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Grain size measurement methods and models for nanograined WC–Co
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International Journal of Refractory Metals & Hard Materials 26 (2008) 152–163 www.elsevier.com/locate/IJRMHM
Grain size measurement methods and models for nanograined WC–Co Seong Jin Park b
a,*
, Kristina Cowan b, John L. Johnson
c,1
, Randall M. German
a
a Center for Advanced Vehicular Systems, Mississippi State University, P.O. Box 5405, Mississippi State, MS 39762-5405, USA Center for Innovative Sintered Products, The Pennsylvania State University, 118 Research West, University Park, PA 16802, USA c ATI Alldyne, 7300 Highway 20 West, Huntsville, AL 35806, USA
Received 18 October 2006; accepted 25 May 2007
Abstract Development of nanograined WC–Co presents challenges for grain size measurement. In this study, standard and nanocrystalline WC–Co powders are processed by conventional and spark sintering. The resulting microstructures are characterized by image analysis of scanning electron microscopy micrographs, X-ray line broadening, and magnetic coercivity. The results are analyzed and a property map relating coercivity to WC grain size is developed. Equations for interface-controlled grain growth are transformed into the master sintering curve form and are used to analyze the grain size data from the three measurement techniques. 2007 Elsevier Ltd. All rights reserved. Keywords: Nanograined WC–Co; Grain size measurement; Scanning electron microscopy; X-ray line broadening; Magnetic coercivity
1. Introduction For WC–Co, strength and hardness generally increase with decreasing grain size for a given cobalt content, but the tradeoff is decreased toughness. Some authors have speculated that decreasing the WC grain size to the nanoscale (below 100 nm) in a cobalt matrix may enable simultaneous increases in both hardness and toughness [1,2], but little data are available to support these assertions due to the difficulty in producing nanograined WC by conventional sintering. An early report by Fang and Eason [3] determined that WC–Co samples produced from a nanocrystalline powder had higher toughnesses than those with the same hardness produced from a standard sub-micron WC–Co powder. A later analysis of 65 commercial and laboratory WC–Co samples by Schubert et al. [4] found that the hardness and toughness combinations of materials produced from nanocrystalline powders did not signifi*
Corresponding author. E-mail address: [email protected] (S.J. Park). 1 Previously Breakthrough Technology, Kennametal Inc., 1600 Technology Way, Latrobe, PA 15650, USA. 0263-4368/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmhm.2007.05.010
cantly deviate from those produced from conventional powders, but noted the need to optimize process conditions for each system. Richter and Ruthendorf [5] found the fracture toughness remained relatively constant at about 4–5 MPa m1/2 as the grain size decreased below 500 nm and was governed by the WC/WC interface toughness. They did not see any indications that the fracture toughness would increase at grain sizes below 100 nm. Still, the issue remains open. New sintering technologies are evolving that may lead to the fabrication of WC–Co with grain sizes below 100 nm that would enable clear determination of any property benefits. One approach is to use a nanocrystalline WC powder with combinations of grain growth inhibitors and sintering cycles that prevent coarsening of the WC grains beyond 100 nm. Combinations of VC and rare earth element additions have shown the capability of producing nanograined WC–Co after liquid phase sintering [6]. Another approach is to use spark sintering, which involves pulsing direct current during heat treatment of powders under pressure in a graphite die. Spark sintering can potentially accelerate consolidation of nanograined WC powders while minimizing grain growth. Early reports
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have shown WC grain sizes on the order of 100 nm for spark sintered WC–Co [7–10]. In addition to the processing challenges, defining and measuring grain sizes at the nanosized level presents an additional challenge. The term ‘‘grain’’ generally refers to a segment of a microstructure that displays clearly visible boundaries in an optical or electron microscope. WC grain sizes are most often quantified from optical micrographs by the linear intercept method, although variations of the area method developed by Jeffries [11] are also used. Additionally, image analysis software is available to quantify average grain size and grain size distribution based on either area or perimeter. Optical microscopy is generally limited to about 2000·, so electron microscopy with magnifications of 10,000· or more is required to resolve nanosized grains. In most cases grains are considered to be single crystals, with the visible boundaries resulting from the interface of either two grains with different crystallographic orientations or one grain with a second phase. In this case, ‘‘grain’’ is synonymous with ‘‘crystallite’’, a coherently diffracting domain the size of which can be measured by different Xray diffraction techniques. On the other hand, the grains may be composed of multiple crystallites with the crystallite boundaries not being easily seen with microscopy. The X-ray line broadening technique is a common method of measuring crystallite size. It provides an average of the crystallite sizes from the width and height of peaks in an X-ray diffraction pattern [12]. These values have been reported in sintering studies of nanocrystalline WC–Co by prior researchers [13,14], but the correlation of crystallite size with properties is not as clearly defined as for grain size. Magnetic coercivity measurements provide another means of characterizing the WC grain size. The WC/Co interface restricts movement of magnetic domain walls within the ferromagnetic Co binder-phase. Thus, the magnetic field required to restore zero magnetization to a magnetically saturated WC–Co hardmetal is proportional to the interfacial area between the Co binder-phase and the WC hard phase and is thus related to the WC grain size [15–20]. This technique is used by the hardmetal industry for non-destructive quality control. Consistent grain size data are important for correlating with both experimental property data and with theoretical models. Many papers involved with sintering of WC–Co present grain size data from just one measurement technique, making cross-comparisons difficult. In this paper, all three measurement techniques are applied to sintered WC–Co samples produced from conventional and nanocrystalline WC–Co powders. Correlations between the different measurement techniques are identified. The results are utilized in a semi-empirical model based on the master sintering curve concept, initially proposed by Su and Johnson [21] for densification and recently formulated by Park et al. [22] for grain growth, to determine which method provides the most consistent results.
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2. Experimental 2.1. Powder characterization Two powders were obtained as the raw materials for this research work. A standard WC–10Co powder (S) produced by carburizing W powder, milling it with Co powder, and spray drying it with 2 wt% paraffin was acquired from Kennametal Inc. (Latrobe, PA). A nanocrystalline WC–12Co (N) was produced by Inframat Corp. (Farmington, CT) by a continuous wet chemical process based on the Spray Conversion Process in which W, C, and Co precursors are mixed and reacted together. Two compositions were prepared from this powder by ball milling it for 24 h with grain growth inhibitors, TiC and TaC. Powder N1 contained 1 wt% TiC, 3 wt% TaC, and 3 wt% paraffin wax, which was added during milling, while Powder N2 contained 0.3 wt% TiC and 0.3 wt% TaC. The powders were characterized for their tap and pycnometer densities and BET surface area. Due to the presence of the wax in Powder S, no BET surface area was possible, but its pycnometer density was measured after binder removal from the as-received powder. The BET equivalent spherical particle diameter (DBET) of Powder N was calculated from the following equation: DBET ¼
6 qp ABET
ð1Þ
where ABET is the specific BET surface area of the powder in m2/g, qp is the pycnometer density of the powder in g/ cm3 and DBET is in lm. The crystallite size was also determined by X-ray diffraction as described later. SEM micrographs of the two as-received powders are shown in Fig. 1. Both powders were agglomerated, so results from laserbased scattering are not reflective of the individual particle sizes and are not given. 2.2. Sample preparation Die pressing was used as the method of compaction. Right cylindrical compacts, approximately 3.20 mm diameter and 30 g mass, were made at three different compaction pressures of 110, 400, and 565 MPa from Powder S with 2 wt% paraffin wax as lubricant and Powder N1 with 3 wt% paraffin wax. Compaction was carried out using a hand press. Twelve samples were compacted at each pressure and a typical variation of 2% was seen in green density at each pressure. The samples were heated at 2 C/min up to 250 C with a 1 h hold, heated again at 3 C/min up to 1000 C with a 1 h hold, and cooled at 10 C/min to room temperature in a H2 atmosphere for wax removal and presintering. Sintering was performed in a H2 atmosphere with four different sintering temperatures of 1100, 1200, 1300, and 1400 C. The samples were heated at 5 C/min up to the designated temperature with a 1 h hold and cooled at 10 C/min to room temperature.
