A model for thermal conductivity kappa, based on phonon lifetimes obtained from infrared reflectivity, replicates experimental data at ambient conditions. The pressure and absolute temperature dependences of transport properties are accurately obtained from the Gruneisen parameter gammaTh, bulk modulus KT, and thermal expansivity alpha: The lattice contribution kappalat equals kappa298(298/T)a exp[-(4gammaTh + 1/3) integral298Talpha(theta)dtheta] with a = 0.33 for silicates (or 0.9 for MgO), and partial differential[ln(kappalat)]/ partial differentialP = (1/3 + 4gammaTh)/KT. The smaller, pressure-independent radiative contribution kapparad equals 0.0175 - 0.0001037T + (2.245T2/10(7)) - (3.407T3/10(11)), in units of watts per meter-kelvin, if Fe2+ is present. The resulting lithospheric geotherm is steep. Consequently, the mantle geotherm is hot if the low-velocity zone is anhydrous, but cold if hydrated.

Abstract.We have analyzed the 8 − 13.5 µm UKIRT CGS3 spectra of 142 M-type stars including 80 oxygenrich AGB stars and 62 red supergiants, with a view to understanding the differences and similarities between the dust features of these stars. We have classified the spectra into groups according to the observed appearance of the infrared features. In each case the normalized continuumsubtracted spectrum has been compared to those of the other stars to find similarities and form groups. The dust features of the AGB stars are classified into six groups: broad AGB, where the feature extends from 8 µm to about 12.5 µm with little structure; broad+sil AGB, which consists of a broad feature with an emerging 9.7 µm silicate bump; and four silicate AGB groups in which a "classic" 9.7 µm silicate feature gets progressively narrower. Likewise, the supergiant spectra have also been classified into groups, however these do not all coincide with the AGB star groups. In the supergiant case we again have six groups: featureless, where there is little or no emission above the continuum; broad Super, where the feature extends from about 9 µm to about 13 µm; and four silicate Super groups, which again show a progression towards the narrowest "classic" 9.7 µm silicate feature. We compare the mean spectrum for each group, which yields two main results. Firstly, while the "classic" silicate feature is essentially identical for both AGB stars and red supergiants, the broad features observed for these two stellar types are quite different. We suggest that the dust in these two environments follows different evolutionary paths, with the dust around Mira stars, whose broad feature spectra can be fit by a combination of alumina (Al 2 O 3 ) and magnesium silicate, progressing from this composition to dust dominated by magnesium silicate only, while the dust around supergiants, whose broad feature can be fit by a combination of Ca-Al-rich silicate and Al 2 O 3 , progresses Send offprint requests to: A.K. Speck from this initial composition to one eventually also dominated by magnesium silicate. The reason for the difference in the respective broad features is not clear as yet, but could be influenced by lower C/O ratios and chromospheric UV radiation fields in supergiant outflow environments. The second result concerns the 12.5 − 13.0 µm feature discovered in IRAS LRS spectra and widely attributed to Al 2 O 3 . This feature is seen predominantly in the spectra of semiregular variables, sometime in Miras and only once (so far) in supergiant spectra. We argue that it is unlikely that this feature is due to Al 2 O 3 or, as has more recently been suggested, spinel (MgAl 2 O 4 ), but could be associated with silicon dioxide or highly polymerized silicates (not pyroxenes or olivines).

The thermal evolution of planetary crust and lithosphere is largely governed by the rate of heat transfer by conduction. The governing physical properties are thermal diffusivity (kappa) and conductivity (k = kapparhoC(P)), where rho denotes density and C(P) denotes specific heat capacity at constant pressure. Although for crustal rocks both kappa and k decrease above ambient temperature, most thermal models of the Earth's lithosphere assume constant values for kappa ( approximately 1 mm(2) s(-1)) and/or k ( approximately 3 to 5 W m(-1) K(-1)) owing to the large experimental uncertainties associated with conventional contact methods at high temperatures. Recent advances in laser-flash analysis permit accurate (+/-2 per cent) measurements on minerals and rocks to geologically relevant temperatures. Here we provide data from laser-flash analysis for three different crustal rock types, showing that kappa strongly decreases from 1.5-2.5 mm(2) s(-1) at ambient conditions, approaching 0.5 mm(2) s(-1) at mid-crustal temperatures. The latter value is approximately half that commonly assumed, and hot middle to lower crust is therefore a much more effective thermal insulator than previously thought. Above the quartz alpha-beta phase transition, crustal kappa is nearly independent of temperature, and similar to that of mantle materials. Calculated values of k indicate that its negative dependence on temperature is smaller than that of kappa, owing to the increase of C(P) with increasing temperature, but k also diminishes by 50 per cent from the surface to the quartz alpha-beta transition. We present models of lithospheric thermal evolution during continental collision and demonstrate that the temperature dependence of kappa and C(P) leads to positive feedback between strain heating in shear zones and more efficient thermal insulation, removing the requirement for unusually high radiogenic heat production to achieve crustal melting temperatures. Positive feedback between heating, increased thermal insulation and partial melting is predicted to occur in many tectonic settings, and in both the crust and the mantle, facilitating crustal reworking and planetary differentiation.

