**6. Discussion**

38 Tungsten Carbide – Processing and Applications

be lesser than that in the original powders.

intermediate stage of sintering.

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

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

**Figure 16.** Sample sintered at 1673 K showing (a) three regions marked 1, 2 and 3 and their

diffuse ring pattern (b) is the DF image from an excited spot in the DP in 2.

removal of the amorphous pockets and pore closure.

corresponding DPs. 1 is an almost defect-free grain imaged along �12�10�, 2 contains GB dislocations as seen from the multi beam condition in the corresponding DP and 3 is an amorphous pocket with a

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, 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 *n*-WC powder. It is seen that densification dominates during the initial stages up to ≈ 1350 K with the relative density increasing from ≈ 68% to 85%. Following this rapid densification, the density then *decreases* slightly; interestingly, grain growth is also insignificant during this stage. This is a surprising observation since while the densification rate (*d/dt*) can decrease owing to many factors (grain growth or the formation of a reaction product etc.), an actual decrease in the measured density cannot occur *unless the compact is subjected to a volumetric expansion or unless there is pore growth in the specimen*. A more clear picture arises when we convert the isothermal strains at different temperatures shown earlier in **Fig. 1** to instantaneous densities as shown in **Fig. 19**. We note immediately that near the vicinity of the first peak in the CRH experiment, while the isothermal densification strains are high, the *initial densities are also lower*. This simply means that the densification rate at any temperature is a function of the green density at that temperature. This behaviour persists over a small temperature range of ≈150 K after which at around 1500 K, the second stage of densification again begins; however, simultaneous grain growth is also observed here. This

multi-stage sintering process can be explained only by a combination of different densifying and non-densifying processes occurring simultaneously and sequentially at different stages. Since the sintering behaviour (*viz*., the sintering kinetics and microstructure evolution) is influenced by the nano size of the particles, nature of the powder (agglomerates) and the activated sintering process – the effects of any of which on either the kinetics or microstructure are not exactly known, - we split the discussion into different segments in order not to mix up the issues and hence lend more clarity and focus to our overall analysis. The chief aims of this section are therefore to interpret the following observed phenomena: (i) the low sintering activation energies, (ii) occurrence of multiple sintering stages and (iii) the decrease in measured density at intermediate temperatures.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 41

**Figure 19.** Comparison of CRH sintering rate and instantaneous densities during isothermal sintering

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 (*c/a*=0.985) with C atoms occupying the interior positions in the unit cell. Yet, carbon cannot be equated to a regular interstitial atom in WC. This is because the tendency for formation of the W-C bond is quite strong. The origin of defects and the lower mechanical strength along the prism planes rather than on the basal planes can be traced back partly to this molecular origin [Nabarro F R N *et al*, 2008]. Yet, many direct and indirect evidences are available to support the fact that at higher temperatures, C is extremely active than W. For instance, the diffusion of tracer Carbon (14C) in WC was found to occur initially by LD and later on by GB diffusion through the WC grains [Bushmer and Crayton, 1971]. Estimated values of *Dv* was very low compared to GB diffusion with the diffusivity ratio, *Dgb/Dv* being of the order of 103 (*Dgb* ~ 10-9 m2 /s at 2238 K). The activation energy for GB diffusion of 14C was estimated to be ≈ 300 kJ/mol. Another estimate provides a value of 10-22 m2/s for lattice diffusion of 14C in WC [Andrievky R A and Spivak I I, 1983]. Activation energies for the diffusion of W can be assumed to be higher. It should be noted that these estimates can be different when a liquid binder like Co is present since the WC molecule has to first dissociate into W and C, dissolve in the liquid and then

*i=(1-)3f*)

(calculated by measuring the final density and using the relation,

**6.1. Size effect on the sintering kinetics** 

**Figure 18.** A sintering map showing variation of grain size and relative density with temperature.

**Figure 19.** Comparison of CRH sintering rate and instantaneous densities during isothermal sintering (calculated by measuring the final density and using the relation, *i=(1-)3f*)

#### **6.1. Size effect on the sintering kinetics**

40 Tungsten Carbide – Processing and Applications

multi-stage sintering process can be explained only by a combination of different densifying and non-densifying processes occurring simultaneously and sequentially at different stages. Since the sintering behaviour (*viz*., the sintering kinetics and microstructure evolution) is influenced by the nano size of the particles, nature of the powder (agglomerates) and the activated sintering process – the effects of any of which on either the kinetics or microstructure are not exactly known, - we split the discussion into different segments in order not to mix up the issues and hence lend more clarity and focus to our overall analysis. The chief aims of this section are therefore to interpret the following observed phenomena: (i) the low sintering activation energies, (ii) occurrence of multiple sintering stages and (iii)

**Figure 18.** A sintering map showing variation of grain size and relative density with temperature.

the decrease in measured density at intermediate temperatures.

