**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.

22 Tungsten Carbide – Processing and Applications

M, 1997, Hulbert D M *et al*, 2008, Hulbert D M *et al*, 2009].

presence of electromagnetic fields.

**2. Activated sintering processes** 

Given that cemented *n*-WC has many such industrial applications particularly owing to its mechanical strength, the microstructure, porosity (density) and grain size inarguably are of extreme significance in tailoring its properties like hardness, toughness and chemical stability. Powder metallurgical processes like Hot Iso-static Pressing (HIP) and high temperature solid state or liquid phase sintering are the usually employed methods of fabricating dense compacts of pure or cemented WC. However, pure WC in the absence of a binder is rather difficult to consolidate completely. While in cemented WC, the liquid phase assists sintering by particle rearrangement, the low diffusivities of W and C under pure solid state sintering conditions retard quick consolidation during sintering or HIP of pure n-WC. Therefore, unnaturally long durations (in the case of isothermal sintering) or very high temperatures in excess of 2000 C (in the case of non- isothermal sintering) are required for consolidation of n-WC. This disadvantage has led researchers to seek alternate or improvised sintering methods [Bartha L *et al*, 2000, Agrawal D *et al*, 2000, Breval E *et al*, 2005, Kim H C *et al*, 2004] like Spark Plasma Sintering (SPS) or microwave sintering to achieve quicker densification at lower time costs. The SPS method, in particular has attracted wide attention owing to its consistently good record of achieving the desired density at surprisingly low times and lower temperatures. The generation of very high current densities leading to a sort of, 'plasma welding' between the particles is suspected to be the chief cause of such a profit in the total energy budget compared to conventional sintering. However, no clear evidence exists for the actual generation of plasma or any surface melting phenomenon in the SPS process although the hypothesis has been widely debated [Tokita

Since the last decade, a number of reports on SPS of *n*-WC have consistently come up in journals and scientific magazines. Not only have the compacts been manufactured to complete density, but the grain size could also be limited to the ultra-fine size (200-400 nm). Usually Hall-Petch hardening is observed at low grain sizes and low cobalt content. This increased capability to constrain the microstructure to the ultrafine regime has been largely aided in part because of the commercial availability of nano powders of WC synthesized by many chemical routes and also partly because of the current popularity of activated sintering instruments that also accommodate high heating rates and pressure along with the

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 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 *temperature controlled* mode, the current to the punch and sample is supplied according to a pre-set temperature programme. The temperature is measured at the die surface with a pyrometer and the feedback is used to adjust the current supply accordingly. In the *current controlled* mode, a constant current is supplied to the sample and the temperature is monitored. Very high heating rates can be achieved limited only by the maximum current available from the power source. However, the actual temperature in SPS can be quite different from the measured temperatures for many reasons: the pyrometer measures the temperature at a niche in the die which is neither exactly on the sample surface nor in the surface interior - certain reports put this difference at ~50-100 K [Bernard and Guizard, 2007]; measured temperatures are usually the average values and give no indication of the very local temperatures that can actually exist between the particles. The overall electrical resistance - including the internal resistance of the voltage source and resistance of the bulk of the apparatus - controls the current flow and consequently, the Joule heating generated in the sample. Hence, in an SPS experiment, the total resistance, *Rtotal* can be written as:

$$(R)\_{total} = (R)\_{internal} + (R)\_{contact} + (R)\_{sample} + (R)\_{bulk} \tag{1}$$

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, *Rcontact* [Giovanni Maizza *et al*, 2007, Munir Z A et al, 2006]. Moreover, the resistance of the sample, *Rsample* is continuously changing (as a function of the instantaneous porosity) and hence, the observed value of current in circuit is a product of the complex interplay of various parameters. The pulse frequency of the DC supply in a typical SPS process is split into an ON/OFF ratio of 12/2. The ON pulse in turn is split into sub pulses of milli second duration. All these parameters can be controlled by the user to achieve the best sintering conditions. Usually, only the heating rate and pressure are varied with the rest of the controls kept according to the factory settings.

