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Showing papers on "Thermal expansion published in 1995"


Journal ArticleDOI
01 Jan 1995-Carbon
TL;DR: In this paper, the tensile and bending stiffness constants of ideal multi-walled and single-wall carbon nano-tubes are derived in terms of the known elastic properties of graphite.

1,275 citations


Journal ArticleDOI
TL;DR: In this article, the electrical conductivity and Seebeck coefficient as a function of the Co Fe ratio and temperature were investigated in the La0.8Sr0.2Co1−yFeyO3 with 0 ≤ y ≤ 1.

746 citations


Journal ArticleDOI
TL;DR: An asymptotic growth rate at high electronic stopping power and low irradiation temperature is derived which correlates the growth rate with a few simple material parameters without introducing any adjustable free parameter.
Abstract: Under energetic ion bombardment, amorphous solids show substantial plastic flow in the form of anisotropic growth. This is attributed to the relaxation of shear stresses coupled to the thermal expansion in cylindrical thermal spikes induced by intense electronic excitations and to the subsequent freezing-in of the associated strain increment upon cooling down. An asymptotic growth rate at high electronic stopping power and low irradiation temperature is derived which correlates the growth rate with a few simple material parameters without introducing any adjustable free parameter. Good agreement with measurements justifies the basic assumptions of the model.

235 citations



Journal ArticleDOI
TL;DR: In this article, the authors report on acoustic-emission experiments that monitor the process of thermal cracking as it occurs during heating, supported by measurements of crack surface area, porefluid permeability, porosity and surface conductivity carried out on rock samples treated to various peak temperatures.
Abstract: SUMMARY It is usually suggested that thermal cracking in a quartz-bearing rock results from the anomalously high volumetric expansion coefficients of quartz (eg Simmons & Cooper 1978) It has also been recognized that thermal expansion mismatch and mineral anisotropy contribute to thermal cracking in materials that consist of a polycrystalline aggregate composed of several anisotropic minerals even in the absence of a temperature gradient (Friedrich & Wong 1986) Experiments investigating thermal cracking in rocks commonly involve imaging and quantitative stereology of crack populations induced in rocks treated to various peak temperatures (eg Friedrich & Johnson 1978; Homand-Etienne & Troalan 1984; Atkinson, McDonald & Meredith 1984; Meredith & Atkinson 1985) Here we report on acoustic-emission experiments that monitor the process of thermal cracking as it occurs during heating, supported by measurements of crack surface area, pore-fluid permeability, porosity and surface conductivity carried out on rock samples treated to various peak temperatures The acoustic-emission measurements show a strong peak of microcracking at the phase transition temperature for quartz (˜573°C) superimposed upon a background of microcracking due to thermal expansion There is also a clear peak of microcracking at higher temperatures (˜800°C) that can be attributed to oxidation-dehydroxylation reactions of hornblende and chlorite Measurements of fluid permeability, pore surface area, porosity and electrical conductivity, made on samples that have been heat treated to various maximum temperatures, show increases associated with a major episode of cracking in the 500-600°C temperature range, indicating that the new cracks form a well-interconnected network This has been confirmed by SEM and optical microscopy These results have implications for the electrical conductivity of the continental crust, providing a mechanism enabling the high pore-fluid connectivity needed to explain zones of high electrical conductivity at depth providing that cracks opened in this way remain open at the high pressures existing at depth It should be recognized, however, that th***se measurements are limited in their direct application since they were obtained under initially dry conditions at laboratory pressures

220 citations


Journal ArticleDOI
TL;DR: In this paper, high-temperature x-ray diffraction was used to study the tetragonal distortion as a function of temperature (25-700 °C) for compositions (x = 0.7) using powders prepared by solid-state reaction in the above system.
Abstract: Compositions in the (Pb1−xBix (Ti1−xFex)O3 solid solution system for x ⋚ 0.7 show unusually large tetragonal distortion. High-temperature x-ray diffraction was used to study the tetragonal distortion as a function of temperature (25–700 °C) for compositions (x = 0–0.7) using powders prepared by solid-state reaction in the above system. Large changes in the lattice parameters were observed over a narrow temperature range near Curie temperature (TC) for compositions near the morphotropic phase boundary (MPB) (x ≃ 0.7). Compositions near MPB showed a c/a ratio of 1.18 at room temperature. Polar plots of lattice constants at different temperatures indicated strong anisotropic thermal expansion with zero thermal expansion along the [201] direction.

