1. Introduction

Owing to its high strength, high hardness, oxidation resistance, superior fracture toughness and chemical stability even in aggressive environments, SiC has applications in many fields such as aerospace industry, nuclear reactors, propulsion applications and heat exchangers^[1–7]. Compared to their bulk forms, nanoparticles have demonstrated novel mechanical, electrical and optical properties^[8–11]. Materials reinforced with SiC nanoparticles have showed improved hardness and fracture strength^{[12, 13]}.

The size effects of nanoparticles in composites have been studied extensively, which demonstrated the significant influences of sizes on mechanical and physical properties of the nano-composites. It was found that the smaller size of silicon carbide (SiC) nanoparticles embedded in Al matrix played a significant role on grain refinement rather than the larger ones^[14]. Timofeeva et al. studied the effect of average nanoparticles sizes on basic macroscopic properties and heat transfer performance of alpha-SiC/water nanofluids. They found that the nanofluids with larger particles have higher thermal conductivity and lower viscosity than those with smaller particles of the same material because of the smaller solid/liquid interfacial area in the former system^[15]. It was also reported that the catalytic activity highly depends on the shape and size of the nanoparticles^[16]. Nanoparticles used as second phase reinforcement also affect the yield strength of the compound material by their size distribution^[17]. Therefore, an accurate measurement of the nanoparticles size distribution has become crucial in many cases.

The average size of the commercial SiC nanoparticles we use in this study was claimed to be 30 nm. We apply the methods of small angle X-ray scattering (SAXS), X-ray diffraction (XRD) and transmission electron microscope (TEM) to investigate the actual size distribution of these nanoparticles, as well as their structures.

2. Material and methods

Commercially available silicon carbide (3C-SiC, also called β-SiC) nanoparticles (99.9%) with a claimed average particle size of 30 nm was chosen for our study. XRD, TEM and small angle X-ray scattering (SAXS) measurements were carried out to study the nanostructure of the material.

SAXS measurement was carried out at beamline BL16B1 at Shanghai Synchrotron Radiation Facility using a three-slit system. The wavelength of the X-ray was 0.124 nm. The 2D SAXS patterns were recorded by a Mar165 CCD at a resolution of 2048 × 2048 pixels and a pixel size of 80 × 80 μm² for quantitative analysis. The sample-to-detector distance was 1920 mm calibrated by a beef tendon standard. This setup provided a scattering vector q range of 0.007 to 0.2 Å, corresponding to real space scale of around 3 to 100 nm. SiC powder was spread on a Scotch tape for measurements. The scattering patterns of SiC powders in the tape and the tape itself were taken separately during the experiment so that the scattering pattern of SiC powders per se can be obtained by subtraction.

X-ray diffraction data were obtained using a Bruker D8 Advance diffractometer with Cu kα radiation (λ = 1.5418 Å) in the 2θrange between 5 and 90, which covered most of the intense diffraction peaks of SiC. The instrument operated at 40 kV and 40 mA.

TEM observations were conducted using an FEI Tecnai G2 S-TWIN (accelerating at 200 kV) microscope. The samples were prepared by dispersing the SiC nanoparticles in ethanol with ultrasonic cleaner to prevent the aggregation of nanoparticles and drying a few drops on a carbon-coated copper grid.

3. Results

3.1 Modeling of SAXS

For a single spherical scatterer, the scattering intensity I₁(q) can be expressed as follows:

${{{I}}_1}\left( {{q}} \right) = {I_{\rm e}}{V^2}{\rho ^2}P\left( {q, r} \right),$

(1)

where

$P\left( {q,r} \right) = {\left\{ {\frac{{3\left[ {\sin \left( {qr} \right) - qr{\rm cos}\left( {qr} \right)} \right]}}{{{{\left( {qr} \right)}^3}}}} \right\}^2} ,$

(2)

is the form factor of a sphere;

${{q}} = \frac{{4\pi }}{\lambda }{\rm{sin}} \theta ,$

(3)

is the scattering vector, where θ is half of the scattering angle. V denotes the scatterer’s volume, ρ is the electron density of the monomer, r is particle radius, and I_e is the intensity scattered by one electron.

In our case, SiC nanoparticles are modeled as the polydisperse spheres. The scattering contrast comes from the density difference between the SiC and vacuum if the background (tape + air) is taken away. The densities of all the spheres are the same.

