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Igneous intrusions are important to the thermomechanical evolution of continents because they inject heat into their relatively cold host rocks, and potentially change the distribution of radiogenic heat production and thermal properties within the crust. To explore one aspect of the complex evolution of the continental crust, this paper investigates the local thermal effects of two intrusive rock types (carbonatites and anorthosites) on the Archean Superior Province of the Canadian shield. We provide new data on their contrasting properties: rock density near 298 K, thermal diffusivity, and heat capacity up to 800 K (which altogether yield thermal conductivity), plus radiogenic element contents. The volumetrically small carbonatites have widely varying radiogenic heat production (2–56 µW m−3) and moderate thermal conductivity at 298 K (~ 1 to 4 W m−1 K−1) which decreases with temperature. The massive Shawmere anorthosite has nearly negligible radiogenic heat production (

Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D&infin, (T)[1 &minus, exp(&minus, bL)]. When L is several mm, D&infin, (T) = FT&minus, G + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D&infin, &minus, 0.477 at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D &rarr, 0 as L &rarr, 0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (&kappa, ) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for &kappa, (T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe &kappa, with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (&part, ln(cP)/&part, P = &minus, linear compressibility), which leads to &part, ln(&kappa, )/&part, P = linear compressibility + &part, ln&alpha, /&part, P, where &alpha, is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light.

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.

Recent work discloses shortcomings in models for heat transport properties. Some errors involve simple numerical factors, but others are substantial, such as not accounting for the finite lifetimes of interactions, nor weighting thermal conductivity in summations, nor realizing that thermal diffusivity depends on thickness. This chapter discusses the consequences in view of the ambiguities contributed by multiplied parameters in models, and provides an improved model for heat transport in solids. We show that radiative diffusion describes all heat transfer, when the association of various processes in matter with limited frequency ranges of light is addressed. Dimensionless thermal conductivity of solids from 0 to ~300K, including the cryogenic peak, is fit by one parameter; but including high temperature data requires more. Theoretical pressure derivatives agree well with reliable data. To better understand heat transport requires measuring transport properties as a function of length and spectra at low frequencies and temperatures.

We provide measurements of thermal diffusivity (D), heat capacity (CP), and viscosity (η) for 12 remelted natural lavas and 4 synthetic glasses and melts, ranging in composition from leucogranite to low-silica basalt, and calculate their thermal conductivity. Both viscosity and the glass transition temperature decrease with decreasing melt polymerization. For basaltic glasses, D is low, ~ 0.5 mm2 s− 1 at room temperature, decreases slightly with increasing temperature, and then drops upon melting to ~ 0.25 to 0.35 mm2 s− 1. Other samples behave similarly. Despite scatter, clear correlations exist between D of glass or melt with Si content, density, NBO/T, and, most strongly, with fragility (m). Glass thermal diffusivity is represented by D = FT− G + HT, where F, G and H are fitting parameters. For melts, ∂ D/∂ T was resolved only for dacite-andesite and MORB: a positive slope is consistent with other iron-bearing samples. Glass and liquid CP depend on density and other physical properties, but not exactly in the same manner as D. We calculate thermal conductivity (k) from these data and demonstrate that k for glasses is described by a Maier-Kelly formula. Large scatter exists for k at 298 K, but silicic to intermediate melts have k between 1.8 and 1.3 Wm− 1 K− 1, whereas basaltic melts are constrained to ~ 1.4 ± 0.1 Wm− 1 k− 1. Low values for thermal diffusivity and viscosity for basaltic melts suggests that basalts transfer heat much more efficiently by advection than by conduction alone, and that partially molten zones in the mantle quickly become more thermally insulating than non-molten zones, potentially contributing to melt localization during decompression melting.