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from magnetic coercivity. The spark sintering was carried out under vacuum at University of California at Davis. Right cylindrical compacts, approximately 20 mm diameter and 10 g mass, were prepared from Powder N2. These samples were subjected to a design of experiments (DOEs) with sintering temperatures ranging from 1000 to 1200 C, holding times ranging from 0 to 10 min, pressures ranging from 40 to 80 MPa, and electric currents ranging from 1000 to 2000 A. Table 1 shows the DOE based on an orthogonal array. Note that these few spark sintered samples are not sufficient by themselves to develop a grain growth model. 2.3. Image analysis
Fig. 1. SEMs of Powders S and N: (a) Powder S and (b) Powder N.
Additional samples were spark sintered from Powder N2 for verifying the developed model to predict grain size
Table 1 Orthogonal array for spark sintering Sample
1 2 3 4 5 6 7 8 9
Factor A
Factor B
Factor C
Factor D
Sintering temperature (C)
Holding time (min)
Pressure (MPa)
Electric current (A)
1000 1000 1000 1100 1100 1100 1200 1200 1200
0 5 10 0 5 10 0 5 10
40 80 60 60 80 40 60 40 80
1000 2000 1500 1500 1000 2000 2000 1500 1000
To obtain a polished microstructure for grain size analysis, the sintered samples were sectioned top-to-bottom and mounted using epoxy resin under vacuum to fill the porosity and to prevent the smearing of the material into the pores. The polishing procedure involved the use of a 9 lm diamond suspension followed by 6, 3, and 1 lm diamond suspensions on a MD-DAC cloth from Struers. A mirror-like finish was obtained by giving a final polish with a 0.04 lm silica colloidal suspension (OP-S from Struers). Next, the microstructure was revealed by chemically etching with a solution of 6 g of potassium ferricyanate and 0.5 g of potassium hydroxide in 50 ml of distilled water. The polished and etched microstructures were imaged using scanning electron microscopy (SEM). For the conventionally sintered samples, five different fields of each sample were taken at a magnification of 10,000· on a TopCon Model ABT-32 SEM (Tokyo, Japan). Example SEMs are shown in Fig. 2. For the spark sintered samples, two different fields of each sample were taken at magnifications of 20,000· on a Philips XL30 SEM. The WC grain size was measured from the fields using image analysis of the average grain area and perimeter. An analysis routine was developed using Clemex (Longueuil, Canada) Version PE 3.5 software. Grain boundaries were visually identified based on penetration by the Co matrix. The grains were then segmented as shown by the example images in Fig. 3. The software provided the cross-sectional area and perimeter of each individual WC grain. The diameter of an equivalent circle was calculated to represent the average WC grain size Gequivalent from the following equation: Gequivalent ¼
4A P
ð2Þ
where A is the average grain area and P is the average grain perimeter. 2.4. X-ray diffraction The WC crystallite size was measured by X-ray line broadening for both raw materials and sintered samples. X-ray diffraction measurements were performed with a Scintag X2 Advanced Diffraction System with a Si (Li)
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Fig. 2. Example SEMs of sintered microstructures: (a) Powder S, 400 MPa, 1100 C, (b) Powder S, 400 MPa, 1400 C, (c) Powder N1, 400 MPa, 1100 C, and (d) Powder N1, 400 MPa, 1400 C.
peltier detector using the Scherrer method. Scans were performed from 5 to 70 at a rate of 2/min. The peak position and full-width at half-maximum (FWHM) were calculated from both the most strongly diffracting peak (48) and from the average of all the peaks using Jade+ version 7.0 software. An X-ray diffraction pattern was collected on a NIST-certified silicon powder to establish and subtract any peak broadening contributed by the instrument itself, and all samples were run on the same instrument to eliminate peak broadening contributions from different machines. Peak broadening is also affected by lattice strain, but its contribution is difficult to separate from that of crystallite size so it was neglected. Data collection parameters remained identical between the reference silicon powder and the WC–Co samples. An example diffraction pattern is shown in Fig. 4 for Powder N1 sintered at 1100 C. The most strongly diffracting peaks of WC, Co, and TaC are indicated.
2.5. Magnetic coercivity A Foerster Model 1.095 coercimeter was used to measure the magnetic coercivities of the samples. The sample diameter was aligned with the long axis of the holder, which was inserted within a 40 mm coil. After adjustment of the residual field strength to obtain a coercive field strength within the display range, two measurements were taken with alternating polarity. The average value is reported. 3. Results and discussion 3.1. Powder characteristics The characteristics of the two as-received powders are summarized in Table 2. The X-ray line broadening measurement for Powder N agrees closely with the manufacturer’s advertised crystallite size of 40–70 nm; however,
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Fig. 3. Example segmented SEM images for grain size measurement: (a) spark sintering, 1100 C, 5 min, 80 MPa, 1000 A and (b) spark sintering, 1200 C, 5 min, 40 MPa, 1500 A.
its BET particle size is significantly larger than 100 nm prior to sintering. X-ray diffraction revealed that the standard powder also has nanocrystalline structure, indicating that the WC particles are composed of multiple crystallites. This shows the ambiguity in defining a powder as ‘‘nanocrystalline’’ based on X-ray diffraction measurements. 3.2. Grain size measurements Image analysis provides data on grain size distributions in addition to the mean grain size. An example distribution for a spark sintered sample is shown in Fig. 5. The distribution is log-normal with 10% of the grains below 128 nm in size, 50% below 230 nm, and 90% below 436 nm. All of the
samples sintered in this study had log-normal grain size distributions, so they can be represented by their mean value in the following analysis. The effects of sintering temperature and compaction pressure on mean WC grain size as measured by image analysis for Powder S and Powder N1 are plotted in Fig. 6. Powder S has a larger initial grain size and coarsens with temperature. Powder N1 shows a significant increase in grain size from 1100 C to 1200 C, but then further increases in temperature up to 1400 C have little effect on grain size, indicating an effective role of the grain growth inhibitor during both solid-state and liquid-phase sintering. For the most part, the effect of compaction pressure on grain size is not significant within measurement
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Fig. 4. Diffraction pattern of Powder N1 sintered at 1100 C.
Table 2 Powder characteristics Powder
S
N
Vendor Composition Pycnometer density (g/cm3) Tap density (g/cm3) (% of pycnometer density) BET surface area (m2/g) BET particle size (nm) Average crystallite size (nm)
Kennametal WC–10Co 14.5 –
Inframat WC–12Co 13.7 2.4 (17.5%)
– – 49 ± 9
2.3 188 57 ± 7
The effect of sintering temperature on the WC crystallite size as measured by X-ray line broadening for Powder S and Powder N1 is plotted in Fig. 7. The data are summarized in Table 3 in comparison to the grain size as determined by image analysis of SEM micrographs. The crystallite area is 6–100 times smaller than the grain area, indicating that each grain is comprised of this many crystallites. Fig. 8 shows the correlation between grain size and crystallite size. The crystallite size increases independently of grain size for Powder N1, while it increases linearly with grain size for Powder S. Achieving a sintered WC grain size of less than 100 nm will require not just a crystallite size below this, but discrete particles with dimensions less than 100 nm. The effect of sintering temperature on the magnetic coercivity for Powder S and Powder N1 is plotted in Fig. 9. The magnetic coercivity, K in kA/m, can be correlated with grain size, GWC in lm, for cobalt contents, wCo between 6 and 25 wt% as follows [18]: K ¼ ðc1 þ d 1 wCo Þ þ ðc2 þ d 2 wCo Þ
Fig. 5. Grain size distribution for spark sintering, 1000 C, 5 min, 80 MPa, 2000 A.
error. At 1400 C, the grain size increases with compaction pressure for Powder S. For powder N1, the grain size decreases with compaction pressure at 1100 C.
