Anisotropic Thermal Expansion Coefficients Research Articles

Thermoelastic strain of the lattice plane spacings in white cast iron

White cast iron consists of the two phases ferrite and cementite. On cooling, strong thermoelastic stresses Δσij occur which-because of equilibrium conditions-have different signs in the two phases. According to the sin2ψ-law of conventional X-ray stress analysis (ψ is the angle between the reflecting lattice plane and the irradiated surface of the specimen), the corresponding thermoelastic strains Δd of the lattice plane spacings, if plotted versus sin2ψ, should yield straight lines with slopes proportional to Δσij components. The slopes observed for the two phases should, therefore, have different signs. Experimentally, the opposite was observed. It is shown that this unexpected behavior is related to the anisotropic microscopic thermal expansion coefficients of the cementite combined with anisotropic macroscopic thermal expansion coefficients of the specimen. The latter is a result of the texture of the cementite phase. This changes more or less the conventionally expected Δd(sin2ψ) curves of the two phases.

極低温用負膨張コイルボビンの開発 高強度ポリエチレン繊維／アルミナ繊維系混合強化複合材料からなるパイプの弾性率及び熱歪特性

Hybrid composite pipes reinforced with high-strength polyethylene fiber (DF) and alumina fiber (AlF) were prepared to develop the coil bobbin for stable superconducting coils. The bobbin in which the circumferential thermal strain expands with cooling and in which the circumferential Young's modulus is large would be effective for stable coils. The unidirectional hybrid composite (ADFRP) showed 0 thermal expansion coefficient when the ratio between DF and AIF volume was 5/5 in fiber direction, and its Young's modulus was larger than that of DF reinforced plastic (DFRP) both in parallel and perpendicular to fiber direction. The circumferential and longitudinal Young's moduli of ADFRP pipe were larger than those of DFRP pipe. The average value of inner and outer circumferential thermal strains with cooling down showed 0 with a filament winding (FW) angle of 90deg when the ratio between DF and AIF volume (D/A) was 5/5. When D/A equals 5/5, the calculated thermal strain with cooling of the pipe showed good agreement with the average of observed inner and outer thermal strains. The circumferential thermal strain showed an expansion with a FW angle of 50-90deg, and an absolute value was smaller than those of DFRP. The inner and outer circumferential thermal strains were different. The difference decreased with an increase of the ratio inner diameter/thickness, and the differences were smaller than those of DFRP with a decrease of the degree of anisotropy of thermal expansion coefficients in UD-FRP. The experimental data were obtained to make it possible to devise a coil bobbin with negative thermal expansion coefficient by ADFRP.

Toughness and thermal shock resistance of YBa 2Cu 3O 7− x composite superconductors containing Y 2BaCuO 5 or Ag particles

Macroscopic toughness measurements and the Vickers indentation technique have been used to characterise sintered or melt-textured superconducting YBa 2Cu 3O 7− x ceramics. A newly developed thermal shock resistance parameter, based on the Vickers indentation technique, has been used. The crack propagation mechanisms observed in sintered ceramics have been analysed with respect to residual stress fields due to the anisotropy in thermal expansion coefficients, or to the difference with that of the Y 2BaCuO 5 (‘211’) inclusions. The addition of the ‘211’ brittle phase does not increase the toughness and thermal shock resistance of sintered ceramics, but toughens the textured materials. An enhancement of the thermal shock resistance, through an increased R-curve behaviour, has been achieved by introducing a metallic silver ductile phase into the microstructure, both in sintered and textured ceramics. The evaluation of the latter needed the extension of the thermal shock resistance parameter to the case of Palmqvist indentation cracks. Parallelly, a modelling of the thermal shock behaviour of textured ceramics is proposed through the description of the microstructure as a stacking of YBa 2Cu 3O 7− x layers cracked along the (001) planes, joined by Y 2BaCuO 5 particles, corresponding to a low-stiffness material.

Analyses of thermal expansion behavior of intergranular two-phase composites

Both analytical modeling and numerical simulations were performed to analyze residual thermal stresses and coefficients of thermal expansion (CTEs) of intergranular two-phase composites in a two-dimensional sense. A composite-circle model was adopted for analytical modeling. Model microstructures consisting of square-array, hexagon-array, and brick wall-array of grains with an intergranular phase as well as an actual microstructure of random-array grains with an intergranular phase were adopted for numerical simulations. The results showed that in predicting CTEs, the simple analytical model represents the two-dimensional composite well except that with brick wall-array grains, which induced significant anisotropic CTEs in the composite. The residual thermal stresses in composites were also discussed.