Heat transport plays a crucial role in igneous processes, and the thermal evolution of terrestrial bodies. Thermal conductivity (k) is a product of density (ρ), thermal diffusivity (D) and specific heat (CP). We measured D and CP as a function of temperature for a suite of planetary analog lavas relevant to the Moon, Mars, Mercury, Io and Vesta. Heat capacity was measured using differential scanning calorimetry on glasses and liquids covering temperatures from 400 to 1750 ​K; ρ was measured using the Archimedean method; and D was measured using laser-flash analysis on glasses from room temperature up to their melting point, which is slightly above the glass transition (Tg). Although the values of D and CP depend on both temperature and composition, we found no systematic variation of D with chemical or structural parameters. Glass data are described by the equation D g l a s s = 2.305 ± 0.22 T − 0.2567 ± 0.015 + 7.796 ± 6.2 × 10 − 5 T where D is in mm2s−1 and T is in K, with 2σ uncertainty of 0.06 ​mm2 ​s−1. Thermal diffusivity of the tholeiitic liquids above Tg is Dliquid ​= ​0.36 ​± ​0.07 mm2s-1, but the temperature-dependence cannot be constrained due to viscous flow and changing sample geometry at higher temperatures. The model for D presented here, in combination with already available models to calculate CP and ρ, allows prediction of thermal conductivity. For tholeiitic glasses, k decreases from ~1.5 ​± ​0.3 ​W ​m−1K−1 ​at ~295 ​K to ~1.3 ​± ​0.3 ​W ​m−1K−1 ​at Tg at ~1000 ​K. For tholeiitic liquids, k decreases from ~1.6 ​± ​0.3 ​W ​m−1K−1 ​at Tg to ~1.3 ​± ​0.4 ​W ​m−1K−1 ​at 1500 ​K. We recommend a generic value of 1.3 ​W ​m−1 K−1 for k of tholeiitic and basaltic lava instead of the commonly assumed 1.0 ​W ​m−1 K−1. Future work should aim to constrain the temperature dependence of D for liquids, for which a novel experimental approach is needed.

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.

We provide new measurements of thermal diffusivity (D) of 8 synthetic glasses and melts along the enstatite–ferrosilite compositional binary, 4 remelted crystals which are close to the binary, plus one synthetic ternary composition (Fs15Wo40En45). Thermal diffusivity of these glasses is between 0.50 and 0.62 mm2 s− 1 at room temperature, decreases to ~ 0.45 to 0.50 mm2 s− 1 near 1000 K, then drops upon melting at 1100 K to ~ 0.34 mm2 s− 1. A roughly linear trend in D exists across the En–Fs binary at 298 K, with Fe-rich compositions having lower D, whereas at high temperatures all melts have similar D. The trend is not smooth, due to variable amounts of crystallites and residual strain in glasses, both of which affect D-values. Above about 700 K, ∂D/∂T is visibly positive for moderate Fe contents (i.e., Fe / (Fe + Mg) = 0.1 to 0.3), which we attribute to diffusive radiative transfer being enhanced by electronic–vibronic coupling. All data are well represented by equations of the form FT − G + HT, where F, G and H are fitting parameters. The fitting reveals a weak increase in D at high T for all of our glasses, consistent with weak radiative transfer in the infrared. Although data could only be collected on melts over a narrow temperature range, they also appear to have a positive ∂D/∂T, which is consistent with previous results on less mafic iron-bearing glasses and melts. Our results suggest that Fe-rich melts in the lower mantle could have thermal diffusivity higher than their crystalline counterparts due to the response of D to temperature.

Combining new measurements of thermal diffusivity ( D ) and viscosity (η) of 13 silica-rich glasses and their melts with previous data reveals specific effects of Al, Ca, and Fe cations on heat and mass transport for diverse glasses and melts. We investigated rhyolites, tektites, leucogranite, haplogranite, and chemically complex commercial glasses. Highly polymerized samples, with high-Al but low-Ca contents, yield high values for η, D , and glass transition temperatures ( T g,12), whereas less polymerized samples with high-Ca but low-Al contents, have low η, D , and T g,12. Upon crossing the glass transition, D decreases substantially, to ~0.35 mm2/s for Ca-rich melts, but D decreases only weakly, to ~0.52 mm2/s for Al-rich melts. The magnitude of the decrease in D at T g,12 correlates with the melt fragility, and also to the configurational heat capacity. High-Ca contents result in low D for glasses and melts, whether or not Al is present. At high T , ∂ D /∂ T is positive for glasses and melts containing Fe2+, which we attribute to diffusive radiative transfer involving electronic-vibronic coupling. Thermal conductivity of all glasses increases with T , flattening out as the transition is approached. For melts with >1 wt% FeOtotal, ∂ k /∂ T is positive. We predict that upon melting, I-type arc granite liquids should have lower thermal diffusivity than calcium-poor A- or S-types, and calc-alkaline basalts will have lower D than tholeiitic basalts, such that D of granitic melts is ~0.2 mm2s−2 higher than basaltic. Ferrous iron enhancing heat transport could alter the predicted order at higher temperatures.