1 GWC
ð3Þ
where c1, c2, d1, and d2 are material constants. Although Eq. (3) was derived from linear intercept data for liquid phase sintered WC–Co, curve fitting the experimental data from image analysis of solid-state sintered and spark sintered samples to Eq. (3) resulted in an R2 value of 0.95 with a maximum error of 4.8% with the following values for the material constants: c1 = 7.873, c2 = 3.421, d1 = 0.125, and d2 = 0.665. Fig. 10 shows the fit between measured coercivity and grain size measured by SEM image analysis
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Fig. 6. Grain size measured by image analysis of SEM micrographs: (a) Powder S and (b) Powder N1.
reported for ‘‘super-ultrafine’’ WC–6Co grades with gain sizes of about 200 nm and hardnesses of 2200 VHN [3,23]. Fig. 10 shows that solid state sintered WC–12Co with a grain size of 200 nm is projected to have a coercivity of just 29.2 kA/m (367 Oe). Extrapolating to a nanograined grade with a WC grain size of 100 nm, the projected coercivity is 52.0 kA/m (653 Oe). In comparison, using the original values [18] for the material constants, c1 = 1.44, c2 = 12.47, d1 = 0.04 and d2 = 0.37, the projected coercivity for liquid phase sintered WC–12Co with a WC grain size of 100 nm is 82 kA/m (1028 Oe). The Vickers hardness number H has been linked to the grain size GWC in lm based on the Hall–Petch relationship via the following equation [20]: Fig. 7. Crystallite size measured by X-ray line broadening for samples compacted at 400 MPa.
for Powder S, Powder N1, and Powder N2. In comparison, the coercivity correlates poorly (average error = 33% and R2 = 0.67) with crystallite size, which is not directly related to the WC/Co interfacial area. The measured coercivity values are generally lower than they would be at the same WC grain size for liquid phase sintered materials with more uniform Co distribution. Coercivities as high as 51.7 kA/m (650 Oe) have been
H ¼ 1178 1326V Co þ ð654 497V Co ÞG0:5 WC
ð4Þ
where VCo is the volume fraction of Co. No such relationship exists for hardness and crystallite size. Combining Eqs. (3) and (4) enables the creation of a hardness–coercivity property map as shown in Fig. 11. Although developed from samples with coercivities of less than 35 kA/m, extrapolating the results to higher coercivities provides some targets for nanograined WC–Co. We propose that nanocrystalline be used to describe a powder or sintered material comprised of crystallites below 100 nm and that the term nanograined be reserved for
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Table 3 Summary of grain size and crystallite size data for samples pressed at 400 MPa Powder
Sintering temperature (C)
Crystallite size
Grain size
Mean (nm)
At 48 peak (nm)
Mean (nm)
Number of measured grains
Crystallites per grain
S
1100 1200 1300 1400
54 ± 4 113 ± 38 131 ± 29 176 ± 64
57 101 124 149
558 ± 13 593 ± 28 729 ± 15 1077 ± 25
1486 1325 1082 749
107 28 31 37
N
1100 1200 1300 1400
69 ± 16 90 ± 23 135 ± 61 127 ± 17
64 85 134 139
254 ± 12 354 ± 16 343 ± 21 374 ± 22
1925 1037 1067 981
14 15 6 9
3.3. Master sintering curve modeling The mean grain size increases with sintering time. For the sintering of hard materials, the classical model for interface-controlled grain growth with isothermal condition is [28]: G2 ¼ G20 þ Kt
Fig. 8. Relationship between grain size and crystallite size for samples compacted at 400 MPa.
sintered materials comprised of individual grains less than 100 nm. Nanocrystalline hardmetals do not necessarily have higher hardness. Based on the above analysis, proposed criteria for the properties of nanograined WC– Co grades are summarized in Table 4. Grain size measurement by linear intercept or equivalent circular diameter may indicate a nanograined material, but if it consists of a large percentage of WC–WC interfacial area instead of WC–Co interfacial area, properties may not be reflective of one. Coercivity is the best indicator of interfacial area, other than time-consuming contiguity measurements. Thus, magnetic coercivity is the recommended technique for extension of grain size measurements into the nanoscale range. The coercivity values given in Table 4 should be obtained in order to expect superior properties. Increased hardness is projected, but whether it can be combined with a unique combination of toughness remains to be seen. The property data for several reports of ‘‘nanocrystalline’’ and ‘‘super-ultrafine’’ WC–Co are summarized in Table 5 in for comparison with the criteria given in Table 4. Despite much activity with nanocrystalline powders, none of these materials achieve the requirements of a nanograined material as defined in Table 4. The reported grain sizes of the WC–6Co prepared by Lin and Yuan [6] are within the nanograin definition, but no supporting property data are given.
ð5Þ
where G is the mean grain size, t is the time, G0 is the particle size at the beginning of the steady-state, and K is the rate constant. K exhibits dependence with temperature that can be expressed as: K0 Q K¼ exp ð6Þ RT T where T is the absolute temperature, K0 is the associated pre-exponential factor, Q is the apparent activation energy, and R is the universal gas constant. The differential form for grain growth under non-isothermal conditions can be derived by substituting Eq. (6) into Eq. (5) and differentiating this equation with respect to time as follows: dG K 0 Q ¼ exp 2G ð7Þ dt RT T Starting with a densification rate equation in a form similar to Eq. (6), Su and Johnson developed the master sintering curve as a practical way of describing the densification of a compact along any given complex sintering cycle [21]. In this kind of equation, it is possible to separate the terms related with the microstructure on the left side and the temperature dependent parameters on the right side. Then, both sides are integrated independently assuming that: (a) microstructural evolution, both grain size and shape, is only a function of mean grain size; and (b) the apparent activation energy (Q) does not change during the sintering thermal cycle. Point (a) is usually true when the same basic atomic transport mechanics are responsible for both densification and microstructural evolution. Point (b) is satisfied when the proportional contribution of these basic mechanisms does not change during the sintering process. When point (b) is not true because of a change of basic mechanisms during the sintering cycle, the cycle can be divided
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Fig. 9. Effect of sintering temperature on magnetic coercivity: (a) Powder S and (b) Powder N1.
When the conditions previously mentioned are fulfilled, the integration of Eq. (7) leads to: Z t K0 Q 2 2 exp G ¼ G0 þ dt ð8Þ RT 0 T Eq. (8) for the grain growth is transformed into the master sintering curve form as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð9Þ G ¼ G20 þ H where Z H¼ 0
Fig. 10. Correlation between grain size as measured by image analysis and magnetic coercivity measurements. Samples from Powders S and N1 were compacted at 400 MPa and sintered at temperatures ranging from 1100 to 1400 C. Samples from Powder N2 were spark sintered.
into several consecutive stages that are integrated separately [22]. An additional condition is that the powders, their processing, and the compaction pressure are the same for all the green compacts, so green density and microstructure are common to all of them.
t
K0 Q exp dt RT T
ð10Þ
The parameters K0 and Q can be determined by curve fitting experimental data with Eqs. (9) and (10). It is noted that in Eq. (9), grain size in the MSC model depends on only the initial grain size of G0, regardless of sintering cycle, K0, and Q. The condition imposed in this fitting is to minimize the following mean residual, R: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 N u1 X GMSC i t ð11Þ RðK 0 ; QÞ ¼ 1 N i¼1 GEXP i
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161
Fig. 11. Property map for hardness and coercivity.
