Decoupling grain growth from densification during sintering of oxide nanoparticles

Abstract

When external pressure is exerted on oxide nanoparticles (NPs), they densify without exhibiting significant grain growth at temperatures lower than half their melting temperature. This type of densification behavior contradicts the usual sintering behavior observed during densification, which is inevitably accompanied by grain growth. It has been found that NPs of various oxides, including ZnO, CuO, TiO₂, SnO₂, Fe₂O₃, and BaTiO₃, show slight low-temperature densification (LTD) at temperatures much lower than half their melting temperature, even when an external pressure is not applied. Here we report that LTD is crucial for the densification of NPs during pressure sintering: without LTD, densification does not progress sufficiently even when a pressure as high as 2 GPa is applied. The phenomenon of LTD can be ascribed to surface and/or boundary diffusion in the NPs because of the low thermal activation energy of LTD as well as its sensitivity to changes in the NP surface morphology. It is likely that the decoupling of grain growth from densification in oxide NPs is related to LTD-assisted yield deformation, that is, the migration of surface atoms, which is not accompanied by significant lattice diffusion.

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Introduction

Sintering is a widely employed process for obtaining densified bulk materials in industry as well as basic research. It is based on the premise that small particles have large surface energies. When a material is heated, its atoms start to diffuse to minimize the surface energy, that is, they move to reduce the free surface, resulting in densification. Meanwhile, small particles may combine into larger ones. As a result, grain growth inevitably follows densification, especially among nanoparticles (NPs).¹

There is a strong demand for the nanostructuring of bulk materials. However, this requires a low degree of grain growth during densification, which remains a challenge. In the case of oxides, pioneering efforts like pressure sintering of NPs enabled sintering with low grain growth.^2–4 In particular, the sintering temperature used was significantly lower than half the melting temperature of the material of subject; however, the density of the sintered material was almost equal to the theoretical value. In 1990, Hahn et al. densified TiO₂ (rutile) NPs with a size of 11 nm at approximately 500 °C by applying a pressure of 1 GPa. This resulted in a pellet with a density equal to 95% of the theoretical density, while the initial crystal size was maintained.² Later, Liao et al. studied the effect of pressure on the sintering of TiO₂ (anatase) NPs at 400 °C and observed gradual grain growth accompanied by a phase transformation.³ Similar sintering behavior was also reported for the Al₂O₃ system.⁴ Liao et al. analyzed the effect of grain boundary creep on densification under pressure as well as grain growth retardation by pore-controlled pinning and concluded that both mechanisms were in reasonable agreement with the experimental results.⁵ However, the deviation of the effects of external pressure on densification from their model is a matter of controversy.⁶

Here, we examine the pressure sintering of oxide NPs to determine the origins of the decoupling of densification and grain growth. In particular, we discuss the impact of the low-temperature densification (LTD) mode, which is manifested as indistinct densification at temperatures well below half the melting temperature of the material in question in the absence of an external pressure. Finally, we propose that the migration of surface atoms and the yield deformation of the NPs are the critical mechanisms responsible for limiting the grain growth of NPs during pressure sintering.

Experimental

Various types of NPs of CuO, SnO₂, TiO₂, ZnO, BaTiO₃, and Fe₂O₃ were used as the starting materials. Among them, the BaTiO₃ NPs⁷ and Fe₂O₃ NPs⁸ were synthesized via the hydrothermal method in the laboratory. The others were obtained commercially. The CuO, SnO₂, and TiO₂ NPs (NanoTek, C. I. Kasei, Japan) were almost spherical, while the ZnO NPs (Pazet GK-40, Hakusui Tech, Japan) were round but elongated. The synthesized BaTiO₃ NPs were cube-shaped and uniformly sized (20 nm). In addition, two types of Fe₂O₃ NPs were prepared: spherical and rhombohedral. Both were synthesized under similar conditions, according to a previously reported method,⁸ except different concentrations of the solution were used. The spherical particles were obtained at a FeCl₃·6H₂O concentration of 0.1 mol L⁻¹ (M), while the rhombohedral ones were synthesized at a concentration of 0.01 M. The crystallite sizes of the NPs were determined from the Williamson–Hall plot, and they are listed in ESI.†

To observe the shrinkage behavior of the NPs after thermal activation, a differential dilatometer (TD-5200SA, Bruker, Japan) was used. The NPs were pressed into a bar with dimensions of 5 × 5 × 20 mm³ by applying a uniaxial pressure of 50 MPa. The bar was then isostatically pressed under a pressure of 100 MPa. The degree of shrinkage was monitored in air using an Al₂O₃ bar as the reference; a load of 5.0 g was applied to ensure proper mechanical contact of the probes. The heating and cooling rates were adjusted to be 5–20 K min⁻¹.