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.

Thermal diffusivity ( D ) was obtained from cristobalite formed via melting slightly hydrous fused silica using laser flash analysis. Natural samples have lower D due to contamination ( e.g. , with feldspar) or to varying amounts of pore space. Data collected from cristobalite from 298 to 1300 K is fit by 14.11×106 T −2.+0.000493 T mm2/s. Values of D ( e.g. , 1.85 mm2/s at 298 K) and thermal conductivity are similar to those for rhyolite and silica glass, but higher than their melt values, consistent with cristobalite being highly disordered, but without the additional degree of freedom for a melt. Formation of snowflake obsidian is discussed in view of our synthesis experiments.

The thermal structure of Archean terranes depends in part on the thermal transport properties of their distinctive rock types. We determined thermal diffusivity ( D ) of a suite of 14 greenstone, mafic granulite and tonalite–trondhjemite–granodiorite (TTG) rocks at temperatures up to 1000 °C at atmospheric pressure using laser flash analysis, which lacks systematic errors associated with conventional contact techniques. At room temperature, D ranges from ∼3.8 mm 2 s −1 for banded iron formation to ∼0.8 mm 2 s −1 for a quartz-poor trondjhemite. For all samples thermal diffusivity decreases with increasing temperature, such that D for the suite converges around ∼0.7 ± 0.1 mm 2 s −1 at ∼700 °C. Combining these results with measured density and heat capacity calculated from modal mineralogy provides thermal conductivity as a function of temperature for each rock suite. Whereas near-surface thermal conductivity varies from 2.7 to 4.2 W m −1 K −1 depending on rock type, thermal conductivity of the lower crust is ∼2 W m −1 K −1 and only weakly dependent on lithology, which is more thermally resistive than the uppermost mantle (∼3.5 W m −1 K −1 ). Use of temperature-dependent thermal transport properties in numerical models reveals that surface geotherms can be relatively insensitive to crustal heat production, because high heat-producing TTG rocks typically have high thermal diffusivity and conductivity at low temperatures and, consequently, are more efficient conductors of the heat they produce. This finding implies that calculations of crustal heat production from surface borehole measurements may entail significant uncertainties.

Thermal diffusivity (D) was measured using laser-flash analysis on pristine and remelted obsidian samples from Mono Craters, California. These high-silica rhyolites contain between 0.013 and 1.10 wt% H2O and 0 to 2 vol% crystallites. At room temperature, D glass varies from 0.63 to 0.68 mm2 s−1, with more crystalline samples having higher D. As T increases, D glass decreases, approaching a constant value of ∼0.55 mm2 s−1 near 700 K. The glass data are fit with a simple model as an exponential function of temperature and a linear function of crystallinity. Dissolved water contents up to 1.1 wt% have no statistically significant effect on the thermal diffusivity of the glass. Upon crossing the glass transition, D decreases rapidly near ∼1,000 K for the hydrous melts and ∼1,200 K for anhydrous melts. Rhyolitic melts have a D melt of ∼0.51 mm2 s−1. Thermal conductivity (k = D·ρ·C P) of rhyolitic glass and melt increases slightly with T because heat capacity (C P) increases with T more strongly than density (ρ) and D decrease. The thermal conductivity of rhyolitic melts is ∼1.5 W m−1 K−1, and should vary little over the likely range of magmatic temperatures and water contents. These values of D and k are similar to those of major crustal rock types and granitic protoliths at magmatic temperatures, suggesting that changes in thermal properties accompanying partial melting of the crust should be relatively minor. Numerical models of shallow rhyolite intrusions indicate that the key difference in thermal history between bodies that quench to obsidian, and those that crystallize, results from the release of latent heat of crystallization. Latent heat release enables bodies that crystallize to remain at high temperatures for much longer times and cool more slowly than glassy bodies. The time to solidification is similar in both cases, however, because solidification requires cooling through the glass transition in the first case, and cooling only to the solidus in the second.