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 (*c/a*=0.985) with C atoms occupying the interior positions in the unit cell. Yet, carbon cannot be equated to a regular interstitial atom in WC. This is because the tendency for formation of the W-C bond is quite strong. The origin of defects and the lower mechanical strength along the prism planes rather than on the basal planes can be traced back partly to this molecular origin [Nabarro F R N *et al*, 2008]. Yet, many direct and indirect evidences are available to support the fact that at higher temperatures, C is extremely active than W. For instance, the diffusion of tracer Carbon (14C) in WC was found to occur initially by LD and later on by GB diffusion through the WC grains [Bushmer and Crayton, 1971]. Estimated values of *Dv* was very low compared to GB diffusion with the diffusivity ratio, *Dgb/Dv* being of the order of 103 (*Dgb* ~ 10-9 m2 /s at 2238 K). The activation energy for GB diffusion of 14C was estimated to be ≈ 300 kJ/mol. Another estimate provides a value of 10-22 m2/s for lattice diffusion of 14C in WC [Andrievky R A and Spivak I I, 1983]. Activation energies for the diffusion of W can be assumed to be higher. It should be noted that these estimates can be different when a liquid binder like Co is present since the WC molecule has to first dissociate into W and C, dissolve in the liquid and then

migrate to the re-deposition surface. Therefore in solid state sintering without Co, it might be expected that the diffusivity of the relatively immobile W should control the effective diffusivity during the sintering of WC. Yet surprisingly, our analysis suggests that the densification processes are activated by energies as low as 100 kJ/mol. There is a substantial body of evidence that suggests similar values of low activation energies that are comparable to our present results during the initial stage sintering of either WC nano particles or by activated sintering of large WC particles (discussed in the following section). Mugenstein and co-workers [Goren-Mugenstein G R *et al*, 1998] studied the initial stage sintering of WC powders with an average particle size 100-500 nm by conventional furnace sintering and employing the Dorn method, determined the activation energy to be 76 kJ/mol. Our calculations described in the earlier sections too showed values to be of the same order. Fang and co-workers [Fang Z *et al*, 2004] studied the sintering of various grades of WC-Co in a vacuum furnace. While they did not measure the kinetics, they did indeed observe that the onset temperature of sintering of the nano sized powders (50 nm particles) started 160 K below that of the micron sized powders. Moreover, since the nature of the sintering curves was similar for both particle sizes, they surmised that the densification steps were similar irrespective of particle size, but that the activation energy decreased with the size of the particles. Therefore, it seems that lowering of the activation energy can be achieved merely by reducing the particle size, atleast during the initial stage. Studies on certain other nano sized oxide ceramics also support the same view. Theunissen and co-workers [Theunissen G S A M. *et al*, 1993] studied conventional sintering of chemically synthesized ultrafine (8-50 nm) Y2O3-ZnO2 ceramics and found that the activation energy was as low as 100 kJ/mol, which again did not correspond to any densifying diffusion mechanism. Comparison of these and many other results available in the literature [see for example, Dominguez O and Bigot J, 1995 (*n*-Fe), Kinemuchi Y and Watari K, 2008 (*n*-CeO2), Victor Zamora *et al*, 2012 (*n*-ZrB2), Li J G and Sun X, 2000 (*n*-Al2O3)] strongly support the view that a mere reduction in particle size can lower the activation energy for sintering. Fundamentally, this relates to a scaling down of a thermodynamic quantity with particle size, which can be analysed using Herring's scaling laws [Rahaman M N, (2003), Wenming Zeng *et al*, (1999)]. These laws basically compare the rate of sintering (densifying and non densifying) in different pathways for two dimensionally different particle systems. **Fig. 20** shows the sintering rates for two systems 1 and 2, as a function of the particle size ratio (R1/R2). The graph shows a cross-over when the particle size decreases (GB and Surface diffusion are significantly enhanced when R1<<R2). All the possible sintering mechanisms in a system can therefore be weighed on this scale simply as a function of particle size, provided all other factors are unchanged. Zeng and co-workers [Wenming Zeng *et al*, (1999)] used a similar type of semiquantitative analysis and pointed out that, theoretically the sintering temperature (and hence activation energy) of pure -Al2O3 can decrease from 1773 K for an initial powder size of 600 nm to 1498 K for LD and even lower to 1423 K for GB diffusion as the particle size decreases to 60 nm. In support of their argument, they even point out to some relevant experimental reports published elsewhere. The most probable explanation for all these various observations is that the surface and GBs of nano powders are easily activated and play a major role in lowering the sintering temperature and activation energy, irrespective Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 43