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 electromigration (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 *et al*, 2009, Di Yang *et al*, 2010, Gupta V K *et al*, 2007]. However, while the outcome has been certainly encouraging, a clear and validated picture of the sintering mechanism under activated sintering is still lacking.

#### **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 (*x/a*) or by measuring the macroscopic shrinkage using a dilatometer with respect to time. A number of theories have been developed to explain both shrinkage and neck growth during sintering [Ashby M F, 1974, Swinkels F B and Ashby M F, 1981, Beere W, 1974, Coble R L, 1958]. Such theories derive explicit relations connecting the shrinkage strain, (=*l/l0*) or neck growth (*x/a*) to the time of sintering, *t* under isothermal conditions. Measurements of neck growth in ultrafine particles are difficult and therefore, the macroscopic shrinkage strain is instead measured and a suitable theory is chosen to study the kinetics. In any case, the sintering kinetics (either solid or liquid phase assisted) can be described by a generic equation of the type:

$$
\varepsilon^m = \left(\frac{\Delta l}{l\_0}\right)^m = \frac{\kappa t}{T} \tag{2}
$$

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 25

) against ln (*t*) at constant *T* is a straight line with slope 1/*m*. The

*<sup>m</sup>*) against 1/*T* at constant values of time, *t* should yield a straight line

/dt) against 1/*T* would yield values of *Q*. Usually the Dorn

����� � (7)

� ��(�) (4)

�� (5)

�� (6)

��(�) <sup>=</sup> �

Therefore a plot of ln (

Hence a plot of ln (*T*

determined by:

so that the slope of a plot of ln(d

Lattice diffusion without grain growth

where *f(*

modelled for the sintering of a pair of spherical particles.

*)* is the shrinkage strain – time curve.

kinetic methods should yield the same values of activation energy.

� �� ��

sintering exponent '*m*' can vary depending on the mechanism (diffusion path) and geometry of the sintering bodies. **Table 1** shows the various values of *m* available in the literature,

The activation energy for sintering, *Q* can be determined in many ways: Utilizing the

��(���) = ��(���) <sup>−</sup> �

from which *Q* can be determined if the sintering exponent, *m* is known. Another equivalent method for determination of the activation energy of sintering in isothermal experiments is the time for constant fraction technique which is based on the measurement of a constant linear shrinkage fraction at different hold temperatures. The activation energy can then be

��(�) = �� �� ����(�)����� �

A more common method of determining the activation energy without *apriori* knowledge of the sintering exponent, *m* is the Dorn's method [Bacmann J J and Cizeron G, 1968]. Here, the densication strain rates are evaluated at a constant time at different sintering temperatures

method is associated with an error of ~8 to 10%. Provided the initial temperature instability during the first few minutes of isothermal hold is eliminated and if the system does not exhibit shrinkage saturation (asymptotic behaviour) very early during the hold period, both

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:

�−�� <sup>=</sup> ������

� � � �

exponential dependence of *K* on *T*, and the *m* value determined earlier, we can write,

�� � �

where '*m*' is the sintering exponent, *t* is the isothermal holding time and *T* is the hold temperature. The higher the value of *m*, the lower is the magnitude of shrinkage. The constant, *K* = *K(T)* is the temperature dependant sintering constant and accommodates the interface energetics and transport kinetics of the sintering process via the surface energy, and the diffusion coefficient, *D*. The form of *K* can be related to temperature by an Arrhenius type equation,

$$K = K\_0 e^{-Q/RT} \tag{3}$$

where *Q* refers to the activation energy for densification and *R* is the gas constant. The kinetic parameters can be evaluated easily by a simple modification of the two equations. Firstly, equation (2) gives:

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 25

$$\ln(\varepsilon) = \frac{1}{m} \ln\left(\frac{\kappa}{\tau}\right) + \frac{1}{m} \ln(t) \tag{4}$$

Therefore a plot of ln () against ln (*t*) at constant *T* is a straight line with slope 1/*m*. The sintering exponent '*m*' can vary depending on the mechanism (diffusion path) and geometry of the sintering bodies. **Table 1** shows the various values of *m* available in the literature, modelled for the sintering of a pair of spherical particles.

