Showing papers on "Thermal expansion published in 1997"

Design of materials with extreme thermal expansion using a three-phase topology optimization method

Abstract: Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases that optimizes an objective function (e.g. thermoelastic properties) subject to certain constraints, such as elastic symmetry or volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material structures are found using the numerical homogenization method based on a finite-element discretization of the base cell. The optimization problem is solved using sequential linear programming. To benchmark the design method we first consider two-phase designs. Our optimal two-phase microstructures are in fine agreement with rigorous bounds and the so-called Vigdergauz microstructures that realize the bounds. For three phases, the optimal microstructures are also compared with new rigorous bounds and again it is shown that the method yields designed materials with thermoelastic properties that are close to the bounds. The three-phase design method is illustrated by designing materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void.

Compressibility, Phase Transitions, and Oxygen Migration in Zirconium Tungstate, ZrW2O8

Abstract: In situ neutron diffraction experiments show that at pressures above 2 kilobars, cubic zirconium tungstate (ZrW2O8) undergoes a quenchable phase transition to an orthorhombic phase, the structure of which has been solved from powder diffraction data. This phase transition can be reversed by heating at 393 kelvin and 1 atmosphere and involves the migration of oxygen atoms in the lattice. The high-pressure phase shows negative thermal expansion from 20 to 300 kelvin. The relative thermal expansion and compressibilities of the cubic and orthorhombic forms can be explained in terms of the “cross-bracing” between polyhedra that occurs as a result of the phase transition.

Design of materials with extreme thermal expansion using a three-phase topology optimization method

Abstract: We show how composites with extremal or unusual thermal expansion coefficients can be designed using a numerical topology optimization method. The composites are composed of two different material phases and void. The optimization method is illustrated by designing materials having maximum thermal expansion, zero thermal expansion, and negative thermal expansion. Assuming linear elasticity, it is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void. We also show that there is no mechanistic relationship between negative thermal expansion and negative Poisson's ratio.

Thermal Expansion of Periclase (MgO) and Tungsten (W) to Melting Temperatures

Abstract: In situ x-ray data on molar volumes of periclase and tungsten have been collected over the temperature range from 300 K to melting. We determine the temperature by combining the technique of spectroradiometry and electrical resistance wire heating. The thermal expansion (α) of periclase between 300 and 3100 K is given by α=2.6025 10−5+1.3535 10−8 T+6.5687 10−3 T−1−1.8281 T−2.

Thermal expansion of periclase (MgO) and tungsten (W) to melting temperatures Sample: T = 298 K

Abstract: Abstract In situ x-ray data on molar volumes of periclase and tungsten have been collected over the temperature range from 300 K to melting. We determine the temperature by combining the technique of spectroradiometry and electrical resistance wire heating. The thermal expansion (α) of periclase between 300 and 3100 K is given by α=2.6025 10−5+1.3535 10−8 T+6.5687 10−3 T−1−1.8281 T−2.For tungsten, we have (300 to 3600 K) α=7.862 10−6+6.392 10−9 T.The data at 298 K for periclase is: molar volume 11.246 (0.031) cm3, α=3.15 (0.07) 10−5 K−1, and for tungsten: molar volume 9.55 cm3, α=9.77 (10.08) 10−6 K−1.

Negative thermal expansion materials

Abstract: The recent discovery of negative thermal expansion over an unprecedented temperature range in ZrW 2 O 8 (which contracts continuously on warming from below 2 K to above 1000 K) has stimulated considerable interest in this unusual phenomenon. Negative and low thermal expansion materials have a number of important potential uses in ceramic, optical and electronic applications. We have now found negative thermal expansion in a large new family of materials with the general formula A 2 (MO 4 ) 3 . Chemical substitution dramatically influences the thermal expansion properties of these materials allowing the production of ceramics with negative, positive or zero coefficients of thermal expansion, with the potential to control other important materials properties such as refractive index and dielectric constant. The mechanism of negative thermal expansion and the phase transitions exhibited by this important new class of low-expansion materials will be discussed.

Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy

Abstract: A new nanofabrication procedure has been developed for making thermocouple probes for high-resolution scanning thermal microscopy. Thermocouple junctions were placed at the end of SiNx cantilever probe tips and were typically 100–500 nm in diameter. Cantilever bending due to thermal expansion mismatch was minimized for Au–Ni, Au–Pt, and Au–Pd thermocouples, by carefully choosing thermal probe materials, film thicknesses, and deposition conditions. A spatial resolution of 24 nm was demonstrated for thermal microscopy although the noise-equivalent limit of 10 nm was estimated from experimental data. Using thermo-power measurements, a simple model was developed to calculate the tip-sample thermal resistance. Model-based calculations, correlations between topographical and thermal features, as well as experiments in different gaseous and humidity environments indicate that the dominant tip-surface heat conduction is most likely through a liquid film bridging the tip and the sample surface, and not through the surrounding gas, solid-solid point contact, or near-field radiation. Dynamic measurements within a 100 kHz bandwidth showed a time constant of about 0.15±0.02 ms which was attributed to the thermal time constant of the whole cantilever. Calculations suggested the RC electrical time constant and the thermal time constant of the thermocouple junction to be on the order of 10 ns which, however, could not be experimentally probed.

The partial molar volume, thermal expansivity, and compressibility of H2O in NaAlSi3O8 liquid: new measurements and an internally consistent model

Abstract: The molar volumes of 19 hydrous albitic liquids (1.9 to 6.1 wt% H2Ototal) were determined at one bar and 505–765 K. These volume data were derived from density measurements on hydrous glasses at 298 K, followed by measurements of the thermal expansion of each glass from 298 K to its respective glass transition temperature. The technique exploits the fact that the volume of a glass is equal to that of the corresponding liquid at the limiting fictive temperature (Tf′), and that Tf′ can be approximated as the temperature near the onset of the rapid increase in thermal expansion that occurs in the glass transition interval. The volume data of this study were combined with available volume data for anhydrous, Na2O-Al2O3-SiO2 liquids to derive the partial molar volume (±1) of the H2O component \(\) in an albitic melt at ∼565 K and one bar. To extend the determination of \(\) to higher temperatures and pressures, the molar volumes of the hydrous albitic liquids determined in this study were combined with those measured by previous authors at 1023–1223 K and 480–840 MPa, leading to the following fitted values (±1) at 1673 K and one bar: \(\) (±0.46)×10−3 cm−3/mol-K, and dV¯H2Ototal/dP=−3.82 (±0.36)×10−4 cm3/mol-bar. The measured molar volumes of this study and those of previous authors can be recovered with a standard deviation of 0.5%, which is within the respective experimental errors. There is a significant difference between the values for \(\) derived in this study as a function of temperature and pressure and those obtained from an existing polynomial, primarily caused by the previous absence of accurate density measurements on anhydrous silicate liquids. The coefficients of thermal expansion (=4.72×10−4/K) and isothermal compressibility (T=1.66×10−5/bar) for the H2O component at 1273 K and 100 MPa, indicate that H2Ototal is the single most expansive and compressible component in silicate liquids. For example, at 1473 K and 70 MPa (conditions of a mid-ocean ridge crustal magma chamber), the presence of just 0.4 wt% H2O will decrease the density of a basaltic liquid by more than one percent. An equivalent decrease in melt density could be achieved by increasing the temperature by 175 degrees or the decreasing pressure by 230 MPa. Therefore, even minor quantities of dissolved water will have a marked effect on the dynamic properties of silicate liquids in the crustal environment.

Method of bonding a III-V group compound semiconductor layer on a silicon substrate

Abstract: Prior to a heat treatment for bonding a III-V group compound semiconductor layer on a silicon substrate, a thermal stress relaxation layer is provided between the silicon layer and the III-V group compound semiconductor layer thermal stress relaxation layer, having a thermal expansion coefficient equal or near to the thermal expansion coefficient of the III-V group compound semiconductor layer and having a rigidity coefficient being sufficiently large to suppress generation of any crystal defects in the III-V group compound semiconductor layer due to a thermal stress generated in the heat treatment and subsequent cooling stage by the difference in the thermal expansion coefficient between the III-V group compound semiconductor layer and the silicon layer.