of whether other diffusion routes (LD, diffusion through defects etc.) dominate sintering in similar systems with a larger initial particle size. The same phenomenon can also be assumed to occur in *n*-WC powders. The presence of excessive planar defects also obfuscates the atomic diffusivity leading to rapid sintering. From the TEM micrographs, it is seen that the SFs dominate the microstructure until 1473 K, which act as short-circuit diffusion paths for sintering. However, while the particle size can be argued to lower the activation energy, it still does not explain the end point densities observed in most of the initial temperature range (shown in **Figs. 1, 19** earlier). Neither does the fact that surface diffusion is enhanced imply that shrinkage is also enhanced, since surface diffusion, unlike GB diffusion, is a non densifying sintering mechanism. Therefore, in addition to the particle size effect, there are other factors that control the sintering of the *n*-WC powders in the

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 *particle rearrangement* (PR) that can induce a rapid initial densification but eventually leads to a saturation density. PR usually occurs at low temperatures, starts with a minor shrinkage and leads to an end point density when the closest packing is reached. This type of densification by rearrangement can be enhanced in the presence of surface diffusion, and GB sliding – both of which can be assumed to occur in the green compact. Most of the defects observed in the powders and low temperature compacts run diametrically across the particles and therefore can be equated to GB dislocations which can easily lead to GB sliding. The low sintering activation energy observed during the initial stage may therefore be attributed to a densication mechanism brought about by a combination of PR assisted by surface diffusion (SD) leading to GB sliding. This mechanism explains not only the low activation energy but also the saturation shrinkage strains observed in the low temperature

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 densication 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 densication.

**Fig. 21** shows a high magnication 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).

present case.

region of the Iso-CRH curves.

**6.2. Influence of agglomeration** 

of whether other diffusion routes (LD, diffusion through defects etc.) dominate sintering in similar systems with a larger initial particle size. The same phenomenon can also be assumed to occur in *n*-WC powders. The presence of excessive planar defects also obfuscates the atomic diffusivity leading to rapid sintering. From the TEM micrographs, it is seen that the SFs dominate the microstructure until 1473 K, which act as short-circuit diffusion paths for sintering. However, while the particle size can be argued to lower the activation energy, it still does not explain the end point densities observed in most of the initial temperature range (shown in **Figs. 1, 19** earlier). Neither does the fact that surface diffusion is enhanced imply that shrinkage is also enhanced, since surface diffusion, unlike GB diffusion, is a non densifying sintering mechanism. Therefore, in addition to the particle size effect, there are other factors that control the sintering of the *n*-WC powders in the present case.

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 *particle rearrangement* (PR) that can induce a rapid initial densification but eventually leads to a saturation density. PR usually occurs at low temperatures, starts with a minor shrinkage and leads to an end point density when the closest packing is reached. This type of densification by rearrangement can be enhanced in the presence of surface diffusion, and GB sliding – both of which can be assumed to occur in the green compact. Most of the defects observed in the powders and low temperature compacts run diametrically across the particles and therefore can be equated to GB dislocations which can easily lead to GB sliding. The low sintering activation energy observed during the initial stage may therefore be attributed to a densication mechanism brought about by a combination of PR assisted by surface diffusion (SD) leading to GB sliding. This mechanism explains not only the low activation energy but also the saturation shrinkage strains observed in the low temperature region of the Iso-CRH curves.

