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The low thermal diffusivity of Earth’s rocks and its large size signify that even today, thermal transport in the lower mantle and core are independent of that in the outer layers. This situation permits construction of thermal profiles of the deep Earth from internal constraints: namely, the two-phase metallic core follows the solidus of iron alloy, and the top of the lower mantle lies below the dry peridotite solidus. Thermal conductivity of the core is irrelevant. Without samples, mantle thermal conductivity is estimated considering data and models for dense solids, leading to “hot silicate” and “cold oxide” geotherms. Temperatures are reasonably constrained, except for the height and position of the local maximum in the lower mantle. Meteoritic values for radionuclide contents of the lower mantle are consistent with present-day temperatures and progressive melting of the core.

Pyroxene crystals are common in meteorites but few compositions have been recognized in astronomical environments. We present quantitative room-temperature spectra of 17 Mg-- Fe-- and Ca--bearing ortho- and clinopyroxenes, and a Ca-pyroxenoid in order to discern trends indicative of crystal structure and a wide range of composition. Data are produced using a Diamond Anvil Cell: our band strengths are up to 6 times higher than those measured in KBr or polyethylene dispersions, which include variations in path length (from grain size) and surface reflections that are not addressed in data processing. Pyroxenes have varied spectra: only two bands, at 10.22~$\mu$m and 15.34~$\mu$m in enstatite (En$_{99}$), are common to all. Peak-wavelengths generally increase as Mg is replaced by Ca or Fe. However, two bands in MgFe-pyroxenes shift to shorter wavelengths as the Fe component increases from 0 to 60 per cent. A high-intensity band shifts from 11.6~$\mu$m to 11.2~$\mu$m and remains at 11.2~$\mu$m as Fe increases to 100~per~cent; it resembles an astronomical feature normally identified with olivine or forsterite. The distinctive pyroxene bands between 13~ and 16~$\mu$m show promise for their identification in MIRI spectra obtained with JWST. The many pyroxene bands between 40 and 80~$\mu$m could be diagnositic of silicate mineralogy if data were obtained with the proposed SPICA telescope. Our data indicate that comparison between room-temperature laboratory bands for enstatite and cold $\sim 10-K$ astronomical dust features at wavelengths $\gtrsim 28~\mu$m can result in the identification of (Mg,Fe)- pyroxenes that contain 7--15 % less Fe-- than their true values because some temperature shifts mimic some compositional shifts. Therefore some astronomical silicates may contain more Fe, and less Mg, than previously thought., Comment: 16 pages, 10 figures.accepted in MNRAS

This chapter evaluates mechanisms for heat transfer in large bodies, which include several processes that occur on scales and/or conditions that cannot be reproduced in the laboratory. Planetary interiors contrast with laboratory conditions by being layered, self-compressed spheroids, and moreover are open systems with internally graded gravitational acceleration, high temperatures, and high pressures. The large time- and length-scales of planets permit diffusion of visible radiation, even within their metallic cores. Advection of fluids coexisting with solids is very important in planets, due to fluid buoyancy, mobility, low viscosity, and their ability to carry latent heat and heat-producing elements: such behavior is covered in detail in this chapter. Theoretical problems in mantle convection models are reviewed, which include not conserving mass, and incorrectly representing the response of condensed matter to differential stress as the diffusion of momentum, rather than as elastic and plastic deformation.

The phonon component of thermal diffusivity (D) was measured up to temperatures (T) of ~1350 K using laser-flash analysis from leucite, analcime, pollucite, nepheline, sodalite, and petalite, many of which were single crystals. From electron microprobe analysis, nepheline is a solid solution, Na2(Na1.2K0.71)Al3.88Si4.10O16, whereas the other minerals have nearly endmember chemical compositions. From near-IR spectra, hydroxyl contents range from ~200 ppm to 1 wt%. At 298 K, D is low (0.51–0.75 mm2 s−1) for the zeolites and the solid-solution nepheline but moderate (1.9–2.2 mm2 s−1) for the endmember feldspathoids. For leucite, D decreases with increasing T until reaching the tetragonal to cubic phase transition whereupon D increases. A complex polynomial is required to describe D(T) for leucite, due to the displacive transition. For the other samples, as observed for most minerals, D decreases up to dehydration which terminated the runs and is described by FT −G + HT where G varies from 0.14 to 1.44 and H is negligible to 0.0006 K−1. Available heat capacity and volumetric data were used to calculate thermal conductivity as a function of T. For sodalite and petalite, k decreases with T, whereas for the remaining phases, k is roughly constant and low, ~1.5 Wm−1 K−1.

Thermal diffusivity (D) was measured up to ~1,800 K of refractory materials using laser-flash analysis, which lacks radiative transfer gains and contact losses. The focus is on single-crystal MgO and Al2O3. These data are needed to benchmark theoretical models and thereby improve understanding of deep mantle processes. Measurements of AlN, Mg(OH)2, and isostructural BeO show that the power law (D = AT −B ) where T is temperature holds for simple structures. Results for more structurally complicated corundum Al2O3 with and without impurity atoms are best fit by CT d + ET f where d ~ −1 and f ~ −4, whereas for isostructural Fe2O3, f is near +3 and multiphase ilmenite Fe1.12Ti0.88O3 is fit by the above power law. The positive temperature response for hematite is attributed to diffusive radiative transfer arising from electronic–vibronic coupling. We find good agreement of k and D data on single-crystal and non-porous ceramic Al2O3. For the corundum structure, D is nearly independent of T at high T. Although D at 298 K depends strongly on chemical composition, at high temperature, these differences are reduced. Thermal conductivity provided for MgO and Al2O3, using LFA data and literature values of density and heat capacity, differs from contact measurements which include systematic errors. The effect of pressure is discussed, along with implications for the deepest mantle.

