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Astron. Astrophys. 329, 1035-1044 (1998)

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3. Laboratory results on SiC powders

In this section, we wish to illustrate and confirm the statements of Sect. 2. For this purpose, we took advantage of the advent of two new synthesis methods used in our laboratories for more general purposes: laser pyrolysis of gaseous precursors, and mechanical synthesis by milling together pure carbon and silicon.

3.1. Laser pyrolysis

Nanosized SiC powder has been synthesized by a gas phase laser driven reaction using silane and acetylene precursors and a high-power continuous wave CO2 laser emitting at 10.6 µm in resonance with an infrared absorption band of silane. Detailed information on the synthesis process was given by Cauchetier et al. (1988). Sample SiC212 was obtained at atmospheric pressure under 600 W laser power, the flow rates being 600 and 300 cm3 /min of silane and acetylene respectively. A gray, cotton-like powder is formed. The specific surface area, as measured by adsorption-desorption of nitrogen (Brunnauer-Emmet-Teller method), is 70 m [FORMULA] /g and corresponds to an equivalent diameter of 27nm, which agrees with transmission electron microscope photographs (Fig. 1).

[FIGURE] Fig. 1. Micrograph of an as-formed pyrolysis powder. Bar=100nm.

Chemical analysis shows the presence of 1.4 wt% of oxygen and 30.3 wt% of carbon. Neglecting hydrogen, the silicon content amounts to the remaining 68.3 wt%. From stoichiometry, the corresponding chemical composition is SiC: SiO2: free carbon = 95.7: 2.7: 1.6 wt%.

[FORMULA] NMR spectra show the main polytype to be [FORMULA] SiC with a much smaller amount of the [FORMULA] variety.

3.2. Mechanical alloying

Mechanical alloying is now a widely used method to prepare all kinds of materials from elemental powder mixtures (Gilman and Benjamin,1983; LeCaer et al., 1990; Koch, 1993). A wide variety of alloys, compounds, composites have been obtained by this dry and high-energy ball-milling process often in a metastable crystalline form with a nanometric crystallite size which is typically of the order of 10 nm. Dry grinding in high-energy ball-mills is also a non-equilibrium method of processing already synthesized materials which induces changes in the ground powders such as formation of nanometre-sized crystallites with a high defect density and interface content, amorphization (Koch 1993), polymorphic transformations (for instance Begin-Colin et al. 1994), order-disorder transformations (Pochet et al. 1995). Both mechanical processes involve repeated welding, fracturing and rewelding of powder particles in a high energy ball charge. In the case of SiC, detailed studies of these processes as a function of various experimental parameters can be found in the recent literature (see for instance LeCaer et al., 1990; Matteazzi et al., 1991; Sherif El-Eskandarany et al., 1995).

[FIGURE] Fig. 2. SEM a and TEM b micrographs of SiC powder ground for 4 hours.

Here, we have used ball-milling to refine and homogenize a commercial product of essentially the same [FORMULA] polytype as in Sect. 3.1 (CERAC, Inc. (France), average initial granulometry [FORMULA] 80 µm). The SiC powder was milled under an argon atmosphere for 4 hours in a planetary ball-mill (Fritsch Pulverisette 7) with hardened steel grinding media consisiting of a 50 cm3 vial and of seven balls of diameter close to 13 mm. The powder to ball weight ratio was 1/20. The resulting sample is designated as SiC4h.

The X-Ray diffraction (XRD) pattern of ground SiC powder is identical to the XRD pattern of the starting powder, but with broadened diffraction peaks related to crystallite sizes and strains. Grinding does not induce change in the lattice parameter of [FORMULA] -SiC: a = 0.4361 nm and a strain [FORMULA] of 1.2 10-3 Å is calculated from the XRD pattern. From a morphological point of view, the ground SiC powder consists of ellipsoidal aggregates of small particles. The average size of aggregates is approximatly 100-500 nm (Fig. 2a). These aggregates are constituted of very small crystallites of about 15-20 nm as deduced from X-ray diffraction patterns and TEM observations (Fig. 2b).

3.3. IR Spectrometry

Transmission spectra were obtained using KBr and CsI pellets in which small quantities of SiC powder were embedded homogeneously. A pellet is obtained by mixing about 1 mg of SiC and 300 mg of matrix powder, grinding for several minutes, and applying about 10 tons of pressure for 5 to 10 mn. The pellet is 13 mm in diameter and about 1 mm thick. It is mounted in the sample beam of a P-E interferometric spectrometer whose resolution is set at 4 cm-1.

