Influence of sintering temperature and pressure on crystallite size and lattice defect structure in nanocrystalline SiC
J. Gubiczaa, S. Nauyoksb, L. Balogha, T. W. Zerdab, and T. Ungára
a Department of Materials Physics, Eötvös Loránd University
Budapest, P.O.B. 32, H-1518, Hungary
b Department of Physics and Astronomy, Texas Christian University
Fort Worth, TX 76129, USA
Microstructure of sintered nanocrystalline SiC is studied by X-ray line profile analysis. The lattice defect structure and the crystallite size are determined as a function of pressure between 2 and 5.5 GPa for different sintering temperatures in the range from 1400 to 1800 C. The sintering process results in an increase of the crystallite size indicating coalescence of powder particles. It is found that in the case of relatively small crystallite size values, i.e. less than about 20 nm, planar faults are the main lattice defects, while for crystallite size larger than 70 nm dislocations are more abundant. At the largest applied pressure and temperature, 8 GPa and 1800 C, the crystallite size decreases probably as a result of subdivision of grains by dislocation boundaries.
Keywords: nanostructure; sintering; defects; x-ray diffraction, XRD
Silicon carbide is frequently used as a functional and structural material at high temperatures. Nanocrystalline SiC offers very high strength in structural applications even at high temperatures . For that reason, silicon carbide often serves as a binding phase in composites, for example in diamond composites. Improvements in mechanical properties of SiC resulting from grain size reduction are expected [2,3]. To modify the grain size of bulk SiC sintered from nanopowders we varied manufacturing pressure and temperature. It is expected that the microstructure of sintered SiC can be tailored by the proper selection of these two parameters .
Influence of defects on mechanical properties of ceramics has been thoroughly investigated experimentally  but no theoretical model describing the relationship between deformations in the lattice, hardness, and grain size dependence exists. The lattice defect structure in microcrystalline SiC have been studied by microscopic and X-ray diffraction methods [6,7]. The appearance of planar faults in SiC has been reported and the density of these defects were estimated by comparing intensities of different X-ray reflections [6,8]. However, results of that procedure become uncertain when microstructure consists of nanograins and lattice defects, especially dislocations, are abundant. Recently, the Convolutional Multiple Whole Profile (CMWP) fitting procedure  worked out for the determination of crystallite size and dislocation structures has been extended to determine the density of stacking faults and twins concomitantly with the first two microstructure components . The extended Convolutional Multiple Whole Profile (eCMWP) fitting procedure was successfully applied to ultrafine grained copper samples processed by different methods .
In the present work a series of sintered nanocrystalline SiC specimens is investigated by X-ray line profile analysis using the CMWP fitting procedure. The effect of sintering temperature and pressure on the crystallite size as well as on the dislocation and planar fault densities is studied here. In the past, we applied this methodology to analyze structure and defects in diamond crystals of different history of pressure and temperature treatments and in the diamond phase of diamond-SiC composites [11,12]. Additional motivation for the present study is the need to better understand the role of the SiC binding phase in diamond-SiC composites. Silicon carbide is the weaker component and its structure and properties determines many physical and mechanical properties of the diamond based composites. It is expected that the results of this study will help to better understand properties of silicon carbide in those composites which are produced under high pressure and high temperature conditions.
2. Experimental materials and procedures
Bulk nanocrystalline SiC specimens were sintered from SiC nanopowder with nominal grain size of 30 nm. The sintering procedure was carried out at temperatures of 1400, 1600 and 1800 C. At each temperature, specimens were sintered at pressures of 2, 4 and 5.5 GPa. This process gave nine bulk sintered SiC samples, in addition to the initial powder. An additional specimen was produced at 1800 C and at a very high sintering pressure of 8 GPa.
Sintering at 2 GPa was conducted in a piston-cylinder cell while those at higher pressures, 4, 5.5 and 8 GPa, in a toroid high pressure cell which consisted of two identical anvils with toroidal grooves and lithographic gasket that matched the contours of the grooves. In each case, silicon carbide powder was placed inside a heater that consisted of a graphite cylinder and two graphite plugs on both ends of the cylinder. The heater was placed inside a piston-cylinder cell or between the anvils which were next pressed together by a hydrostatic press. Pressure and temperature calibrations were run prior to the experiments according to the procedure described in Ref. 12. Precision of temperature measurements was 50oC and pressure was stable within 10%.