The activation energy for sintering, *Q* can be determined in many ways: Utilizing the exponential dependence of *K* on *T*, and the *m* value determined earlier, we can write,

$$\ln\left(T\varepsilon^{m}\right) = \ln\left(K\_{0}t\right) - \frac{Q}{RT} \tag{5}$$

Hence a plot of ln (*T<sup>m</sup>*) against 1/*T* at constant values of time, *t* should yield a straight line from which *Q* can be determined if the sintering exponent, *m* is known. Another equivalent method for determination of the activation energy of sintering in isothermal experiments is the time for constant fraction technique which is based on the measurement of a constant linear shrinkage fraction at different hold temperatures. The activation energy can then be determined by:

$$\ln \text{l}(\mathbf{t}) = \ln \left( \int\_0^f [k\_0 f(\boldsymbol{\varepsilon})]^{-1} d\mathbf{y} \right) + \frac{\mathcal{Q}}{\mathcal{R}\mathbf{T}} \tag{6}$$

where *f()* is the shrinkage strain – time curve.

24 Tungsten Carbide – Processing and Applications

mechanism under activated sintering is still lacking.

equation of the type:

Arrhenius type equation,

Firstly, equation (2) gives:

**3. Isothermal and non-isothermal sintering** 

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 electromigration (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 *et al*, 2009, Di Yang *et al*, 2010, Gupta V K *et al*, 2007]. However, while the outcome has been certainly encouraging, a clear and validated picture of the 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 (*x/a*) or by measuring the macroscopic shrinkage using a dilatometer with respect to time. A number of theories have been developed to explain both shrinkage and neck growth during sintering [Ashby M F, 1974, Swinkels F B and Ashby M F, 1981, Beere W, 1974, Coble

neck growth (*x/a*) to the time of sintering, *t* under isothermal conditions. Measurements of neck growth in ultrafine particles are difficult and therefore, the macroscopic shrinkage strain is instead measured and a suitable theory is chosen to study the kinetics. In any case, the sintering kinetics (either solid or liquid phase assisted) can be described by a generic

where '*m*' is the sintering exponent, *t* is the isothermal holding time and *T* is the hold temperature. The higher the value of *m*, the lower is the magnitude of shrinkage. The constant, *K* = *K(T)* is the temperature dependant sintering constant and accommodates the interface energetics and transport kinetics of the sintering process via the surface energy,

and the diffusion coefficient, *D*. The form of *K* can be related to temperature by an

where *Q* refers to the activation energy for densification and *R* is the gas constant. The kinetic parameters can be evaluated easily by a simple modification of the two equations.

 (=*l/l0*) or

� (2)

�=����� �� <sup>⁄</sup> (3)

R L, 1958]. Such theories derive explicit relations connecting the shrinkage strain,

�� = ��� �� � � <sup>=</sup> �� A more common method of determining the activation energy without *apriori* knowledge of the sintering exponent, *m* is the Dorn's method [Bacmann J J and Cizeron G, 1968]. Here, the densication strain rates are evaluated at a constant time at different sintering temperatures so that the slope of a plot of ln(d/dt) against 1/*T* would yield values of *Q*. Usually the Dorn method is associated with an error of ~8 to 10%. Provided the initial temperature instability during the first few minutes of isothermal hold is eliminated and if the system does not exhibit shrinkage saturation (asymptotic behaviour) very early during the hold period, both kinetic methods should yield the same values of activation energy.