Laser-flash analyses (LFA) of oriented sections of six natural plagioclase crystals provide thermal diffusivity ( D ) as function of temperature (to ~1300–1500 K) and composition (An5–95). Plagioclase has low-thermal diffusivity; our measurements indicate that plagioclase is more insulating than other major igneous rock-forming minerals. Over much of the solid solution, room-temperature D ranges from 0.751 to 0.979 mm2/s along c , 0.722 to 0.919 mm2/s along b , and 0.632 to 0.868 mm2/s perpendicular to b and c . The directionally averaged D is 30–45% lower than D of Amelia albite. Thermal conductivities calculated using measured D values are almost the same for all samples with 18 ≤ An ≤ 65, ranging from 1.5 to 1.9 W/m/K and changing little with temperature. Increasing Al-Si disorder causes D to decrease with increased An content, although sample structure causes more ordered samples to have higher D than more disordered samples. Anorthite is a special case. Although ordered, the larger unit cell provides many lattice modes, leading to low diffusivity. Structure dictates whether D along the b -axis is greater or less than that along the c -axis, possibly because ordering in An-like domains increases D more along c relative to b . Inflections in 1/ D ( T ) are connected with lattice distortion during heating, and occur near temperatures expected for phase transitions; for example, the lattice stretch occurring at the temperature of the transition to C 1 structure lowers diffusivity. Likewise, lattice distortion during heating decreases D in albite along c but has little impact on D in the other directions. The anharmonic lattice effects that dictate both thermal expansivity and D are masked by effects of disorder; the latter plays a major role in heat transport in plagioclase.

Thermal diffusivity (D) was measured using laser-flash analysis (LFA) from oriented single-crystal albite and glasses near LiAlSi3O8, NaAlSi3O8, CaAl2Si2O8, LiAlSi2O6 and CaMgSi2O6 compositions. Viscosity measurements of the supercooled liquids, over 2.6 × 108 to 8.9 × 1012 Pa s, confirm strongly non-Arrhenian behavior for CaAl2Si2O8, and CaMgSi2O6, and near-Arrhenian behavior for the others. As T increases, D glass decreases, approaching a constant near 1,000 K. Upon crossing the glass transition, D decreases rapidly. For feldspars, D for the melt is ~15% below D of the bulk crystal, whereas for pyroxenes, this difference is ~40%. Thermal conductivity (k lat = ρC P D) of crystals decreases with increasing T, but k lat of glasses increases with T because heat capacity (C P ) increases with T more strongly than density (ρ) and D decrease. For feldspars, k lat for the melt is ~10% below that of the bulk crystal or glass, whereas this decrease for pyroxene is ~50%. Therefore, melting substantially impedes heat transport, providing positive thermal feedback that could promote further melting.

To determine which factors affect thermal diffusivity ( D ) of mineral aggregates, we compared accurate measurements of D for five quartzites, two microcrystalline samples (chert and agate), chalcedony, and two partially crystalline opal specimens (of type opal-CT) with single-crystal quartz. Samples were characterized using infrared (IR) spectroscopy, electron microprobe analysis, optical microscopy, and X-ray powder diffractometry (XRD). Using laser flash analysis, we measured D of the quartzites and microcrystalline samples between room temperature and 1000 °C, and D of the opal specimens and chalcedony up to the temperatures where these samples failed (300 and 650 °C, respectively). Data between 20 and 500 °C can be fit by 1/ D = AT + B . Values of A and B for quartzites, microcrystalline samples, opal specimens, and chalcedony are distinct from each other and from those of directionally averaged quartz single-crystals. Lower D at room temperature correlates with inflated B values of polycrystalline samples and results from porosity (all samples), hydration (all samples), grain boundaries (microcrystalline samples and chalcedony), and disorder (opal specimens and chalcedony). Dehydration and pore space reduction alter the temperature derivatives of D ; dehydration causes the low A in chalcedony and opal. Above 600 °C, D changes negligibly with temperature and is lower than directionally averaged quartz, suggesting an increase in contact resistance as cracks open during heating. Thermal cracking is greatest in samples with large grain sizes and abundant, fluid-filled pores. The prevalence of cracking in polycrystalline samples suggests that high-temperature laboratory measurements generally underestimate heat transport properties in geologic environments, wherein confining pressures limit thermal expansion.

The phonon component of thermal diffusivity ( D ) from 12 single crystals in the spinel family was measured at temperatures ( T ) of up to ~2000 K, using laser-flash analysis. Synthetic disordered spinel, 4 gemstones near MgAl 2 O 4 , nearly ZnAl 2 O 4 , 4 “hercynites” [(Mg,Fe 2+ )(Al,Fe 3+ ) 2 O 4 ], and 2 magnetites (nearly Fe 3 O 4 ) were characterized using optical spectroscopy and electron microprobe analysis. The magnetic transition in Fe 3 O 4 is manifest as a lambda curve in 1/ D , but otherwise, D decreases with increasing T and approaches a constant ( D sat ) at high T . Part of the decrease in D as T increases results from disordering above ~700 K: these two effects were distinguished by making multiple heating runs. At 298 K, D decreases strongly as either cation substitution or Mg-Al disorder increases, whereas D sat is moderately perturbed by substitutions. For both ordered and (equilibrium) disordered spinels and hercynites, the temperature dependence of 1/ D is best described by low-order polynomial fits. For spinel, combining our data with previous cryogenic studies of thermal conductivity ( k ) constrains the T dependence of D and k from ~0 K to melting. The response of D to disorder, impurity content, and cation mass for the aluminates is used to constrain D ( T ) for γ-Mg 2 SiO 4 and ringwoodite. Pressure derivatives are provided by relationships such as ∂ln( k lat )/∂ P = ∂ln( K T )/∂ P . Our results show that the phonon contribution to heat transport in Earth’s transition zone is high, particularly for large proportions of ringwoodite.