Table 4 Proposed criteria for a WC–Co grade to be designated ‘‘nanograined’’ Composition Linear intercept grain size (nm)
Equivalent Magnetic Crystallite Hardness circular coercivity size (nm) (VHN) diameter (kA/m) (nm)
WC–6Co WC–8Co WC–10Co WC–12Co
<100 <100 <100 <100
<100 <100 <100 <100
104 97 89 82
<100 <100 <100 <100
2955 2863 2774 2688
where N is the number of experimental grain size data points, i is a dummy variable for summation, GMSC_i is the ith grain size predicted by the master sintering curve model with given K0 and Q values, and GEXP_i is the ith experimentally measured grain size. The advantage of this method is to obtain more accurate values for Q and K0 with the consideration of the full thermal cycle, that is, with any combination of heating rate and holding temperature. The method is valid when all the grain growth data from different sintering cycles lie on a single master sintering
curve, the resulting activation energy (Q) has a reasonable value, and the mean residual term (R) is small. In the case of hardmetals, a significant contribution to grain growth results from variables such as gross carbon content, growth inhibitors, and matrix contents, which require reconstructing a new MSC for each composition with new experiments and new curve-fitted parameters Q and K0. The above MSC approach was performed based on the mean grain size from image analysis of SEM micrographs. The MSC approach based on magnetic coercivity data are almost the same since image analysis data were used to develop the correlation between grain size and magnetic coercivity. The BET particle size of 188 nm was used for the initial grain size for Powder N1. Since no BET particle size was available for Powder S, an initial grain size of 480 nm was obtained from curve fitting based on Eq. (11), which means that three parameters (K0, Q, and G0) were considered in case of Powder S. The MSC approach showed a high average error of 31% using crystallite size data from X-ray line broadening as for the case of predicting crystallite size from magnetic coercivity.
Table 5 Reported properties of nanocrystalline and super-ultrafine WC–Co Composition
Reference
Grain size (nm)
Grain size measurement technique
Coercivity (kA/m)
Hardness
Toughness (MPa m1/2)
WC–6Co WC–6Co
[3] [6]
Linear intercept Linear intercept
611 NRa
2150 VHN NR
NR NR
WC–10Co WC–6Co WC–10Co WC–7Co WC–9.45Co WC–7Co
[13] [23] [24] [25] [26] [27]
400 45 87 300 220 330 220 200–300 200–240
X-ray diffraction NR Image analysis Linear intercept NR Linear intercept
NR 651 NR NR 27.4 NR
WC–10Co
[8]
100
NR
NR
1950 VHN 2220 VHN 1900 VHN 2093 VHN 92.8 HRA 94.7 HRA 94.2 HRA 1887 VHN
NR NR NR 10.4 NR 10.2 11.2 11.5
a
NR, not reported.
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Fig. 12. Master sintering curves of grain growth for Powders S and N1.
Table 6 Material parameters used in MSC analysis of grain growth Powder
Die compaction pressure (MPa)
Q (kJ/mol)
K0 (m2 K/s)
Mean residual (%)
S
110 400 565
171 209 224
1.47 · 108 4.39 · 107 1.81 · 106
2.48 2.54 3.05
N1
110 400 565
64 88 65
9.96 · 1013 5.85 · 1012 9.56 · 1013
3.27 3.80 2.59
Fig. 12 shows the master sintering curves of grain growth for Powder S and Powder N1. The average errors are 2.73% for Powder S and 3.32% for Powder N1 and the maximum errors are 3.05% for Powder S and 3.80% for Powder N1, respectively. These low error values indicate that the classical model of interface-controlled grain growth, described above, can well explain grain growth in the WC–Co system. In addition, the BET particle size and the proposed equivalent diameter determined from image analysis, expressed in Eq. (2), seem to be reasonable for this model, indicating that the polycrystalline WC grains do not disintegrate into multiple grains during sintering. Table 6 shows the activation energies and the associated pre-exponential factors, which supports quantitatively the explanation of Fig. 8 in Section 3.2. Finally, the asymptotic character of Fig. 12 at low levels of thermal work (H) indicates that it is impossible to consolidate these powders to full density with a nanoscale grain size; a suggestion already given by the research of Hayashi and Matsuika [29]. Combining the MSC grain growth model with the MSC densification model provides an estimate of the minimum starting particle size required to achieve a specific combination of density and sintered grain size [30]. From the optimization results, the minimum grain size that can be achieved at a sintered density of 97% of theoretical is 332 nm for Powder N1 with a compaction pressure of 565 MPa. This value is 1.8 times larger than the initial grain size, which suggests that a WC powder with
discrete particles less than 50 nm in diameter is required in order to obtain nanograined WC–Co with the properties shown in Table 4. 4. Conclusion The mean grain size of solid-state sintered and spark sintered WC–Co can be determined by image analysis and correlated with magnetic coercivity, which is related to the WC–Co interfacial area. With sufficient data, empirical expressions for coercivity can be extrapolated into the nanograined range and related to properties such as hardness and toughness. WC grains can be polycrystalline, thus the crystallite size as determined by X-ray diffraction can be substantially smaller than the grain size measured by image analysis and does not correlate with magnetic coercivity or properties. Despite much activity with nanocrystalline powders, sintered WC–Co with nanoscale grains has not yet been achieved. Traditional coarsening models for WC–Co are based on interface-controlled grain growth and are not suitable for predicting coarsening of crystallite sizes determined by Xray diffraction. A model based on master sintering curve theory indicates that a powder with discrete particles below 50 nm is needed to produce an average grain size of less than 100 nm. Future characterizations of sintered nanocrystalline WC–Co powders should include magnetic coercivity measurements as well as hardness and toughness data for development of models to link microstructure and properties at the nanoscale level. Acknowledgments This study was supported by Kennametal, Inc. and the CAVS Chair at Mississippi State University. Special thanks go to Yixiong Liu, Tim Muller, Tracy Potter, Don Heaney, Lou Campbell, and Joanna Groza for their help with providing experimental data and valuable advice.
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References [1] Yao Z, Stiglich JJ, Sudarshan TS. Nanosized WC–Co holds promise for the future. Metal Powder Rep 1998;3:26–33. [2] Seo O, Kang S, Laverinia EJ. Growth inhibition of nano WC particles in WC–Co alloys during liquid-phase sintering. Mater Trans 2003;44:2339–45. [3] Fang Z, Eason JW. Study of nanostructured WC–Co composites. Int J Refract Hard Mater 1995;13:297–303. [4] Schubert WD, Neumeister H, Kinger G, Lux B. Hardness to toughness relationship of fine-grained WC–Co hardmetals. Int J Refract Hard Mater 1998;16:133–42. [5] Richter V, Ruthendorf MV. On hardness and toughness of ultrafine and nanocrystalline hard materials. Int J Refract Hard Mater 1999;17:141–52. [6] Lin C, Yuan G. Effects of rare earths on the microstructure of nanocrystalline WC–VC–10Co hardmetals. In: Kneringer G, Roedhammer P, Wildner H, editors. Plansee seminar, vol. 2. Reutte, Austria: Plansee; 2005. p. 363–77. [7] Wang X, Xie Y, Guo H, Van der Biest O, Vleugels J. Sintering of WC–Co powder with nanocrystalline WC by spark plasma sintering. Rare Metals 2006;25:246–52. [8] Zhu LH, Huang QW, Zhao HF. Preparation of nanocrystalline WC– 10Co–0.8VC by spark plasma sintering. J Mater Sci Lett 2003;22:1631–3. [9] Park CD, Kim HC, Shon IJ, Munir ZA. One-step synthesis of dense tungsten carbide – cobalt hard materials. J Am Ceram Soc 2002;88:2670–7. [10] Basu B, Lee JH, Kim DY. Development of WC–ZrO2 nanocomposites by spark plasma sintering. J Am Ceram Soc 2004;87:317–9. [11] Engqvist H, Uhrenius B. Determination of the average grain size of cemented carbides. Int J Refract Hard Mater 2003;21:31–5. [12] German RM. Powder metallurgy and particulate materials processing. Princeton (NJ): MPIF; 2005. p. 30–32. [13] Xueming MA, Gang JI, Ling Z, Yuanda D. Structure and properties of bulk nano-structured WC–Co alloy by mechanical alloying. J Alloy Compd 1998;264:267–70. [14] Maheshwari P, Fang ZZ, Sohn HY. Early-stage densification and grain growth of nanosized WC–Co powders during sintering. In: Bose A, Dowding RJ, editors. International conference on tungsten, refractory, and hardmetals. Princeton (NJ): MPIF; 2006. p. 98–106. [15] Porat R, Malek J. Binder mean-free-path determination in cemented carbide by coercive force and material composition. Mater Sci Eng 1988;105–106:289–92.