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

$$P - P\_0 = \frac{N\_A D\_v \Omega \mathcal{Y}}{k\_B T G^3} \mathbf{t} \tag{7}$$

Lattice diffusion with grain growth

$$P - P\_0 = \frac{N\_A D\_\vartheta \Omega \mathcal{Y}}{k\_B T G^3} \ln(t) \tag{8}$$

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 27

1873 K. The samples were held at these temperatures for a period of 30 minutes while their shrinkage was continuously monitored using a dilatometer. For the non-isothermal sintering studies, two heating rates – 20 K/min and 50 K/min – were employed and the sintering process was assumed to be complete when the dilatometer showed no further change in shrinkage during two successive temperature measurements. All the samples were allowed to cool down to room temperature inside the chamber. Before analysis, the samples were first polished with fine diamond paste (1m) and subsequently cleaned with ethanol in an ultrasonic bath. The densities of the samples were determined by the Archimedes method. All densities are reported relative to the density of pure WC (15.8 g/cc). Fractured and etched samples were used for the microstructure analysis. Before etching, the samples were cross sectioned, polished and cleaned as earlier. Conventional Murakami solution (H2O+KOH+K3[Fe(CN)6] in a volumetric ratio of 10:1:1) was used for etching the compacts. For TEM analysis, the cross sectioned samples were mechanically thinned to 100 m, dimpled to a depth of 20 m and then milled with Ar ions to electron transparency. Microstructure and phase analyses were carried out using XRD, FE SEM, EBSD and TEM. Grain size evaluation was performed using the FE SEM images (15000 X magnification) of the etched samples with the aid of an image analysis software (Image Pro-Plus). Approximately 150-200 grains from three different locations of a sample were randomly selected for the measurements. The boundaries were delineated either manually or auto segmented and the average diameter (average value of the diameters measured at 2 intervals

and passing through the centroid of the selected grain) of the grains was calculated.

process, it does indeed show at first glance, the occurrence of sub-stages.

**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

**5. Results** 

**5.1. Analysis of the sintering kinetics** 

Grain boundary diffusion without grain growth

$$P - P\_0 = \left(\frac{\kappa\_{A^0B^0W^{\Omega}\mathcal{Y}}}{k\_B T G^4}\right)^{2/3} t^{2/3} \tag{9}$$

where the terms have the following meanings: *P0* – initial porosity at *t = 0* in the intermediate stage, *P* – nal porosity, *Dv*, *Db* – volume, grain boundary diffusivities, – surface energy, *w* –grain boundary width, – atomic volume, *G* – grain size and the other terms have the usual meanings.

Non isothermal (also called *constant rate of heating*, CRH) sintering can also be analysed by suitable models. In this work, we employed the method of Young and Cutler [Young W S and Cutler I B, 1970] to determine the activation energy from a plot of ln(d/dt) against 1/*T*. The slope determined from the plot is *mQ* (effective activation energy) and if either the mechanism (*m* is ½ for LD and ⅓ for GB diffusion) or activation energy (*Q*) is known *apriori* (from isothermal experiments), the other unknown can be determined. We used a combination of both isothermal and non-isothermal sintering to complement each for the kinetic studies reported in this work.