216 citations


BookDOI
01 Jan 1995
TL;DR: Zerodur as discussed by the authors is a low-thermal glass ceramic for optical precision applications, which can be used for household appliances and is shown to be a good choice for indoor lighting applications.
Abstract: 1. Overview 2. The Scientific Basis 3. Transparent and Tinted Glass Ceramics for Household Appliances 4. Zerodur(R) - A Low Thermal Glass Ceramic for Optical Precision Applications

212 citations


Patent
29 Dec 1995
TL;DR: In this paper, a defect-free permanent bond formation method without the use of adhesives as well as devices formed by this method is disclosed, where similar or dissimilar crystalline, vitreous or dense polycrystalline ceramic, metallic or organic polymeric components are first joined by optical contacting and then heat treated to stabilize the bond.
Abstract: A method of forming defect-free permanent bonds without the use of adhesives as well as devices formed by this method is disclosed. In general, the disclosed process allows similar or dissimilar crystalline, vitreous or dense polycrystalline ceramic, metallic or organic polymeric components to be first joined by optical contacting and then heat treated to stabilize the bond. The heat treatment can be performed at a low enough temperature to prevent interdiffusion between species, thus insuring that the bond is not subjected to excessive mechanical stresses and that the materials do not undergo phase changes. Therefore stable bonds can be formed using the disclosed process between materials of widely differing physical, mechanical, thermal, optical and electro-optical properties such as different hardness, chemical durability, mechanical strength, coefficients of thermal expansion, thermal conductivity, crystal structure, refractive indices, optical birefringence, nonlinear optical coefficients, electrical conductivity, or semiconducting properties.

147 citations


Journal ArticleDOI
TL;DR: Calculations based on a newly developed elastic strain model reveal that the main reason temperature stability of the center wavelengths exhibits substrate dependency is due to a reduction in film packing density brought about by volumetric distortion of the film, which is caused by stress induced from the substrate.
Abstract: Four types of single-cavity, thin-film, narrow-bandpass filter whose full width at half-maximum ranges from 0.5 to 1.1 nm are produced by ion-assisted deposition of alternating TiO(2)/SiO(2) or Ta(2)O(5)/SiO(2) layers upon eight substrates having differing coefficients of linear expansion, and the temperature stability of their center wavelengths is examined in the 1540-nm wavelength region. The temperature stability is shown to be greatly dependent on the coefficient of linear expansion of the substrate upon which the filter is deposited. For the eight substrates whose coefficients of linear expansion range from 0 to 142 × 10(-7)/°C, the temperature stability of the filters ranges from +0.018 to -0.005 nm/°C. Calculations based on a newly developed elastic strain model reveal that the main reason temperature stability of the center wavelengths exhibits substrate dependency is due to a reduction in film packing density brought about by volumetric distortion of the film, which is caused by stress induced from the substrate.

131 citations


Book
31 Jan 1995
TL;DR: In this article, the authors present a list of general polymer features and their relationship with specific heat properties, including the Grueneisen relation and the thermal expansion and thermal conductivity of polymers.
Abstract: Introduction and General Polymer Features. Phonon Structure and Polymers. Specific Heat. Thermal Expansion and the Grueneisen Relation. Thermal Conductivity. Molecular Place Changes and Dampening Spectra. Mechanical Deformation Behavior. Dielectric Properties and their Correlations. Fracture Behavior of Polymers. Cryogenic Measuring Methods. Polymers as Matrix for Composites. Appendix. Index.

125 citations


Journal ArticleDOI
TL;DR: In this paper, a molecular-dynamics simulation method is described that permits space-filling, fully dense 3D nanocrystalline materials to be grown by crystallization from the melt.
Abstract: A molecular‐dynamics simulation method is described that permits space‐filling, fully dense three‐dimensional nanocrystalline materials to be grown by crystallization from the melt. The method is illustrated by computer synthesis of an eight‐grain polycrystal of Cu with a grain size of 43 A. At the beginning of the simulation, eight small pre‐oriented single‐crystal seeds are embedded in the melt which is subsequently cooled below the melting point to enable crystal growth under an applied external pressure. The fully relaxed nanocrystalline material contains large perfect‐crystal regions separated by well‐defined grain boundaries, most of which have approximately the same width and energy. In spite of the rather small number of grains in the simulation cell, the thermal expansion of the material is practically isotropic, and almost identical to that of the perfect crystal. The elastic moduli are also almost isotropic and are somewhat lower than in the coarse‐grained material. The material exhibits a low‐temperature anomaly in the specific heat.