Infrared absorbance spectra over ∼100 to 1,800 cm−1 were collected from optically thin films of 21 samples with compositions spanning the forsterite–fayalite binary. Polarization information from previous specular reflectance data on end-members was used in tracing the peaks across the entire binary. Peak positions (νi) were constrained by Lorentzian decompositions. Fitting also constrained widths for singlet peaks but for doublets and triplets, variation in νi with composition among the constituent polarizations alters widths from intrinsic. Because film thicknesses of 0.6–1.4 μm were estimated, our band strengths are approximate; however, relative intensities should be correct. Only for a few peaks does νi vary smoothly across the entire binary; instead, distinct linear trends exist for Fe- and Mg-rich olivines. Discontinuities and kinks in νi(X) occur at X = Mg/(Fe + Mg) = 0.7 and are accompanied by a change in intensity patterns. This interesting behavior was not revealed in previous spectra of powder dispersions. The contrasting character of IR vibrations for Fe- and Mg-rich olivines is inferred to arise from structural variations because (1) frequency is related to bond length, (2) other factors affecting frequency (cation mass and probably bonding type) vary linearly across the binary, and (3) available data on unit cell parameters are consistent with distinct trends for forsterites and fayalites. Vibrational components of heat capacity (C V) and enthalpy (H) calculated from νi, were found to be slightly more negative than linear interpolations between values for forsterite and fayalite. Our computations give smaller negative excesses from ideality in H than do previous calorimetric measurements, but are equal within experimental uncertainties.

Thermal diffusivity ( D ) data from 12 oriented single crystals and seven polycrystalline samples of olivine group minerals were acquired with the laser-flash method at temperatures ( T ) of up to ~1500 °C. Samples included forsterite, Fe-Mg binary olivines, sinhalite, and chrysoberyl; specimens were characterized using infrared spectroscopy and electron microprobe analysis. Crystal orientation and chemistry both affect D . For our single crystals, D [100] > D [001] > D [010] at all temperatures. Thermal diffusivity decreases with increasing T and becomes virtually constant at high temperatures. At room temperature, D [001] of pure forsterite has the highest observed values, but substitution of a small amount of Co in forsterite (0.3 wt% CoO) lowers D by ~20%. Substitution of ~10% Fe for Mg in forsterite, as in typical mantle olivine, lowers D by ~50%. At room temperature, mantle olivine has D = 3.25, 1.66, and 2.59 mm2/s for the [100], [010], and [001] orientations, respectively. The values decrease to 0.93–0.87 mm2/s at 790–985 °C for [100], 0.54–51 mm2/s at 590–740 °C for [010] and 0.83–0.79 mm2/s at 740–890 °C for [001]. Two dunite samples have D of 0.55–0.56 mm2/s at 890–1080 °C, showing the effect of preferred orientation of grains dominated by [010]. Thermal diffusivity of polycrystalline samples is controlled by the large amounts of olivine present; minor phases offset the curves for D ( T ) from the value of the olivine mineral. Our laser-flash measurements isolate the phonon component of heat transfer from radiative transfer and show that the phonon contribution becomes nearly constant for the high temperatures expected in the mantle. The other microscopic component (diffusive radiative transfer) depends strongly on temperature and this temperature dependence likely exerts greater control on mantle convection.

Absorption coefficients associated with atomic motions of species expected in astronomical environments are determined from infrared measurements of various hydrosilicates, hydrated magnesium oxide, and the Al-bearing chain silicate, sapphirine. Band types measured include O‐H stretching modes near 3 μm, Si‐O stretching motions near 10 μm, Si‐O‐Si bends near 14 μm, O‐Si‐O bends near 20 μm, and translations of cations such as Mg and Ca near 50‐200 μm. We obtain data from films of varying thickness and use a ratioing method. First, bandstrengths of O‐H fundamentals were determined from spectra obtained from films of controlled thicknesses, generally 6 μm. The O‐H absorbance strength was then used to accurately determine thickness for a thinner film of each mineral (found to be

The distinct patterns, relatively low intensities and peak positions of overtone-combination bands of silicates and oxides suggest that the 5-8 μm spectral region can provide clues for the dust composition when near optically thick conditions exist for the 10-μm silicate feature. We present 1000-2500 cm -1 room-temperature laboratory spectra obtained from powders of silicate, aluminate and nitride minerals and silicate glasses. The spectra exhibit overtone absorption bands with mass absorption coefficients ∼ 100 times weaker than the fundamentals. These data are compared with the 5-8 μm spectra of deeply embedded young stellar objects observed with the Short Wavelength Spectrometer on the Infrared Space Observatory. Fits of the laboratory data to the observations, after subtraction of the 6.0-μm H 2 O ice feature and the 6.0-μm feature identified with organic refractory material, indicate that crystalline melilite (a silicate) or metamict hibonite (a radiation-damaged crystalline aluminate) may be responsible for much of the 6.9-μm absorption feature in the observations, with melilite providing the best match. A weaker 6.2-μm absorption in the young stellar object spectra is well matched by the spectra of hydrous crystalline amphibole silicates (actinolite and tremolite). Relative abundances of Si-O in room-temperature amphiboles to low-temperature H 2 O ice are in the range 0.46-3.9 and in melilite are in the range 2.5-8.6. No astronomical feature was matched by the overtones of amorphous silicates because these bands are too broad and peak at the wrong wavelength. Hence, this analysis is consistent with the 10-μm features of these objects being due to a mixture of crystalline and amorphous silicates, rather than only amorphous silicates.

