Infrared (IR) observations of evolved red giant stars (AGB stars) have shown that many are surrounded by dust envelopes, which are ejected into the interstellar medium and seed the next generation of stars and planets. By studying these one can understand the origins of interstellar and solar system materials. AGB stars fall into two main categories: oxygen-rich and carbon-rich. The prominent features of the IR spectra of AGB stars are: the 11.3μm feature of C-stars, attributed to silicon carbide (SiC); and the 9.7μm feature of O-rich stars, attributed to silicates. There are also various minor features with less secure identifications. Identifying dust around stars requires the use of laboratory spectra of dust species analogous to those one expects to observe. I have compiled a database of such spectra, and thereby constrained the identifications of circumstellar dust, which I have also tried to ensure are compatible with data from meteoritic presolar grains. Some laboratory spectra need to be modified before they are relevant to the problem in hand, i.e. stardust. The techniques used for such modifications are outlined in the thesis. In order to fully comprehend the problems that can arise from using laboratory spectra, the way in which light interacts with matter must be understood. To this end the optical properties of matter are discussed. While the mineral constituents of the Earth have been reprocessed so extensively that they no longer contain any evidence of their stellar origins, the same is not true of primitive meteorites which contain "presolar" dust grains with isotopic fingerprints identifying their stellar sources. By comparing these presolar grains with nucleosynthesis models, grains expected to form around various stars and observational evidence of dust, we can gain a better picture of the formation mechanisms and sites of the various dust grains. I have investigated the mineralogy of SiC of 32 C-stars and its relationship to meteoritic dust by using a x2-minimisation routine to fit the observed SiC features, using laboratory optical constants that have been published for a variety of SiC samples. In addition to the extreme carbon star AFGL 3068, the only C-star previously known to show the 11.3μm SiC feature in absorption, I have discovered three further examples of sources that show SiC in net absorption. Previous attempts to identify the type of SiC present around carbon stars have all identified it with a-SiC. However, 1 have found that the previous work is based on flawed laboratory data and that a better fit is achieved using β-SiC, which agrees with meteoritic data. I have also used the same techniques to investigate the mineralogy of 80 O-rich stars. Dust mineralogy around O-rich stars is considerably more complicated. The 9.7μm feature attributed to silicates varies greatly in shape and intensity as well as exact peak position from star to star, and the number of possible laboratory analogues is much greater than for SiC. Most of these spectra have been fitted using some form of forsterite (Mg2SiO4) and/or enstatite (MgSiO3), although constraining the mineralogy further was not possible. There is little evidence of Al2O3 around these stars, contrary to theoretical predictions and previous radiative transfer models. Relating the O-rich dust species to meteoritic data is also more complicated, as most of the silicate material was reprocessed in the early solar system, although data on a small number of O-rich presolar grains have been used for this purpose. I have also discovered a previously unrecognized feature in the spectra of O-rich stars at 9.25μm. This feature, and the 12.5-13.0μm feature previously attributed to Al2O3, have been attributed to SiO2- Implications of the new attributions for both C- and O-rich stars are discussed