Journal ArticleDOI
TL;DR: In this paper, the effect of thermal expansion mismatch stress between silicon nitride and different grain boundary phases on the fracture toughness of silicon polysilicon was investigated, and the presence of tensile residual stress at the grain boundary caused by thermal expansion mismatches between the silicon and grain boundary phase enhanced crack deflection and grain bridging.
Abstract: The effect of thermal expansion mismatch stress between silicon nitride and different grain boundary phases on the fracture toughness of silicon nitride was investigated. Different sintering aids in the Y-Mg-Si-Al-O-N system produced silicon nitride specimens with very similar microstructures but different grain boundary phase compositions and different values of fracture toughness. The fracture toughness of the silicon nitride increased as the thermal expansion coefficient of the grain boundary phase increased. The presence of tensile residual stress at the grain boundary caused by thermal expansion mismatch between the silicon nitride and the grain boundary phase enhanced crack deflection and grain bridging.

Journal ArticleDOI
TL;DR: In this paper, the density and the coefficient of thermal expansion of pure liquid Mn, Fe, Ni, Cu, Al and Sn at temperatures between melting and 1973K using the γ-ray attenuation technique are reported.
Abstract: New experimental data for the density and the coefficient of thermal expansion of pure liquid Mn, Fe, Ni, Cu, Al and Sn at temperatures between melting and 1973K using the γ-ray attenuation technique are reported. An extensive study of sources of random and systematic errors has shown a maximum error of 0.75% in absolute density measurements. In the temperature range studied, the density behaves linearly with temperature. The density at the melting point and the coefficient of thermal expansion are in accordance with those of other studies. Comparison of the specific heat ratios γ calculated with the results of this study with those obtained using structural data from diffraction experiments shows large and even non-physical discrepancies, e.g., in the case of Mn. Solid-like viscoelastic behavior in the low-Q region is suggested as a possible cause of such anomaly while shear components would contribute noticeably to reduce the liquid compressibility. It is shown that expansivities of the present...

Journal ArticleDOI
TL;DR: In this paper, the temperature dependence of the thicknesses and densities of ultrathin deuterated PMMA films under high vacuum on Si(111) substrates was investigated via neutron reflectometry in situ.
Abstract: The temperature dependence of the thicknesses and densities of ultrathin deuterated PMMA films under high vacuum on Si(111) substrates was investigated via neutron reflectometry in situ. The increase in film thickness and concurrent decrease in film density, with increasing temperature in such films was observed directly for the first time. The degree of thermal expansion observed differs below and above the approximate T g of the polymer

Journal ArticleDOI
TL;DR: In this article, the properties and structure of (45 - x)RO · xNa2O · 2.5Al2O3 · 52.5P2O5 (R = Mg, Ca, Sr, Ba, 0 ⩽ x⩽ 31 mol%) glasses were investigated.
Abstract: The properties and structure of (45 - x)RO · xNa2O · 2.5Al2O3 · 52.5P2O5 (R = Mg, Ca, Sr, Ba, 0 ⩽ x ⩽ 31 mol%) glasses were investigated. The variation in the molar volumes of glasses in the MgO series is closely related to the formation of the end groups in the glasses with the substitution of Na+ ions for Mg2+ ions, resulting in a variation of the density and refractive index of the glasses. The properties of glasses containing CaO in terms of Na2O substitution depend mainly on the low field strength of Na+ ions substituting for CaO even though the end groups occurring in the glasses increased. The variation in properties of the glasses containing SrO and BaO, some of which were substituted by Na2O, could be explained by differences in masses, field strength and polarizability between the Na+ ions and the alkaline-earth ions due to a small variation in the structure of the glasses despite Na2O substitution.