Heat capacity (CV) and entropy (S) as a function of temperature were calculated for phases in the CaO-Al2O3 system from vibrational spectra using a quasi-harmonic model. Calculated values of CV at 298 K for the calcium aluminates may have uncertainties as small as ±1%, based on comparison with published calorimetric data for CaO, Al2O3, and CaAl2O4. For hibonite (CaAl12O19), we predict CP as 519.3 J/mol-K and S as 391.7 J/mol-K, at 298 K. For grossite (CaAl4O7), calculated values of CP as 195.9 J/mol-K and of S as 172.0 J/mol-K are slightly smaller than the available calorimetric data at 298 K, consistent with calorimetric data having been obtained from samples containing ∼10 wt% hibonite impurities. Thermal conductivity at 298 K (k0) is predicted from peak widths of the vibrational modes using the damped harmonic oscillator model of a phonon gas. Calculations of k0 for CaO and Al2O3 differ from the measurements by 17% and 5%, respectively. The discrepancy for lime is larger due to uncertainties in its peak widths. This comparison suggests that our results for the calcium aluminates should be more accurate than conventional measurements of k0 which are commonly uncertain by ∼25%.

Infrared (IR) spectra of phases found in calcium-aluminum rich inclusions in meteorites are incomplete, yet such data are needed to ascertain the mineralogy of astronomical environments. To better characterize the system CaO-Al2O3, we obtained IR thin-film absorption data, partially polarized Raman scattering spectra, and single-crystal X-ray structure refinements from small single-crystals of end-member hibonite (CaAl12O19) and grossite (CaAl4O7), synthesized by laser-heating. Vibrational spectra were also acquired from natural samples of Th-bearing hibonite, synthetic corundum (Al2O3), 17O-enriched grossite, CaAl2O4, and CaO. Spectral fitting provided band positions and widths. The true absorbance of strong IR peaks in calcium aluminates is 1–2/μm, based on thickness determined from interference fringes and on comparison with absorption coefficients calculated from reflectivity data on natural hibonite. Our data on the lattice vibrations of hibonite reveal that the terrestrial samples are partially metamict: their spectra cannot be used for comparison with astronomical objects because of peak broadening and changes in the polarization of the vibrations. Direct comparison of our IR data of synthetic samples with astronomical observations shows that grossite and hibonite are present in the proto-planetary nebula NGC 6302. That spectral patterns match provides a strong case. Corundum, spinel, and melilite-group minerals also could be present in the nebula. Because spectra of melilites resemble those of pyroxenes, the latter assignment is less certain. We limit our compositional analysis of the nebula to matching spectral patterns, because detailed spectral modeling of the mineralogy would be both premature (due to a lack of cryogenic IR data), and uncertain (due to the occurrence of dust in clumps large enough to emit as blackbodies). The inferred mineralogy of NGC 6302 follows the condensation sequence for a nebula of solar composition, and contains mineral types known to be presolar.

Diffusion of heat by radiation in the mantle has previously been associated with absorption of light by Fe 2+ . The near-IR absorptions of structurally incorporated OH − provide another mechanism to convert the energy of photons into lattice vibrations. The effective diffusive radiative thermal conductivity due to protonation ( k rdf,wet ) may be important within the mantle because low absorption strengths, as expected for trace to minor OH − contents, allow light to travel long distances in the medium. Available calibrations of band strength with OH − content are used to develop a formula for k rdf,wet as a function of temperature, grain size, and hydroxyl concentration that is generally applicable to mantle phases. These results are compared to new data on the phonon contribution for olivine and to calculations of Fe 2+ radiative transfer. As T increases, k rdf,wet increases. As OH − content increases, k rdf,wet initially increases, reaches a maximum near 100–1000 ppm hydroxyl content as H 2 O, and then decreases at higher concentrations. A similar dependence on grain size exists, with the maximum k rdf,wet near d ∼ 1 cm. Grain sizes and OH − contents of hydrous upper mantle samples foster radiative transport via protonation. For example, at 1500 K, sub-cm grain sizes with ∼10–100 ppm H 2 O, provide k rdf,wet that is ∼1/4 of k rdf arising from the combined effect of overtones and Fe 2+ transitions, and ∼1/8 of the lattice contribution to k of olivine. Given that OH − concentrations vary among mantle minerals, the above results suggest that mantle heat flow is heterogeneous and anisotropic. The dependence of both k rdf and viscosity on grain size and hydration suggests that the dynamical behavior in or near subducting slabs will be complex.

Infrared reflectance, thin-film absorbance, and polarized Raman spectra were acquired from ~100 to ~4000 cm−1 from polycrystalline garnets along the pyrope (Py = Mg3Al2Si3O12)-majorite [Mj = Mg3(MgSi)Si3O12 ] join. We measured Py100, Mj39, Mj45, Mj80, and natural single-crystal, nearly end-member pyrope. Consistency is obtained between measured absorption spectra and absorption coefficients calculated through Kramers-Kronig analysis of reflectivity ( R ) data, if R -values are scaled to account for losses through scattering. The widths of the lattice modes double from each end-member toward the middle of the binary, whereas frequencies are nearly independent of composition. Strong polarization of Raman peaks of all our samples except pyrope shows that the space group is reduced from cubic, even for the Al-rich majorites. The largest number of IR or Raman peaks is observed for Mj80. The number of peaks for Al-rich majorites lies between those seen for cubic pyrope and I 41/ a majorite. The behavior of symmetry-breaking modes supports the I 41/ acd space group, which was inferred from X-ray data for Mj contents near 30 to 45% (Nakatsuka et al. 1999a). Also, the internal mode types that are expected for isolated SiO4 tetrahedra in any garnet-like structure do not fully describe the patterns of peaks seen for some intermediate compositions along the Py-Mj join. The appearance of Sioct-O-Sitet bending modes in the available spectral data for Mj contents near 30–40 and 80–90%, but not near 45–50%, is attributed to two-mode behavior. Specifically, disruption of the structural chain -Sioct-O-Sitet-O-Sioct-O-Sitet-in Si-rich majorites by units such as ![Graphic][1] alters the electrostatic balance so that the internal modes are not entirely described by motions of isolated SiO4 tetrahedra. Short chains are formed at both high and low Al contents, promoting coupling of Si octahedral and tetrahedral vibrations. Near Mj50, each tetrahedron is linked (on average) to four octahedra containing two Al-, one Si-, and one Mg, and the Sioct-O-Sitet bending modes disappear. Order-disorder in majorite garnets is characterized not only by increased peak widths, but also by the presence of modes due to the bridging O atoms, whereas splittings and the appearance of new peaks indicate the space group for non-cubic garnets. [1]: /embed/inline-graphic-1.gif