The phase composition of the specimens was determined by X-ray diffraction using a Philips X'pert powder diffractometer with a Cu anode. The microstructure of the specimens were studied by X-ray diffraction line profile analysis. The X-ray line profiles were measured by a high-resolution diffractometer (Nonius, FR 591) using CuK?1 radiation. The line profiles were evaluated by the extended Convolutional Multiple Whole Profile (eCMWP) fitting procedure described in detail in Ref. 10. In this method, the experimental pattern is fitted by the convolution of the instrumental pattern and the theoretical size and strain line profiles. Because of the nanocrystalline state of the studied samples, the physical broadening of the profiles was much higher than the instrumental broadening; therefore, instrumental correction was not applied in the evaluation. The theoretical profile functions used in this fitting procedure are calculated on the basis of a model of the microstructure, where the crystallites have spherical shape and log-normal size distribution, and the lattice strains are assumed to be caused by dislocations and planar faults. The method gives the area-weighted mean crystallite size, <χarea> area, the density of dislocations, ρ, and the density of planar fault, in this case twins, α.
3. Results and discussion
The X-ray diffraction pattern of the SiC specimen sintered at 2 GPa at 1800°C is shown in Fig.1a. The diffractograms corresponding to the other samples have similar qualitative features. The X-ray diffraction patterns show that beside the SiC main phase the sintered specimens contain graphite with the concentration between 2 to 5 (±0.5) vol.%. These are remnants from the graphite heater which was difficult to remove after the sintering. Because the specimens and the heater were compressed together by the anvils it was very difficult to remove all graphite without discarding also the specimen. The X-ray diffraction pattern shown in Fig. 1a is re-plotted in Fig. 1b with logarithmic intensity scale for the 2 range between 30 and 45 degrees. A shoulder can be observed on the left-tail of the 111 SiC peak at about 2 =33.6°. Previous experimental results [6,8] showed that this peak appears when planar faults exist in the microstructure. To justify the correspondence between this small peak and the planar faults, we calculated the X-ray diffraction pattern for SiC assuming that the microstructure contains planar faults. The calculation was carried out for intrinsic and extrinsic stacking faults and twins by the DIFFaX  software. The X-ray diffraction pattern calculated for 10 % twins is plotted in Fig. 2 for the 2 range between 30 and 45°. The small peak at 33.6° is unambiguously related to planar faults. The same peak appears also when intrinsic or extrinsic stacking faults are assumed in the microstructure.
For revealing the type of lattice defects in the microstructure, the Full Width at Half Maximum (FWHM) was plotted as a function of the length of the diffraction vector, K=2sinθ/λ , in the Williamson-Hall plot. A typical example of the Williamson-Hall plots of the present SiC samples is shown for the specimen sintered at 2 GPa and 1800°C in Fig. 3. It can be seen that, within experimental error, the FWHM values of the 111/222 and 200/400 reflection pairs are order-independent indicating that line broadening, in this case, is mainly caused by small crystallite size and/or planar faults. This is also the case for the initial powder and the specimens sintered at pressures lower than 4 GPa and temperatures below 1600°C. At the same time, for the SiC specimen sintered at higher pressures and temperatures, i.e. 5.5 GPa and 1800°C, there is a strong order-dependence of the FWHM values, as shown in Fig. 4a. Using the average dislocation contrast factors, C, the FWHM data can be arranged along a smooth curve in the modified Williamson-Hall plot (see, e.g. Fig. 4b) indicating that lattice distortions originate basically from dislocations.
The microstructure parameters of SiC in the initial powder and the sintered specimens were determined by the eCMWP fitting method. For all eleven specimens the fitting procedure was carried out for extrinsic, intrinsic and twin planar faults. The final sum of squared residuals after the fitting was the smallest for each sample when twins were assumed. Moreover, for the first two types of planar defects the diffraction lines should show a systematic asymmetry while in the case of the twins, the peak profiles are expected to be symmetrical . Our profiles were observed to be almost completely symmetrical for all samples. Taking into account that the smallest values of the final sum of squared residuals were obtained for twins, and that the measured profiles are symmetrical we conclude that the planar defects are twins. Hereafter, only results obtained by assuming twins as planar faults are shown. Two typical examples of the fitting, one for order-independent and another for order-dependent FWHM behavior are shown in Figs. 5a and 5b for the samples sintered at 2 and 5.5 GPa at 1800°C, respectively. The differences between the measured and fitted patterns are also plotted at the bottom of the figures. The quality of the fitting can also be checked in the Williamson-Hall plot of Fig. 3 where the breadths of the fitted profiles (open triangles) are in good agreement with the experimentally determined FWHM values (open squares).