Proceedings ArticleDOI
31 May 1995
TL;DR: In this paper, the Q-factor of LGS resonators was measured in temperature range -200 to 100/spl deg/C and single and double rotated Z temperature cuts were calculated.
Abstract: Refined data of temperature dependences, elastic, dielectric, piezoelectric and thermal expansion coefficients were received for temperature range -100 to 100/spl deg/C. Single and double rotated Z temperature cuts were calculated. Q-factor of LGS resonators was measured in temperature range -200 to 100/spl deg/C.

Journal ArticleDOI
TL;DR: Theoretical results for the temperature dependence of the thermal expansion coefficient for 3C-SiC were reported using a phenomenological lattice dynamical theory in the quasiharmonic approximation.
Abstract: Theoretical results for the temperature dependence of the thermal expansion coefficient for 3C–SiC are reported using a phenomenological lattice dynamical theory in the quasiharmonic approximation. The linear thermal expansion coefficient α of 3C–SiC exhibits a variation with temperature much like that of the specific heat and, unlike other tetrahedrally coordinated materials, it does not attain a negative value at lower temperatures.

Patent
30 Jun 1995
TL;DR: In this paper, a flip-chip bonding structure is obtained in a semiconductor device where the semiconductor element and mounting substrate are bonded to each other by the wire bump electrodes.
Abstract: In a semiconductor device and a method for manufacturing the same according to the present invention, a bonding wire is bonded to an electrode pad of a semiconductor element by ball bonding. The bonding wire is cut to have a predetermined length, and compressed and crushed into a bump. By doing so, a wire bump electrode is formed on each electrode pad of the semiconductor element. The wire bump electrodes formed on the electrode pads are then bonded to the respective substrate electrodes on a mounting substrate by melting a low-melting metal. As a result, a flip chip bonding structure wherein the semiconductor element and mounting substrate are bonded to each other by the wire bump electrodes, is obtained. Even in a semiconductor device wherein a semiconductor element is bonded to a resin type mounting substrate whose thermal expansion coefficient greatly differs from that of the semiconductor element, a flip chip bonding structure, which is strong in a heat cycle test and has high reliability, can be achieved.

Journal ArticleDOI
TL;DR: X-ray single-crystal diffraction data for synthetic pyrope garnet over the temperature range 30-973 K was presented in this paper, where the structure refinements allowed a detailed geometrical analysis of the polyhedral distortions over this temperature range, and the determination of the thermal expansion for bond distances.
Abstract: X-ray single-crystal diffraction data are presented for synthetic pyrope garnet over the temperature range 30-973 K, which extends the range previously studied The structure refinements allow a detailed geometrical analysis of the polyhedral distortions over this temperature range, the determination of the thermal expansion for bond distances, and the determination of atomic displacement parameters The problem of static or dynamic disorder of the Mg site is discussed on the basis of the temperature behavior of the atomic displacement tensors, which show no evidence of static disorder on this site The hightemperature anharmonic contribution to the thermal vibrations is investigated by the use of Gram-Charlier high-order expansion terms of the displacement parameter tensor

Journal ArticleDOI
TL;DR: In this article, the residual stresses induced in composites when cooling down from the processing temperature were determined using a cylinder model and using a finite element computer program, and the influence of factors such as interphase thickness and uncertainty in interphase properties (including Young's modulus and coefficient of thermal expansion) was analyzed.
Abstract: The residual stresses induced in composites when cooling down from the processing temperature were determined using a cylinder model and using a finite element computer program. Various specimen geometries were examined: microcomposites, unidirectional composites and flat substrates coated with one or two layers. Various combinations were investigated involving MoSi2 as an interphase, SiC as a fiber, a matrix, a substrate or an external coating layer and C as a fiber, a substrate, an interphase or an intermediate coating layer. The influence of factors such as interphase thickness and uncertainty in interphase properties (including Young's modulus and coefficient of thermal expansion) was analyzed. It was shown that trends in distribution of thermal residual stresses (TRS) prevailing in 1D composites can be satisfactorily predicted using the analytical cylinder model. The presence of a MoSi2 interphase induces the highest interfacial stresses but it relieves stresses in the matrix. The presence of a C interphase essentially reduces the interfacial stresses.