Using IR radiation from a synchrotron source, high-quality absorbance spectra were obtained from polycrystalline powder of chloritoid (cld) from ambient conditions up to pressures of 10 GPa over 50 to 4000 cm −1 . The idealized chemical composition of the chloritoid group is M 2 Al 4 O 2 (SiO 4 ) 2 (OH) 4 where M = Fe or Mg in our experiments. All of the 42 expected fundamental IR modes were observed. These data, combined with the response of the IR bands to substitutions of Fe for Mg, and of D for H, constrained the band assignments. Heat capacity ( C P ) and entropy ( S o ) for the triclinic and monoclinic polymorphs of Fe- and Mg-cld were calculated from the Kieffer-type model, using our detailed band assignments. The calculated heat capacity and entropy for the monoclinic and triclinic polymorphs differ negligibly. The results at temperatures above 298 K are described by the following polynomial expressions in J/(mol·K): C P = 7.835 · 10 2 − 5.170 · 10 3 T −0.5 −1.648 · 10 7 T −2 + 1.934 · 10 9 T −3 for Mg-cld and C P = 7.848 · 10 2 − 5.185 · 10 3 T −0.5 − 1.548 · 10 7 T −2 + 1.783 · 10 9 T −3 for Fe-cld. At room temperature, S s = 293 J/mol·K for Mg-cld and 335 J/mol·K for Fe-cld. These values differ somewhat from entropy estimated from various internally consistent databases (−3 to −9% for Mg-cld and −9 to +5% for Fe-cld). However, using our new S o and C P values in conjunction with the enthalpy of formation, H f = −7101 kJ/mol for Mg-cld or H f = −6422 kJ/mol for Fe-cld (estimated in this study), we can closely reproduce the experimental data for the reactions Mg-chloritoid + talc = clinochlore + kyanite (Chopin 1985) and Fe-chloritoid = almandine + diaspore + water (Vidal et al. 1994).

A band of pure crystalline forsterite (100 per cent Mg2SiO4) occurs at 69.67 μm at room temperature (295 K); for olivines with ≳10 per cent Fe the corresponding feature is at ≳73 μm. The Mg-rich forsterite feature is observed in a variety of ISO LWS spectra, but the corresponding Fe-rich olivine feature is not. For the 10 astronomical sources in our sample, the forsterite band peaks in the 68.9–69.3 μm range and narrows with decreasing peak wavelength. This is consistent with the shortwards shifting of the peak observed when laboratory samples are cooled to 77 K (69.07 μm) and 3.5 K (68.84 μm). The shifted peak is produced by lattice contraction and the sharpening is due to a decrease in phonon density at lower temperatures. However, the astronomical bands are narrower than those of the laboratory samples. By comparing the laboratory and astronomical peak wavelengths, we deduce characteristic forsterite 69-μm band temperatures that are in the 27–84 K range for the eight post-main-sequence objects in our sample. These values are shown to be consistent with the local continuum temperatures derived using a β=1.5 dust emissivity index, similar to derived interstellar values of the opacity index. For the pre-main sequence-objects HD 100546 and MWC 922, the characteristic 69-μm forsterite band temperatures (127±18 and 139±10 K, respectively) are significantly higher than those of the post-main-sequence objects and are more than twice as high as their local continuum temperatures deduced using β=1.5. The assumption of large grains (β=0) can produce agreement between the derived 69-μm and continuum temperatures for one of these objects but not for the other – a spatial separation between the forsterite and continuum-emitting grains may therefore be implied for it. We conclude that observations of the peak wavelength and FWHM of the 69-μm forsterite band show great promise as a new diagnostic of characteristic grain temperatures.

The damped harmonic oscillator model for thermal conductivity of insulators is improved, leading to a formula that predicts thermal conductivity at ambient conditions ( k ) from various physical properties, most of which are commonly measured. Specifically, k = [ρ/(3 ZM )] C V [( u P + u S)/2]2/ , where ρ is density, Z is the number of formula units in the primitive unit cell, M is the molar weight, C V is heat capacity, u is the sound speed (P denotes compression; S denotes shear), and is the average of the damping coefficients determined from peak widths in infrared reflectivity spectra, or from suitable Raman and Brillouin spectra. The classical physics and quantum-mechanical basis for this model is discussed, with emphasis on the effect of phonon-phonon interactions on mode properties. The calculated values of k all lie within the experimental uncertainty of the measurements for all samples with the spinel or olivine structure examined by Horai (1971) with known or approximately correct chemical compositions. Other divergent measurements of k for MgAl2O4 are discounted for various reasons. Early studies of Fe-bearing spinels are not generally reliable, but rough estimates from the above equation are consistent with all data, and good agreement is obtained for samples such as Mg0.5Fe0.5Al2O4 and γ-Fe2SiO4 for which the previous authors obtained chemical data, and for which IR reflectivity data exist. The theory reproduces the measured dependence of k on composition and structure. Anisotropy in k results mainly from differences in lattice constants ( j ): the equation for olivine is k j/ k =( V 1/3/ j )0.73 which predicts the ratios within 3%. For solid solutions between Fe and Mg, the model provides a non-linear dependence of k on mol% Fe, with the damping coefficient being the key factor producing non-linearity. Predicted ambient values are 11.3 ± 0.4 W/m-K for γ-Mg2SiO4 , 6.5 ± 0.7 W/m-K for β-Mg1.2Fe0.8SiO4, and 6.9 ± 0.3 W/m-K for β-Mg2SiO4. The high k for ringwoodite suggests that heat in Earth’s transition zone should be conducted twice as efficiently as in the adjacent upper and lower mantles: this discontinuous depth dependence of k could impact thermal models of conduction in subducting slabs and of mantle convection