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.

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) at high temperature (T) was measured from 15 samples of commercial SiO2 glasses (types I, II, and III with varying hydroxyl contents) using laser-flash analysis (LFA) to isolate vibrational transport, in order to determine effects of impurities, annealing, and melting. As T increases, Dglass decreases, approaching a constant (~ 0.69 mm2s− 1) above ~ 700 K. From ~ 1000 K to the glass transition, the slope of D is small but variable. Increases of D with T of up to 6% correlate with either low water and/or low fictive temperature and are attributed to removal of strain and defects during annealing. Upon crossing the glass transition, D substantially decreases to 0.46 mm2s− 1 for the anhydrous melt. Hydration decreases Dglass, makes the glass transition occur over wider temperature intervals and at lower T, and promotes nucleation of cristobalite from supercooled melt. Due to the importance of thermal history, a spread in D of about 5% occurs for any given chemical type. Combining prior steady-state, cryogenic data with our average results on type I glass provides thermal conductivity (klat = ρCPD) for type I: klat increases from ~ 0 K, becoming nearly constant above 1500 K, and drops by ~ 30% at Tg. We find that D− 1(T) correlates with thermal expansivity times temperature from ~ 0 K to melting due to both properties arising from anharmonicity.

We explore the conductive cooling rates of plutons and temperature-time paths of their wall rocks using numerical methods that explicitly account for the temperature dependence of thermal diffusivity ( α ) and heat capacity (C P ). We focus on α because it has the strongest influence on the temperature-dependence of thermal conductivity (k = ρ·C P · α ) at high temperatures. Latent heats of crystallization are incorporated into the models as apparent C P 's. Two sets of models are presented, one for a 50 m thick basalt sill emplaced into rocks with diffusivity of the average crust, and one for a 5 km wide and 2 km thick granite pluton emplaced into dolostones. The sill's liquidus is 1230 °C, the solidus 980 °C, and the sill is emplaced into wall rocks that are at 150 °C. The pluton's liquidus is 900 °C, the solidus 680 °C, and the pluton is emplaced into wall rocks with initial geothermal gradient of 30 °C/km. The top of the pluton is at 3 km depth. Incorporating appropriate α = f(T) into calculations can more than double the solidification times of intrusions in comparison with incorporating constant α of 1 mm 2 ·s − 1 that is used in most petrologic heat transport models. The instantaneously emplaced basalt sill takes ~ 51 a to completely solidify, whereas the granite pluton takes ~ 52 ka to completely solidify. The solidification time is longer because of low thermal diffusivity of magma and because wall rocks become more insulating as temperature rises. In contact aureoles, maximum temperatures reached with α = f(T) are somewhat lower in comparison with α = 1 mm 2 ·s − 1 ; however, temperatures in inner aureoles stay elevated significantly longer with α = f(T), and consequently promote approach to mineralogical and textural equilibrium. The elevated temperature regime in inner aureoles enhances temperature gradients that may promote greater fluid fluxes if fluid pore pressures are controlled by temperatures. The results demonstrate the need to incorporate temperature-dependent transport properties of magmas and wall rocks into models of metamorphism and fluid flow in contact aureoles.

Examining length and time scales reveals ruinous problems in diverse determinations of thermal conductivity (k) involving the diamond anvil cell (DAC). (1) Conditions in laboratory experiments are optically thick (diffusive) for low-frequency phonons, but optically thin (ballistic) for high-frequency photons. Because speeds of photons are about ×105 those of phonons, ballistic photons transport heat over the short length and time scales of pulse-heating measurements in the DAC intended to measure phonons. Ballistic transport was confirmed by conducting pulse-heating experiments under various conditions. Not accounting for this time-dependent effect produces fallacious values for the lattice contribution to k. (2) In DAC optical spectroscopy, strong refraction was misinterpreted as sample absorption and its affect on path length went unnoticed, resulting in invalid calculations of the radiative diffusive component of k. Better estimates of lower mantle k are summarized. Scaling aspects point to the controls exerted by radiative transfer early in Earth's history and the importance of mantle layers to Earth's present thermal state. Diffusion of radiation is fast, making retention of primordial heat improbable: thus today's Earth is in quasi-steady-state, wherein its emitted heat is derived solely from current radiogenic contents.