Journal ArticleDOI
TL;DR: In this paper, the optical temperature properties of glasses were analyzed in a physically meaningful model for four standard reference glasses and vitreous silica, and the optical band gaps, such as excitonic and isentropic, contributed to the thermo-optic coefficients rather than the temperature coefficient of the electronic polarizability.
Abstract: The thermo-optic coefficients, d n d T , define the optical temperature properties of glasses. These coefficients are analyzed in a physically meaningful model for four standard reference glasses and vitreous silica. In this model, the optical band gaps, such as excitonic and isentropic, and the thermal expansion coefficient, contribute to the thermo-optic coefficients rather than the temperature coefficient of the electronic polarizability.

Journal ArticleDOI
TL;DR: In this paper, a modified Birch-Murnaghan equation of state for MgSiO3 orthoenstatite is described by a modified version of the BME for diverse temperatures.
Abstract: P-V-T data of MgSiO3 orthoenstatite have been measured by single-crystal X-ray diffraction at simultaneous high pressures (in excess of 4.5 GPa) and temperatures (up to 1000 K). The new P-V-T data of the orthoenstatite, together with previous compression data and thermal expansion data, are described by a modified Birch-Murnaghan equation of state for diverse temperatures. The fitted thermoelastic parameters for MgSiO3 orthoenstatite are: thermal expansion ∂α/∂P with values of a=2.86(29)×10-5 K-1 and b=0.72(16)×10-8 K-2; isothermal bulk modulus K T o =102.8(2) GPa; pressure derivative of bulk modulus K′=∂K/∂P=10.2(1.2); and temperature derivative of bulk modulus K=∂K/∂T=-0.037(5) GPa/K. The derived thermal Gruneisen parameter is γ th=1.05 for ambient conditions; Anderson-Gruneisen parameter is δ T o =11.6, and the pressure derivative of thermal expansion is ∂α/∂P=-3.5×10-6K-1 GPa-1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at two constant pressures of 1.5 GPa and 4.0 GPa are calculated. The resulting pressure dependence of thermal expansion is Δα/ΔP=-3.2(1)× 10-6 K-1 GPa-1. The significantly large values of K′, K, δ T and ∂α/∂P indicate that compression/expansion of MgSiO3 orthoenstatite is very sensitive to changes of pressure and temperature.

Journal ArticleDOI
TL;DR: In this paper, PALS measurements were conducted on polycarbonate subjected to either thermal expansion or to tensile and compressive strains, and it was found that thermal expansion affected both the nanometer hole size and the hole number density, whereas mechanical stress affected mainly the size of existing holes and did not generate or eliminate holes in the quasielastic deformation region.
Abstract: Positron Annihilation Lifetime Spectroscopy (PALS) measurements were conducted on polycarbonate subjected to either thermal expansion or to tensile and compressive strains. It was found that thermal expansion affected both the nanometer hole size and the hole number density, whereas mechanical stress affected mainly the size of existing holes, and did not generate or eliminate holes in the quasielastic deformation region. The effect of stress on yield and postyield behavior of this glassy material was also investigated. The deduced hole volume fraction of this polymer at 25°C was 6.8 ± 0.5% from the thermal expansion experiment and 7.2 ± 1.2% from the mechanical loading experiment. When the specimen was under compression, the hole volume fraction was found to continuously decrease. This can be considered as evidence of the inability of the free volume concept in explaining the yield behavior of glassy polymers. ©1995 John Wiley & Sons, Inc.


Journal ArticleDOI
TL;DR: In this article, the effect of barium-substituted lanthanum manganite (La1−xBaxMnO3) powders have been synthesized by a novel autoignition technique.
Abstract: Barium-substituted lanthanum manganite (La1−xBaxMnO3) powders have been synthesized by a novel autoignition technique, and the effect of barium content on the autoignition characteristics, stability of the compound, and the powder characteristics have been investigated. X-ray examinations show that the material exists as a single phase having perovskite structure up to 40 at. % substitution of Ba for La, beyond which mixed phases of LaMnO3 and BaMnO3 are formed at least up to the highest limit of substitution (50 at. %) and calcination temperature (1350 °C) investigated. Electrical conductivity and thermal expansion behavior of the material have been studied for plausible use as cathode material in solid oxide fuel cells.