Thermal expansion coefficients of Mo-Si compounds by first-principles calculations

Taking Mo-Si compounds as model systems, we show that the coefficients of thermal expansion (CTEs) of complex structures can be calculated precisely from first principles by incorporating the Debye model for acoustic response. Specifically, we obtain a nearly isotropic CTE in MoSi2 but a highly anisotropic CTE in Mo5Si3. The CTE anisotropy in Mo5Si3 is due to an elastically more rigid basal plane and a higher anharmonicity along the c axis. As the structure of 5-3 compounds is modified from D8m to D8l by boron substitutions (Mo5SiB2), we predict a significant decrease in the CTE anisotropy, which is confirmed by experiments.

Physical weathering of marbles caused by anisotropic thermal expansion

Marbles as building stones as well as in their natural environments show complex weathering phenomena. The most important damage scenario is based on the highly anisotropic thermal expansion coefficient α of calcite, i.e. extreme expansion parallel and contraction normal to the crystallographic c-axis. Therefore, the rock fabric and especially the lattice-preferred orientation (texture) of calcite and/or dolomite as the predominant mineral phases in marbles have a significant influence on the mechanical weathering. The textures of marbles from five different locations vary from a more or less perfect prolate to moderate oblate shape of the [006] pole figure tensor. Accordingly, the texture-derived bulk thermal dilatation anisotropy covers a broad range from –0.048 to 0.680. The modelled thermal dilatations correlate with those obtained from experimental measurements. The difference in magnitude is basically explained by the microcrack fabrics which was not considered in the computations. All samples show a deterioration due to thermal treatment regardless of the strength of texture. The directional dependence of (a) the total magnitude of the thermal dilatation coefficient and (b) of the residual strain is highest in marbles with a strong texture, whereas the Carrara marble with a weak texture exhibits a uniform crack formation. The progressive loss of cohesion along grain boundaries due to dilatancy may serve as an example for the initial stage of physical weathering.

Studies of Zirconium Alloy Oxide Layers Using Synchrotron Radiation

The aim of this study is the determination of the residual stress state and the analysis of the microstructure of ZrO 2 oxide layers (mainly the tetragonal to monoclinic phase ratio) formed on different zirconium alloy plates oxidized in steam at 400°C for several lengths of time, using x-ray diffraction techniques. The marked texture and the large stress and phase distribution gradients in the zirconia layer did not allow to use a conventional x-ray apparatus, especially for local analyses. These difficulties have been overcame using the French Synchrotron Radiation (SR) facility LURE (Laboratoire pour l'Utilisation du Rayonnement Electromagnetique) at Orsay, France. The distribution in the oxide layer was determined by varying both the incident angle and the wavelength of the beam. A preferential localization of the tetragonal phase close to the metal/oxyde interface was observed when comparing the x-ray diffraction peaks of the monoclinic phase (mainly (111)) to the (111) reflection of the tetragonal phase. The same type of analysis has been performed to determine the residual stresses. These studies reveal the existence of a high in plane compressive stress state in the oxide layer and a lower one in the metal. A significant effect of the composition in the metal plates was observed on the tetragonal to monoclinic phase ratio as well as on the evolution of the compressive stress level in the ZrO 2 layer with oxidation time. But these stresses are measured at room temperature and because of the anisotropy of thermal expansion coefficients, elastic constants and texture of Zr and ZrO 2 , these stresses are certainly not representative of the ones spreading out during the growth of the oxide scale. Therefore, in a first approximation a macroscopic calculation of the thermal stress has been performed, but the results obtained can not explain the stress reduction due to cooling observed elsewhere. In fact, the local stresses developing both in the metal and the oxide for particular crystallographic orientation (especially epitaxial orientations) have to be taken into account during the cooling. They may be determined using a thermoelastic self-consistent model.

Tailoring the thermal expansion anisotropy of Mo5Si3

ABSTRACTThe silicide Mo5Si3, with the W5Si3 structure, exhibits a high anisotropy of its coefficients of thermal expansion (CTEs) in the a and c directions, namely, CTE(c)/CTE(a)=2.2. In order to determine whether the CTE anisotropy can be controlled, molybdenum was partially substituted with Nb. CTEs were determined by high temperature x-ray powder diffraction. Partial substitution with 44 at. % Nb reduced the value of CTE(c)/CTE(a) to a value near 1. For higher Nb concentrations, CTE(c)/CTE(a) increased again. When nearly all the Mo was replaced by Nb, the crystal structure changed to the Cr5B3 structure type and the CTE anisotropy decreased to a value near 1. Our thermal expansion results are interpreted in terms of the site occupation of Nb, the Nb-induced increase in the interatomic spacing of the Mo atom chains along the c-direction, and the reduction in the anisotropy of the lattice anharmonicity in the a and c directions.