The absorbance spectra shown here were obtained by subtracting the spectrum of a KBr (or CsI) blank from the spectrum of an SiC-loaded pellet. Absorbances at the feature's peak range between 0.5 and 2.5. The extinction coefficient is obtained from the absorbance, A, by writing

[EQUATION]

where S =1.3 cm2 is the pellet cross-section area, [FORMULA] =3.2 g/cm3 is the density of [FORMULA] C and m, the mass of embedded [FORMULA] C (measured to 20% accuracy). Note that [FORMULA] equals [FORMULA], the cross-section per unit volumeof the particles in the mixture and not of bulk SiC. If the embedded SiC particles aresmall, isolated spheres of radius a, their reduced optical extinction efficiency is [FORMULA]

[EQUATION]

If the particles are big by construction or by agglomeration, in the matrix, the spectrum can suffer dramatic changes: thus, Fig. 3 shows the full spectra of SiC from laser pyrolysis (sample SiC 212) embedded in KBr by careful grinding (a), and the same powder crammed over a blank KBr pellet (b). The effects predicted by theory (Sect. 2) are all observed on curve 3b. Similar effects are exhibited by embedded mechanically prepared SiC, when not ground or ground for excessively long times: 4 hours seems to be an optimum in avoiding size and agglomeration effects (hence sample SiC4h). By contrast, laser pyrolysis seems to produce consistently small particles.Note the very weak underlying continuum absorbance across the whole spectrum.

[FIGURE] Fig. 3. Transmission spectra of SiC212 synthesized by laser pyrolysis: a  homogeneously embedded in a KBr matrix; b  crammed upon a Kbr blank pellet

In the following, therefore, we consider only sample powders SiC212 and SiC4h and restrict the spectral range to the feature extent, 700 to 1000 cm-1, as in Fig. 4 and 5 [FORMULA]

[FIGURE] Fig. 4. Spectral details of SiC212 powder embedded in: a  KBr, b  CsI.

[FIGURE] Fig. 5. Spectral details of SiC4h powder embedded in: a  KBr, b  CsI.

3.4. Discussion

In order to lay down sound bases for the comparison of laboratory with astronomical spectra (Sect. 4), we wish first to use our results as a test of the fundamental assumptions that: 1) the feature shape is determined mainly by the distribution of particle shapes and 2) the bulk optical constants (Eq. 12) apply to our powders.

Indeed, as expected, all extinction features are confined between [FORMULA] 780 and [FORMULA] 970 cm-1, nearly the values of [FORMULA] and [FORMULA]. Extinction outside this range is weak, (especially for SiC212), confirming the absence of other fundamental oscillators or electronic conduction in the IR.

The red shift of the feature on going from a KBr matrix ([FORMULA]) to the stronger dielectric CsI ([FORMULA]), is not uniform but decreases to zero towards the edges of the feature. This test can be further quantified by using Sect. 2 to infer theexpected feature of SiC embedded in one matrix from the measured feature of the same powder in the other matrix. The procedure is as follows.

1) Considering the weakness of the damping constant, [FORMULA], we assume that each shape parameter, L, contributes a single Dirac- [FORMULA] resonance to the extinction spectrum, at a wavenumber [FORMULA] depending on the matrix according to (8) (In this approximation, it is not possible to deal with wavenumbers outside, or near, the edges of the interval [FORMULA] ce the wings of the Frohlich resonance are artificially [FORMULA] pressed).

2) For each wavenumber [FORMULA] of a spectrum taken in matrix m, compute [FORMULA] and, inverting Eq. 8, deduce the corresponding shape parameter

[EQUATION]

3) Using (8), compute the corresponding resonance wavenumber in the other matrix, n:

[EQUATION]

where [FORMULA] assuming the [FORMULA] distribution is the same in both matrices.

4) Note that the ratio of spectral intensities, [FORMULA] and [FORMULA], at corresponding wavenumbers [FORMULA] and [FORMULA] is equal to the ratio of embedded SiC masses multiplied by the ratio of the corresponding cross-sections, [FORMULA], in matrices m and n. Hence, using (7),

[EQUATION]

where [FORMULA]. An intensity peak in one spectrum does not necessarily transform into an intensity peak in the other spectrum.

This procedure was applied to the spectrum (Fig. 2b) of SiC212 in CsI (matrix m) to deduce the expected spectrum in KBr (matrix n), which is compared in Fig. 6 to the measured spectrum (Fig. 4a). The fit is particularly sensitive to the exact value assumed for [FORMULA] ; here, the best fit was obtained for 798 cm-1, in agreement with Spitzer et al.'s value to instrumental accuracy. The small discrepancies in intensity are most likely ascribed to inevitable differences in particle aggregation.

[FIGURE] Fig. 6. Spectra of SiC212 in KBr. Continuous line: predicted from the measured spectrum in CsI (Fig. 2b); dashes: measured (Fig. 2a).