Patent
06 Apr 1995
TL;DR: In this paper, a flexible outer skin formed from a metal super alloy is designed to flex and accommodate thermal growth in the vehicle structure, which is made from a plurality of hexagonal shaped cups which are welded together at the edges in a honeycomb type of array with thermal expansion gaps provided between the outermost surfaces of the hexagonal cups.
Abstract: A method and apparatus are disclosed for providing an aircraft thermal protection system for hypersonic cruise and space launch vehicles. A flexible outer skin formed from a metal super alloy is designed to flex and accommodate thermal growth in the vehicle structure. The flexible super alloy skin is made from a plurality of hexagonal shaped cups which are welded together at the edges in a honeycomb type of array with thermal expansion gaps provided between the outermost surfaces of the hexagonal cups. Gap covers extend across the thermal expansion gaps to reduce aerodynamic drag. The flexible outer skin extends over hexagonal shaped, high temperature ceramic blocks, which provide both an insulation layer and support for the outer skin. The flexible outer skin distributes airloads across various ones of the rigid ceramic blocks. A strain isolation pad extends across the ends of the blocks, opposite the flexible outer skin, to absorb strains induced by thermal expansion of the ceramic blocks and the materials beneath. A closed cell foam sheeting extends adjacent to the strain isolation pads, opposite the ceramic blocks, to provide a moisture barrier for preventing liquid formation and freezing on cryogenic fuel tanks. A thin super alloy backing foil extends along the closed cell foam sheeting, opposite the strain isolation pads. The flexible outer skin is secured to the backing foil by super alloy rods.

Journal ArticleDOI
TL;DR: In this article, the authors measured the temperature dependence of the cell parameter of cubic β-cristobalite up to 1300°C by high-precision X-ray powder diffraction.
Abstract: We have measured the temperature dependence of the cell parameter of cubic β-cristobalite up to 1300° C by high-precision X-ray powder diffraction. The thermal expansion coefficient decreases on heating, until above 1000° C the cell parameter is virtually constant in value. We discuss this change in the thermal expansion with reference to the behaviour of low-frequency rigid unit modes and fluctuations associated with the α-β phase transition.

Journal ArticleDOI
TL;DR: In this paper, high-resolution X-ray diffraction measurements were performed at variable temperatures and pressures of gallium nitride, which is a wide-band semiconductor, for an evaluation of the basic physical properties, namely lattice constants, thermal expansion and compressibility.
Abstract: High-resolution X-ray diffraction measurements can be performed at variable temperatures and pressures. The usefulness of such experiments is shown when taking gallium nitride, which is a wide-band semiconductor, as an example. The GaN samples were grown at high pressures (bulk crystals) and as epitaxial layers on silicon carbide and sapphire. The X-ray examinations were done at temperatures of 293-750 K and at pressures of up to 8 kbar. The results served for an evaluation of the basic physical properties of gallium nitride; namely lattice constants, thermal expansion and compressibility. The comparison of monocrystals with epitaxial layers grown on highly mismatched substrates provided important information about the influence of the substrate on the crystallographic perfection of the layers.

Journal ArticleDOI
TL;DR: In this paper, the phase boundary between spinel+stishovite and perovskite is estimated to be P (GPa) = (24.0±0.5) - (0.0025±0.0025) T-800.
Abstract: A double-stage multianvil system was developed to conduct in situ X ray diffraction study at high pressures. The system generates pressures and temperature above 25 GPa and 1200°C and has been used in conjunction with intense synchrotron radiation to study the phase transitions of MgSiO3 and the thermal expansion of MgSiO3 perovskite. At pressures between 20 and 30 GPa, we observed a series of phase transitions from spinel+stishovite through ilmenite to perovskite. Spinel+stishovite transforms into ilmenite at 20.0±1.0 GPa, and ilmenite transforms into perovskite at 24.0±0.5 GPa at 800°C. The phase boundary between ilmenite and perovskite is estimated to be P (GPa) = (24.0±0.5) - (0.0025±0.0025)(T-800)(°C) by combining the present results and previous constraints on the slope of the phase boundary from the thermodynamic properties. Measured unit cell parameters of MgSiOs perovskite indicate that the average volumetric thermal expansion coefficient of MgSiOs perovskite over 25°–1200°C is 2.0±0.4×10−5 K−1 at 25 GPa. These results provide the phase stability relation of MgSiO3 and the thermal equation of state of MgSiO3 perovskite at pressures corresponding to the boundary between the upper and lower mantle. However, uncertainties involved in extrapolating to the actual mantle temperatures do not allow evaluation of the chemical structure near the 670 km discontinuity in the mantle.