Positive Coefficient Of Thermal Expansion Research Articles

Analytical Solutions to Estimate the Temperature Sensitivity of Arrayed Waveguide Gratings With Stress Plates

Controlling thermal stress is a promising way to reduce the temperature instability of arrayed waveguide gratings (AWGs). A simple method to apply thermal stress is to attach stress plates on the arrayed waveguides. In this paper, a general analytical method to study the temperature sensitivity of the central wavelength in modified AWGs with stress plates is developed. The complete analysis shows that the temperature sensitivity can be controlled effectively by tuning the material parameters and the thickness of the stress plates. To obtain athermal AWGs, a stress plate with large positive thermal expansion coefficient and small Young's modulus should be attached on the bottom of the arrayed waveguides. The material with large negative thermal expansion coefficient suggests another potential scheme.

Thermal expansion of Cr 2xFe 2−2xMo 3O 12, Al 2xFe 2−2xMo 3O 12 and Al 2xCr 2−2xMo 3O 12 solid solutions

The transition temperature from monoclinic to orthorhombic and the thermal expansion of the orthorhombic phase were investigated for three systems of the family A 2M 3O 12: Cr 2 x Fe 2−2 x Mo 3O 12, Al 2 x Fe 2−2 x Mo 3O 12 and Al 2 x Cr 2−2 x Mo 3O 12. It was possible to obtain a single-phase solid solution in all studied samples ( x=0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1). A linear relationship between the transition temperature and the fraction of A 3 + cations ( x) was observed for each system. In all orthorhombic solid solutions studied here the observed thermal expansion was anisotropic. These anisotropic thermal expansion properties of crystallographic axes a , b and c result in a low positive or near-zero overall linear coefficient of thermal expansion ( α l= α V /3). The relationship between the size of A 3 + cations in A 2M 3O 12 and the coefficient of thermal expansion is discussed. Near-zero thermal expansion of Cr 2Mo 3O 12 is explained by the behavior of Cr–O and Mo–O bond distances, Cr–Mo non-bond distances and Cr–O–Mo bond angles with increasing temperature, estimated by Rietveld analysis of synchrotron X-ray powder diffraction data.

Structures, Thermal Expansion Properties and Phase Transitions of ErxFe2‐x(MoO4)3 (0.0 ≤ x ≤ 2.0).

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Structures, thermal expansion properties and phase transitions of Er xFe 2− x(MoO 4) 3 (0.0 ≤ x ≤ 2.0)

Structures, thermal expansion properties and phase transitions of Er x Fe 2− x (MoO 4) 3 (0.0 ≤ x ≤ 2.0) have been investigated by X-ray diffraction and differential thermal analysis. The partial substitution of Er 3+ for Fe 3+ induces pronounced decreases in the phase transition temperature from monoclinic to orthorhombic structure. Rietveld analysis of the XRD data shows that both the monoclinic and orthorhombic Fe 2(MoO 4) 3, as well as the orthorhombic Er x Fe 2− x (MoO 4) 3 ( x ≤ 0.8) have positive thermal expansion coefficients. However, the linear thermal expansion coefficients of Er x Fe 2− x (MoO 4) 3 ( x = 0.6–2.0) decrease with increasing content of Er 3+ and for x ≥ 1.0, compounds Er x Fe 2− x (MoO 4) 3 show negative thermal expansion properties. Attempts for making zero thermal expansion coefficient materials result in that very low negative thermal expansion coefficient of −0.60 × 10 −6/°C in Er 1.0Fe 1.0(MoO 4) 3 is observed in the temperature range of 180–400 °C, and zero thermal expansion is observed in Er 0.8Fe 1.2(MoO 4) 3 in the temperature range of 350–450 °C. In addition, anisotropic thermal expansions are found for all the orthorhombic Er x Fe 2− x (MoO 4) 3 compounds, with negative thermal expansion coefficients along the a axes.

Connected Triangles Exhibiting Negative Poisson's Ratios and Negative Thermal Expansion