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[16] Fang Z, Eason JW. Nondestructive evaluation of WC–Co composites using magnetic properties. Int J Powder Metall 1993;29:259– 65. [17] Roebuck B, Bennett EG, Gee MG. Grain size measurement methods for WC/Co hardmetals. In: Bildstein H, Eck R, editors. Plansee seminar, vol. 2. Reutte, Austria: Plansee; 1993. p. 273–92. [18] Roebuck B. Magnetic coercivity measurements for WC/Co hardmetals. In: NPL CMMT(MN)042. National Physical Laboratory UK; 1999. [19] Sundin S, Haglund S. A comparison between magnetic properties and grain size for WC/Co hard materials containing additives of Cr and V. Int J Refract Hard Mater 2000;18:297–300. [20] Roebuck B. Hardmetals: hardness and coercivity property maps. In: NPL MATC(MN)14. National Physical Laboratory UK; 2002. [21] Su H, Johnson DL. Master sintering curve: a practical approach to sintering. J Am Ceram Soc 1996;79:3211–7. [22] Park SJ, Martin JM, Guo JF, Johnson JL, German RM. Grain growth behavior of tungsten heavy alloys based on master sintering curve concept. Metall Mater Trans A 2006;37A:3337–46. [23] Carroll DF. Sintering and microstructural development in WC/Cobased alloys made with superfine WC powder. Int J Refract Hard Mater 1999;17:123–32. [24] Cha S, Hong SH, Ha GH, Kim BK. Microstructure and mechanical properties of nanocrystalline WC–10Co cemented carbides. Scripta Mater 2001;44:1535–9. [25] Zhang F, Shen J, Sun S. Processing and properties of carbon nanotubes–nano-WC–Co composites. Mater Sci Eng A 2004;381: 86–91. [26] Shao GQ, Duan XL, Xie JR, Yu XH, Zhang WF, Yuan RZ. Sintering of nanocrystalline WC–Co composite powder. Rev Adv Mater Sci 2003;5:281–6. [27] Zhang F, Shen J, Sun J. The effect of phosphorus additions on densification, grain growth, and properties of nanocrystalline WC– Co composites. J Alloy Compd 2004;385:96–103. [28] German RM. Liquid phase sintering. New York: Plenum Press; 1985. p. 136. [29] Hayashi K, Matsuika N. Grain size condition for abnormal grain growth in fine-grained WC–Co hardmetal extinated by numerical calculation based on two kinds of grain size alloy model. J Adv Mater 2002;34:38–48. [30] Park SJ, Johnson JL, German RM. Unified molding and simulation for nano-structured tungsten carbide. In: Powder metallurgy world congress, PM, Busan, Korea; 2006. p. 362–3 [part I].
International Journal of Refractory Metals & Hard Materials 26 (2008) 152–163 www.elsevier.com/locate/IJRMHM
Grain size measurement methods and models for nanograined WC–Co Seong Jin Park b
a,*
, Kristina Cowan b, John L. Johnson
c,1
, Randall M. German
a
a Center for Advanced Vehicular Systems, Mississippi State University, P.O. Box 5405, Mississippi State, MS 39762-5405, USA Center for Innovative Sintered Products, The Pennsylvania State University, 118 Research West, University Park, PA 16802, USA c ATI Alldyne, 7300 Highway 20 West, Huntsville, AL 35806, USA
Received 18 October 2006; accepted 25 May 2007
Abstract Development of nanograined WC–Co presents challenges for grain size measurement. In this study, standard and nanocrystalline WC–Co powders are processed by conventional and spark sintering. The resulting microstructures are characterized by image analysis of scanning electron microscopy micrographs, X-ray line broadening, and magnetic coercivity. The results are analyzed and a property map relating coercivity to WC grain size is developed. Equations for interface-controlled grain growth are transformed into the master sintering curve form and are used to analyze the grain size data from the three measurement techniques. 2007 Elsevier Ltd. All rights reserved. Keywords: Nanograined WC–Co; Grain size measurement; Scanning electron microscopy; X-ray line broadening; Magnetic coercivity
1. Introduction For WC–Co, strength and hardness generally increase with decreasing grain size for a given cobalt content, but the tradeoff is decreased toughness. Some authors have speculated that decreasing the WC grain size to the nanoscale (below 100 nm) in a cobalt matrix may enable simultaneous increases in both hardness and toughness [1,2], but little data are available to support these assertions due to the difficulty in producing nanograined WC by conventional sintering. An early report by Fang and Eason [3] determined that WC–Co samples produced from a nanocrystalline powder had higher toughnesses than those with the same hardness produced from a standard sub-micron WC–Co powder. A later analysis of 65 commercial and laboratory WC–Co samples by Schubert et al. [4] found that the hardness and toughness combinations of materials produced from nanocrystalline powders did not signifi*
Corresponding author. E-mail address: [email protected] (S.J. Park). 1 Previously Breakthrough Technology, Kennametal Inc., 1600 Technology Way, Latrobe, PA 15650, USA. 0263-4368/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmhm.2007.05.010
cantly deviate from those produced from conventional powders, but noted the need to optimize process conditions for each system. Richter and Ruthendorf [5] found the fracture toughness remained relatively constant at about 4–5 MPa m1/2 as the grain size decreased below 500 nm and was governed by the WC/WC interface toughness. They did not see any indications that the fracture toughness would increase at grain sizes below 100 nm. Still, the issue remains open. New sintering technologies are evolving that may lead to the fabrication of WC–Co with grain sizes below 100 nm that would enable clear determination of any property benefits. One approach is to use a nanocrystalline WC powder with combinations of grain growth inhibitors and sintering cycles that prevent coarsening of the WC grains beyond 100 nm. Combinations of VC and rare earth element additions have shown the capability of producing nanograined WC–Co after liquid phase sintering [6]. Another approach is to use spark sintering, which involves pulsing direct current during heat treatment of powders under pressure in a graphite die. Spark sintering can potentially accelerate consolidation of nanograined WC powders while minimizing grain growth. Early reports
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have shown WC grain sizes on the order of 100 nm for spark sintered WC–Co [7–10]. In addition to the processing challenges, defining and measuring grain sizes at the nanosized level presents an additional challenge. The term ‘‘grain’’ generally refers to a segment of a microstructure that displays clearly visible boundaries in an optical or electron microscope. WC grain sizes are most often quantified from optical micrographs by the linear intercept method, although variations of the area method developed by Jeffries [11] are also used. Additionally, image analysis software is available to quantify average grain size and grain size distribution based on either area or perimeter. Optical microscopy is generally limited to about 2000·, so electron microscopy with magnifications of 10,000· or more is required to resolve nanosized grains. In most cases grains are considered to be single crystals, with the visible boundaries resulting from the interface of either two grains with different crystallographic orientations or one grain with a second phase. In this case, ‘‘grain’’ is synonymous with ‘‘crystallite’’, a coherently diffracting domain the size of which can be measured by different Xray diffraction techniques. On the other hand, the grains may be composed of multiple crystallites with the crystallite boundaries not being easily seen with microscopy. The X-ray line broadening technique is a common method of measuring crystallite size. It provides an average of the crystallite sizes from the width and height of peaks in an X-ray diffraction pattern [12]. These values have been reported in sintering studies of nanocrystalline WC–Co by prior researchers [13,14], but the correlation of crystallite size with properties is not as clearly defined as for grain size. Magnetic coercivity measurements provide another means of characterizing the WC grain size. The WC/Co interface restricts movement of magnetic domain walls within the ferromagnetic Co binder-phase. Thus, the magnetic field required to restore zero magnetization to a magnetically saturated WC–Co hardmetal is proportional to the interfacial area between the Co binder-phase and the WC hard phase and is thus related to the WC grain size [15–20]. This technique is used by the hardmetal industry for non-destructive quality control. Consistent grain size data are important for correlating with both experimental property data and with theoretical models. Many papers involved with sintering of WC–Co present grain size data from just one measurement technique, making cross-comparisons difficult. In this paper, all three measurement techniques are applied to sintered WC–Co samples produced from conventional and nanocrystalline WC–Co powders. Correlations between the different measurement techniques are identified. The results are utilized in a semi-empirical model based on the master sintering curve concept, initially proposed by Su and Johnson [21] for densification and recently formulated by Park et al. [22] for grain growth, to determine which method provides the most consistent results.
