Trasmission and Reflection (ATR)Far-Infrared Spectroscopy Applied in the Analysis of Cultural Heritage Materials

FIR spectroscopy is an alternative way of collecting spectra of many inorganic pigments and corrosion products found on art objects, which is not normally observed in the MIR region. Most FIR spectra are traditionally collected in transmission mode but as a real novelty it is now also possible to record FIR spectra in ATR (Attenuated Total Reflectance) mode. In FIR transmission we employ polyethylene (PE) for preparation of pellets by embedding the sample in PE. Unfortunately, the preparation requires heating of the PE in order to produces at transparent pellet. This will affect compounds with low melting points, especially those with structurally incorporated water. Another option in FIR transmission is the use of thin films. We test the use of polyethylene thin film (PETF), both commercial and laboratory-made PETF. ATR collection of samples is possible in both the MIR and FIR region on solid, powdery or liquid samples. Changing from the MIR to the FIR region is easy as it simply requires the change of detector and beamsplitter (which can be performed within a few minutes). No preparation of the sample is necessary, which is a huge advantage over the PE transmission method. The most obvious difference, when comparing transmission with ATR, is the distortion of band shape (which appears asymmetrical in the lower wavenumber region) and intensity differences. However, the biggest difference can be the shift of strong absorbing bands moving to lower wavenumbers in ATR mode. The sometimes huge band shift necessitates the collection of standard library spectra in both FIR transmission and ATR modes, provided these two methods of collecting are to be employed for analyses of unknown samples. Standard samples of 150 pigment and corrosion compounds are thus collected in both FIR transmission and ATR mode in order to build up a digital library of spectra for comparison with unknown samples. XRD, XRF and Raman spectroscopy assists us in confirming the purity or impurity of our standard samples. 24 didactic test tables, with known pigment and binder painted on the surface of a limestone tablet, are used for testing the established library and different ways of collecting in ATR and transmission mode. In ATR, micro samples are scratched from the surface and examined in both the MIR and FIR region. Additionally, direct surface contact of the didactic tablets with the ATR crystal are tested together with water enhanced surface contact. In FIR transmission we compare the powder from our test tablet on the laboratory PETF and embedded in PE. We also compare the PE pellets collected using a 4x beam condenser, focusing the IR beam area from 8 mm to 2 mm. A few samples collected from a mural painting in a Nepalese temple, corrosion products collected from archaeological Chinese bronze objects and samples from a mural paintings in an Italian abbey, are examined by ATR or transmission spectroscopy.

Refined Gelfand models for some finite complex reflection groups

In 'Involutory reflection groups and their models' (F. Caselli, 2010), a uniform Gelfand model is constructed for all complex reflection groups G(r,p,n) satisfying GCD(p,n)=1,2 and for all their quotients modulo a scalar subgroup. The present work provides a refinement for this model. The final decomposition obtained is compatible with the Robinson-Schensted generalized correspondence.