Vibrational spectra are used to determine key physical properties of phases thought to be important in Earth’s transition zone. Single-crystal infrared (IR) reflectance spectra were measured for synthetic Mg, Fe, Ni, or Co-bearing silicates with the spinel structure. Peak parameters (frequency, damping coefficient, and oscillator strength) were determined for the fundamentals, and for overtones, up to 3rd order. On average, the frequencies and damping coefficients of the overtones are simple multiples of the corresponding parameters of the fundamental modes. Absorption spectra of thin films were measured at pressures ( P ) up to 370 kbar for γ-Mg2SiO4 and up to 200 kbar for γ-Fe2SiO4. Widths are nearly constant, but frequencies (νi) increase either linearly or quadratically with P . For weak peaks, the absorption widths have values close to their corresponding damping coefficients. For γ-Fe2SiO4, ambient IR data predict heat capacity ( C V = 126 ± 2.5 J/mol·K), shear modulus ( G = 875 ± 15 kbar), and sound velocities ( u P = 8.20 ± 0.05, u S = 4.25 ± 0.06 km/s) at 298 K; pressure data give ∂ G /∂ P = 0.06, 0.44, or 0.91 if for the bulk modulus, ∂ K /∂ P = 5, 4.5, or 4, respectively, and an average mode Gruneisen parameter of = 1.45 ± 0.4, which implies that thermal expansivity is (21 ± 1) × 10−6/K. For γ-Mg1.2Fe0.8SiO4, ambient IR data predict G = 1120 ± 50 kbar, u P = 9.12 ± 0.20, and u S = 5.18 ± 0.20 km/s at 298 K, assuming that the frequency of the acoustic mode is 225 to 240 cm−1. This calculation uses K S = 1995 kbar, which was obtained from recent compression data by assuming ∂ K /∂ P = 4. The above values provide a smooth quadratic dependence of K S and G on Fe/(Fe + Mg). The trends suggest that ∂ K /∂ P remains at 4 whereas ∂ G /∂ P drops from ~1 to ~0.5 as Fe content increases in ringwoodite. Acoustic fundamentals or overtones were used successfully here to provide u , G , and their P and T derivatives for silicate spinels. This method should work for other simple structures, and may be generally applicable.

High-pressure infrared (IR) spectra of most lattice modes and of hydrous impurities of Fe-bearing wadsleyite were measured from O to 23 GPa. At ambient conditions, 29 of the 35 expected IR bands were revealed through a combination of reflection and absorption measurements. Absorption spectra of a magnesium end-member at ambient conditions were similar. The pressure dependence of eight OH vibrations were established to 12 GPa. The degree of hydrogen bonding is inferred from the values of the hydroxyl frequencies and their response to pressure: Five hydroxyls with low v have negative ∂v/∂P and thus moderate to strong hydrogen bonding, whereas three OH groups with high v have near-zero or positive values of ∂v/∂P and thus weak or no hydrogen bonding. This information, the response of the OH bands to Fe/Mg exchange, and X ray data were used to assign the most intense OH bands to the structural sites, O(1) and O(2). These assignments of hydroxyl vibrations are consistent with previous theoretical models. Our study of high-pressure OH vibrations in nominally anhydrous wadsleyite indicates that hydrogen impurities in wadsleyite are stable during compression. Our data are consistent with the previously observed minor structural change at around 9 GPa which is possibly due to a slight change in the compression mechanism.

Infrared (IR) spectroscopy, in combination with magnetic methods, was used to study the thermally induced transformation of synthetic lepidocrocite (3,-FeOOH) to maghemite (~-Fe203). Mag- netic analyses showed that the thermal conversion began at about 175"C with the formation of super- paramagnetic maghemite clusters. The overall structural transformation to ferrimagnetic'y-Fe203 occurred at 200"C and was complete around 300"C. At higher temperatures, the maghemite converted into hematite (a-Fe203). Observation of the transformation from 3,-FeOOH to "y-Fe203 using variable-temperature IR spectroscopy indicated that dehydroxilation on a molecular level was initiated between 145"C and 155*C. The lag time between the onset of the breaking of OH bonds and the release of H20 from lepidocrocite around 1750C can be explained by diffusive processes. Overall dehydroxilation and the subsequent break- down of the lepidocrocite structure was complete below 219*(3. The comparison of the magnetic and IR data provides evidence that the dehydroxilation may precede the structural conversion to maghemite.