**Table 1.** 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).

### **4. Experiments**

Commercially purchased *n*-WC powders without any pre-treatment were used for sintering. The particle size measured by BET was 70 nm and the powder composition included 0.4% O, 5 ppm Cr, 27 ppm Fe, 4 ppm Mo, 3 ppm Ca, 2 ppm Ni, <5 ppm Si and < 2 ppm Sn. Approximately 2.5 – 3 g of the powder was filled into a 10 mm diameter graphite die for spark plasma sintering (SPS) in a Dr SINTER LAB instrument. This SPS instrument has a dilatometer with an accuracy of 0.01 mm for measuring the instantaneous linear shrinkage. Temperature measurements were carried out using a radiation thermometer (pyrometer) that was focused on a small niche in the carbon die. Graphite sheets were used as spacers to separate the powder sample from the punch and die. After initial temperature stabilization at 873 K for 3 minutes, sintering was carried out in vacuum (< 4 Pa) at a constant heating rate of 50 K/min and a compressive stress of 40 MPa to various temperatures from 1073K to 1873 K. The samples were held at these temperatures for a period of 30 minutes while their shrinkage was continuously monitored using a dilatometer. For the non-isothermal sintering studies, two heating rates – 20 K/min and 50 K/min – were employed and the sintering process was assumed to be complete when the dilatometer showed no further change in shrinkage during two successive temperature measurements. All the samples were allowed to cool down to room temperature inside the chamber. Before analysis, the samples were first polished with fine diamond paste (1m) and subsequently cleaned with ethanol in an ultrasonic bath. The densities of the samples were determined by the Archimedes method. All densities are reported relative to the density of pure WC (15.8 g/cc). Fractured and etched samples were used for the microstructure analysis. Before etching, the samples were cross sectioned, polished and cleaned as earlier. Conventional Murakami solution (H2O+KOH+K3[Fe(CN)6] in a volumetric ratio of 10:1:1) was used for etching the compacts. For TEM analysis, the cross sectioned samples were mechanically thinned to 100 m, dimpled to a depth of 20 m and then milled with Ar ions to electron transparency. Microstructure and phase analyses were carried out using XRD, FE SEM, EBSD and TEM. Grain size evaluation was performed using the FE SEM images (15000 X magnification) of the etched samples with the aid of an image analysis software (Image Pro-Plus). Approximately 150-200 grains from three different locations of a sample were randomly selected for the measurements. The boundaries were delineated either manually or auto segmented and the average diameter (average value of the diameters measured at 2 intervals and passing through the centroid of the selected grain) of the grains was calculated.

## **5. Results**

26 Tungsten Carbide – Processing and Applications

Lattice diffusion with grain growth

Grain boundary diffusion without grain growth

surface energy, *w* –grain boundary width,

terms have the usual meanings.

kinetic studies reported in this work.

**4. Experiments** 

���� <sup>=</sup> ������

���� = ��������

and Cutler I B, 1970] to determine the activation energy from a plot of ln(d

**Diffusion pathway Value of** *m* **Reference**

refer to lattice diffusion (i.e., volume) and grain boundary respectively).

����� �

where the terms have the following meanings: *P0* – initial porosity at *t = 0* in the intermediate stage, *P* – nal porosity, *Dv*, *Db* – volume, grain boundary diffusivities, –

Non isothermal (also called *constant rate of heating*, CRH) sintering can also be analysed by suitable models. In this work, we employed the method of Young and Cutler [Young W S

The slope determined from the plot is *mQ* (effective activation energy) and if either the mechanism (*m* is ½ for LD and ⅓ for GB diffusion) or activation energy (*Q*) is known *apriori* (from isothermal experiments), the other unknown can be determined. We used a combination of both isothermal and non-isothermal sintering to complement each for the

**LD** 0.46 Johnson and Cutler, 1963a

**GB** 0.31 Johnson and Cutler, 1963b

**Table 1.** Values of the initial stage sintering exponent developed for model geometries. (LD and GB

Commercially purchased *n*-WC powders without any pre-treatment were used for sintering. The particle size measured by BET was 70 nm and the powder composition included 0.4% O, 5 ppm Cr, 27 ppm Fe, 4 ppm Mo, 3 ppm Ca, 2 ppm Ni, <5 ppm Si and < 2 ppm Sn. Approximately 2.5 – 3 g of the powder was filled into a 10 mm diameter graphite die for spark plasma sintering (SPS) in a Dr SINTER LAB instrument. This SPS instrument has a dilatometer with an accuracy of 0.01 mm for measuring the instantaneous linear shrinkage. Temperature measurements were carried out using a radiation thermometer (pyrometer) that was focused on a small niche in the carbon die. Graphite sheets were used as spacers to separate the powder sample from the punch and die. After initial temperature stabilization at 873 K for 3 minutes, sintering was carried out in vacuum (< 4 Pa) at a constant heating rate of 50 K/min and a compressive stress of 40 MPa to various temperatures from 1073K to

0.5 Coble R L, 1958

0.33 Coble, 1958

0.4 Kingery W D and Berg M, 1955

���

����� ��(�) (8)

– atomic volume, *G* – grain size and the other

���� (9)

/dt) against 1/*T*.