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.

Contact-free, laser-flash analysis (LFA) accurately (±2%) measures lattice thermal diffusivity ( D ) at high temperature ( T ). Conventional measurements of minerals underestimate D by ∼20% near 298 K due to interface resistance, although simultaneously existing direct radiative transfer artificially elevates D as T rises. Pressure ( P ) determinations possess these and other problems; however, reproduced values of ∂ D /∂ P agree the damped harmonic oscillator model. Models combined with new LFA data on perovskite compounds show that lattice thermal conductivity ( k lat ) is high and independent of T , increasing from 7.5 to 30 W/m K (±25%) across the lower mantle (LM) due to compression. Diffusive radiative transfer is estimated from a recent model: For expected fine grain-size, spectral characteristics do not play a strong role, indicating that k rad increases from ∼1 to ∼5 W/m K across the LM, estimated from olivine spectra. Although greater accuracy through improved measurements is needed, our results demonstrate that the LM is an efficient conductor of heat. Even a low, adiabatic temperature gradient can carry the power inferred to run the dynamo. Mantle convection may be limited to above 670 km.

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 ) was measured from 8 single-crystals and 2 polycrystalline clinopyroxene samples at temperatures ( T ) up to a maximum of ~1000 to 1600 K, using laser-flash analysis. Electron microprobe analysis shows that we have two samples of near end-member diopside, two augites, one end-member and one impure jadeite, aegerine, and three near end-member spodumenes. Hydroxyl contents determined from near-IR spectroscopy range from ~ 0 to 70 ppm as H 2 O. Two directions constrain D for clinopyroxenes, consistent with phonon symmetry. Anisotropy = ( D ⊥c − D ||c )/ D ||c is near 40 % for all samples and independent of T , where || and ⊥ indicate the direction heat flows relative to the c -axis. Thermal diffusivity decreases with increasing T and approaches a constant ( D sat ) near 1400 K. The temperature dependence of 1/ D is well described by low-order polynomial fits. At 298 K and for near end-member compositions, cation mass and bond lengths strongly affect D ⊥c whereas D ||c is essentially constant and large, 3.9 mm 2 s −1 . For solid solutions, D at 298 K decreases from end-member values as impurity content increases, but D at saturation is little affected. Excluding Li-rich clinopyroxenes, D ⊥c,sat ~ 0.5 mm 2 s −1 and D ||c,sat ~ 0.9 mm 2 s −1 . The values pertain to lithospheric and mantle compositions of clinopyroxene above 1400 K, and lead to bulk thermal conductivity at saturation being 2.4 W m −1 K −1 . Pressure deriviatives are predicted from models as ∂(ln k )/∥ P = 4.2 to 4.7 %GPa −1 .

Thermal diffusivity (D) was measured using laser-flash analysis from oriented single-crystal low-sani- dine (K0.92Na0.08Al0.99Fe 3+ Si2.95O8), and three glasses near KAlSi3O8. Viscosity measurements of the three super- cooled liquids, in the range 10 6.8 to 10 12.3 Pa s, confirm near- Arrhenian behavior, varying subtly with composition. For crystal and glass, D decreases with T, approaching a constant near 1,000 K: Dsat * 0.65 ± 0.3 mm 2 s -1 for bulk crystal and *0.53 ± 0.03 mm 2 s -1 for the glass. A rapid decrease near 1,400 K is consistent with crossing the glass transition. Melt behavior is approximated by D = 0.475 ± 0.01 mm 2 s -1 . Thermal conductivity (klat) of glass, calculated using previous heat capacity (CP) and new density data, increases with T because CP strongly increases with T. For melt, klat reaches a plateau near 1.45 W m -1 K -1 , and is always below klat of the crystal. Melting of potassium feldspars impedes heat transport, providing positive thermal feedback that may promote further melting in continental crust.

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.