Wadsleyite (β-(Mg,Fe)2SiO4) is a major constituent of the Earth's transition zone and is known to accommodate OH. The portion of the transition zone between 400–550 km could be an important source or sink for hydroxyl in plumes and slabs intersecting this region. Micro-infrared spectroscopy has been carried out on the β-phase and coexisting metastable olivine synthesized in a multianvil apparatus at 14 GPa and 1550–1650 K under hydrous conditions. Single-crystal and polycrystal specimens of both phases were analyzed in the 1800–8500 cm−1 frequency region to determine the speciation, abundances, and partitioning behavior of the hydrous components in coexisting β-phase and olivine. β-phase spectra consistently show three distinct OH bands at 3329, 3580, and 3615 cm−1. OH concentrations range from 10000–65000 H/106 Si. A strong positive correlation of grain size and extent of transformation with OH concentration in the β-phase indicates that grain-growth and transformation rates are enhanced in a hydrous environment. Olivine spectra are variable, but consistently show a prominent broad-band absorbance representing molecular H2O, consistent with the infrared signature of the starting material. OH concentrations in olivine range from

Thermal diffusivity ( D ) as a function of temperature ( T ) was determined from common and brittle micas both parallel and perpendicular to the basal plane using laser-flash analysis, which does not suffer from problems with contact losses and radiative gains. Samples were characterized using the electron microprobe and visible spectroscopy. For the two orientations, D differs by almost a factor of 10, such that for flow within the cleavage plates D is ∼2 mm 2 s –1 , similar to many silicate minerals. Thermal diffusivity decreases as F or Fe contents increase. Data are best described as D = F T –G + H T , where F, G, and H are fitting parameters. Thermal conductivity up to 1000 K is calculated from D , density, and heat capacity for muscovite, phlogopite, and biotite. The pressure dependence of k is inferred from recent data from muscovite for flow across the basal plane.

[1] Laser-flash measurements show that hydration lowers the lattice component of thermal diffusivity (D) for calcic and Fe-Mg garnets, and glasses. Hydration depresses D above the glass transition, suggesting that melts respond likewise. For garnets, which have a wide range of total water and OH− contents (X), ∂(lnD)/∂X = −0.003%/ppm H2O. For olivine and quartz, D is constant, but thermal conductivity (k = ρCPD) decreases because hydration lowers density (ρ) but negligibly changes heat capacity (CP). This finding is geophysically significant: specifically, it suggests that hydration leads to heat retention, promoting convective instabilities and melting.

Far-infrared spectra of laboratory silicates are normally obtained at room temperature even though the grains responsible for astronomical silicate emission bands seen at wavelengths >20 micron are likely to be at temperatures below ~150 K. In order to investigate the effect of temperature on silicate spectra, we have obtained absorption spectra of powdered forsterite and olivine, along with two orthoenstatites and diopside clinopyroxene, at 3.5+-0.5 K and at room temperature (295+-2K). To determine the changes in the spectra the resolution must be increased from 1 to 0.25 cm^-1 at both temperatures since a reduction in temperature reduces the phonon density, thereby reducing the width of the infrared peaks. Several bands observed at 295 K split at 3.5 K. At 3.5 K the widths of isolated single bands in olivine, enstatites and diopside are ~ 90% of their 295 K-widths. However, in forsterite the 3.5-K-widths of the 31-, 49- and 69-micron bands are, respectively, 90%, 45% and 31% of their 295 K widths. Due to an increase in phonon energy as the lattice contracts, 3.5-K-singlet peaks occur at shorter wavelengths than do the corresponding 295-K peaks; the magnitude of the wavelength shift increases from \~ 0-0.2 micron at 25 micron to ~0.9 micron at 80 micron. Changes in the relative absorbances of spectral peaks are also observed. The temperature dependence of lambda_pk and bandwidth shows promise as a means to deduce characteristic temperatures of mineralogically distinct grain populations. In addition, the observed changes in band strength with temperature will affect estimates of grain masses and relative mineral abundances inferred using room-temperature laboratory data., 11 pages, 7 figures including figures 3a and 3b. includes latex and eps files. Accepted by MNRAS on 15th March 2001

Infrared absorption measurements were taken from 100 to 5000 cm−1 of a natural chondrodite and three dense hydrous magnesium silicates: phase A, phase B, and superhydrous phase B (shy-B). Raman spectra were also acquired from phase B and the chondrodite. Roughly half of the lattice modes are represented and our data are the first report of the low frequency modes. Comparison of our new spectra to symmetry analyses suggests that multiple sites for hydrogen exist for all the phases. The shy-B we examined crystallizes in P21nm with two OH sites. Models for the density of states are constructed based on band assignments for the lattice modes and for the OH stretching vibrations. Heat capacity CP and entropy S calculated using Kieffer's formulation should be accurate within 3% from 200 to 800 K. Model values for CP at 298 K are 299.6 J/mol-K for chondrodite, 421.5 J/mol-K for phase A, 529.4 J/mol-K for shy-B, and 618.9 J/mol-K for phase B. Model values for S2980 are 234.2 J/mol-K for chondrodite, 303.5 J/ mol-K for phase A, 377.9 J/mol-K for shy-B, and 473.3 J/mol-K for phase B. Debye temperatures are near 1000 K.

Single-crystal Raman and infrared reflectivity data including high pressure results to over 200 kbar on a natural, probably fully ordered MgAl2O4 spinel reveal that many of the reported frequencies from spectra of synthetic spinels are affected by disorder at the cation sites. The spectra are interpreted in terms of factor group analysis and show that the high energy modes are due to the octahedral internal modes, in contrast to the behavior of silicate spinels, but in agreement with previous data based on isotopic and chemical cation substitutions and with new Raman data on gahnite (∼ ZnAl2O4) and new IR reflectivity data on both gahnite and hercynite (∼Fe0.58Mg0.42Al2O4). Therefore, aluminate spinels are inappropriate as elastic or thermodynamic analogs for silicate spinels. Fluorescence sideband spectra yield complementary information on the vibrational modes and provide valuable information on the acoustic modes at high pressure. The transverse acoustic modes are nearly pressure independent, which is similar to the behavior of the shear modes previously measured by ultrasonic techniques. The pressure derivative of all acoustic modes become negative above 110 kbar, indicating a lattice instability, in agreement with previous predictions. This lattice instability lies at approximately the same pressure as the disproportionation of spinel to MgO and Al2O3 reported in high temperature, high pressure work.