### **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 *m* values are not consistent. Careful observation of the sintering strain curves revealed that at those temperatures where the *m* values were unreasonably large, the curves reached saturation and flattened at longer hold times. At those temperatures where the shrinkage did not saturate, the sintering exponents were estimated to be m1173=1.46 and m1273=2.14 (LD through defects and GB recreation respectively, in accordance with the models of Kingery et al, 1975 and Coble RL, 1958). This temperature range seems to be a transition regime between defectassisted LD and the initiation of GB diffusion at higher temperatures. Irrespective of the sintering mechanism, the initial temperature range shows two characteristics: presence of a non densifying mechanism and end point densities.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 29

**Figure 2.** (a) Linear densification strains from 1073 K – 1273 K and (b) the corresponding sintering

**Figure 3.** Porosity and relative densities at different intermediate temperatures.

**Figure 4.** Plots of *P-P0* vs. *tm* according to eqns. (7)-(9) between (a) 1373 – 1473 K and (b) 1573-1873 K.

exponents calculated according to eqn. (4).

**Figure 1.** Isothermal and CRH sintering curves at different temperatures.

non densifying mechanism and end point densities.

**Figure 1.** Isothermal and CRH sintering curves at different temperatures.

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 *m* values are not consistent. Careful observation of the sintering strain curves revealed that at those temperatures where the *m* values were unreasonably large, the curves reached saturation and flattened at longer hold times. At those temperatures where the shrinkage did not saturate, the sintering exponents were estimated to be m1173=1.46 and m1273=2.14 (LD through defects and GB recreation respectively, in accordance with the models of Kingery et al, 1975 and Coble RL, 1958). This temperature range seems to be a transition regime between defectassisted LD and the initiation of GB diffusion at higher temperatures. Irrespective of the sintering mechanism, the initial temperature range shows two characteristics: presence of a

**Figure 2.** (a) Linear densification strains from 1073 K – 1273 K and (b) the corresponding sintering exponents calculated according to eqn. (4).

**Figure 3.** Porosity and relative densities at different intermediate temperatures.

**Figure 4.** Plots of *P-P0* vs. *tm* according to eqns. (7)-(9) between (a) 1373 – 1473 K and (b) 1573-1873 K.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 31

the results of the Dorn method shown earlier, there was a narrow range with negative slope in the CRH experiments also between the second and third regions. The activation energy for sintering controlled by lattice diffusion (*m* = 1/2) in the I stage is *Q* I = 113.4 kJ/mol which agrees very well with the calculations of the Dorn method for isothermal sintering (*Q* = 111 kJ/mol). In the second stage, assuming GB diffusion (*m* = 1/3), *Q* I = 310.5 kJ/mol which closely corresponds to the activation energy for GB diffusion of C in WC [Bushmer C P and Crayton P H, 1971]. It should be mentioned however, that the appearance of this, 'second stage' depends on the heating rate (and consequently, the activation energy of the second stage is also a function of the heating rate). At low heating rates, a clear division between the first and second stages can be discerned by a change in slope, but at higher heating rates, it is impossible to differentiate between the first and second stage. The third stage clearly shows a very low activation energy, which could not be correlated to any reported solid

state diffusion mechanism.

**5.2. Microstructure analysis** 

**Figure 6.** Calculation of effective activation energy from CRH experiments.

cross section SEM image and composition map of the sample by EPMA.