Thermal expansion of isotropic multiphase composites and polycrystals

Abstract: Sharp bounds on the effective thermal expansion coefficients of isotropic multiphase composites and isotropic polycrystals are obtained by using classical variational principles and the translation method. Our bounds are appreciably narrower than the known Schapery-Rosen-Hashin bounds. Conditions are formulated that guarantee a one-to-one correspondence between the bulk modulus and thermal expansion coefficient of a polycrystal. All of our results can be readily applied to the poroelasticity problem. Generalizations of the results to treat anisotropic composites comprised of anisotropic phases are discussed.

First-principles calculations of the thermal expansion of metals

Abstract: We present first-principles calculations of the thermal expansion of several simple metals (Al, Li, and Na) within the quasiharmonic approximation. Linear-response theory is used to determine the volume-dependent phonon frequencies within the density-functional framework. Our results indicate that the treatment of anharmonic effects at the quasiharmonic level provides a remarkably good description of the structural and elastic properties of these materials up to their melting points.

Theory of thermal expansivity and bulk modulus for MgO and other minerals at high temperatures

Abstract: The Gruneisen theory of thermal expansion as formulated by Born and Huang has been modified by including higher-order terms for the change in volume in the expansion of potential energy. New expressions are obtained for the thermal expansivity and bulk modulus, and used to estimate these quantities for MgO and other minerals in the temperature range 300–1800 K. The results are found to present close agreement with the experimental data.

Silicate melts: Relaxation, rheology, and the glass transition

Abstract: Movement of magma within the Earth depends upon the density, compressibility, thermal expansion, viscosity, diffusivity, heat capacity, and thermal conductivity of silicate melts as a function of temperature, pressure, and composition. These physical properties are controlled by the atomic coordination and bond strengths of the melt. To contribute more to our understanding of geological processes than numerous measurements of physical properties of individual magmas of local interest, the relationship between melt structure and physical properties needs to be understood. In geological settings where the viscosity of the molten component is high (108-1014 Pa s), the melt structure requires a long time (seconds to weeks) to equilibrate in response to changes in pressure, temperature, and composition. The effects of this structural equilibration upon the viscosity, density, and compressibility of magmas and the time required for equilibration need to be included in discussions of magma ascent and emplacement and of crystal nucleation, growth, and segregation within magmas. The structural relaxation discussed here is the slowest relaxation process occurring in a silicate melt at a specific temperature and therefore represents the glass transition, which is a kinetic transition whose temperature is not a constant specific to a melt composition but depends upon the timescale on which measurements are performed. On the basis of the agreement between nuclear magnetic resonance measurements of Si-O bond exchange timescales and measured structural relaxation timescales, the structural equilibration observed in silicate melts appears to be due to the lifetime of the Si-O bonds in the melt. The following is a discussion of a range of different studies to determine the density, viscosity, thermal expansion, and compressibility of silicate melts, based on a central theme of the structural relaxation phenomenon and its use to calculate the physical properties of a melt, for example, using calorimetry data to calculate viscosity, volume, and thermal expansion in silicate melts at temperatures 50 K above the glass transition. This results in the determination of melt properties at conditions of direct geological interest, for example, the densities of granitic melts at 1050 K and viscosities of 109–1012 Pa s; observations of anomalously low, non-Newtonian viscosities and compressibilities in melts at conditions of high strain rate; the viscosities of volatile-bearing melts; and the viscosity of the melt phase in natural crystal- and bubble-bearing obsidians.

The thermal expansion of the zeolites MFI, AFI, DOH, DDR, and MTN in their calcined and as synthesized forms

Abstract: The thermal expansion coefficients of the silica zeolites MFI, DOH, DDR, and MTN and of the alumophosphate AFI were determined using the X-ray Guinier technique. At low temperatures the as synthesized microporous materials show positive volume expansion coefficients of the order of magnitude of 10·10−6K−1 which are in the expected range for silicates or phosphates. After calcination the thermal expansion of these materials is positive below the displacive phase transitions to their high symmetry forms. The high temperature phases, however, contract with increasing temperature. Their volume expansion coefficients are negative and in the order of −10·10−6K−1.