The pressure sintering of the NPs was performed using a spark plasma sintering apparatus (SPS 1050, Sumitomo Coal Mining, Japan), which allowed for a maximum load of 10 t. Using a piston cylinder with a diameter of 8 mm, a nominal pressure of up to 2 GPa could be achieved in the experimental setup. In order to apply a pressure this high, cobalt–tungsten-carbide (Co–WC) was used to fabricate the piston and cylinder. The sintering pressures listed in this paper are the nominal pressures. Heating was performed by the joule heating of Co–WC. The process temperature was measured using a thermocouple mounted in the cylinder that was covered with a thermal insulator made of graphite fiber to ensure temperature homogeneity. Heating and cooling proceeded at a rate of 50 K min⁻¹, with a hold time of 5 min at each desired temperature. A vacuum (<10 Pa) was maintained within the chamber throughout the experiment. After the completion of the sintering process, the samples were observed using a scanning electron microscope (SEM; S-4300, Hitachi, Japan) and a transmission electron microscope (TEM; 3000F, JEOL, Japan). Their densities were measured on the basis of their dimension and weight or using the Archimedes method (or using both methods).

Results and discussion

Fig. 1 shows images of the ZnO NPs and their microstructure after densification at 200 °C under a pressure of 500 MPa. Since the melting temperature of ZnO is 1980 °C, the process temperature was well below half the melting temperature of ZnO. Considering that the rate of atomic diffusion increases exponentially with the temperature, it is difficult to explain why densification occurred at such a low process temperature. For instance, conventional sintering of ZnO requires temperatures above 1000 °C, and the diffusion coefficient of oxygen is lower than that of zinc in the ZnO lattice. As a result, diffusion phenomena such as sintering are controlled by oxygen, whose coefficient is approximately 10⁻¹⁹ m² s⁻¹ at 1000 °C. However, it should be 10⁻⁴⁴ m² s⁻¹ at 200 °C if one extrapolates the high-temperature data.^9,10 Because the sintering rate is a linear function of the diffusion coefficient,¹ such a large difference suggests a sintering duration that is 10²⁵ times longer. Even if we consider the effect of the particle size on the sintering rate, this slow diffusion practically means no densification can occur. On the other hand, the surface and grain boundaries exhibit much higher diffusion coefficients than does the lattice, with diffusion being estimated to be four to seven orders of magnitude faster in the ZnO cyrstal.¹⁰ However, this is still very slow for practical densification. It is possible that NPs exhibit a different sintering mechanism owing to an enhanced surface effect. To investigate this issue, Ewsuk et al. analyzed the apparent activation energy of sintering for ZnO NPs and concluded that the lowering of their sintering-onset temperature was attributable to a scaling (i.e., particle size) effect only.¹¹ In other words, the diffusion mechanism of ZnO NPs is similar to that of microcrystalline particles, and the NPs do not exhibit any anomalies during pressure-less sintering.

Fig. 1 (a) TEM images of the ZnO NPs and (b) their microstructure after densification via pressure sintering at 200 °C.

Contrary to what one might expect with regard to the sintering of ZnO NPs, the nanostructure of the sintered pellet had a neck-like formation: the grains were polyhedrons while the NPs were initially round. It is also remarkable that the size of the grains in the densified pellet was almost similar to that of the NPs. This is characteristic of NPs that are pressure-sintered at temperatures lower than half their melting temperature: densification occurs without grain growth.^{2–4,12–14} This densification behavior can be clearly observed in Fig. 2. In the absence of pressure, grain growth was accompanied by densification, indicating that neck growth caused by the densification raised the amount of diffusive atoms because of the enlargement of the diffusion path from one particle to the others. Meanwhile, diffusion from the small particles to the larger ones through the Ostwald ripening mechanism occurred, leading to substantial grain growth. On the other hand, the density increased monotonously with pressure without simultaneous grain growth during pressure sintering. It is widely accepted that both densification and grain growth are difficult to decouple, especially at relative densities (RDs) above 0.9. To our knowledge, this type of decoupling can be observable in pressure sintering of NPs only.

Fig. 2 Grain size (d) of sintered ZnO as a function of its relative density (RD).