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

Clearly, huge abnormal grains populate the microstructure from the surface to a depth of nearly 30-40 m. 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

**Figure 5.** Calculation of apparent activation energy by Dorn's method.

For analysing the intermediate stage, the porosity fraction was estimated as *P = 1 -* , where *f* is the instantaneous density and *<sup>f</sup>* is the nal density expressed as a fraction of the theoretical density. **Fig. 3** shows the porosity and relative densities of the samples at different temperatures in the intermediate stage. At the start of the isothermal hold period, the porosity was ≈35 to 42% (at various temperatures) which decreases to a value between 6 and 18% at the end of the hold period. It is interesting to note that although the density increases with the hold time, they are almost constant in a narrow range of temperature (1400 to 1573 K). The end density seems to be a strong function of the initial density at *t* = 0. **Fig. 4a,b** shows the subsequent kinetic analysis of the intermediate stage obtained by plotting *P-P0* against *tm*. Most of the data points fall in a straight line when *m*=0.66, suggestive of Coble's grain boundary dominated sintering mechanism.

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**), *Q* = 111 kJ/mol. In the nal stages (1673– 1823 K), a small activation energy of 45 kJ/mol was calculated (gure not shown). The other temperature ranges could not be analyzed without ambiguity since sintering strains between the temperatures varied rapidly and our sampling interval (every 50 or 100 K) was inadequate to collect sufcient data points. The CRH experiments were hence considered for analysis at higher temperatures.

The sintering kinetics from the CRH experiments was also analysed. **Fig. 6** shows a plot of ln(*Td/dT*) vs. *1/T* along with the measured values of the effective activation energy. Low heating rates were found to show transition stages clearly. Three different sintering stages can be identied from 1173 K to 1873 K by the change in slope: a rst stage ranging from 1173 to 1273 K with *mQ* = 56.7 kJ/mol, a second stage from 1323 to 1473 K and *mQ* = 103.5 kJ/mol and a third stage with *mQ* = 41.35 kJ/mol between 1673 and 1823 K. Consistent with the results of the Dorn method shown earlier, there was a narrow range with negative slope in the CRH experiments also between the second and third regions. The activation energy for sintering controlled by lattice diffusion (*m* = 1/2) in the I stage is *Q* I = 113.4 kJ/mol which agrees very well with the calculations of the Dorn method for isothermal sintering (*Q* = 111 kJ/mol). In the second stage, assuming GB diffusion (*m* = 1/3), *Q* I = 310.5 kJ/mol which closely corresponds to the activation energy for GB diffusion of C in WC [Bushmer C P and Crayton P H, 1971]. It should be mentioned however, that the appearance of this, 'second stage' depends on the heating rate (and consequently, the activation energy of the second stage is also a function of the heating rate). At low heating rates, a clear division between the first and second stages can be discerned by a change in slope, but at higher heating rates, it is impossible to differentiate between the first and second stage. The third stage clearly shows a very low activation energy, which could not be correlated to any reported solid state diffusion mechanism.

**Figure 6.** Calculation of effective activation energy from CRH experiments.

#### **5.2. Microstructure analysis**

30 Tungsten Carbide – Processing and Applications

ln(*Td*  

**Figure 5.** Calculation of apparent activation energy by Dorn's method.

suggestive of Coble's grain boundary dominated sintering mechanism.

*f* is the instantaneous density and

For analysing the intermediate stage, the porosity fraction was estimated as *P = 1 -* 

the theoretical density. **Fig. 3** shows the porosity and relative densities of the samples at different temperatures in the intermediate stage. At the start of the isothermal hold period, the porosity was ≈35 to 42% (at various temperatures) which decreases to a value between 6 and 18% at the end of the hold period. It is interesting to note that although the density increases with the hold time, they are almost constant in a narrow range of temperature (1400 to 1573 K). The end density seems to be a strong function of the initial density at *t* = 0. **Fig. 4a,b** shows the subsequent kinetic analysis of the intermediate stage obtained by plotting *P-P0* against *tm*. Most of the data points fall in a straight line when *m*=0.66,

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**), *Q* = 111 kJ/mol. In the nal stages (1673– 1823 K), a small activation energy of 45 kJ/mol was calculated (gure not shown). The other temperature ranges could not be analyzed without ambiguity since sintering strains between the temperatures varied rapidly and our sampling interval (every 50 or 100 K) was inadequate to collect sufcient data points. The CRH experiments were hence considered for analysis at higher temperatures.