### **6.2. Influence of agglomeration**

42 Tungsten Carbide – Processing and Applications

migrate to the re-deposition surface. Therefore in solid state sintering without Co, it might be expected that the diffusivity of the relatively immobile W should control the effective diffusivity during the sintering of WC. Yet surprisingly, our analysis suggests that the densification processes are activated by energies as low as 100 kJ/mol. There is a substantial body of evidence that suggests similar values of low activation energies that are comparable to our present results during the initial stage sintering of either WC nano particles or by activated sintering of large WC particles (discussed in the following section). Mugenstein and co-workers [Goren-Mugenstein G R *et al*, 1998] studied the initial stage sintering of WC powders with an average particle size 100-500 nm by conventional furnace sintering and employing the Dorn method, determined the activation energy to be 76 kJ/mol. Our calculations described in the earlier sections too showed values to be of the same order. Fang and co-workers [Fang Z *et al*, 2004] studied the sintering of various grades of WC-Co in a vacuum furnace. While they did not measure the kinetics, they did indeed observe that the onset temperature of sintering of the nano sized powders (50 nm particles) started 160 K below that of the micron sized powders. Moreover, since the nature of the sintering curves was similar for both particle sizes, they surmised that the densification steps were similar irrespective of particle size, but that the activation energy decreased with the size of the particles. Therefore, it seems that lowering of the activation energy can be achieved merely by reducing the particle size, atleast during the initial stage. Studies on certain other nano sized oxide ceramics also support the same view. Theunissen and co-workers [Theunissen G S A M. *et al*, 1993] studied conventional sintering of chemically synthesized ultrafine (8-50 nm) Y2O3-ZnO2 ceramics and found that the activation energy was as low as 100 kJ/mol, which again did not correspond to any densifying diffusion mechanism. Comparison of these and many other results available in the literature [see for example, Dominguez O and Bigot J, 1995 (*n*-Fe), Kinemuchi Y and Watari K, 2008 (*n*-CeO2), Victor Zamora *et al*, 2012 (*n*-ZrB2), Li J G and Sun X, 2000 (*n*-Al2O3)] strongly support the view that a mere reduction in particle size can lower the activation energy for sintering. Fundamentally, this relates to a scaling down of a thermodynamic quantity with particle size, which can be analysed using Herring's scaling laws [Rahaman M N, (2003), Wenming Zeng *et al*, (1999)]. These laws basically compare the rate of sintering (densifying and non densifying) in different pathways for two dimensionally different particle systems. **Fig. 20** shows the sintering rates for two systems 1 and 2, as a function of the particle size ratio (R1/R2). The graph shows a cross-over when the particle size decreases (GB and Surface diffusion are significantly enhanced when R1<<R2). All the possible sintering mechanisms in a system can therefore be weighed on this scale simply as a function of particle size, provided all other factors are unchanged. Zeng and co-workers [Wenming Zeng *et al*, (1999)] used a similar type of semiquantitative analysis and pointed out that, theoretically the sintering temperature (and hence activation energy) of pure -Al2O3 can decrease from 1773 K for an initial powder size of 600 nm to 1498 K for LD and even lower to 1423 K for GB diffusion as the particle size decreases to 60 nm. In support of their argument, they even point out to some relevant experimental reports published elsewhere. The most probable explanation for all these various observations is that the surface and GBs of nano powders are easily activated and play a major role in lowering the sintering temperature and activation energy, irrespective

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 densication 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 densication.

**Fig. 21** shows a high magnication 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 substages are introduced in the intermediate stage by the differences in the sintering kinetics of the inter and intra agglomerate pores.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 45

**Figure 21.** FE-SEM image of WC powder and compact sintered at 1073 K showing agglomeration. On

**Fig. 22(a–c)** shows the high magnication 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 nal sintering stage (**Fig. 22e**). It is clear that the intermediate stage and much of the entire densification process is

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 densication 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

the right is a schematic of the general low temperature microstructure.

governed by agglomerate evolution.

**Figure 20.** Dominance of various sintering mechanisms as a function of particle size calculated using Herring's scaling law.

the inter and intra agglomerate pores.

Herring's scaling law.

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 substages are introduced in the intermediate stage by the differences in the sintering kinetics of

**Figure 20.** Dominance of various sintering mechanisms as a function of particle size calculated using

**Figure 21.** FE-SEM image of WC powder and compact sintered at 1073 K showing agglomeration. On the right is a schematic of the general low temperature microstructure.

**Fig. 22(a–c)** shows the high magnication 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 nal 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 densication 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

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 47

between 30̊ and 120̊ [Gurland J, 1977]. WC (and in general, most of the transition metal carbides) exhibit facetted GBs and therefore the dihedral angle can vary drastically between

value for the critical pore co-ordination number, *Nc* can then be calculated from [Kingery et

�� <sup>=</sup> ���

this case is 3.6. Our microstructural observation show agglomerates that are co-ordinated by a far larger number of particles (**Fig. 22**) which clearly explains why the agglomerate sintering rate faces a thermodynamic barrier. This inter-agglomerate pore stability retards the shrinkage rate in the intermediate stage. Following the dip in shrinkage strain rate, there is a passive period over which the system tries to evolve by *particle growth within the agglomerates*. The massive grain growth leads to a breakup of the agglomerate identity into large grains and the stable inter agglomerate pores now start to sinter. As the agglomerates continuously convert into large grains, the pores start to shrink rapidly, surpassing the grain growth rate. Hence concurrent grain growth supports shrinkage until the continuous pores are eliminated and the isolated pore structure resembling the nal stage appears. The relative densities increase to nearly 94% during this stage. The nal stage of sintering is reached at temperatures above 1773 K when the pore phases are pinched off which again results in a reduction of the densication rate. Bimodal shrinkage rates seem to be a signature trait of agglomeration-induced densification and have been commonly reported in the literature [Lanfredi S *et al*, 2000, Jiang X X, 1994]. Non agglomerated powders show only one sintering rate maxima while agglomerated powders usually show double maxima for the bimodal pore size distributions [Nobre M A L *et al*, 1996, Shi J L *et al*, 1994, Duran P *et al*,

