Values of the initial stage sintering exponent developed for model geometries. (LD and GB refer to lattice diffusion (i.e., volume) and grain boundary respectively).
Nano grained cemented tungsten carbide (
Given that cemented
Since the last decade, a number of reports on SPS of
2. Activated sintering processes
Sintering methods involving the presence of an electric field are generally called Field Assisted Sintering Techniques (FASTs). Unlike conventional sintering - in which the sample is heated from the outside (furnace) - in FAST, the sample is heated internally by the passage of an electric current. Compared to the hot pressing process, FAST methods can have extremely high heating rates, sometimes even upto 2000 K/min [Tokita M et al, 2007, Cramer G D, 1944 and a host of other patents, a review of which can be found in the paper by Salvatore Grasso et al, 2009]. This is achieved by using current pulses from a few micro seconds to milli seconds but charged with an extremely high current density of about 10,000 A/cm3. External pressures can also be applied from a few MPa to typically 1000 MPa making the sintering process rapid and effective. Generally, the electric field can be applied in a number of ways: pure DC (also called resistive sintering), pulsed DC or Microwave. Activated sintering using a pulsed DC has also been often referred to as Spark Plasma Sintering (SPS) in the literature, since the high current density is thought to induce a plasma at the inter-particle neck region. However, the generic term, Pulsed Electric Current Sintering (PECS) is also commonly used in reference to any type of current waveform other than pure DC.
In a typical SPS process, the powder sample is loaded in a cylindrical die and closed on the two sides by electrically conductive punches. For ease of separation after sintering and also to avoid any reaction between the punch and the sample, graphite papers are used as spacers. Sintering is carried out in vacuum and both pressure and electric current through an external power source is applied to the punches. The electric field control can be achieved in two ways: in the
It has been found that for a constant applied current, the maximum resistance (and thereby the maximum joule heating) occurs at the punch/graphite contact surface,
While the quantum of publications on/using SPS has been steadily increasing, the basic process is far from being well understood; the answer to the fundamental question of whether a plasma is generated at the inter-particle contact area is still elusive. Another intriguing fact is the observation of very low sintering activation energies, enhanced sintering rates and low sintering temperatures when the sample is subjected to a simultaneous pressure and electric field as in SPS. While some authors attribute this observation to electro-migration (i.e., diffusion under an electric field gradient) as a, ‘sintering enhancer’, it must be noted that electro-migration can be expected to play a serious role in the sintering of highly ionic compounds. But the observation that the activation energy can be equally low in predominantly covalent compounds like WC (the ionicity according to the Pauling scale is only ~1%) suggests that the field effect may not be the sole cause for the observed rapid kinetics. Thermodynamic arguments suggest that the applied pressure drives sintering while the electric field retards grain growth thereby achieving full densification with limited grain growth. A number of alternate mechanisms, which treat the GB as a separate phase have also been put forth [Dillon S J
3. Isothermal and non-isothermal sintering
Sintering, like coarsening and grain growth is also a thermally activated process and hence an Arrhenius type of dependence on temperature is observed. The kinetics of fusion of two particles during sintering is usually studied either by measuring the neck to particle size ratio (
Therefore a plot of ln (
The activation energy for sintering,
Hence a plot of ln (
A more common method of determining the activation energy without