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2. Experimental 2.1. Powder characterization Two powders were obtained as the raw materials for this research work. A standard WC–10Co powder (S) produced by carburizing W powder, milling it with Co powder, and spray drying it with 2 wt% paraffin was acquired from Kennametal Inc. (Latrobe, PA). A nanocrystalline WC–12Co (N) was produced by Inframat Corp. (Farmington, CT) by a continuous wet chemical process based on the Spray Conversion Process in which W, C, and Co precursors are mixed and reacted together. Two compositions were prepared from this powder by ball milling it for 24 h with grain growth inhibitors, TiC and TaC. Powder N1 contained 1 wt% TiC, 3 wt% TaC, and 3 wt% paraffin wax, which was added during milling, while Powder N2 contained 0.3 wt% TiC and 0.3 wt% TaC. The powders were characterized for their tap and pycnometer densities and BET surface area. Due to the presence of the wax in Powder S, no BET surface area was possible, but its pycnometer density was measured after binder removal from the as-received powder. The BET equivalent spherical particle diameter (DBET) of Powder N was calculated from the following equation: DBET ¼
6 qp ABET
ð1Þ
where ABET is the specific BET surface area of the powder in m2/g, qp is the pycnometer density of the powder in g/ cm3 and DBET is in lm. The crystallite size was also determined by X-ray diffraction as described later. SEM micrographs of the two as-received powders are shown in Fig. 1. Both powders were agglomerated, so results from laserbased scattering are not reflective of the individual particle sizes and are not given. 2.2. Sample preparation Die pressing was used as the method of compaction. Right cylindrical compacts, approximately 3.20 mm diameter and 30 g mass, were made at three different compaction pressures of 110, 400, and 565 MPa from Powder S with 2 wt% paraffin wax as lubricant and Powder N1 with 3 wt% paraffin wax. Compaction was carried out using a hand press. Twelve samples were compacted at each pressure and a typical variation of 2% was seen in green density at each pressure. The samples were heated at 2 C/min up to 250 C with a 1 h hold, heated again at 3 C/min up to 1000 C with a 1 h hold, and cooled at 10 C/min to room temperature in a H2 atmosphere for wax removal and presintering. Sintering was performed in a H2 atmosphere with four different sintering temperatures of 1100, 1200, 1300, and 1400 C. The samples were heated at 5 C/min up to the designated temperature with a 1 h hold and cooled at 10 C/min to room temperature.
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from magnetic coercivity. The spark sintering was carried out under vacuum at University of California at Davis. Right cylindrical compacts, approximately 20 mm diameter and 10 g mass, were prepared from Powder N2. These samples were subjected to a design of experiments (DOEs) with sintering temperatures ranging from 1000 to 1200 C, holding times ranging from 0 to 10 min, pressures ranging from 40 to 80 MPa, and electric currents ranging from 1000 to 2000 A. Table 1 shows the DOE based on an orthogonal array. Note that these few spark sintered samples are not sufficient by themselves to develop a grain growth model. 2.3. Image analysis
Fig. 1. SEMs of Powders S and N: (a) Powder S and (b) Powder N.
Additional samples were spark sintered from Powder N2 for verifying the developed model to predict grain size
Table 1 Orthogonal array for spark sintering Sample
1 2 3 4 5 6 7 8 9
Factor A
Factor B
Factor C
Factor D
Sintering temperature (C)
Holding time (min)
Pressure (MPa)
Electric current (A)
1000 1000 1000 1100 1100 1100 1200 1200 1200
0 5 10 0 5 10 0 5 10
40 80 60 60 80 40 60 40 80
1000 2000 1500 1500 1000 2000 2000 1500 1000
To obtain a polished microstructure for grain size analysis, the sintered samples were sectioned top-to-bottom and mounted using epoxy resin under vacuum to fill the porosity and to prevent the smearing of the material into the pores. The polishing procedure involved the use of a 9 lm diamond suspension followed by 6, 3, and 1 lm diamond suspensions on a MD-DAC cloth from Struers. A mirror-like finish was obtained by giving a final polish with a 0.04 lm silica colloidal suspension (OP-S from Struers). Next, the microstructure was revealed by chemically etching with a solution of 6 g of potassium ferricyanate and 0.5 g of potassium hydroxide in 50 ml of distilled water. The polished and etched microstructures were imaged using scanning electron microscopy (SEM). For the conventionally sintered samples, five different fields of each sample were taken at a magnification of 10,000· on a TopCon Model ABT-32 SEM (Tokyo, Japan). Example SEMs are shown in Fig. 2. For the spark sintered samples, two different fields of each sample were taken at magnifications of 20,000· on a Philips XL30 SEM. The WC grain size was measured from the fields using image analysis of the average grain area and perimeter. An analysis routine was developed using Clemex (Longueuil, Canada) Version PE 3.5 software. Grain boundaries were visually identified based on penetration by the Co matrix. The grains were then segmented as shown by the example images in Fig. 3. The software provided the cross-sectional area and perimeter of each individual WC grain. The diameter of an equivalent circle was calculated to represent the average WC grain size Gequivalent from the following equation: Gequivalent ¼
4A P
ð2Þ
where A is the average grain area and P is the average grain perimeter. 2.4. X-ray diffraction The WC crystallite size was measured by X-ray line broadening for both raw materials and sintered samples. X-ray diffraction measurements were performed with a Scintag X2 Advanced Diffraction System with a Si (Li)
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Fig. 2. Example SEMs of sintered microstructures: (a) Powder S, 400 MPa, 1100 C, (b) Powder S, 400 MPa, 1400 C, (c) Powder N1, 400 MPa, 1100 C, and (d) Powder N1, 400 MPa, 1400 C.
peltier detector using the Scherrer method. Scans were performed from 5 to 70 at a rate of 2/min. The peak position and full-width at half-maximum (FWHM) were calculated from both the most strongly diffracting peak (48) and from the average of all the peaks using Jade+ version 7.0 software. An X-ray diffraction pattern was collected on a NIST-certified silicon powder to establish and subtract any peak broadening contributed by the instrument itself, and all samples were run on the same instrument to eliminate peak broadening contributions from different machines. Peak broadening is also affected by lattice strain, but its contribution is difficult to separate from that of crystallite size so it was neglected. Data collection parameters remained identical between the reference silicon powder and the WC–Co samples. An example diffraction pattern is shown in Fig. 4 for Powder N1 sintered at 1100 C. The most strongly diffracting peaks of WC, Co, and TaC are indicated.
2.5. Magnetic coercivity A Foerster Model 1.095 coercimeter was used to measure the magnetic coercivities of the samples. The sample diameter was aligned with the long axis of the holder, which was inserted within a 40 mm coil. After adjustment of the residual field strength to obtain a coercive field strength within the display range, two measurements were taken with alternating polarity. The average value is reported. 3. Results and discussion 3.1. Powder characteristics The characteristics of the two as-received powders are summarized in Table 2. The X-ray line broadening measurement for Powder N agrees closely with the manufacturer’s advertised crystallite size of 40–70 nm; however,
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Fig. 3. Example segmented SEM images for grain size measurement: (a) spark sintering, 1100 C, 5 min, 80 MPa, 1000 A and (b) spark sintering, 1200 C, 5 min, 40 MPa, 1500 A.
its BET particle size is significantly larger than 100 nm prior to sintering. X-ray diffraction revealed that the standard powder also has nanocrystalline structure, indicating that the WC particles are composed of multiple crystallites. This shows the ambiguity in defining a powder as ‘‘nanocrystalline’’ based on X-ray diffraction measurements. 3.2. Grain size measurements Image analysis provides data on grain size distributions in addition to the mean grain size. An example distribution for a spark sintered sample is shown in Fig. 5. The distribution is log-normal with 10% of the grains below 128 nm in size, 50% below 230 nm, and 90% below 436 nm. All of the
samples sintered in this study had log-normal grain size distributions, so they can be represented by their mean value in the following analysis. The effects of sintering temperature and compaction pressure on mean WC grain size as measured by image analysis for Powder S and Powder N1 are plotted in Fig. 6. Powder S has a larger initial grain size and coarsens with temperature. Powder N1 shows a significant increase in grain size from 1100 C to 1200 C, but then further increases in temperature up to 1400 C have little effect on grain size, indicating an effective role of the grain growth inhibitor during both solid-state and liquid-phase sintering. For the most part, the effect of compaction pressure on grain size is not significant within measurement
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Fig. 4. Diffraction pattern of Powder N1 sintered at 1100 C.