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

refers to the energy of either a GB or pore and *A*gb, *A*s-v are the corresponding areas.

there is oxidation of the particles at high temperatures that reduces the surface energy of the particles. X-ray diffractograms of the samples at various temperatures are shown in **Fig 23**. At about 1300 K, it is observed that small peaks of WO3 show up. In addition, from the earlier TEM micrographs, it is clear that there is a tendency for dissociation of WC leading to

�� = �������� ����������� (11)

gb, pore growth can occur. This can happen particularly when

is the dihedral angle between the particles in the agglomerate. It turns out that *Nc* in

) in WC– Co is reported to vary

. The approximate

����� (10)

large pore co-ordination number *Nc*. The dihedral angle (

al, 1975]:

where

1996, Knorr P *et al*, 2000].

powder system:

Under conditions, when

s-v < 

where, 

different GBs. However, a statistical average of 75̊ can be assumed for

**Figure 22.** High magnification FE-SEM images of the intermediate sintering stage showing evolution of agglomerates.

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 densication rate. But this is also prevented because of the large pore co-ordination number *Nc*. The dihedral angle () in WC– Co is reported to vary between 30̊ and 120̊ [Gurland J, 1977]. WC (and in general, most of the transition metal carbides) exhibit facetted GBs and therefore the dihedral angle can vary drastically between different GBs. However, a statistical average of 75̊ can be assumed for . The approximate value for the critical pore co-ordination number, *Nc* can then be calculated from [Kingery et al, 1975]:

46 Tungsten Carbide – Processing and Applications

agglomerates.

**Figure 22.** High magnification FE-SEM images of the intermediate sintering stage showing evolution of

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 densication rate. But this is also prevented because of the

$$N\_c = \frac{^{360}\text{L}}{^{160-\varphi}}\tag{10}$$

where is the dihedral angle between the particles in the agglomerate. It turns out that *Nc* in this case is 3.6. Our microstructural observation show agglomerates that are co-ordinated by a far larger number of particles (**Fig. 22**) which clearly explains why the agglomerate sintering rate faces a thermodynamic barrier. This inter-agglomerate pore stability retards the shrinkage rate in the intermediate stage. Following the dip in shrinkage strain rate, there is a passive period over which the system tries to evolve by *particle growth within the agglomerates*. The massive grain growth leads to a breakup of the agglomerate identity into large grains and the stable inter agglomerate pores now start to sinter. As the agglomerates continuously convert into large grains, the pores start to shrink rapidly, surpassing the grain growth rate. Hence concurrent grain growth supports shrinkage until the continuous pores are eliminated and the isolated pore structure resembling the nal stage appears. The relative densities increase to nearly 94% during this stage. The nal stage of sintering is reached at temperatures above 1773 K when the pore phases are pinched off which again results in a reduction of the densication rate. Bimodal shrinkage rates seem to be a signature trait of agglomeration-induced densification and have been commonly reported in the literature [Lanfredi S *et al*, 2000, Jiang X X, 1994]. Non agglomerated powders show only one sintering rate maxima while agglomerated powders usually show double maxima for the bimodal pore size distributions [Nobre M A L *et al*, 1996, Shi J L *et al*, 1994, Duran P *et al*, 1996, Knorr P *et al*, 2000].

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:

$$
\Delta G = \chi\_{gb} \Delta A\_{gb} + \chi\_{\text{s-v}} \Delta A\_{\text{s-v}} \tag{11}
$$