Lattice thermal diffusivities of eleven orientated natural and synthetic quartz samples were measured using a laser-flash apparatus (LFA). For α-quartz, thermal diffusivity (D) decreases with temperature, so that directionally averaged values of D(T) between 20° and 500°C can be fit with D(T) = 1/(0.0017T + A), where A varies from 0.12 to 0.18 among the samples and D is in mm2/s. For β-quartz, D decreases very slightly or is constant with temperature. Values of D measured along [001] exceed those measured along [100] at all temperatures studied. A sharp decrease of D(T) marks the α-β phase transition, consistent with correlation of 1/D with C P in the damped harmonic oscillator model. Due to the rapidity of the laser-pulse and the dynamic nature of the measurements, the raw data show evidence of latent heat being released at the transition temperature over ∼50 ms. D(T) values within 10 K of the transition are affected both by latent heat release and by the phase change. For our suite of samples, D at all temperatures varies by ±7% from the overall average. This range is outside the 2% experimental uncertainty. To ascertain causes of D variations, we characterized out samples using infrared absorption spectroscopy, electron microprobe analyses and secondary ion mass spectrometry. Differences between the samples seem to result from the interplay of different impurity types: cations that replace Si in the silicate tetrahedra, cations squeezing into the lattice, and OH. Although limitations in quantifying amounts of trace impurities and poor understanding of where impurities reside in the lattice hamper interpretation, it seems that samples containing more substitutional impurities (e.g., Al3+) have higher diffusivities along [001], those with more interstitial defects (e.g., Li+) have higher diffusivities along [100], and that OH reduces D.

Pressure ( P ) derivatives of thermal conductivity ( k ) and thermal diffusivity ( D ) are important to geophysics but are difficult to measure accurately because minerals, being hard and partially transparent, likely incur systematic errors through thermal losses at interfaces and spurious radiative transfer. To evaluate accuracy, repeat experiments for olivine [(Mg 0.9 Fe 0.1 ) 2 SiO 4 ], quartz (SiO 2 ), and NaCl are examined in detail: these and other data on electrical insulators are compared with theory. At ambient conditions, D is underestimated in proportion to the number of contacts. As temperature ( T ) increases, spurious radiative transfer more than offsets contact loss. Compression of pore space and contact losses affect pressure derivatives, but these seem independent of T . Accurate (±2%) values of D ( T ) at 1 atm are obtained with the contact-free, laser-flash method. Other optical techniques do not pinpoint D but provide useful pressure derivatives. Published data on ∂(ln k )/∂ P at ambient conditions agree roughly with all available models, the simplest of which predicts ∂(ln k )/∂ P ∼ ∂(ln K T )/∂ P , where K T is the bulk modulus. However, derivatives verified by multiple measurements are reproduced accurately only by the damped harmonic oscillator model. An improved database is needed to refine this model and to confidently extrapolate these difficult measurements to geophysically relevant conditions.

This chapter reviews measurements and theory of heat transport properties (thermal conductivity, k , and thermal diffusivity, D ) of electric insulators that are partially transparent to light (i.e., most minerals in Earth's mantle). We focus on the effects of temperature ( T ) because the specific dependence of k or D on T largely determines conductive and convective model outcomes.

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.

Thermal diffusivity (D) of garnets with diverse chemical compositions was measured using the laser-flash technique, which is accurate (±2%) and isolates the lattice component from direct radiative transfer. Temperatures ranged from ~290 to ~1,600 K (unless limited by melting). Seven synthetic (e.g., YAG, GGG) and 15 natural garnets with two types of ionic substitution [Ca3(Fe,Al)2Si3O12 and (Mg,Fe,Ca)3Al2Si3O12] and varying amounts of OH- were examined. Cation substitution or hydroxyl incorporation lowers D from end-member values. Thermal diffusivity is constant once the temperature (T) exceeds a critical value (T sat) of ~1,100 to 1,500 K. From ~290 K to T sat, the measurements are best represented by 1/D=A+BT+CT 2 where A, B, and C are constants. These constants vary little among diverse chemical compositions, suggesting that the oxygen sublattice controls heat transport. Higher order terms are needed only when T sat is low, such as Ant Hill garnet wherein 1/D=0.049403+0.0032299T−2.3992T 2×10−6+6.0168T 3×10−10(1/D in s/mm2; T in K). The mean free path (λ, computed from D and sound velocities) is slightly larger than the lattice parameter above T sat, in accord with phonon–phonon interactions requiring non-localized modes. At most temperatures, λ is nm-sized. Large values of λ are obtained by extrapolation to a few Kelvins, suggesting that boundary scattering can only be important at extremely cold temperatures. The observed behavior with T and chemical composition is consistent with the damped harmonic oscillator model. Phonon transport is best represented by inverse thermal diffusivity wherein 1/D goes as T n where n is between 1 and 3 up to ~200 K, depends on a quadratic or cubic polynomial at moderate T, but is constant above T sat. The predicted and observed temperature response of 1/D mimics the well-known form for heat capacity, in that acoustic modes control heat transport near cryogenic temperatures, optic phonons dominate above ambient temperature, and a limit analogous to that of Dulong and Petit is reached at very high temperature, due to full population of discrete phonon states.