極低温用負膨張コイルボビンの開発 高強度ポリエチレン繊維系複合材料からなるパイプの熱歪特性

High-strength polyethylene-fiber-reinforced plastic (DFRP) pipes show different circumferential thermal strains between outer and inner surfaces with cooling. The strains were measured by means of strain gage on DFRP, glass-fiber-reinforced plastics (GFRP) and DF/GF hybrid composite (DGFRP) pipes to establish the design methodology of the coil bobbin showing negative thermal expansion coefficient in circumferential direction at the outer surface. The difference of outer and inner circumferential thermal strain decreased with increase of the ratio of inner diameter vs. thickness. The difference increased with the increase of the degree of anisotropy of thermal expansion coefficients in UD-FRP. The difference of outer and inner circumferential thermal strains was shown the largest value by DFRP, and the smallest one by GFRP. The difference was confirmed to be designed with the material parameters of UD-FRP.

X-ray diffraction study of anisotropic thermal expansion in ZrMo2O8

Temperature-dependent X-ray diffraction measurements are reported for ZrMo2O8in the trigonal phase from 80 to 925 K. The measurements reveal highly anisotropic thermal expansion coefficients with average values of −3.9 × 10−6and 52 × 10−6 K−1for theaandccell parameters, respectively.

Anisotropic plastic deformation of polycrystalline Fe 3Al during high-temperature oxidation

Anisotropic plastic deformation of polycrystalline Fe 3Al was observed during high-temperature oxidation. The direction of main plastic deformation observed in Fe 3Al, after oxidation, differs with grain orientation. This may be due to anisotropic thermal expansion coefficient of each grain in Fe 3Al substrate. Based on the experimental results, anisotropic plastic deformation of the substrate is discussed and interpreted in terms of elastic modulus and thermal expansion coefficient.

Distinctive features of the monitoring of microstructural and strength properties of ceramics

An efficient method for the evaluation and prediction of microstructural and strength properties of ceramic materials with anisotropic coefficient of linear thermal expansion of grains is described for an Al2O3 hot-pressed ceramic used as an example. We analyze the effects caused by spontaneous microcracking in the process of cooling and formation of bridges behind the crack front and affecting the strength characteristics of the ceramic. In the realization of a scheme of computer monitoring of the microstructural and strength properties of hot-pressed ceramics, we used the parameter of inhibition of grain growth and the length of the bridge span as basic parameters that can be used for the optimization of the properties of noncubic ceramics.

First principles calculations of structural and defect properties of high‐temperature intermetallics†

First principles quantum mechanical calculations based on the local‐density‐functional (LDF) theory have been used to investigate the electronic, structural, and defect properties of transition‐metal aluminides and silicides. Three examples are given to show the predictive capability of modern LDF calculation: (1) interfacial properties of two‐phase Ti‐Al alloys, (2) point defect structure of NiAl and FeAl, and (3) elastic constants and coefficient of thermal expansion (CTE) of Mo5Si3. Emphasis is placed on the effect of interfaces on the planar fault energies in Ti‐Al, the interaction between vacancies in B2 aluminides, and the interplay between bonding and the anisotropy in CTE in Mo5Si3. We show that first principles calculation not only yields results in excellent agreement with experiments (if available), but offers information on electronic structure from which a clearer understanding of atomic‐level interactions that govern alloy behavior can be made.

Thickness dependence of the anisotropy in thermal expansion of PMDA-ODA and BPDA-PDA thin films

The thickness dependence of the anisotropy in thermal expansion of poly(pyromellitic dianhydride oxydianiline) (PMDA-ODA) with flexible chains and poly(biphenylene tetracarboxylic dianhydride p-phenylene diamine) (BPDA-PDA) ranging from 2.5 to 20 μm has been investigated. The lateral (in-plane) coefficient of thermal expansion (CTE) of PMDA-ODA and BPDA-PDA increases with increasing film thickness; in contrast, the vertical (out-of-plane) CTE of PMDA-ODA and BPDA-PDA decreases with increasing film thickness. The vertical CTE of PMDA-PDA is 4–7 times larger than the lateral CTE. The vertical CTE of BPDA-PDA is 14–20 times larger than the lateral CTE. It is believed that the thickness dependence of the anisotropy in CTE is caused by the in-plane orientation of the polyimide main chain. Since BPDA-PDA has a rigid-rod-like structure, this leads to a better in-plane orientation and a larger anisotropy in CTE than PMDA-ODA.

Phase stability, bonding mechanism, and elastic constants of Mo 5Si 3 by first-principles calculation

We present results of first-principles local-density-functional calculations of the structural and elastic properties of Mo 5Si 3. Among the three different structures (D8 m, D8 8, and D8 l ), the D8 m structure (referred to as the T1 phase) has the greatest binding with a high heat of formation of −3.8 eV/formula unit. The bonding in Mo 5Si 3 is found to have pronounced covalent components, characterized by the planar Mo–Si–Mo triangular bonding units on the (001) plane and by the unusually short Mo–Mo bonds directly along the c-axis. The calculated six elastic constants of the D8 m structure are in excellent agreement with the experimental values. While the bonding in the (001) basal plane is stronger than the bonding along the [001] direction (i.e. C 11+ C 12> C 33 and C 66> C 44), the crystal anharmonicity is found to be higher along the [001] direction. The implication of our results on the anisotropy of thermal expansion coefficients is briefly discussed.