where, refers to the energy of either a GB or pore and *A*gb, *A*s-v are the corresponding areas. Under conditions, when s-v < gb, pore growth can occur. This can happen particularly when there is oxidation of the particles at high temperatures that reduces the surface energy of the particles. X-ray diffractograms of the samples at various temperatures are shown in **Fig 23**. At about 1300 K, it is observed that small peaks of WO3 show up. In addition, from the earlier TEM micrographs, it is clear that there is a tendency for dissociation of WC leading to oxidation of the particles. Therefore, it is probable that the oxidation of the WC particles could have led to the growth of pores. WO3 has a high vapour pressure and therefore evaporates as it forms. It is probable that this continuous formation and evaporation of WO3 leads to an increase in porosity (which lowers the density) while isothermal holding at these temperatures leads to an increase in densification due to the applied stress and continuous repacking of agglomerates. Liu *et al* [Dean-Mo Liu *et al*, 1999] reported a detailed study on the influence of agglomeration of zirconia (ZrO2) powder. Their observation corresponds very well with our experiments: systems with a lower green density and which consequently are highly agglomerated show the maximum sintering rate and reach full density. The densification rate below the first maximum in the CRH curve corresponds to regions where isothermal sintering can be carried out. Similar results have been reported for *n*-MgO too by Itatani *et al*, [Itatani K *et al*, 1993] who show that a lower green density increases final densities of compacts. While these previous reports have not studied the isothermal and non-isothermal sintering behaviour at any particular temperature, they assume that coarsening could be the reason for the low densities at certain temperatures. This point is still ambiguous and requires further detailed investigations to clarify the actual mechanism. But as Kellet and Lange have pointed out earlier, for a fixed sintering temperature and time, the end point density is proportional to the bulk density of the powder [Kellet B J and Lange F F, 1983].

#### **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:

$$
\nabla T = \frac{1}{G + r\_p} \sqrt{\frac{E^2 \Delta t \lambda\_a T\_0}{2nC}} \tag{12}
$$

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 49

*<sup>e</sup>* were obtained from the literature: *C1300K*0.0175 J/K/m3

*e(0,T)[(1-P)/(1+2P)]* [Eugene Olevsky and Froyen,

*H* arising from the phase transformation of

*t*=46.2 ms, *n*=120220,

*<sup>e</sup>* =1/) of a sample with residual

*T*).

time and 6.6 ms OFF time. The ON pulse comprises twelve 3.3 ms pulses. Other

[Andon et al, 1975]. For a sample with residual porosity *P*, the heat capacity is given by *C*=(1-*P*)*C1300K* [Eugene Olevsky and Froyen, 2009, Yann Aman *et al*, 2011]. Since data on the electrical resistivity of WC at high temperatures were unavailable, with a knowledge of the room temperature resistivity of WC (*300K*20 m) and the temperature coefficient of resistivity 4500 /K [Grebenkina and Denbnovetskaya, 1968], a linear approximation was applied from 300 K to the temperature of interest (1300 K) using the relation =*300K* (1+

This approximation, although slightly in error, may yield a variation of one order of

2009]*.* Using these values, *T*60x106 K/m. Owing to these large gradients, a plasma is more likely to form at the neck area. However, the temperature can be rapidly conducted over the particle surfaces leading to surface melting in a zone of 5-10 nm at the periphery of the grains as observed near the neck of the sintered particles. These regions can then enhance sintering by reducing inter-granular friction leading to more compact packing (densification by particle rearrangement) and provide easy routes for GB diffusion. At higher temperatures or in densely compacted regions, the term, 'grains' is more appropriate than, 'particles'. It was observed that such regions where the microstructure can be described as 'grains', are not surrounded by the recrystallized phase. While the actual observation of a GB phase during SPS of WC has not been reported yet, certain recent investigations by Demiriskyi and co-workers [Demirskyi D et al, 2012] on micrometre sized spherical balls of WC did reveal anomalous diffusion at the inter-particle neck regions. The group conducted some fundamental studies to understand the sintering mechanism in WC during SPS, conventional sintering and Microwave sintering. They measured both the linear shrinkage during the initial stage and also the neck growth rate (by SEM observations). Using the experimentally observed neck growth rate, they calculated the diffusion coefficient and arrived at the surprising result that the diffusion coefficient during SPS was *orders of magnitude higher* than during conventional sintering. This anomalous behaviour was attributed to a highly active surface and recrystallization at the neck region was clearly observed by SEM. Another recent report is from the group of Guyot and co-workers [Guyot P *et al*, 2012], who demonstrated micro welding at inter-particle areas of micron-sized Cu powders. They attribute this to the inductive coupling of the electromagnetic field leading to a decrease in electrical resistivity of the powders by several orders of magnitude (the *Branly effect*). These recent reports clearly suggest that particle overheating can lead to a GB complexion [Jian Luo,

approximate values were also plugged in: *G*100 nm, *rp*50 nm,

magnitude in the final result. The electrical conductivity (

*e(P,T)=*

2008, Shen Dillon *et al*, 2009] particularly during the initial stages of SPS.

activation energy for sintering (component of

Our observations of the low temperature sintered samples clearly show that the local fieldinduced 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

solid to liquid), this surface melting that is expected to occur in SPS is a totally nonequilibrium melting phenomenon which occurs rapidly. As Chaim [Rachman Chaim, 2007]

