in proportion to the amount of liquid, the high Ostwald frequency factor gives different result to Figs. 11(a) and 16(a). The high frequency factor about Ostwald trial at initial setting of simulation results in the deviation to experimental results, where larger solid grain diameter is clearly obtained in proportion to liquid glass fraction for copper system as shown is Fig. 11(b). Similarly, the diameter of grain sizes are almost same at the final stage of holding temperature 585°C even if the presence or the amounts of glass fraction are different as shown in Fig. 16(b). From these simulation results, the Ostwald ripening does not seem to the dominant grain growth mechanism. Whereas in simulation case of the frequency factor of the Ostwald trial is set to zero, the spatial distribution of the glass got scattered for copper and silver cases. As a result, simulation with zero frequency of Ostwald cannot reproduce the experimental microstructure, which has liquid configuration at triple junction. From these simulation results, although the Ostwald ripening does not seem to the dominant grain growth mechanism, their contribution may not zero.
Finally, the difference of the dependence between copper and silver system on the presence of glass is explained by simulation results, where the presence of glass does not make difference on copper grain size, but makes difference on silver grain size. In condition of parameter setting in this study, the reduction of total system energy for copper and silver system is obtained when liquid penetrates into solid grain boundaries. This configuration makes reduction of the solid grain boundary ratio compared to that initial as shown in Figs. 8(a) and 13(a). By this increment of solid-liquid interfaces, the number of simulation trial about rearrangement of solid particle is more frequently occurred [13]. As a result, the solid particles come close to each other and the number of solid grain boundary increase (Fig. 8(b)). This increments of the number of solid grain boundary as a function of MCS are almost same even if the presence or the fractions of liquid are different for copper system. Consequently, it is supposed that the grain growth behavior by solid phase diffusion progresses in proportion to the number of the increment of solid grain boundary, then copper grain diameter at final stage does not make difference. On the other hand, in case of silver system, significant increase of the number of the solid grain boundary is observed after 3000MCS (Fig. 13(b)), where the frequency factor of rearrangement trial set large at this holding temperature above the softening temperature of glass. Since same frequency factor about Ostwald (FGG = 0.05) is used for initial and later half of 3000 MCS, the observed larger grain diameter for glass containing condition than that of no glass is attributed to the solid diffusion between the solid grain boundary, where the increment of silver grain boundaries are explained above.
From these considerations, the dominant mechanism of grain growth is attributed to solid diffusion between the solid grain boundaries in case of materials in this study. However, in case of metal alloys, the amount of liquid is different between temperatures, and metal alloy is partially melted or solidified [17]. In future study, the simulation model is revised so that these difficult phenomena are simulated.
Microstructures of sintered specimen for copper or silver system containing glass were experimentally observed for each glass fractions. The experimental microstructures were numerically reproduced by using the Monte Carlo method. The following findings are observed:
We greatly appreciate to Dr. Sota Terasaka (JFCC) about valuable discussions.