The sintering kinetics from the CRH experiments was also analysed. **Fig. 6** shows a plot of

*/dT*) vs. *1/T* along with the measured values of the effective activation energy. Low heating rates were found to show transition stages clearly. Three different sintering stages can be identied from 1173 K to 1873 K by the change in slope: a rst stage ranging from 1173 to 1273 K with *mQ* = 56.7 kJ/mol, a second stage from 1323 to 1473 K and *mQ* = 103.5 kJ/mol and a third stage with *mQ* = 41.35 kJ/mol between 1673 and 1823 K. Consistent with

, where

*<sup>f</sup>* is the nal density expressed as a fraction of

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 m. 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

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 33

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.

**Figure 8.** Hardness and fracture toughness of sintered *n*-WC compacts at different loads.

**Figure 9.** Brittle two-phase regions on the surface leading to indentation cracking.

**Figure 7.** A cross-sectional composition map by EPMA near the graphite/WC interface of a completely sintered compact.

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.

32 Tungsten Carbide – Processing and Applications

sintered compact.

**Figure 7.** A cross-sectional composition map by EPMA near the graphite/WC interface of a completely

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

**Figure 8.** Hardness and fracture toughness of sintered *n*-WC compacts at different loads.

**Figure 9.** Brittle two-phase regions on the surface leading to indentation cracking.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 35

**Figure 12.** Microstructures of the compacts interrupted at various temperatures during sintering.

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 nal 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

**Figure 10.** Unique colour grain map of the surface and interior of the samples by EBSD clearly showing larger grain size on the surface of the specimens.

**Figure 11.** Grain size distributions by EBSD showing a bimodal distribution both on the surface and interior of the samples.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 35

34 Tungsten Carbide – Processing and Applications

larger grain size on the surface of the specimens.

interior of the samples.

**Figure 10.** Unique colour grain map of the surface and interior of the samples by EBSD clearly showing

**Figure 11.** Grain size distributions by EBSD showing a bimodal distribution both on the surface and

**Figure 12.** Microstructures of the compacts interrupted at various temperatures during sintering.

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 nal 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.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 37

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

**Figure 14.** TEM micrographs of a sample sintered to 1323 K showing (a) necking (b) SFs with a thin amorphous GB phase and (c) Diffraction pattern (DP) and a dark field (DF) image confirming that the

**Figure 15.** Sample sintered at 1473 K showing (a) a large grain with 3 or more sub grains and (b) SFs on

too (**Fig. 14a-c**).

SFs populate the prismatic planes only.

prism planes.

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�101�0� planes and the basal �0001� planes were relatively free of defects.

**Figure 13.** TEM micrographs of the *n*-WC powder showing agglomeration and stacking faults.

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**).

36 Tungsten Carbide – Processing and Applications

were relatively free of defects.

the low activation energies measured by the kinetic analysis.

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

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�101�0� planes and the basal �0001� planes

**Figure 13.** TEM micrographs of the *n*-WC powder showing agglomeration and stacking faults.

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

**Figure 14.** TEM micrographs of a sample sintered to 1323 K showing (a) necking (b) SFs with a thin amorphous GB phase and (c) Diffraction pattern (DP) and a dark field (DF) image confirming that the SFs populate the prismatic planes only.

**Figure 15.** Sample sintered at 1473 K showing (a) a large grain with 3 or more sub grains and (b) SFs on prism planes.

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.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 39

**Figure 17.** Sample sintered to almost full density at 2073 K showing a few SFs, but mostly well- formed

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

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

*/dt*) can decrease

stage. This is a surprising observation since while the densification rate (*d*

faceted grains.

**6. Discussion** 

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.

**Figure 16.** Sample sintered at 1673 K showing (a) three regions marked 1, 2 and 3 and their 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 diffuse ring pattern (b) is the DF image from an excited spot in the DP in 2.

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.

Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 39

**Figure 17.** Sample sintered to almost full density at 2073 K showing a few SFs, but mostly well- formed faceted grains.