The requirement of high pressure for obtaining high density indicates the occurrence of dislocation-induced deformation,¹⁵ although this phenomenon does not occur readily in other nanomaterials.⁶ Fig. 3a shows a high-resolution TEM image of the sintered pellet; it can be observed that the lattice fringes were distorted and discontinuous in some grains. On the other hand, an image of the NPs as a starting material, shown in Fig. 1a, contains only straight lattice fringes. The emergence of distorted and discontinuous lattice fringes after sintering suggests that the lattice spacing was inhomogeneous and there were variations in the crystal orientation, that is, there was a strong residual strain in the grains. Another characteristic of the microstructure was the step-like structure of the grain boundaries, as shown in Fig. 3b. Such grain boundaries are typically observed near grains with a high dislocation density or large strain (or both).¹⁶ Thus, it is clear that a large strain and dislocations were induced during the densification process when the high pressure was applied. Because ZnO is a known wide-band-gap semiconductor, one might anticipate it to exhibit a brittle nature instead of undergoing ductile deformation. However, ZnO does undergo ductile deformation at elevated temperatures.¹⁷ According to previous studies, the stress–strain curve of ZnO rises linearly at the beginning. Subsequently, ZnO exhibits smooth yielding behavior, with the curve rising gradually, owing to the work hardening. The yield stress along the (0001) basal slip plane was determined to be 15 MPa at 650 °C. An extrapolation of the high-temperature data showed that the yield stress at 200 °C was 200 MPa and roughly 1 GPa at 100 °C; this stress range is comparable to the pressure applied during the present process. Hence, yield deformation owing to the pressure applied is a plausible mechanism behind the observed densification.

Fig. 3 High-resolution TEM image of densified ZnO. The distortion and discontinuity of the lattice fringes are evident in (a). The step-like structure of the grain boundaries can be seen in (b).

To directly observe the yield deformation mechanism, cubic NPs of BaTiO₃ were densified in a similar manner. Here, the NPs were randomly packed initially so that the shape deformation of the NPs would be significant after densification (an SEM image of the NPs is shown in ESI†). Contrary to our expectations, face-to-face particle packing and subsequent bonding were observed, as shown in Fig. 4. Regarding the crystallographic relation, the surfaces of these NPs belonged to the {1 0 0} plane,⁷ while the glide plane of BaTiO₃ is {1 1 0}.¹⁸ Owing to dislocation gliding under pressure, the difference in the sizes of the NPs may be adjustable within a certain range, leading to the densification of the system. Indeed, an image contrast caused by the strain is evident in some of the grains. However, the dislocation gliding mechanism cannot have caused the ordering of the NP structure. Instead, rotation of the NPs predicted by molecular dynamics simulations is the mechanism responsible for the densification and ordering.¹⁹

Fig. 4 TEM image of the densified BaTiO₃ NPs with cubic microstructures. An image of the NPs before densification is given in ESI.†

The above-mentioned mechanism is considered to play the role of the external pressure. Another aspect is the role of the NPs. Given that final density attainable through yield deformation is a simple function of the pressure,¹⁵ the final density must reach a certain value independent of the starting material. We found experimentally that the microcrystalline particles and heat-annealed NPs did not reach the same density under identical sintering conditions (see ESI†). This strongly suggests that the NPs exhibited unique characteristics with respect to densification. Since the pressure sintering utilizes brute force, it is difficult to investigate minute differences. Therefore, we monitored the densification behavior of NPs in the absence of pressure. The results for ZnO NPs are shown in Fig. 5. Significant shrinkage was observed at temperatures above 600 °C, while a small degree of shrinkage was observed at approximately 200 °C. Hereafter, we refer to this later-stage shrinkage as LTD. Since microcrystalline particles with a size of 150 nm prepared via the annealing of the NPs did not exhibit LTD, as shown in Fig. 5, LTD is regarded as a characteristic of NPs.

Fig. 5 Shrinkage rate (dε/dt) of ZnO as a function of the temperature (T). The red line represents the NPs, and the blue line represents a powder consisting of submicrometer-sized particles.

It was found that LTD has a pronounced effect on densification during pressure sintering, as shown in Fig. 6. Below the temperature corresponding to LTD, densification did not proceed beyond the limit of the closest-packing density, which was approximately 0.75: the packing of the NPs by the external pressure occurred predominantly in this temperature region. On the other hand, at temperatures higher than that corresponding to LTD, the density was effectively higher than the packing limit. Thus, pore filling through diffusion or dislocation gliding contributed to the densification phenomenon. The same phenomenon was also observed in CuO NPs (Fig. 7). Thus, it is obvious that LTD plays a crucial role in the densification process of NPs in general.

Fig. 6 Relative density (RD) of the pressure-sintered ZnO NPs (P: pressure). The inset shows the shrinkage rate near LTD for these NPs.

Fig. 7 Relative density (RD) as a function of the pressure (P) of the pressure-sintered CuO NPs. The inset shows the shrinkage rate near LTD for these NPs. A TEM image of the CuO NPs is also shown.