From femtosecond spectroscopy (fs-spectroscopy) of metals, electrons and phonons reequilibrate nearly independently, which contrasts with models of heat transfer at ordinary temperatures ([Formula: see text] K). These electronic transfer models only agree with thermal conductivity [Formula: see text] data at a single temperature, but do not agree with thermal diffusivity [Formula: see text] data. To address the discrepancies, which are important to problems in solid state physics, we separately measured electronic (ele) and phononic (lat) components of [Formula: see text] in many metals and alloys over [Formula: see text]290–1100 K by varying measurement duration and sample length in laser-flash experiments. These mechanisms produce distinct diffusive responses in temperature versus time acquisitions because carrier speeds [Formula: see text] and heat capacities [Formula: see text] differ greatly. Electronic transport of heat only operates for a brief time after heat is applied because [Formula: see text] is high. High [Formula: see text] is associated with moderate [Formula: see text], long lengths, low electrical resistivity, and loss of ferromagnetism. Relationships of [Formula: see text] and [Formula: see text] with physical properties support our assignments. Although [Formula: see text] reaches [Formula: see text] near 470 K, it is transient. Combining previous data on [Formula: see text] with each [Formula: see text] provides mean free paths and lifetimes that are consistent with [Formula: see text] K fs-spectroscopy, and new values at high [Formula: see text]. Our findings are consistent with nearly-free electrons absorbing and transmitting a small fraction of the incoming heat, whereas phonons absorb and transmit the majority. We model time-dependent, parallel heat transfer under adiabatic conditions which is one-dimensional in solids, as required by thermodynamic law. For noninteracting mechanisms, [Formula: see text]. For metals, this reduces to [Formula: see text] above [Formula: see text]20 K, consistent with our measurements, and shows that Meissner’s equation [Formula: see text] is invalid above [Formula: see text]20 K. For one mechanism with multiple, interacting carriers, [Formula: see text]. Thus, certain dynamic behaviors of electrons and phonons in metals have been misunderstood. Implications for theoretical models and technological advancements are briefly discussed.

The rate of heat transfer by conduction is the dominant factor that determines the thermal evolution of planetary crust and lithosphere. Most thermal models of the Earth's crust assume constant values for thermal diffusivity, owing to large experimental uncertainties in measuring this property of rocks at high temperature. Whittington et al. have used recent advances in laser-flash analysis on three different crustal rocks types to show that thermal diffusivity strongly decreases with increasing temperature. They find thermal diffusivity to be about half that commonly assumed at mid-crustal temperatures and therefore conclude that the hot middle and lower crust is a much more effective thermal insulator than previously thought. They also present models of lithospheric thermal evolution during continental collision, and demonstrate that the temperature dependence of rock properties leads to a 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. The thermal evolution of planetary crust and lithosphere is governed by the rate of heat transfer by conduction, which is determined by the rock's thermal diffusivity, usually assumed to remain constant. Alan Whittington and colleagues show that thermal diffusivity in fact decreases strongly with increasing temperature, concluding that the hot middle and lower crust is a much more effective thermal insulator than previously thought; this removes the requirement for unusually high radiogenic heat production to achieve crustal melting temperatures. The thermal evolution of planetary crust and lithosphere is largely governed by the rate of heat transfer by conduction1,2,3. 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 temperature4,5, 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)6,7 owing to the large experimental uncertainties associated with conventional contact methods at high temperatures. Recent advances in laser-flash analysis8,9 permit accurate (±2 per cent) measurements on minerals and rocks to geologically relevant temperatures10. 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 materials11. 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 differentiation12.