Thermoelastic equation of state of jadeite NaAlSi2O6: An energy‐dispersive Reitveld Refinement Study of low symmetry and multiple phases diffraction

Abstract: We report the first measurement of a complete set of thermoelastic equation of state of a clinopyroxene mineral. We have conducted an in situ synchrotron x-ray diffraction study of jadeite at simultaneous high pressures and high temperatures. A modified Rietveld profile refinement program has been applied to refine the diffraction spectra of low symmetry and multiple phases observed in energy dispersive mode. Unit cell volumes, measured up to 8.2 GPa and 1280 K, are fitted to a modified high-temperature Birch-Murnaghan equation of state. The derived thermoelastic parameters of the jadeite are: bulk modulus K=125 GPa with assumed pressure derivative of bulk modulus K′ = ∂K/∂P = 5.0, temperature derivative of bulk modulus , and volumetric thermal expansivity α = a + bT with values of a=2.56×10−5K−1 and b=0.26x10−8 K−2. We also derived thermal Gruneisen parameter γth=1.06 for ambient conditions; Anderson-Gruneisen parameter δTo=5.02, and pressure derivative of thermal expansion ∂α/∂P = −1.06×10−6 K−1 GPa−1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at five constant pressures of 1.0, 2.5, 4.0, 5.5, and 7.5 GPa are calculated. The derived pressure dependence of thermal expansion is: Δα/ΔP = −0.97×10−6K−1GPa−1, in good agreement with the thermodynamic relations.

Elastic constants and thermal expansion of single crystal γ-TiAl from 300 to 750 K

Abstract: The six independent elastic constants of a γ -TiAl (Ti 44 Al 56 ) single crystal have been measured for the first time from room temperature to 750 K using a resonant ultrasound spectroscopy technique. The values of C 12 and C 13 are virtually temperature independent, whereas C 11 , C 33 , C 44 , and C 66 decrease between 6 and 9% from 300 to 750 K. The two independent linear thermal expansion coefficients α 1 (along [100] direction) and α 2 (along [001] direction) of single crystal γ -TiAl have been measured from 4 to 750 K using two different apparatus. The elastic constants have been corrected for the effect of thermal expansion, and the corrected C ij have been used to calculate the Young's and shear moduli along various crystal directions. The elastic constants and moduli values have also been extrapolated to 1273 K. Finally, the elastic anisotropy has also been calculated as a function of temperature.

Thermal expansion responses of pressure infiltrated SiC/Al metal-matrix composites

Abstract: Aluminium-matrix composites containing thermally oxidized and unoxidized SiC particles featuring four average particle diameters ranging from 3 to 40 μm were produced by vacuum assisted high pressure infiltration. Their thermal expansion coefficient (CTE) was measured between 25 and 500°C. Oxidation of the SiC particles in air produces the formation at their surface of silicon oxide in quantities sufficient to bond the particles together, and confer strength to preforms. After infiltration with pure aluminium, the composites produced showed no sign of significant interfacial reaction. The CTE of the composite reinforced with unoxidized SiC particles featured an abrupt upward deviation upon heat-up near 200°C, and a second abrupt decrease near 400°C. The first transition is attributed to an inversion of stress across particle contact points. When composites are produced with oxidized SiC particles, these two transitions were removed, their CTE varying smoothly and gradually from the lower elastic bound to the upper elastic bound as temperature increases. With both composite types, the CTE decreased as the average particle size decreased. This work illustrates the benefits of three-dimensional reinforcement continuity for the production of low-CTE metal matrix composites, and shows a simple method for producing such composites.