LTD is a thermally activated phenomenon, and hence its activation energy can be evaluated based on a sintering model.^11,20 For instance, the heating rate during dilatometer analysis can be used to estimate the activation energy: a higher heating rate would shift the shrinkage behavior towards a higher temperature, with the thermal activation energy determining the extent of the shift. Fig. 8 shows the heating-rate dependence of the shrinkage rate of ZnO NPs. An obvious peak shift, attributable to a difference in the heating rate, was observed at approximately 800 °C (Fig. 8b); however, a shift was not observed in the case of LTD (Fig. 8a). This indicates that the activation energy of LTD was much lower than that of the other higher-temperature shrinkage modes. In fact, the activation energies calculated for LTD (Fig. 8a) and conventional shrinkage (Fig. 8b) based on the master sintering curve analysis^20,21 were 126 and 562 kJ mol⁻¹, respectively. Furthermore, as in the case for LTD of ZnO, a peak shift was not observed in LTD of the other oxides. This suggests that LTD originates in the diffusion of atoms that are weakly bonded to the lattice, namely, the surface atoms.

Fig. 8 Shrinkage rate (dε/dT) near the peak for several heating rates: (a and b) ZnO NPs, (c) TiO₂ NPs, and (d) SnO₂ NPs. (a, c and d) The shift in LTD is not significant. (b) An obvious shift in the peak is observed in the case of high-temperature shrinkage.

In order to verify the origin of LTD, the effect of the surface energy on LTD was investigated. Here, we synthesized hematite NPs with different morphologies, namely, spherical and rhombohedral NPs (Fig. 9). Both types of NPs were assumed to be chemically identical because the synthesis conditions such as the temperature, source material, and pH used during the hydrothermal process were identical. The difference in their shapes was caused by the difference in the solution concentration, which governed the growth rate and subsequently the morphology. In addition, the average sizes of the NPs were also similar. The rhombohedral shape can be attributed to the crystal structure with R3̄c symmetry, that is, the crystal habit of Fe₂O₃ hematite. Hence, the surfaces of the rhombohedral NPs were atomically flat so that their surface energy was low. On the other hand, owing to their round shape, the spherical NPs had energetically unstable surfaces. As a result, the two types of NPs exhibited different types of LTD as well, as can be seen from Fig. 9: the shrinkage of the spherical NPs began at a temperature lower than that at which the rhombohedral NPs started shrinking. At temperatures above 500 °C, the two types of NPs exhibited similar shrinkage rates. This result strongly suggests that LTD was connected to the migration of the surface atoms.

Fig. 9 Shrinkage rate of hematite near LTD for spherical and rhombohedral NPs. The insets show SEM images of the hematite NPs; the scale bars correspond to 100 nm.

Summarizing the above experimental findings, the unique densification of oxide NPs is illustrated in Fig. 10. Because of the significant contribution of the surface atoms and inactive lattice diffusion during the process, grain growth of NPs became negligible. Yield deformation resulting from the high pressure partly contributed to the densification, which did not increase the grain size. It is worth nothing that such significant contribution of surface atoms originated from the large surface area; therefore micrometer-sized particles do not show the same densification behavior.

Fig. 10 Schematic image of oxide NP densification.

Conclusions

Pressure sintering of oxide NPs with a size of 20–50 nm was performed at low temperatures, that is, temperatures lower than half the melting temperature. As reported in earlier studies, the application of an external pressure resulted in densification even at such low temperatures. In particular, the NPs exhibited negligible grain growth, in contrast to the case during conventional sintering. TEM observations of the densified samples revealed the existence of dislocations as well as strain, indicating that yield deformation was primarily responsible for the observed densification. A dilatometer analysis of the NP densification process in the absence of an applied pressure revealed that the oxide NPs exhibited slight shrinkage; this is called LTD and it occurred at approximately 100–500 °C. A direct connection between LTD and the densification process during pressure sintering indicates that the NPs densified not only because of the pressure but also because of a thermally activated process. No clear temperature shift in the LTD was observed when the heating rate was varied, indicating that the LTD process had a low thermal activation energy. This suggests that the LTD originated from atomic diffusion on the surfaces of the NPs. Indeed, the LTD was sensitive to the shape of the NPs. As stated above, LTD is believed to arise because of surface diffusion. Thus, the surface area of the NPs plays a significant role. For either yield deformation or surface diffusion, lattice diffusion is apparently not required, thus limiting grain growth. Furthermore, by combining yield deformation with surface diffusion, grain growth is decoupled from densification.

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Footnote

† Electronic supplementary information (ESI) available: Table listing types of nanoparticles used in the study; SEM image of cubic BaTiO₃ NPs; pressure sintering of ZnO microcrystals as control. See DOI: 10.1039/c5ra27844a

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