Magnetic Field Orientation of Liquid Crystalline Epoxy Thermosets.

The effect of magnetic fields on the orientation and properties of 4,4'-bis(2,3-epoxypropoxy)-alpha-methylstilbene cured with sulfanilamide has been studied. This epoxy system is initially isotropic and forms a smectic A phase upon curing. A magnetic field was applied during the cure reaction, resulting in alignment of the molecules along the direction of the applied field. Measurement of the orientation parameter of the fully cured material by wide-angle X-ray scattering (WAXS) showed that orientation improved with an increase in field strength. The orientation parameters of the smectic layer normals calculated from the inner reflection of the WAXS pattern attained a maximum level of approximately 0.8 at a field strength of approximately 12 T. The orientation parameters calculated from the outer reflection of the WAXS pattern were considerably lower, possibly due to the presence of amorphous regions associated with domain boundaries or the loss of molecular alignment within the smectic layers due to topological restrictions of the cross-linking sites. Orientation resulted in an anisotropic linear thermal expansion coefficient after curing, although the overall volumetric expansion was constant. The elastic tensile modulus increased with the square of the orientation parameter, attaining a maximum value of 8.1 GPa, compared to 3.1 GPa for the unoriented material. The change in modulus with orientation could be fit with a simple model for the modulus of anisotropic materials.

A process-structure-property study of anisotropic PMDA-ODA films

A practical methodology for the correlation and prediction of the process–property performance of advanced materials is developed. The model polymer studied is PMDA-ODA polyimide. The connecting link between the process and the properties is the structural state of the polymer. An essential ingredient for a quantitative characterization of the system is a knowledge of its phase state and intrinsic molecular properties. The intrinsic molecular properties define the limiting performance properties available to the polymer. Anisotropic films and sheets produced by five different fabrication processes are examined. Maps of the molecular symmetry axis, the orientation function, and the thickness distributions of two 50-in.-wide sheets fabricated differently are measured nondestructively for process comparison. Four other film fabrication processes are examined and their three-dimensional orientation states determined and correlated. A three-dimensional orientation function triangular plot permits simultaneous representation of the different fabrication processes on the same figure and allows the investigator to choose the most economic and efficient fabrication route. The structure–property study includes the structural correlation and intrinsic molecular property determination of the anisotropic coefficient of thermal expansion (CTE), the anisotropic mechanical moduli and compliances, and the anisotropic dielectric constants. 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 777–788, 1997

On the thermal problem for composite beams using a finite element semi-discretisation

Abstract The paper deals with steady state thermo-elastic problems in beam-like structures and it is composed of three theoretical sections. The first part presents a two-dimensional finite element procedure to compute the temperature distribution within a beam cross section subjected to prescribed boundary conditions. It allows the beam cross section to be modelled taking into account any kind of thermal anisotropy or inhomogeneity. The second part is devoted to the structural thermo-elastic problem in a beam having arbitrary non-homogeneous, anisotropic material properties over the cross section but constant along the axis; the extension of a well-known semi-discretisation procedure to take into account anisotropic thermal expansion coefficients is presented. In this way it is possible to compute strains and stresses related to temperature distributions on the cross section computed, using the method outlined in the first part of the paper. The third part describes the procedure to evaluate thermal equivalent loads suitable for a three dimensional frame analysis. Some examples are presented and the results are compared either with their theoretical counterparts or with numerical results obtained from a full three-dimensional finite element analysis.

An ultrasonic and thermal expansion study of the quasi-one-dimensional compound

We report ultrasonic and thermal expansion measurements on quasi-one-dimensional . The elastic constant exhibits strong anomalies over a wide temperature range around the Peierls transition. Anisotropic behaviour of the slow shear mode propagating along and perpendicular to the chain direction is observed around . Elastic constants, like electrical resistance, are very sensitive to a small Nb content substituted for Ta. Anomalous behaviour of at low temperatures is reported. We also present measurements of the anisotropic thermal expansion coefficients.

Grain Size Dependence of the Martensitic Transformation of Yttria Doped Tetragonal Zirconia Polycrystals

The influences of the particle size and grain size on the phase stability were studied on powder specimens of Y-TZP. The phase stability estimated from the A s and M s did not appreciably change with particle size, but significantly decreased for the coarse grained powders. The latter was attributed to the incipient phase separation introduced during the annealing for the grain coarsening. A probable stress due to the anisotropic thermal expansion coefficient did not appear to influence the transformation temperatures of the present specimens. A few other minor effects caused by the particle size and grain size are discussed.