Equations (2)-(6), hold only during the initial stages of sintering. At later stages of sintering, the free energy reduction accompanying grain growth exceeds that of neck growth. When neck formation is succeeded by interconnected pore structures, the intermediate stage is said to have started. This stage is usually reached after the compact attains 80% or greater of the final density. Compared to the initial stage, fewer models are available for this stage owing to two primary reasons: complicated pore/particle geometry and concurrent grain growth. Densification strain equations for the intermediate stage are primarily based on pore/particle geometries and the inter-relation between them. The frequently referred intermediate stage model is the tetrakaidecahedron model of Coble [Coble R L, 1961a, Coble R L, 1961b]. The appropriate shrinkage kinetics is derived in terms of porosity (pore fraction) rather than linear shrinkage and expressed for different mechanisms as follows:
Lattice diffusion without grain growth
Lattice diffusion with grain growth
Grain boundary diffusion without grain growth
where the terms have the following meanings:
Non isothermal (also called
|0.46||Johnson and Cutler, 1963a|
|0.5||Coble R L, 1958|
|0.4||Kingery W D and Berg M, 1955|
|0.31||Johnson and Cutler, 1963b|
5.1. Analysis of the sintering kinetics
Fig.1 shows the combined isothermal and non-isothermal shrinkage curves. The immediate point worthy of interest is that the CRH strain rate curve does not exhibit a unimodal, gaussian type behaviour that is generally observed in the non-isothermal sintering of many ceramics [Wang J and Raj R, 1990, Panda et al, 1989, Raj R and Bordia R K, 1984]. Instead, there are two peaks (at around 1450 K and 1900 K) leading to a broad plateau covering a rather large temperature interval (from approximately 1400 K to 1900 K). At the peak points in the CRH curve, the corresponding isothermal curves also show a large increase in strain which varies proportionally with the relative magnitude of the CRH sintering strain rate; in most of the low temperature regime, the isothermal sintering strains show saturation, implying that the sintering strains are critically dependant on the heating rate and the temperature of isothermal hold. In conventional sintering, the heating rate is usually assumed to be irrelevant to the kinetics as the sample is presumed to reach the isothermal sintering temperature very swiftly. Our comparison shows the explicit dependence of the isothermal curves on the non-isothermal sintering trajectory and sintering temperature. These preliminary results confirm that the sintering behaviour is not governed by a simple, single mechanism. In the same Fig.1, the stages are marked as Initial, Intermediate I and II for ease of analysis. Although the curve does not resemble the typical three stage sintering process, it does indeed show at first glance, the occurrence of sub-stages.
As mentioned in the previous sections, the relevant equations of sintering have to be applied only to the corresponding sintering stages. Delineating a particular sintering stage (initial, intermediate or final) can be carried out by real time observation of the microstructure. However, such a process is tedious and quite ambiguous, particularly if the particle size is of the order of a few tens or hundreds of nm. As a general rule, when the measured linear shrinkage strains are less than 5%, the dynamics can be assumed to be in the initial stage. With this presumption, the subsequent analysis was carried out for the temperature range 1073-1273 K. Linear shrinkage strains and calculated sintering exponent in the initial stage are shown in Fig. 2a,b. Clearly, while the net shrinkage strains are less than 5%, the
For analysing the intermediate stage, the porosity fraction was estimated as
The apparent activation energy of sintering was calculated using the Dorn method. Only positive values of slope were considered. In the designated initial stage from 1173 K to 1323 K (Fig. 5),
The sintering kinetics from the CRH experiments was also analysed. Fig. 6 shows a plot of ln(
5.2. Microstructure analysis
A preliminary examination of the cross sections of the samples revealed that the edges of the completely densified compact was different from the bulk of the sample. Fig. 7 shows the cross section SEM image and composition map of the sample by EPMA.