The eCMWP fitting analysis carried out for the initial powder gives the mean crystallite size of 8.3±0.7 nm and the twin density of 7.4±0.6 %. As the order-independent FWHM values suggested, the dislocation density (or, in other words: microstrain) in the present specimen is below the limit of detection by X-ray line broadening, i.e. ρ<1013 m-2. Table 1 shows the microstructure parameters of nine SiC specimens sintered at pressures below 5.5 GPa. From the results it can be concluded that in the initial SiC nanopowder the main lattice defects are planar faults, in particular, twin boundaries. The crystallite size increases during sintering because of the coalescence of nanoparticles. At the constant temperature, the higher the sintering pressure the larger the crystallite size is. This phenomenon can be explained by the assistance of pressure in the process of particle fusion. At low pressure values, twins are formed during sintering and the dislocation density remains below the detection limit of line profile analysis. At 1600°C and 1800°C, and above a certain pressure limit, the planar fault density decreases to a very low level, i.e. to about 0.1±0.1 %, and dislocations become the main type of lattice defects. This pressure limit decreases with the increase of temperature. The pressure limits are 5.5 and 4 GPa at 1600°C and 1800°C, respectively. It should be noted, however, that for the specimens where dislocations were observed in abundance, the diffraction peak at 33.6° does not disappear completely indicating small concentration of planar defects in the microstructure. This peak is shown in Fig. 6 in the diffraction pattern for the specimen sintered at 1800°C and 5.5 GPa.
For the specimen prepared at 8 GPa and 1800 C the microstructural data are: <x>area=73±8 nm, α=1.8±0.3 % and ρ=15±2x1014 m-2. The crystallite size decreased while both the dislocation and the planar fault densities increased compared to the sample processed at 5.5 GPa at the same temperature. The highest applied pressure, i.e. 8 GPa, induced the largest dislocation density. The large microstrains at high temperature most probably result in the rearrangement of dislocations into subgrains which is similar to the phenomenon observed in metals during severe plastic deformation . The subdivision of SiC grains into subgrains causes the decrease of crystallite size determined by X-ray line profile analysis, since the coherently scattering domains correspond to subgrains or dislocation cells, as shown previously by Ungar and coworkers [15,16].
The samples containing a significant amount of dislocations are marked by light grey color in Table 1. It seems that at high temperatures and pressures the relatively large crystallite size enables the formation of dislocations during the sintering process. The elimination of planar faults when grain growth takes place during firing at high temperatures has already been observed for SiC . This result is also in line with previous observations for metals . Zhu et al. observed that planar faults are formed in small grain size while for grains larger than 40 nm dislocations are activated during severe plastic deformation . The value of the grain size where that transition takes place depends on the properties of materials. For example, for Cu on the basis of the model calculation and the experimental values of stacking fault energy Zhu and coworkers suggest 40 nm as the critical grain size below which deformation proceeds by twinning instead of by dislocation glide . This conclusion was confirmed by Balogh et al.  who used X-ray line profile analysis. In Fig. 7 the ratio of the twin density and the dislocation density, ρ/α, is shown as a function of the crystallite size for the SiC specimens investigated in this paper. Where the dislocation density was under the detection limit of line profile analysis, the limit was used as the value of the dislocation density. It means that the ρ/α value are probably underestimated, which, however, does not affect the conclusions drawn from Fig. 7. The figure suggests that with increasing crystallite size the formation of dislocations instead of planar defects is preferred. The current study did not allow us to precisely identify the critical grain size for which dislocations become prevalent, but it is appears to be bounded between 25 and 70 nm.
It has been mentioned above that the pressure limit where dislocations become the main lattice defects decreases with increasing temperature. This phenomenon can be explained by the promoting effect of temperature for the growth of crystallites. It is interesting to note that when the crystallite size decreases, e.g. for sintering at 8 GPa and 1800°C, the planar defects have significant densities, which again supports the observed correlation between the crystallite size and the defect structure. During the sintering process of the latter sample, most probably the dislocations are formed first and then are arranged into subgrain boundaries. Once the crystallite size decreases by subgrain formation, the deformation proceeds, at least partly, by twinning.
The effect of sintering temperature and pressure on the microstructure of bulk SiC manufactured from 30 nm powder was studied by X-ray line profile analysis. It has been found that the crystallite size increases during sintering as a result of particle fusion. A correlation between the crystallite size and the lattice defect structure has been established. When the crystallite size increases dislocations gradually become the main lattice defects instead of planar defects. Since increase of pressure and increase of temperature assist grain-growth, above critical value of grain size, deformation proceeds by dislocation glide instead of twinning. That critical value was estimated to be between 25 nm and 70 nm.
This work was partially supported by the Hungarian Scientific Research Fund, OTKA, Grant No. F-047057 and by a grant NSF-DMR 0502136. JG is grateful for the support of a Bolyai Janos Research Scholarship of the Hungarian Academy of Sciences.
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