Anne M. Hofmeister

Temperature-dependent thermal diffusivity of the Earth's crust and implications for magmatism

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 (κ) and conductivity (k = κρCP), where ρ denotes density and CP denotes specific heat capacity at constant pressure. Although for crustal rocks both κ and k decrease above ambient temperature, most thermal models of the Earth’s lithosphere assume constant values for κ (∼1 mm2 s-1) and/or k (∼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 κ strongly decreases from 1.5–2.5 mm2 s-1 at ambient conditions, approaching 0.5 mm2 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 α–β phase transition, crustal κ 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 κ, owing to the increase of CP with increasing temperature, but k also diminishes by 50 per cent from the surface to the quartz α–β transition. We present models of lithospheric thermal evolution during continental collision and demonstrate that the temperature dependence of κ and CP 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.

Thermal diffusivity of olivine-group minerals at high temperature

Abstract Thermal diffusivity (D) data from 12 oriented single crystals and seven polycrystalline samples of olivine group minerals were acquired with the laser-fl ash 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-fl ash 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.

PROCESSING OF PRESOLAR GRAINS AROUND POST-ASYMPTOTIC GIANT BRANCH STARS: SILICON CARBIDE AS THE CARRIER OF THE 21 MICRON FEATURE

Some proto–planetary nebulae (PPNs) exhibit an enigmatic feature in their infrared spectra at � 21 m. This feature is not seen in the spectra of either the precursors to PPNs, the asymptotic giant branch (AGB) stars, or the successors of PPNs, ‘‘normal’’ planetary nebulae (PNs). However, the 21 m feature has been seen in the spectra of PNs with Wolf-Rayet central stars. Therefore, the carrier of this feature is unlikely to be a transient species that only exists in the PPN phase. This feature has been attributed to various molecular and solid-state species, none of which satisfy all constraints, although titanium carbide (TiC) and polycyclic aromatic hydrocarbons (PAHs) have seemed the most viable. We present new laboratory data for silicon carbide (SiC) and show that it has a spectral feature that is a good candidate for the carrier of the 21 m feature. The SiC spectral feature appears at approximately the same wavelength (depending on the polytype/grain size) and has the same asymmetric profile as the observed astronomical feature. We suggest that processing and cooling of the SiC grains known to exist around carbon-rich AGB stars are responsible for the emergence of the enigmatic 21 m feature. The emergence of this feature in the spectra of post-AGB stars demonstrates the processing of dust due to the changing physical environments around evolving stars.

Single-crystal IR spectroscopy of pyrope-almandine garnets with minor amounts of Mn and Ca

Abstract Mg2+ - Fe2+ substitution in the dodecahedral interstice of eight natural single crystals and two synthetic polycrystalline garnets was investigated by measurement of mid- and farinfrared (IR) reflectance spectra across the pyrope-almandine [Py-Al = (Mgx- Fe1-x)3Al2Si3O12] binary. The effect of minor Mn and Ca substitution was investigated by comparison with spectra of four additional natural garnets, Py8Al82SP10 and Py10Al76SP14, where Sp denotes spessartine (Mn3Al2Si3O12) and Py72Al18Gr10and Py54Al36Gr10where Gr denotes grossular (Ca3Al2Si3O12. Data obtained from the two synthetic polycrystals are in excellent agreement with data from the single crystals. Frequencies of all 17 IR active fundamental modes were observed in all specimens except pyrope. Of the 17 modes, 16 show linear correlations between frequency and composition along the pyrope-almandine join. The remaining mode, assigned to translations of the divalent cations against the O framework, exhibits two-mode behavior. The trends show that two modes in pyrope are accidentally degenerate. Frequencies of garnets with up to 10 mol% spessartine and grossular contents lie on the trends defined by the pyrope-almandine samples with negligible impurities. However, one to three additional modes are seen for some intermediate compositions, apparently resulting from either resonances among combination modes or two-mode behavior due to high Ca contents. The nearly linear behavior of the modes indicates that mixing should be close to ideal for the pyrope-almandine series because the lattice contribution dominates heat capacity, entropy, and compressibility.

Single-crystal IR spectroscopy of grossular-andradite garnets

Abstract Fe3+-Al3+ substitution in the octahedral site of 14 natural garnet samples was investigated through measurement of complete single-crystal infrared (IR) reflectance spectra across the grossular-andradite [Ca3 (AlxFe1-x)2 Si3O12] binary. Frequencies of all 17 IR- active fundamental modes depend nearly linearly on composition. Two peaks assigned to translations of the octahedral cations against the O framework exhibit two-mode behavior. Observation of similar frequencies for bands involving A1 and Fe3+ and of much larger intensities for bands associated with Fe3+ suggests that the Fe-O bond has greater strength, which compensates for the greater mass of Fe. The nearly linear behavior of the modes indicates that mixing should approach ideality for this series, as was previously observed in thermodynamic studies. The existence of ideal mixing suggests that high degrees of ordering are not present, and thus that ordering might not cause the anomalous birefringence associated with this series.