Clearly, huge abnormal grains populate the microstructure from the surface to a depth of nearly 30-40 μm. Interestingly, the chemical analysis of the surface by wavelength dispersive EPMA (Electron Probe Micro Analysis) also revealed a C deficient, W2C layer on the surface. (It should be noted that the spatial resolution of the EPMA is rather low and therefore, while the W-rich layer on the surface is shown to be continuous, the region may actually comprise
many small clusters of W2C grains). Such differences in microstructure can occur by temperature gradients in the sample, resulting in a change in chemical composition at the punch/sample interface owing to the high activity of carbon in WC. Both hardness and fracture toughness measured on the surface and the interior showed that the surface was softer than the latter. With increasing heating rate, the grain size decreased with a corresponding increase in hardness, in accordance with the Hall-Petch effect, as reported elsewhere [Kumar A K N et al, 2010]. At higher loads, the hardness saturated to ≈2700 HV for the sample with the smallest grain size (with a sintering rate of 150 K/min, the final measured grain size was <300 nm), as shown in Fig. 8. The microstructure was also not uniform on the surface. The two phase regions existed as patches and were clearly discernible in the optical microscope. Indentation in these areas led to brittle fracture at the corners of the indent (Fig. 9). Such a drastic change in the mechanical properties confirms the existence of W2C, which is an embrittling phase in the W-C system [Luca Girardini et al, 2008]. More quantitative measurements of grain size and distribution were made using EBSD. The unique grain map (Fig. 10a,b) and quantitative grain size histogram plots measured from the area fraction of the grains (Fig. 11) showed a bimodal grain size distribution in the surface with the peaks at ≈700 nm and 1500 nm, while in the interior, the grain size distribution was also bimodal but with the two peaks at ≈250 nm and 480 nm. The bimodal size distribution arises because of abnormal grain growth (AGG) – a characteristic trait of the carbides that exhibit facetted grain boundaries [Li et al, 2007, Byung-Kwon Yoon et al, 2005]. It is also interesting to note that the average grain size of both the normal and abnormal grains is higher on the surface than in the interior.
Fractured surfaces of the sintered compacts at various temperatures, observed by SEM are shown in Fig. 12. From 1173 K to 1323 K, the individual particles and bonded particles with necking can be discerned as a dispersed phase indicating the initial sintering stage. A few agglomerates can also be seen. From around 1373 K to 1773 K, large continuous pores were evident and this temperature range was considered to represent the intermediate stage of sintering. At 1873 K, most of the pore phase is pinched off, leading to the ﬁnal sintering stage. However, the actual transition from the initial to intermediate stage sintering is rather vague as there are strong density gradients in the microstructure due to agglomeration. But as a preliminary estimate, micrographs from these temperature ranges combined with the CRH-Iso sinter curves mentioned earlier can be assumed to represent the different sintering stages. While the SEM analysis does reveal the formation of agglomerates – thereby partly explaining the humps and dip in the CRH curve - the observation still does not account for the low activation energies measured by the kinetic analysis.
To probe the structure of the sintering particles further, the interrupted samples were also observed by TEM. A few samples were selected to understand the sintering behaviour: the original WC powder, samples sintered to 1323 K, 1473 K, 1673 K and the final densified compact. The WC powder was simply put on a grid and observed. Fig. 13 shows a few micrographs of the powder sample viewed under the TEM. It was surely not a mono disperse powder. Agglomeration was clearly obvious and interestingly, a substantial fraction of particles containing stacking faults (SFs) were also seen. The extensive streaking of the spot patterns confirm that the steps observed on the particles are indeed SFs. The faults extended right across several grains diametrically to a length of nearly 2X the particle size, resembling shear bands. As no mechanical milling was conducted, it is likely that the SFs were introduced into the particles during the production stage itself. The clear proof of the occurrence of SFs in the initial particles is an important observation since lattice defects can impact the activation energy for diffusional sintering. Diffraction studies also revealed that the SFs were present only on the prismatic planes and the basal planes were relatively free of defects.
The sample sintered at 1323 K was observed next. It clearly showed signs of undergoing initial stage sintering (necking) in some of the separate particles that could be observed. The necks between particles were almost 5 nm thick and interestingly, the neck and the entire surface of most of the particles showed a sort of spotty, recrystallized-like phase. This phase was marked by its characteristic dull appearance and hardly showed any diffraction contrast. While particle re-deposition during PIPS is most probably the reason for this observation of an amorphous surface layer, in a later section we also consider the effect of local temperature gradients leading to surface overheating of the powders that can be expected in SPS. There was a high density of thin SFs on the prism planes in these samples too (Fig. 14a-c).