Table 2 Powder characteristics Powder
S
N
Vendor Composition Pycnometer density (g/cm3) Tap density (g/cm3) (% of pycnometer density) BET surface area (m2/g) BET particle size (nm) Average crystallite size (nm)
Kennametal WC–10Co 14.5 –
Inframat WC–12Co 13.7 2.4 (17.5%)
– – 49 ± 9
2.3 188 57 ± 7
The effect of sintering temperature on the WC crystallite size as measured by X-ray line broadening for Powder S and Powder N1 is plotted in Fig. 7. The data are summarized in Table 3 in comparison to the grain size as determined by image analysis of SEM micrographs. The crystallite area is 6–100 times smaller than the grain area, indicating that each grain is comprised of this many crystallites. Fig. 8 shows the correlation between grain size and crystallite size. The crystallite size increases independently of grain size for Powder N1, while it increases linearly with grain size for Powder S. Achieving a sintered WC grain size of less than 100 nm will require not just a crystallite size below this, but discrete particles with dimensions less than 100 nm. The effect of sintering temperature on the magnetic coercivity for Powder S and Powder N1 is plotted in Fig. 9. The magnetic coercivity, K in kA/m, can be correlated with grain size, GWC in lm, for cobalt contents, wCo between 6 and 25 wt% as follows [18]: K ¼ ðc1 þ d 1 wCo Þ þ ðc2 þ d 2 wCo Þ
Fig. 5. Grain size distribution for spark sintering, 1000 C, 5 min, 80 MPa, 2000 A.
error. At 1400 C, the grain size increases with compaction pressure for Powder S. For powder N1, the grain size decreases with compaction pressure at 1100 C.
1 GWC
ð3Þ
where c1, c2, d1, and d2 are material constants. Although Eq. (3) was derived from linear intercept data for liquid phase sintered WC–Co, curve fitting the experimental data from image analysis of solid-state sintered and spark sintered samples to Eq. (3) resulted in an R2 value of 0.95 with a maximum error of 4.8% with the following values for the material constants: c1 = 7.873, c2 = 3.421, d1 = 0.125, and d2 = 0.665. Fig. 10 shows the fit between measured coercivity and grain size measured by SEM image analysis
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Fig. 6. Grain size measured by image analysis of SEM micrographs: (a) Powder S and (b) Powder N1.
reported for ‘‘super-ultrafine’’ WC–6Co grades with gain sizes of about 200 nm and hardnesses of 2200 VHN [3,23]. Fig. 10 shows that solid state sintered WC–12Co with a grain size of 200 nm is projected to have a coercivity of just 29.2 kA/m (367 Oe). Extrapolating to a nanograined grade with a WC grain size of 100 nm, the projected coercivity is 52.0 kA/m (653 Oe). In comparison, using the original values [18] for the material constants, c1 = 1.44, c2 = 12.47, d1 = 0.04 and d2 = 0.37, the projected coercivity for liquid phase sintered WC–12Co with a WC grain size of 100 nm is 82 kA/m (1028 Oe). The Vickers hardness number H has been linked to the grain size GWC in lm based on the Hall–Petch relationship via the following equation [20]: Fig. 7. Crystallite size measured by X-ray line broadening for samples compacted at 400 MPa.
for Powder S, Powder N1, and Powder N2. In comparison, the coercivity correlates poorly (average error = 33% and R2 = 0.67) with crystallite size, which is not directly related to the WC/Co interfacial area. The measured coercivity values are generally lower than they would be at the same WC grain size for liquid phase sintered materials with more uniform Co distribution. Coercivities as high as 51.7 kA/m (650 Oe) have been
H ¼ 1178 1326V Co þ ð654 497V Co ÞG0:5 WC
ð4Þ
where VCo is the volume fraction of Co. No such relationship exists for hardness and crystallite size. Combining Eqs. (3) and (4) enables the creation of a hardness–coercivity property map as shown in Fig. 11. Although developed from samples with coercivities of less than 35 kA/m, extrapolating the results to higher coercivities provides some targets for nanograined WC–Co. We propose that nanocrystalline be used to describe a powder or sintered material comprised of crystallites below 100 nm and that the term nanograined be reserved for
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Table 3 Summary of grain size and crystallite size data for samples pressed at 400 MPa Powder
Sintering temperature (C)
Crystallite size
Grain size
Mean (nm)
At 48 peak (nm)
Mean (nm)
Number of measured grains
Crystallites per grain
S
1100 1200 1300 1400
54 ± 4 113 ± 38 131 ± 29 176 ± 64
57 101 124 149
558 ± 13 593 ± 28 729 ± 15 1077 ± 25
1486 1325 1082 749
107 28 31 37
N
1100 1200 1300 1400
69 ± 16 90 ± 23 135 ± 61 127 ± 17
64 85 134 139
254 ± 12 354 ± 16 343 ± 21 374 ± 22
1925 1037 1067 981
14 15 6 9
3.3. Master sintering curve modeling The mean grain size increases with sintering time. For the sintering of hard materials, the classical model for interface-controlled grain growth with isothermal condition is [28]: G2 ¼ G20 þ Kt
Fig. 8. Relationship between grain size and crystallite size for samples compacted at 400 MPa.
sintered materials comprised of individual grains less than 100 nm. Nanocrystalline hardmetals do not necessarily have higher hardness. Based on the above analysis, proposed criteria for the properties of nanograined WC– Co grades are summarized in Table 4. Grain size measurement by linear intercept or equivalent circular diameter may indicate a nanograined material, but if it consists of a large percentage of WC–WC interfacial area instead of WC–Co interfacial area, properties may not be reflective of one. Coercivity is the best indicator of interfacial area, other than time-consuming contiguity measurements. Thus, magnetic coercivity is the recommended technique for extension of grain size measurements into the nanoscale range. The coercivity values given in Table 4 should be obtained in order to expect superior properties. Increased hardness is projected, but whether it can be combined with a unique combination of toughness remains to be seen. The property data for several reports of ‘‘nanocrystalline’’ and ‘‘super-ultrafine’’ WC–Co are summarized in Table 5 in for comparison with the criteria given in Table 4. Despite much activity with nanocrystalline powders, none of these materials achieve the requirements of a nanograined material as defined in Table 4. The reported grain sizes of the WC–6Co prepared by Lin and Yuan [6] are within the nanograin definition, but no supporting property data are given.
ð5Þ
where G is the mean grain size, t is the time, G0 is the particle size at the beginning of the steady-state, and K is the rate constant. K exhibits dependence with temperature that can be expressed as: K0 Q K¼ exp ð6Þ RT T where T is the absolute temperature, K0 is the associated pre-exponential factor, Q is the apparent activation energy, and R is the universal gas constant. The differential form for grain growth under non-isothermal conditions can be derived by substituting Eq. (6) into Eq. (5) and differentiating this equation with respect to time as follows: dG K 0 Q ¼ exp 2G ð7Þ dt RT T Starting with a densification rate equation in a form similar to Eq. (6), Su and Johnson developed the master sintering curve as a practical way of describing the densification of a compact along any given complex sintering cycle [21]. In this kind of equation, it is possible to separate the terms related with the microstructure on the left side and the temperature dependent parameters on the right side. Then, both sides are integrated independently assuming that: (a) microstructural evolution, both grain size and shape, is only a function of mean grain size; and (b) the apparent activation energy (Q) does not change during the sintering thermal cycle. Point (a) is usually true when the same basic atomic transport mechanics are responsible for both densification and microstructural evolution. Point (b) is satisfied when the proportional contribution of these basic mechanisms does not change during the sintering process. When point (b) is not true because of a change of basic mechanisms during the sintering cycle, the cycle can be divided
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Fig. 9. Effect of sintering temperature on magnetic coercivity: (a) Powder S and (b) Powder N1.