Thermal diffusivity of aluminous spinels and magnetite at elevated temperature with implications for heat transport in Earth’s transition zone

Abstract 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 MgAl2O4, nearly ZnAl2O4, 4 “hercynites” [(Mg,Fe2+)(Al,Fe3+)2O4], and 2 magnetites (nearly Fe3O4) were characterized using optical spectroscopy and electron microprobe analysis. The magnetic transition in Fe3O4 is manifest as a lambda curve in 1/D, but otherwise, D decreases with increasing T and approaches a constant (Dsat) 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 Dsat 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-Mg2SiO4 and ringwoodite. Pressure derivatives are provided by relationships such as ∂ln(klat)/∂P = ∂ln(KT)/∂P. Our results show that the phonon contribution to heat transport in Earth’s transition zone is high, particularly for large proportions of ringwoodite.

Thermal diffusivity of oxide perovskite compounds at elevated temperature

The phonon component of thermal diffusivity (D) for eleven compounds (synthetic SrTiO3, SrTiO3:Fe3+, BaTiO3, KTaO3, KNbO3, NdGaO3, YAlO3, YAlO3:Tm, LaAlO3, La0.29Sr0.66Al0.65Ta0.35O3, and natural Ca1.01Mn0.001Fe0.007Ti0.99O3) with various perovskite structures was measured from ambient temperature (T) up to ∼2000 K using contact-free, laser-flash analysis, from which effects of ballistic radiative transfer were removed. Structural transitions (e.g., orthorhombic to tetragonal) below 800 K were manifest as sharp steps in 1/D. Above 800 K, structural transitions occur over intervals of ∼150 K. Similarly broad peaks accompany changes from colorless to black, attributable to partial reduction in Ti, Nb, or Ta from contact with graphite coatings. Otherwise, D decreases with increasing T and, if substitutional disorder exists, approaches a constant (Dsat) near 1600 K. Our data are best described as D−1 following a low order polynomial in T. Ordered, cubic perovskites occupy a single trend for D(T)−1, defining t...

Thermal diffusivity of orthopyroxenes and protoenstatite as a function of temperature and chemical composition

The phonon component of thermal diffusivity ( D ) was measured up to temperatures ( T ) of ~1000–1500 K from laser-flash analysis from four chemically distinct, gem quality single crystals and six cleavage flakes or mats of orthopyroxenes, plus synthetic protoenstatite. From electron microprobe analysis, Mg/(Mg + Fe) varies from 0.65 to 1.0 and Al, Mn, Cr, Ti, and Na occur as minor impurities. From visible spectroscopy, Fe 3+ content is small to negligible. From near-IR spectroscopy, hydroxyl contents range from ~ 0 to 600 ppm. Heating large crystals redistributes H + among various sites: thus, thermal history influences speciation. For Mg/(Mg + Fe) ~ 0.9, at 298 K, D is 1.8, 1.9, and 3.2 mm 2 s −1 along [010], [100], and [001]. For all samples, D decreases with increasing T. Roughly, anisotropy is independent of T , and unaffected by transition to the protoenstatite structure, which causes D to drop by ~10 %. Low-order polynomials describe D −1 ( T ) for orthopyroxenes. A second-order polynomial describes the dependence of D 298 on Mg content. Only 300 ppm OH suffices to lowers D by ~10 % whereas Fe 3+ makes D decrease more rapidly with T but coupled Al substitution has the opposite effect. Available heat capacity and volumetric data were used to calculate orthopyroxene and protoenstatite thermal conductivity.

High-pressure IR-spectra and the thermodynamic properties of chloritoid

Abstract 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 M2Al4O2(SiO4)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 (CP) and entropy (So) 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): CP = 7.835 · 102 - 5.170 · 103T-0.5 - 1.648 · 107T-2 + 1.934 · 109T-3 for Mg-cld and CP = 7.848 · 102 - 5.185 · 103T-0.5 - 1.548 · 107T-2 + 1.783 · 109T-3 for Fe-cld. At room temperature, So = 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 So and CP values in conjunction with the enthalpy of formation, Hf = -7101 kJ/mol for Mg-cld or Hf = -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).

Thermal diffusivity of alkali and silver halide crystals as a function of temperature

The phonon component of thermal diffusivity (D) for ten synthetic single-crystals (LiF, NaCl, NaI, NaI:Tl, KCl, KBr, CsI, CsI:Tl, AgCl, and AgBr) with the B1 and B2 structures was measured from ambient temperature (T) up to ∼1093 K using contact-free, laser-flash analysis, from which effects of ballistic radiative transfer were removed. We investigated optical flats from different manufacturers as well as pellets made from compressed powders of most of the above chemical compositions plus LiI, NaBr, KI, RbCl, RbBr, RbI, CsCl, CsBr, and AgI. Impurities were characterized using various spectroscopic methods. With increasing T,D decreases such that near melting the derivatives ∂D/∂T are low, −0.0006±0.0004 mm2 s−1 K−1. Our results are ∼16% lower than D298 previously obtained with contact methods, which are elevated by ballistic radiative transfer for these infrared (IR) windows, and are well described by either D−1 following a low order polynomial in T, or by D−1∝T+n, where n ranges from 1.0294 to 1.9429. In...