Compatibility of alkaline earth metal (Mg, Ca, Sr)-doped lanthanum chromites as separators in planar-type high-temperature solid oxide fuel cells

Abstract: The mechanical, electrical and thermal properties of alkaline earth metal (Mg, Ca and Sr)-doped LaCrO3 have been examined as separators in planar-type high-temperature solid oxide fuel cells. The maximum three-point bending strength at 1000°C in air was measured and found to be 186 MPa for LaCr0.9Mg0.1O3, 36 MPa for La0.9Ca0.1CrO3 and 77 MPa for La0.9Sr0.1CrO3. The La0.8Sr0.2CrO3 separator placed in both an oxidizing and a reducing environment at 1000°C showed almost the same electrical conductivities of the H2 atmosphere, and the conductivity was independent of sample thickness in the range 0.5–3.0 mm. For all the doped LaCrO3 perovskites, a difference between the thermal expansion behaviours of air and the H2 atmosphere was observed. In particular, the thermal expansion slope for the first heating cycle under the H2 atmosphere showed a marked change. The volume changes were due to the formation of oxygen defects in the perovskite structure.

Preparation and characterization of Pr1-xSrxMnO3 ± δ (x = 0, 0.15, 0.3, 0.4, 0.5) as a potential SOFC cathode material operating at intermediate temperatures (500–700 °C)

Abstract: The crystal structure, thermal expansion and electrical conductivity of Sr-doped praseodymium manganites (Pr1-xSrxMnO3 ± δ where x = 0, 0.15, 0.3, 0.4, 0.5) were studied in air, and their potential use as cathodes in intermediate temperature SOFCs was evaluated. All compositions have an orthorhombic perovskite-type structure (Pbnm space group). The lattice parameters were determined at room temperature by X-ray powder diffraction. The thermal expansion is almost linear for compositions with x≥0.15. The electrical conductivity can be described by the small polaron hopping conductivity model. The conductivity increases with temperature for all compositions. Both the thermal expansion coefficient (TEC) and the electrical conductivity increase with increasing Sr content, while the activation energy decreases. The low values of the calculated activation energies are in agreement with the small polaron hopping mechanism. Among the compositions studied, Pr0.5Sr0.5MnO3±δ, with a TEC value of 12.2 × 10−6 cm (cm °C)−1 and a conductivity value of 226 S cm−1 at 500 ° C, seems to be the most promising material that can function as cathode in the intermediate temperature SOFC.

Thermal expansion of mgsio3 and fesio3 ortho- and clinopyroxenes

Abstract: Unit-cell parameters of synthetic (Mg,Fe)SiO3 ortho- and clinopyroxenes were determined at regular intervals in the temperature range 293‐1094 K using powder X-ray diffraction techniques. Volume thermal expansion coefficients calculated from these data show that orthopyroxenes expand faster than clinopyroxenes (i.e., aopx .a cpx), irrespective of their composition along the MgSiO3-FeSiO3 join. For both ortho- and clinopyroxenes, exceeds . Axial thermal expansion coefficients calculated for each of the pyaa MgSiO FeSiO 33 roxene phases studied here are a complex function of the changes in structure at high temperature. Thermodynamic calculations of the position of the phase boundary between MgSiO3 ortho- and clinopyroxene show excellent agreement with the experimentally reversed boundary.

The Effect of Compositional Tailoring on the Thermal Expansion and Tribological Properties of PS300: A Solid Lubricant Composite Coating

Abstract: This paper describes a research program in which the goal is to alter the thermal expansion coefficient of a composite solid lubricant coating, PS300, by compositional tailoring. PS300 is a plasma sprayed coating consisting of chrome oxide, silver and barium fluoride/calcium fluoride eutectic in NiCr binder. By adjusting the composition, the thermal expansion coefficient can be altered, and hence chosen, to more closely match a selected substrate preventing coating spallation at extreme temperatures. Thermal expansion coefficients (CTE) for a variety of compositions were measured from 25 to 800 C using a commercial dilatometer. The CTE's ranged from 7.0 to 13 x lO(exp -6)/deg C depending on the binder content. Subsequent tribological testing of a modified composition indicated that friction and wear properties were relatively insensitive to compositional tailoring.