Astron. Astrophys. 330, 1080-1090 (1998)

4. Monochromatic absorption coefficient

The monochromatic absorption coefficient can be derived from the Beer-Lambert law,

where and I are the intensities of the incident and transmitted light, respectively, is the density of the absorbing substance, l is the path length of the absorbing substance and is the monochromatic absorption coefficient.

For the UV/VIS measurements the absorption is measured as log₁₀ (I₀ /I), this give the following expression for the monochromatic absorption coefficient after Eq. (1):

The bulk density of the presolar diamonds have been found by Lewis et al. (1989) to be 2.22 - 2.33 g/cm³. The path length l through the diamonds can be found as the volume of diamond sample divided by the area of the sample. The area of the diamond sample is identical to the area of the sample cell if the diamond sample is dispersed evenly in the sample cell. l is then the effective path length of the radiation through an equivalent, thin diamond film of the equivalent thickness V /A = V /A = /A , so that m /A .

The transmittance, T, is:

and the absorbance, D, is given by

Since the transmittance measurement give the monochromatic extinction coefficient (extinction = absorption + scattering) it is necessary to correct for scattering before the monochromatic absorption coefficient can be derived. The measured IR-spectra were corrected for scattering by performing a base-line correction on the measured transmittance spectrum, before it was converted into an absorbance spectrum. In the base-line method a base line is drawn tangent to the spectrum at the wings of the analytical band, and its intersection with a vertical line at the analytical wavenumber is used for . No correction for scattering was performed for the UV/VIS measurements, since the amount of scattering in the experiment was very small.

The primary reason for scattering in the measured IR transmittance spectrum is that when the sample is incorporated in a KBr matrix the size of the KBr grains will force the sample grains to lay around the much larger KBr grains, resulting in some clumping of the sample. The scattering is therefore mainly a matrix effect, and not a property of the diamond that we should expect to observe in stellar environments.

With the measured , being dimensionless, and and l given in the units described above, the monochromatic absorption for the presolar diamonds comes out in units of cm² per gram of diamonds which is shown in Fig. 5. We notice that with the correction for scattering, the value of the absorption coefficient at the upper wavenumber of our infrared measurements is almost identical to the value at the low-wavenumber end of the UV/VIS measurements. Further, Mutschke et al. (1995) notice that this spectral region in their measurements of the presolar diamonds from Murchison, is featureless, which is a well known characteristic of terrestrial diamonds, too. A good approximation of the absorption coefficient in the region from 4000 cm^-1 to 12200 cm^-1 is therefore to approximate it with a constant value, = 220 cm² /g, which we have also done in the computations of the stellar models and synthetic stellar spectra presented in the next chapter. The full set of data is obtainable on anonymous ftp ¹ from stella.nbi.dk.

Fig. 5. The monochromatic absorption coefficient for the presolar diamonds, as derived from the IR and UV/VIS absorbance spectra.

4.1. The uncertainty on

The uncertainty of the monochromatic absorption coefficient, , as determined from Eq. (4) and (5) includes the uncertainty in; (1) the estimate of the mass, (2) the assumption that the grains are homogeneously distributed in the sample, and (3) the uncertainty in the measurement of I/I₀. Of these three we estimate, that the uncertainty in is the dominant factor. The mass of our presolar diamond sample for the UV measurements was determined to be 350 25 µg, giving an uncertainty of 7.1% and for the IR measurement to be 300 45 µg implying an uncertainly of 15%. The overall uncertainty on as determined from Eq. (4) and (5) is therefore around 15%.

© European Southern Observatory (ESO) 1998

Online publication: January 27, 1998
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