When the conditions previously mentioned are fulfilled, the integration of Eq. (7) leads to: Z t K0 Q 2 2 exp G ¼ G0 þ dt ð8Þ RT 0 T Eq. (8) for the grain growth is transformed into the master sintering curve form as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð9Þ G ¼ G20 þ H where Z H¼ 0
Fig. 10. Correlation between grain size as measured by image analysis and magnetic coercivity measurements. Samples from Powders S and N1 were compacted at 400 MPa and sintered at temperatures ranging from 1100 to 1400 C. Samples from Powder N2 were spark sintered.
into several consecutive stages that are integrated separately [22]. An additional condition is that the powders, their processing, and the compaction pressure are the same for all the green compacts, so green density and microstructure are common to all of them.
t
K0 Q exp dt RT T
ð10Þ
The parameters K0 and Q can be determined by curve fitting experimental data with Eqs. (9) and (10). It is noted that in Eq. (9), grain size in the MSC model depends on only the initial grain size of G0, regardless of sintering cycle, K0, and Q. The condition imposed in this fitting is to minimize the following mean residual, R: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 N u1 X GMSC i t ð11Þ RðK 0 ; QÞ ¼ 1 N i¼1 GEXP i
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161
Fig. 11. Property map for hardness and coercivity.
Table 4 Proposed criteria for a WC–Co grade to be designated ‘‘nanograined’’ Composition Linear intercept grain size (nm)
Equivalent Magnetic Crystallite Hardness circular coercivity size (nm) (VHN) diameter (kA/m) (nm)
WC–6Co WC–8Co WC–10Co WC–12Co
<100 <100 <100 <100
<100 <100 <100 <100
104 97 89 82
<100 <100 <100 <100
2955 2863 2774 2688
where N is the number of experimental grain size data points, i is a dummy variable for summation, GMSC_i is the ith grain size predicted by the master sintering curve model with given K0 and Q values, and GEXP_i is the ith experimentally measured grain size. The advantage of this method is to obtain more accurate values for Q and K0 with the consideration of the full thermal cycle, that is, with any combination of heating rate and holding temperature. The method is valid when all the grain growth data from different sintering cycles lie on a single master sintering
curve, the resulting activation energy (Q) has a reasonable value, and the mean residual term (R) is small. In the case of hardmetals, a significant contribution to grain growth results from variables such as gross carbon content, growth inhibitors, and matrix contents, which require reconstructing a new MSC for each composition with new experiments and new curve-fitted parameters Q and K0. The above MSC approach was performed based on the mean grain size from image analysis of SEM micrographs. The MSC approach based on magnetic coercivity data are almost the same since image analysis data were used to develop the correlation between grain size and magnetic coercivity. The BET particle size of 188 nm was used for the initial grain size for Powder N1. Since no BET particle size was available for Powder S, an initial grain size of 480 nm was obtained from curve fitting based on Eq. (11), which means that three parameters (K0, Q, and G0) were considered in case of Powder S. The MSC approach showed a high average error of 31% using crystallite size data from X-ray line broadening as for the case of predicting crystallite size from magnetic coercivity.
Table 5 Reported properties of nanocrystalline and super-ultrafine WC–Co Composition
Reference
Grain size (nm)
Grain size measurement technique
Coercivity (kA/m)
Hardness
Toughness (MPa m1/2)
WC–6Co WC–6Co
[3] [6]
Linear intercept Linear intercept
611 NRa
2150 VHN NR
NR NR
WC–10Co WC–6Co WC–10Co WC–7Co WC–9.45Co WC–7Co
[13] [23] [24] [25] [26] [27]
400 45 87 300 220 330 220 200–300 200–240
X-ray diffraction NR Image analysis Linear intercept NR Linear intercept
NR 651 NR NR 27.4 NR
WC–10Co
[8]
100
NR
NR
1950 VHN 2220 VHN 1900 VHN 2093 VHN 92.8 HRA 94.7 HRA 94.2 HRA 1887 VHN
NR NR NR 10.4 NR 10.2 11.2 11.5
a
NR, not reported.
162
S.J. Park et al. / International Journal of Refractory Metals & Hard Materials 26 (2008) 152–163
Fig. 12. Master sintering curves of grain growth for Powders S and N1.
Table 6 Material parameters used in MSC analysis of grain growth Powder
Die compaction pressure (MPa)
Q (kJ/mol)
K0 (m2 K/s)
Mean residual (%)
S
110 400 565
171 209 224
1.47 · 108 4.39 · 107 1.81 · 106
2.48 2.54 3.05
N1
110 400 565
64 88 65
9.96 · 1013 5.85 · 1012 9.56 · 1013
3.27 3.80 2.59
Fig. 12 shows the master sintering curves of grain growth for Powder S and Powder N1. The average errors are 2.73% for Powder S and 3.32% for Powder N1 and the maximum errors are 3.05% for Powder S and 3.80% for Powder N1, respectively. These low error values indicate that the classical model of interface-controlled grain growth, described above, can well explain grain growth in the WC–Co system. In addition, the BET particle size and the proposed equivalent diameter determined from image analysis, expressed in Eq. (2), seem to be reasonable for this model, indicating that the polycrystalline WC grains do not disintegrate into multiple grains during sintering. Table 6 shows the activation energies and the associated pre-exponential factors, which supports quantitatively the explanation of Fig. 8 in Section 3.2. Finally, the asymptotic character of Fig. 12 at low levels of thermal work (H) indicates that it is impossible to consolidate these powders to full density with a nanoscale grain size; a suggestion already given by the research of Hayashi and Matsuika [29]. Combining the MSC grain growth model with the MSC densification model provides an estimate of the minimum starting particle size required to achieve a specific combination of density and sintered grain size [30]. From the optimization results, the minimum grain size that can be achieved at a sintered density of 97% of theoretical is 332 nm for Powder N1 with a compaction pressure of 565 MPa. This value is 1.8 times larger than the initial grain size, which suggests that a WC powder with
discrete particles less than 50 nm in diameter is required in order to obtain nanograined WC–Co with the properties shown in Table 4. 4. Conclusion The mean grain size of solid-state sintered and spark sintered WC–Co can be determined by image analysis and correlated with magnetic coercivity, which is related to the WC–Co interfacial area. With sufficient data, empirical expressions for coercivity can be extrapolated into the nanograined range and related to properties such as hardness and toughness. WC grains can be polycrystalline, thus the crystallite size as determined by X-ray diffraction can be substantially smaller than the grain size measured by image analysis and does not correlate with magnetic coercivity or properties. Despite much activity with nanocrystalline powders, sintered WC–Co with nanoscale grains has not yet been achieved. Traditional coarsening models for WC–Co are based on interface-controlled grain growth and are not suitable for predicting coarsening of crystallite sizes determined by Xray diffraction. A model based on master sintering curve theory indicates that a powder with discrete particles below 50 nm is needed to produce an average grain size of less than 100 nm. Future characterizations of sintered nanocrystalline WC–Co powders should include magnetic coercivity measurements as well as hardness and toughness data for development of models to link microstructure and properties at the nanoscale level. Acknowledgments This study was supported by Kennametal, Inc. and the CAVS Chair at Mississippi State University. Special thanks go to Yixiong Liu, Tim Muller, Tracy Potter, Don Heaney, Lou Campbell, and Joanna Groza for their help with providing experimental data and valuable advice.
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