The sample sintered at 1473 K showed evidence of necking, agglomeration and slight grain growth. In addition, a number of SFs could also be detected on similar prismatic planes – a continuation of the feature observed in the powders and the previous sample (Fig. 15a-d). The faults were well-formed and the fault line density in the observed grains was found to be lesser than that in the original powders.
The fourth sample that was investigated (1673 K) also showed the same features as that of the earlier sample sintered at 1473 K (Fig. 16). Necking was not observed, while the SFs were rather few and the grains were more facetted and clearly visible. In essence, the features were quite similar to the previous sample, except for a slight variation in the fraction of the phases and size of the grains. This sample also appeared to be in the intermediate stage of sintering.
The final sintered sample (2073 K) showed well-formed grains (Fig. 17). While the specimen still contained some SFs in the small grains, in some of the larger grains instead of the SFs, twins were also observed (confirmed from the DPs which showed twin reflections). Interestingly, small grains of the semi-carbide W2C measuring ≈50-100 nm could be seen in the sample (TEM samples were prepared from the cross section and not surface). All the grains were faceted and had sharp GBs. The grain growth into such well-formed structure seems to occur rather rapidly in the final stages of sintering with the annihilation of SFs, removal of the amorphous pockets and pore closure.
The significant results of the kinetic and microstructural analyses detailed earlier are presented in an integrated way in Fig. 18. The measured relative densities and the corresponding grain size evolution together represent the sintering trajectory of the
6.1. Size effect on the sintering kinetics
Sintering of compounds (both ionic and covalent) occurs by the slowest species diffusing through the fastest route to establish the chemical equilibrium associated with the stoichiometry of the compound. In WC, carbon is generally considered to be more mobile than W. The crystal structure of WC is hcp (
Direct observation of the presence of hard agglomerates (described in the following section) and the flattening of the shrinkage strain curves at low temperatures point to a mechanism of
6.2. Influence of agglomeration
Nano powders, owing to their high surface area to volume ratio, are characterized by a high surface energy. This leads to a difference in the chemical potential of the atomic species constituting the particle at the interior and surface and forms the chief driving force for agglomeration or aggregation. Such agglomerated nano powders are characterised by small groups of particles demarcated by GBs that in turn coalesce to form larger aggregates with pore boundaries [Lange F F, 1984]. This results in a totally non uniform microstructure leading to differential densiﬁcation and multiple routes to sintering. Hence, the concept of the fastest diffusion route during sintering becomes complicated as intra agglomerate pores may densify easily while the larger pores may require higher energies for densiﬁcation.
Fig. 21 shows a high magniﬁcation FE-SEM micrograph of a compact interrupted at 1073 K and also the initial powder, which shows a composite phase consisting of both individual particles and clusters of connected particles that have undergone necking. The clusters are hard agglomerates that persist even after the application of external pressure (40-50 MPa). Unlike the soft agglomerates that form by weak van der Waals/electrostatic bonding and constitute inter agglomerate bridges, the hard agglomerates are formed by solid state diffusional bonding. In all the samples studied, the green density (before sintering) was less than 43%. It is clear that while the initial stage may be controlled by PR, the intermediate stage is governed by agglomerate evolution. When agglomerates form, internal density gradients are set up leading to a large pore size distribution. Consequently, sintering sub-stages are introduced in the intermediate stage by the differences in the sintering kinetics of the inter and intra agglomerate pores.
Fig. 22(a–c) shows the high magniﬁcation microstructure of the samples from 1373 K to 1573 K. The agglomerates are enhanced and importantly, two different types of pore morphologies can be clearly distinguished: long, continuous inter-agglomerate pores and small disconnected intra-agglomerate pores (inter-particle pores). With increase in temperature, the individual agglomerates densify by sintering and slight grain growth, while there is not much observable change in the nature of the inter-agglomerate pores. At 1673 K, the grains can be clearly discerned and the intra-agglomerate pores have almost vanished, replaced by continuous pores (Fig. 22d). At still higher temperatures, (1873 K), the continuous pores become isolated and pinched-off resembling the ﬁnal sintering stage (Fig. 22e). It is clear that the intermediate stage and much of the entire densification process is governed by agglomerate evolution.