So the total scattering intensity is

${{{I}}_0} = \Delta {\rho ^2}\mathop \sum \limits_{i = 1}^{{N_0}} {V_i}{\left( r \right)^2} {P_i}\left( {{q_i}, {r_i}} \right),$

(4)

where $\Delta \rho = \rho _{\rm SiC}^2 {I_{\rm e}}$ is the scattering length density of SiC.

3.2 SAXS and TEM results

Fig. 1(a) shows the 2D SAXS signal of in-tape SiC nanoparticles collected by a CCD camera. One can see the shadows of two beam stops, which was discarded during data analysis. The background scattering from the tape and air was recorded separately on another CCD image, as seen in Fig. 1(b). It was used to subtract from the total scattering image. After correction with the background and dark current, the pure scattering profile I versus q of SiC nanoparticles was plot in Fig. 2, together with the result of the particle size distribution after modeling. The two-dimensional SAXS data were reduced using the Nika package developed in Igor Pro^[18]. Data modelling was carried out using the Irena package developed in Igor Pro^[19].

After the data reduction, the scattering profile of the SiC nanoparticles is plot in Fig. 2, together with the modeling result. Size distribution is described by the volume ratio as a function of the particle size. It suggests that nearly all of the SiC nanoparticles are in diameter of 10–100 nm, in which 20–50 nm is the most popular size range. The size profile follows a log-normal distribution.

Fig. 3(a) shows the bright-field TEM micrograph of the SiC powder, where β-SiC particles with various sizes can be clearly seen and counted. The statistics of the size distribution by TEM observation was summarized in Fig. 3(b) as histogram and compared with the result from SAXS. The trends of the distribution as a function of the size coincide between two methods.

3.3 XRD result

Fig. 4 shows the X-ray diffraction pattern of the SiC powder. Most of it is 3C-SiC (β-SiC) and there is a small amount of 6H-SiC (α-SiC) in it, indicated by the tiny peak (101) appearing on the left of the major 3C-SiC (111) peak. Due to its small content in the sample, this peak from the impurity is negligible in the following size estimation.

Scherrer’s equation is commonly used to determine the crystal size, which is:

$L= \frac{{{K}\lambda }}{{\beta {\rm cos}\theta }},$

(5)

where $K$ is Scherrer’s constant, $\lambda$ is wavelength of X-ray, β is the FWHM, and θ is the diffraction angle. Here we choose 0.94 for K as β-SiC is spherical crystals with cubic symmetry^[20].

Applying the equation on the three main peaks: (111), (220) and (311) respectively, we can get the size of the crystals as 20.2, 22.4, and 21.2 nm respectively. Each value refers to the crystallite dimension in the direction perpendicular to the planes that produced the diffraction peak. So, the crystallite size can be estimated from the average of the three values, which is 21.3 nm.

4. Discussion

The mean particle size determined from SAXS, TEM and XRD is 42, 37, and 21 nm, respectively. The difference of SAXS and TEM are within 10%, but the value given by XRD is only around half of the formers. This is due to the different principles underlining the three measurements. SAXS detects the scattering contrast; TEM image is created by the density contrast; XRD peaks are created by the interference of X-ray scattered from the periodic planes within the same crystal. Hence, if there was a particle composed of several crystalline domains, i.e. a polycrystalline particle, SAXS and TEM would measure the size of the whole particle while XRD peaks would provide the average size of all the crystalline domains. HRTEM micrographs of the sample shown in Fig. 5 verified our argument, where one can see single crystals as well as polycrystals with twins and stacking faults.

There are various methods to synthesize SiC nanoparticles, including Acheson, thermal plasma processing, rice hull conversion, CVD processes, combustion synthesis, sol-gel^[21–24]. Among them, Acheson and thermal plasma processing tend to produce micrometer-sized particles, while other methods produce more uniform particles in size of nanometers. What is more, the nanoparticles by sol–gel method are usually reported to follow the log-normal distribution^[24], as our present study shows.

5. Conclusion

Microstructure and size distribution of SiC nanoparticles were characterized with multiple characterization techniques. TEM provides the morphology of the particles, and suggests the existence of many crystalline defects within particles, including the twins and stacking faults; XRD identifies the phase of the sample to be β-SiC mixed with a small amount of α-SiC, and suggests the average size of the single crystalline domain to be around 21 nm; SAXS result shows that the size distribution of the particles follows log-normal function, and the average particle size to be around 42 nm.

Acknowledgement

The authors also appreciate the beam time provided by 16B of Shanghai Synchrotron Radiation Facility for the SAXS measurements.