[CH]

When you look at spectra from TIR instruments like the Nicolet FTIR, for example, published spectra of rocks and minerals, the reflectance spectra have high value peaks at the wavelengths (or wave numbers, if you prefer), where the subject has strong vibrational absorptions.

If the subject is absorbing strongly at that wavelength, why is there a reflectance peak?

[rwiew]

Can you post an example of such spectrum you're talking about? I've done a bunch of work with reflectance FTIR and this sounds weird, they usually have down pointing peaks which drop from high to low reflectance where absorption occurs.

[CH]

Here is a bidirectional spectra for calcite, you can see the ~11.3 micron vibrational mode showing up as a reflectance peak.  This is from the ASTER spectral library if you'd like to see the data source.  http://speclib.jpl.nasa.gov/

[mjc123]

If you search that library there is quite a variety in the spectra of calcite samples, depending on things like particle size, measurement mode etc. Reflectance is a complicated thing and different modes (specular reflectance, diffuse reflectance, ATR) can give quite different-looking spectra - it's not as simple as "high absorbance = low reflectance". Your spectrum came from a sample comprising large (2 cm) crystals, so I'm assuming specular reflectance. The reflectance depends on the refractive index (look up Fresnel equations), and in the vicinity of an absorption band the RI is complex (the imaginary part accounts for the absorption). The result is that the RI (and the reflectance) varies non-linearly with wavelength, and reflectance peaks tend to look like "derivative peaks", i.e. having both a positive and negative peak - like the 14 µm band in your spectrum. A Kramers-Kronig transform can be applied to derive the absorbance spectrum from the measured reflectance spectrum. (See for example http://www.perkinelmer.co.uk/CMSResources/Images/44-153348TCH_reflection-Measurements.pdf - compare the spectra of PMMA before and after KK.) The physical processes of DR and ATR are different, so the appearance of the spectrum would be different.
Also check obvious things like correct labelling of axes. One of those calcite samples was measured in transmission, yet the y-axis is labelled "reflectance"!

[rwiew]

Thanks for the explanation mjc123, I was reading the same things (that pdf is a really good start) last night, but couldn't understand it enough to post an explanation here. Would someone have some time to talk a bit more about the Frenkel equations and do a more thorough derivation of how to get from absorbance to reflectance? I'd be really interested to see what's going on there as well.

[mjc123]

Fresnel equations can get very complicated - depends on (i) complex refractive index (ii) angle of incidence (iii) polarisation of incident light. You might have more luck trying on Physics Forums (http://www.physicsforums.com/index.php). I think physicists are more likely than chemists to have looked at this in detail.