Polarized single-crystal absorption and reflection spectra of fundamental modes in both the mid- and far-infrared are presented for microscopic crystals of forsterite and fayalite. All modes predicted by symmetry were observed for forsterite, but two B3u modes were not observed for fayalite. Consideration of previously determined frequency shifts for isotopically and chemically substituted olivines, along with symmetry analysis, produced a complete set of band assignments satisfying all constraints for forsterite. A plausible assingment was derived for fayalite by analogy. The frequency shifts from forsterite to fayalite are consistently small for bands assigned to SiO4 stretching and bending, moderate for rotations, and large for translations of M-site ions, suggesting that in olivine, SiO4 groups vibrate separately from the lattice. Allocating the bending and external modes among multiple continua in Kieffer's (1979c) model considerably improves prediction of quasiharmonic heat capacityC v and entropy for forsterite (∼1% discrepancy from 200–1000 K). The experimental entropy of fayalite is closely accounted for (1.8 to 0.1%) by summing lattice, electronic (from Burns' (1985) optical band assignment), and constant magnetic contributions above 200 K.S magnetic determined from the difference of the experimental and model lattice entropies shows inflection points at the two magnetic transition temperatures (23 and 66 K) and indicates that complete spin disorder is not achieved below 680 K.

Radiation-induced smoky color and associated electron paramagnetic resonance (EPR) signals develop only in potassium feldspar (KalSi_3O_8) free of structurally bound molecular water. Fluid inclusion water does not influence coloration. The integrated intensity of each of the four bands (11,600, 16,200, 19,100, and 27,200 cm^(−1)) in the optical absorption spectra are linearly correlated with the doubly-integrated intensity of a broad, asymmetric first derivative at g_(eff)=2.027 in EPR spectra. In microcline, the EPR pattern is resolved into an asymmetric six-line pattern at g_(eff)=2.024 and a single derivative at g_(eff)=2.009 which, based on analogy to alkali-silicate glass, are due respectively to [SiO_4/K^+]^(2+) and a hole shared between two nonbonding oxygens on Si. We propose that structural water inhibits formation of smoky centers in feldspar by releasing atomic hydrogen during irradiation which destroys centers while diffusing towards a stable site.

Far-infrared, mid-IR, and Raman powder spectra were measured on six phases (bromellite, chrysoberyl, phenakite, bertrandite, beryl, and euclase) in the system BeO-Al2O3-SiO2-H2O. A single-crystal absorption spectrum of IR fundamentals in beryl is also presented, which more closely resembles the powder absorption spectrum than it does absorption spectra calculated from single-crystal reflection data. Assignments of the SiO4 and BeO4 internal vibrations are made in accordance with each mineral's symmetry and composition and by comparison to structural analogs. Heat capacities C v calculated for these partial band assignments agree with C v derived from experimental C p for all six phases, provided that Kieffer's (1979c) model is slightly modified to correctly enumerate both Si-O and Be-O stretching modes in the high frequency region (>750 cm−1). Si-O stretching bands were found to out-number Be-O stretching modes in the high-energy region of the vibrational spectra with two exceptions: (1) For those phases containing oxygen ions not coordinated to silicon, vibrations occurring at v>1,080 cm−1 that are attributable to Be-O (H) stretching must be treated separately in the model in order to calculate C v accurately. (2) Minerals consisting entirely of interlocking Si and Be tetrahedra (i.e., phases without Al or OH) can be modeled by one optic continuum representing all optical modes. These results, along with the occurrence of very low energy lattice vibrations for Be-silicates within Al, suggests that although Be-O bonds are generally weaker than neighboring Si-O bonds, Be mimics the network-forming characteristic of Si to a limited extent.

Ferrous and ferric iron concentrations in feldspars with low total iron content (

Optical functions (n and k) of cosmic dust species like forsterite (Mg2SiO4) are required at all wavelengths to quantify the temperature and amount of dust. Astronomers combine optical functions of forsterite and olivine in different ways, which will affect radiative transfer models. We investigated what recent updates to the ultraviolet-visible-near-infrared (UV-VIS-NIR) laboratory spectra of forsterite and the choice of forsterite n, k dataset will have on radiative transfer models. We measured the UV-VIS-NIR transmission spectra of synthetic forsterite, MgO, SiO2, olivine (Fo90), and meteoritic olivine (pallasite). We derived optical functions for these and compared the UV-IR behavior of our k, absorption cross-section 〈Cabs〉, and total flux to that of “astronomical silicate” and olivine. Laboratory-derived k is substantially lower than “astronomical silicate” k at λ ~ 0.2–5 µ m. In the IR, different laboratory n and k produce equivocal 〈Cabs〉, whereas total flux is different for “astronomical silicate” versus laboratory n, k. From 0.35–5 µ m, the choice of “forsterite” k values has the most effect on modeled quantities. For environments with significant UV flux, astronomers should use recent UV-VIS-NIR laboratory n, k.

Some gem-quality labradorite phenocrysts in Miocene basaltic lava from Lake County, Oregon, have a pink schiller due to metallic copper; some have a transparent red or green color. The copper content of the crystals varies systematically with color: pale-yellow labradorite sections have 0–40 ppm CuO; greens have about 100 ppm CuO; reds have 150 to 200 ppm CuO; schiller-bearing laths have 80 to 300 ppm CuO. The variation of Cu content among different crystals is primary and reflects a variation in magma chemistry during plagioclase fractionation. Similarity of absorption spectra of the red zones to that of copper-ruby color in glass shows that the red arises from the intrinsic absorption of colloidal Cu^0 particles that are too small to scatter light (