Abstract. Infrared reflectance (IR) and Raman spectra were collected on small (ca. 500 micron) single crystals of 5 natural garnets with nearly end-member compositions: pyrope (98% Mg3A12Si3Olz), almandine (83% Fe3A12Si3Oj2), spessartine (98% Mn3A12Si3012), grossular (97% Ca3A12SiaO~2), and andradite (99% Ca3Fe2Si30~2). Frequencies and symmetry assignments were determined for all 17 IR modes and all 25 Raman modes. By using factor group analysis and by correlating the bands by their intensities, bands were assigned to either one of the SiO 4 internal motions, as a rotation, or to a type of translation. The assignments are supported by (1) the distinct trends of frequencies with cell size and cation masses for each of the different types of motion, (2) the similarity of garnet energies for each of the different types of motion to those of olivine with the same cation, and (3) the closeness of the T~u IR frequencies to the T2g Raman frequencies. Mode mixing appears to be weak. Correlations between frequencies and structural parameters suggests a direct dependence of force constants on lattice parameter. This relationship arises from bond lengths in the garnet structure being constrained by the size and compressibility of adjacent polyhedra through edge-sharing. Comparison of our endmember data with previous powder IR studies of intermediate garnets indicates that dodecahedral (X) and octahedral (Y) sites alone exhibit two-mode behavior for those solid solutions involving two ions with considerably different masses. However, for solid solutions involving cations of much different ionic radii, two-mode behavior is found for the translations of SiO 4 groups. This is the first report of two-mode behavior that is unrelated to mass, and instead is due to significantly different force constants in the pyralspites compared to the ugrandites.Anomalies in mixing volumes are linked to two-mode behavior of the SiO4 translations, which leads to the suggestion that the mixing volume behavior is caused by the resistance of the Si-O bond to expansion and compression, as well as to changes in the dodecahedral site. Crystal-field effects may also play an important role within the ugrandite series. Deviation of molar volume dependence on composition from a linear to a asymmetric, non-linear (sometimes sigmoidal) dependence can be linked to solid solutions that possess slightly non-equivalent cation sites.

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Oxide and sulphide minerals are expected to occur in diverse astronomical environments. However, optical constants for such minerals are either lacking or poorly characterized. Minimizing errors in laboratory data, while extrapolating over wide frequency ranges, is the focus of this report. We present reflection and absorption spectra of single‐crystal MgO from about ∼100 to 18 000 cm−1 (∼100 to 0.5 μm), and derive emissivity, dielectric and optical functions (n and k) using classical dispersion analysis and supplementary data to ensure that the reflectivity values are correct at the low‐ and high‐frequency limits. Absorbance spectra of thin films of oxides (MgO, CaO, FeO and ZnO) and sulphides (MgS, CaS and FeS) are in good agreement with available reflectivity measurements, and provide information on the various effects of chemical composition, structure and optical depth. The greatest mismatch occurs for MgO, connected with this compound having the broadest peak in reflectance. The ferrous compounds (FeO and FeS) have relatively weak infrared features and may be difficult to detect in astronomical environments. Previous optical data based on transmission spectra of dispersions have underestimated the strength of the main infrared features because this approach includes spectral artefacts that arise from the presence of opaque particulates, or from non‐uniform optical depth. We show that areal coverage, not grain size, is the key factor in altering absorption spectra from the intrinsic values, and discuss how to account for ‘light leakage’ in interpreting astronomical data. Previous reflectivity data on polycrystals differ from intrinsic values because of the presence of additional, internal reflections, creating errors in the derived optical functions. We use classical dispersion analysis and supplemental data from optical microscopy to provide correct n‐ and k‐values for FeO from the far‐infrared to the visible, which can then be used in radiative transfer models. Thin‐film absorption data are also affected by internal reflections in the transparent regions: we show how to recognize these features and how to obtain the absorption coefficient, n, and k from thin‐film infrared data on CaO, CaS and MgS using the damped harmonic oscillator model.

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