Presence of hard agglomerates can partly explain the occurrence of sub-stages observed in the sintering rate curves. Initially, at low temperatures (T≤1423 K), there is a rapid increase in the densiﬁcation rate of the compact. This occurs both by compaction of the agglomerates (contribution of intra-agglomerate sintering, which is expected to be low) and by rearrangement of agglomerates (inter-agglomerate sintering). The end densities increase to around 80%. This initial rapid shrinkage is followed by a saturation of the densification rate in the CRH curve. But interestingly, isothermal holds at these temperatures seem to induce high sintering strains. From this until ≈1623 K, the sintering rate decreases while the
isothermal sintering strains continuously increase. The decrease in the non-isothermal shrinkage rate can be explained on the basis of the energetics of the sintering of agglomerated powders: following the formation of stable agglomerates, the fraction of intra agglomerate pores is significantly reduced. From this point, the sinterability of inter agglomerate pores controls the densiﬁcation rate. But this is also prevented because of the large pore co-ordination number
However, while the agglomerate evolution mechanism explains the sintering rate curve, it does not explain the instantaneous densification curves derived from the isothermal shrinkage data. As mentioned previously, the observation that the measured densities decrease with increase in temperature implies pore growth. Sometimes, coarsening can also lead to a decrease in density. But actual measurements do not show significant coarsening to occur in this temperature interval. Pore growth occurs to reduce the total free energy of the powder system:
6.3. Influence of pulsed electric current
While the preceding discussions on particle size and agglomeration explains the multi-step sintering and partly explains the lowering of the activation energy, the effect of an electric field and high currents during sintering and their implications on sintering are discussed in this section. A thin recrystallized region between the WC particles can result by overheating at the neck regions – a characteristic of the SPS method. In the actual experiment, the external current flowing through the sample was found to increase continuously as the compact densified. The small particle size and the high current (~ 700 A at peak densification) can be expected to induce very high current densities on the particle surface. An approximate calculation of the local temperature gradient between the interior and surface of a nano particle can be carried out using a recent model of SPS proposed by Olevsky and Froyen [Eugene Olevsky and Froyen, 2009]. In their model of heat conduction in SPS, the local temperature gradient, without considering heat loss is given by:
Our observations of the low temperature sintered samples clearly show that the local field-induced temperature gradients can cause spontaneous melting and welding near the neck regions at temperatures as low as 1323 K. While the process of equilibrium melting (i.e., melting WC particles by slow heating to their melting point) may be expected to increase the activation energy for sintering (component of
The SPS behaviour of
The presence of excessive planar defects in the powder suggests that the quality of the nano powder is crucial for determining the sintering kinetics. In addition to defects, powder agglomeration controls sintering for most of the temperature range.
The low activation energies observed encourage efforts to consolidate nano powders to full density. However, not all temperatures are suitable for the sintering process, as agglomerates strongly impede densification at low temperatures. In those temperature ranges where agglomerates retard shrinkage, active surface diffusion and particle rearrangement acts to increase the compact density.
While at low temperatures the current assisted, over-heated surface is most likely the active diffusion route, at higher temperatures, grain growth acts to reduce the retarding effect of agglomerates leading to enhanced sintering.
The net sintering rate in the
While the sintering mechanisms detailed in this work are not conclusive, it can be regarded as a pointer for furthering our understanding of the sintering behaviour of
This work was carried out while AKNK was a foreign researcher at Hokkaido University, Japan. The project was partly funded by the Ohtaseiki Co., Ltd., Japan. AKNK also wishes to express his deep sense of gratitude to Prof. K Kurokawa, for having introduced him to this work and for providing financial support during his stay in Japan. Profs. A Yamauchi and N Sakaguchi are also gratefully acknowledged for their timely help with the SPS and TEM work and also for many discussions during the course of this work.
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