This chapter reviews measurements and theory of heat transport properties (thermal conductivity, k, and thermal diffusivity, D) of electrical insulators, for example, mantle minerals. Recent developments regarding the highly accurate, contact-free laser-flash method for measuring D permit isolation of the lattice contribution (Dlat) for partially transparent silicate and oxide minerals from spurious (direct or boundary-to-boundary) radiative transfer effects. Laser-flash measurements, which provide absolute values, give Dlat near room temperature for hard minerals that is ∼20% higher than methods involving multiple contacts, and ∼10% higher than single-contact methods. Contact methods underestimate Dlat near 298 K due to loss of heat at interfaces. Use of long cylinder geometries mixes the directional dependences of Dlat for anisotropic samples, due to differences in coupling between the longitudinal and transverse components of the lattice vibrations with the transverse electromagnetic field of the propagating phonons. As temperature (T) increases, data obtained using contact methods are increasingly contaminated with spurious radiative transfer, sometimes even at 298 K. Pressure determinations share these problems, but numerous studies of olivine and NaCl set constraints. Picosecond transient grating spectroscopy also underestimates Dlat, possibly due to electronic–vibronic coupling. Reliable laser-flash data exist for few minerals (olivine, garnet, and quartz). We provide new results for MgO and MgAl2O4. Trustworthy, verified data agree with the damped harmonic oscillator model. This model and laser-flash data of structural analogs set constraints on D for high-pressure phases. Diffusive radiative transport (krad,dif), as occurs in the mantle, is not constrained by laboratory experiments, and is therefore calculated. The latest model accounts for grain-size and emissivity. Spectral data needed for model input are inadequate, so results for olivine are generalized to other mantle phases at the expense of accuracy. For all phases, krad,dif depends nonlinearly on T, grain-size, and Fe content. In summary, not only has klat been grossly underestimated at room temperature, but also the high-temperature responses of both the lattice and radiative components for silicates and oxides have been misrepresented to varying degrees in mineral physics experiments and calculations. Heat transport in the core is uncertain because available measurements on Fe and Ni metals at low pressure do not agree with the Weidemann–Franz model used to extrapolate k to core conditions. Improved measurements of diverse types of Earth materials are needed, which will improve our understanding of microscopic processes, and will impact lithospheric studies, estimation of the global power, and the outcome of geodynamic models.

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.

We show that laser-flash analysis measurements of the temperature (T) dependence of thermal diffusivity (D) for diverse non-metallic (e.g., silicates) single-crystals is consistently represented by D(T) = FT−G + HT above 298 K, with G ranging from 0.3 to 2, depending on structure, and H being ∼10−4 K−1 for 51 single-crystals, 3 polycrystals, and two glasses unaffected by disorder or reconstructive phase transitions. Materials exhibiting this behavior include complex silicates with variable amounts of cation disorder, perovskite structured materials, and graphite. The high-temperature term HT becomes important by ∼1300 K, above which temperature its contribution to D(T) exceeds that of the FT−G term. The combination of the FT−G and HT terms produces the nearly temperature independent high-temperature region of D previously interpreted as the minimal phonon mean free path being limited by the finite interatomic spacing. Based on the simplicity of the fit and large number of materials it represents, this finding has repercussions for high-temperature models of heat transport. One explanation is that the two terms describing D(T) are associated with two distinct microscopic mechanisms; here, we explore the possibility that the thermal diffusivity of an electrical insulator could include both a contribution of lattice phonons (the FT−G term) and a contribution of diffusive bulk phonon-polaritons (BPP) at infrared (IR) frequencies (the HT term). The proposed BPP diffusion exists over length scales smaller than the laboratory sample sizes, and transfers mixed light and vibrational energy at a speed significantly smaller than the speed of light. Our diffusive IR-BPP hypothesis is consistent with other experimental observations such as polarization behavior, dependence of D on the number of IR peaks, and H = 0 for Ge and Si, which lack IR fundamentals. A simple quasi-particle thermal diffusion model is presented to begin understanding the contribution from bulk phonon-polaritons to overall heat conduction.

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...

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...