*E*1000 V/m. The values of *C* and

porosity, *P* was calculated as

where, *G* is the grain size, *rp* is the pore radius, *C* is the specific heat capacity, *T0* is the temperature from which sintering is assumed to start (873 K, in this case), *E* is the electric field (V/m), *e* is the electrical conductivity, *t* is the total (ON+OFF) pulse sequence duration and *n* is the number of pulses required to reach the desired temperature. When applied to oxide ceramics with low conductivity like Al2O3, local temperature gradients of the order of 106 K/m were determined during SPS [Eugene Olevsky and Froyen, 2009].. In our experiments, we used an ON/OFF pulse ratio of 12/2 which corresponds to 39.6 ms ON

powder [Kellet B J and Lange F F, 1983].

field (V/m),

**6.3. Influence of pulsed electric current** 

oxidation of the particles. Therefore, it is probable that the oxidation of the WC particles could have led to the growth of pores. WO3 has a high vapour pressure and therefore evaporates as it forms. It is probable that this continuous formation and evaporation of WO3 leads to an increase in porosity (which lowers the density) while isothermal holding at these temperatures leads to an increase in densification due to the applied stress and continuous repacking of agglomerates. Liu *et al* [Dean-Mo Liu *et al*, 1999] reported a detailed study on the influence of agglomeration of zirconia (ZrO2) powder. Their observation corresponds very well with our experiments: systems with a lower green density and which consequently are highly agglomerated show the maximum sintering rate and reach full density. The densification rate below the first maximum in the CRH curve corresponds to regions where isothermal sintering can be carried out. Similar results have been reported for *n*-MgO too by Itatani *et al*, [Itatani K *et al*, 1993] who show that a lower green density increases final densities of compacts. While these previous reports have not studied the isothermal and non-isothermal sintering behaviour at any particular temperature, they assume that coarsening could be the reason for the low densities at certain temperatures. This point is still ambiguous and requires further detailed investigations to clarify the actual mechanism. But as Kellet and Lange have pointed out earlier, for a fixed sintering temperature and time, the end point density is proportional to the bulk density of the

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:

�� � � � ����

*e* is the electrical conductivity,

<sup>√</sup>��������

where, *G* is the grain size, *rp* is the pore radius, *C* is the specific heat capacity, *T0* is the temperature from which sintering is assumed to start (873 K, in this case), *E* is the electric

duration and *n* is the number of pulses required to reach the desired temperature. When applied to oxide ceramics with low conductivity like Al2O3, local temperature gradients of the order of 106 K/m were determined during SPS [Eugene Olevsky and Froyen, 2009].. In our experiments, we used an ON/OFF pulse ratio of 12/2 which corresponds to 39.6 ms ON

��� (12)

*t* is the total (ON+OFF) pulse sequence

time and 6.6 ms OFF time. The ON pulse comprises twelve 3.3 ms pulses. Other approximate values were also plugged in: *G*100 nm, *rp*50 nm, *t*=46.2 ms, *n*=120220, *E*1000 V/m. The values of *C* and *<sup>e</sup>* were obtained from the literature: *C1300K*0.0175 J/K/m3 [Andon et al, 1975]. For a sample with residual porosity *P*, the heat capacity is given by *C*=(1-*P*)*C1300K* [Eugene Olevsky and Froyen, 2009, Yann Aman *et al*, 2011]. Since data on the electrical resistivity of WC at high temperatures were unavailable, with a knowledge of the room temperature resistivity of WC (*300K*20 m) and the temperature coefficient of resistivity 4500 /K [Grebenkina and Denbnovetskaya, 1968], a linear approximation was applied from 300 K to the temperature of interest (1300 K) using the relation =*300K* (1+*T*). This approximation, although slightly in error, may yield a variation of one order of magnitude in the final result. The electrical conductivity (*<sup>e</sup>* =1/) of a sample with residual porosity, *P* was calculated as *e(P,T)=e(0,T)[(1-P)/(1+2P)]* [Eugene Olevsky and Froyen, 2009]*.* Using these values, *T*60x106 K/m. Owing to these large gradients, a plasma is more likely to form at the neck area. However, the temperature can be rapidly conducted over the particle surfaces leading to surface melting in a zone of 5-10 nm at the periphery of the grains as observed near the neck of the sintered particles. These regions can then enhance sintering by reducing inter-granular friction leading to more compact packing (densification by particle rearrangement) and provide easy routes for GB diffusion. At higher temperatures or in densely compacted regions, the term, 'grains' is more appropriate than, 'particles'. It was observed that such regions where the microstructure can be described as 'grains', are not surrounded by the recrystallized phase. While the actual observation of a GB phase during SPS of WC has not been reported yet, certain recent investigations by Demiriskyi and co-workers [Demirskyi D et al, 2012] on micrometre sized spherical balls of WC did reveal anomalous diffusion at the inter-particle neck regions. The group conducted some fundamental studies to understand the sintering mechanism in WC during SPS, conventional sintering and Microwave sintering. They measured both the linear shrinkage during the initial stage and also the neck growth rate (by SEM observations). Using the experimentally observed neck growth rate, they calculated the diffusion coefficient and arrived at the surprising result that the diffusion coefficient during SPS was *orders of magnitude higher* than during conventional sintering. This anomalous behaviour was attributed to a highly active surface and recrystallization at the neck region was clearly observed by SEM. Another recent report is from the group of Guyot and co-workers [Guyot P *et al*, 2012], who demonstrated micro welding at inter-particle areas of micron-sized Cu powders. They attribute this to the inductive coupling of the electromagnetic field leading to a decrease in electrical resistivity of the powders by several orders of magnitude (the *Branly effect*). These recent reports clearly suggest that particle overheating can lead to a GB complexion [Jian Luo, 2008, Shen Dillon *et al*, 2009] particularly during the initial stages of SPS.