Finally, compare the measured and expected extinctions. The measured values of [FORMULA] at the peak of the feature are (in cm-1)

[EQUATION]

If the SiC particles were all small spheres, we would, from Eq. 7, expect their peak extinction coefficient, [FORMULA], in KBr and CsI respectively, to be 6.8 105 and 8.2 105 cm-1. Thus, the ratios of expected to measured peak extinction efficiencies are, for SiC212 and SiC4h, respectively

[EQUATION]

Similar huge "discrepancies" were previously blamed on the use of bulk SiC optical constants to interpret the spectra of powders. Note, however, that micrographs show that the particles are not mostly isolated spheres. Besides, if they were, their spectrum would be a Lorentzian curve of width [FORMULA] =4.8 cm-1, peaking at [FORMULA] 900 cm [FORMULA]

Given the purity and crystallinity of our materials, the observed spectral profiles should rather be interpreted in terms of continuous distributions of grain shapes. In this case, it is indeed expected that the feature peak should be depressed relative to [FORMULA] [FORMULA], with the area under the peak remaining the same as in the case of spheres. In other words, the feature peak height should be inversely proportional to its width. Here, the observed widths are 137 and 102 cm-1, for SiC212 and 4h, respectively, as compared with the Lorentzian width of 4.8 cm-1. Hence, the expected peak extinction coefficients corrected for the shape effect

[EQUATION]

in agreement with the numbers in (17), to within errors on SiC masses embedded in the pellets.

Since our fundamental assumptions are validated by this test and previous remarks, we retain these assumptions for further discussion. Thus, Fig. 7 gives, for each wavenumber, a) the calculated red shift [FORMULA] of the feature, due to embedding in KBr, relative to vacuum, b) the depolarization factor, L.

[FIGURE] Fig. 7. Predictions for any SiC powder in KBr. a  Red shift [FORMULA] relative to powder in vacuum; b  depolarization parameter, L ; both as a function of wavenumber read from the spectrum of a loaded KBr pellet.

We now proceed to discuss the spectra within this framework. First note that the "blue" peak of SiC212 in KBr (Fig. 4a) occurs at [FORMULA] 905 cm-1, close to the expected position for spheres (cf. Fig. 7). This indicates a shape probability distribution favouring nearly spherical shapes, in agreement with micrographs of laser-produced powders.

The other peak in Fig. 4 (820 cm-1 or12.2 µm) and the single peak of Fig. 5 (870 cm-1 or 11.5 µm) must be due to oblate and/or prolate spheroids. The position of this peak mainly depends on the particular shape distribution, i.e. on the production process and preparation technique. Thus, the single peak in the spectra of Friedman et al. (1981) occurs near 840 cm-1 while that of 600GWS, the purest and finest powder of Borghesi et al. (1985), falls at 860 cm-1. The samples of Koike (1987) cover the whole range from 820 to 885 cm-1. Since all these spectra were taken in KBr matrices, it can be deduced from Fig. 5 that the corresponding L 's range from 0.05 to 0.25. For ellipsoids, the corresponding ellipticities fall between 0.7 and 0.88 (Bohren and Huffman, 1983), and the ratio of large to small size, between 1.4 and 50. This is compatible with the flakes and /or strings of spheroids seen under the microscope.

To us, the correlation that seems to exist between polytype and feature peak position (Kaito et al., 1994) only implies that crystal polytypes may come in prefered shapes of particles, not that they have different bulk optical constants. This is borne out by the large variety of spectra that can be obtained by the same laboratory, for the same polytype.

Only exceptionally does the literature mention a strong peak near [FORMULA] =795 cm-1 (12.6 µm). One such case is Pultz and Hertl (1966), who studied matts of fibers deposited upon a transparent substrate. The main peak occured at 795 cm-1, corresponding to the electric field parallel to the fiber axis (L =0). The single, secondary peak occured at 941 cm-1 ([FORMULA] 0.5) as expected if the small dimension of the fiber is parallel to the electric field. For both peaks, the width was [FORMULA] 40 cm-1, much less than [FORMULA], indicating a relatively discrete distribution of shapes, as expected for this sample.

Neither small nor large spheres exhibit the 12.6 µm feature; only intermediate-sized spheres do so, but this feature is then dwarfed by the characteristic feature of spheres at L =1/3 (Bohren and Huffman, Fig. 12.1).

Finally, it is useful to recall here the attempt of Pégourié (1988) to infer the optical constants of [FORMULA] -SiC from spectra of Borghesi et al. for this polytype, using a Kramers-Kronig analysis. The indeces he obtained were distinctly different from those of Spitzer et al. for the bulk material. This paradox can be explained away by noting that Pégourié assumed the sample particles to be spherical, although micrographs show they were not. As a consequence, the damping constant of his equivalent oscillator had to increase considerably so that the resonance could cover the whole feature width. Moreover, a near IR peak was forced into his extinction index, k, by the steep rise, towards short wavelengths, of the experimental spectrum he used. Such a rise is most probably due to scattering by large agglomerates, and is not visible in our spectra (Fig. 3a); neither is it compatible with Spitzer et al.'s measurements.

We conclude that all observed laboratory spectra, to our knowledge, can be interpreted by using the bulk optical properties and allowing for the distribution of particle shapes. If the latter is unknown, it can be inferred from the extinction spectrum (cf. Fig. 6), provided the particles are small enough. However, there is no way to infer the bulk optical properties from the spectrum, if the shape distribution is unknown. The assumption that the particles are spherical is generally not tenable. Even a continuous distribution is a better approximation.

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© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997
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