Our observations of the low temperature sintered samples clearly show that the local fieldinduced 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 *H* arising from the phase transformation of solid to liquid), this surface melting that is expected to occur in SPS is a totally nonequilibrium melting phenomenon which occurs rapidly. As Chaim [Rachman Chaim, 2007]

and Chaim and Reinharz [Chaim R and Reinharz Bar-Hama, 2010] have suggested, this GB complexion leads to a plastically softened surface layer which can activate rapid atomic diffusion and promote particle rearrangement and creep leading to very low activation energies during sintering. At high temperatures, the 'particle' identity is lost and grain growth rate also increases. The thickness of the recrystallized layer decreases in comparison to the grain size, although the GB is still an active diffusion route until complete densification is achieved. This idea is consistent with our observed kinetic results and the microstructure.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 51

1. 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,

2. 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

3. 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

4. The net sintering rate in the *n*-WC powder can be equated to the sum of three factors:

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 *n*-WC. The experimental observations do suggest that alternate, yet novel mechanisms are active during the SPS of *n*-WC, and certain factors that can be responsible have been discussed at length. However, a consistent theory of nano sintering specific to *n*-WC is still necessary. Such a description should therefore include the effects of GB plasticity and creeping induced by dislocation climb and glide in addition to the surface overheating phenomenon in nano materials during SPS. These points are motivated by the fact that even in a brittle material like WC, plasticity effects can be significantly enhanced as the 'GB phase' fraction

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

powder agglomeration controls sintering for most of the temperature range.

rearrangement acts to increase the compact density.

effect of agglomerates leading to enhanced sintering.

*Dept. of Materials Science and Engineering, Case Western Reserve University,* 

*USACentre for Advanced Research of Energy and Materials, Faculty of Engineering, Hokkaido University, Sapporo, Japan* 

*Centre for Advanced Research of Energy and Materials, Faculty of Engineering, Hokkaido University, Sapporo, Japan* 

���)����� � ���)������� � ���)����� � ���)��.

increases.

**Author details** 

A.K. Nanda Kumar

Kazuya Kurokawa

**Acknowledgement** 

*Cleveland, Ohio,* 

**Figure 23.** XRD of the samples interrupted at different temperatures. The WO3 phase is seen at almost all low temperatures, while the final compact only shows WC and graphite. All the primary peaks are from the WC phase.

### **7. Conclusions**

The SPS behaviour of *n*-WC appears to be a complex process involving size effects, field effects, chemical reactions and anomalously rapid diffusion. Experimental observations described in this work show evidence of planar defects, possible GB reconstruction and agglomeration that can contribute to the lowering of the sintering activation energy. In our analysis and from the current volume of literature cited to support our view, it is clear that the fundamental aspects of sintering pertaining to nano particles particularly in the presence of an electromagnetic field can be largely different, for which an exact theory is yet to be developed. A few significant results of this work are given below to summarize our findings:


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 *n*-WC. The experimental observations do suggest that alternate, yet novel mechanisms are active during the SPS of *n*-WC, and certain factors that can be responsible have been discussed at length. However, a consistent theory of nano sintering specific to *n*-WC is still necessary. Such a description should therefore include the effects of GB plasticity and creeping induced by dislocation climb and glide in addition to the surface overheating phenomenon in nano materials during SPS. These points are motivated by the fact that even in a brittle material like WC, plasticity effects can be significantly enhanced as the 'GB phase' fraction increases.