Materials normally get thinner when stretched (positive Poisson’s ratio) and expand when heated (positive thermal expansion coefficients). However, not all systems behave in this way and systems (materials or structures) which defy common expectation and become wider when stretched (negative Poisson’s ratios, NPR, commonly referred to as auxetic) or contract when heated (negative thermal expansion, NTE) do exist and are now well documented. Materials exhibiting one of these unusual properties are known to be very useful in various practical applications. For example it has been shown that the presence of a negative Poisson’s ratio gives auxetic materials various enhanced physical characteristics over their conventional counterparts ranging from increased indentation resistance and a natural ability to form dome-shaped surfaces to improved acoustic damping properties. Similarly, negative thermal expansion materials can be extremely useful in various applications, such as in the manufacture of composites exhibiting some pre-determined thermal expansion coefficients since the presence of a component with negative thermal expansion lowers the overall thermal expansion of a composite. Although in recent years considerable progress and developments were made in the distinct fields of NPR and NTE, so far, research on systems which could exhibit both of these anomalous properties simultaneously is still in its infancy. Nevertheless, it is known that NTE and NPR are not mutually exclusive properties and in fact, single-crystalline polyacetylene networks (hypothetical carbon allotropes, which so far have not been synthesised) have been predicted to exhibit both properties. Here we will show how existing knowledge on systems exhibiting negative Poisson’s ratios and negative thermal expansion can be combined to produce a novel and easily constructible system which can exhibit both negative properties simultaneously. In particular, we note that as we have recently shown, the construct made from beams connected as illustrated in Fig. 1(a) can exhibit NPR since when it is uniaxially stretched, the beams will flex as illustrated in Fig. 1(b) with the net effect that the triangles rotate relative to each other to produce a more open structure (the ‘‘rotating triangles’’ effect, resulting in negative Poisson’s ratios of 1 in-plane if the triangles are equilateral. In such systems, the straight beams of length 2l can either be welded together or connected through the use of ‘‘pin joint’’-type connections at ends and centres of the beams (corresponding to the vertices of the triangles) where the axes of the ‘‘pin joints’’ are orthogonal to the plane of the structure. The use of such ‘‘pin joints’’ is possible since the formation of the triangles reduces the degrees of freedom of the system and give the structure its characteristic shear rigidity. The presence of these triangles also provide us with a route for turning this auxetic structure into one which can also exhibit negative thermal expansion since as recently proposed, equilateral triangles constructed in such a way that their base is made from a material with a thermal expansion coefficient being at least four times that of the other two sides will get shorter when heated (the ‘‘shortening of triangles’’ mechanism). In fact, it has been shown that dh, the change in height h when the equilateral triangle in Fig. 2 is subjected to a temperature change dT is given by:

Simultaneous measurement of bending and temperature based on a single sampled chirped fiber Bragg grating embedded on a flexible cantilever beam

We propose and experimentally demonstrate a simple and practical scheme for simultaneous measurement of bending and temperature based on a single sampled chirped fiber Bragg grating with multiple resonant peaks, which is embedded on a flexible cantilever beam. The wavelength spacing of the grating can be changed by adjusting the bending curvature change, since the compressive strain gradient induced by the bending of the cantilever beam changes the chirp ratio of the fiber grating. However, the wavelength spacing of the fiber grating is not changed by the temperature variation; the multiple resonant wavelengths are only shifted into the longer wavelength because of the positive thermal-expansion and thermo-optic coefficients of the fiber grating. Consequently, the proposed scheme allows for discrimination between two effects of bending and temperature.

Influence of Nitride on Sinterability of the Composite of Lithium Aluminum Silicate and Silicon Carbide

Ceramics with zero thermal expansion coefficients at room temperature (293K) were investigated. We found the thermal expansion coefficient was controlled by a compounding ratio of lithium aluminum silicate (LAS) and silicon carbide (SiC), which have negative and positive thermal expansion coefficients respectively. Although it was difficult to densify the composite of the LAS and SiC (LAS/SiC) in the sintering process, an addition of nitride improved the sinterability of the LAS/SiC. In order to examine the effect of the nitride additive, at first, the melting point of the LAS with silicon nitride (Si3N4) or aluminum nitride was measured by TG-DTA. The melting point of the LAS decreased with existence of nitride. It is believed that the densification of the LAS/SiC was promoted by the nitride, because the nitride causes the LAS/SiC to form a liquid phase, thereby decreasing the melting point. Next, the lattice constant of the LAS with Si3N4 was measured by XRD and it was verified that the a-axis was longer and the c-axis was shorter than those of the LAS without additive. It is supposed that this phenomenon is due to the substitution of nitrogen for oxygen in the LAS lattice, and the decrease of the melting point of the LAS with nitride seems to be influenced by this substitution of nitrogen.

Tunable Linear Thermal Expansion Coefficient of Amorphous Zirconium Tungstate

Zirconium tungstate (α‐ZrW2O8) exhibits isotropic negative thermal expansion over a wide range of temperatures. Under high pressure it transforms to a metastable amorphous phase with positive thermal expansion coefficient. α‐ZrW2O8 can be fully recovered by annealing the amorphous phase at temperatures slightly above 600°C, at room pressure. In this work, we describe the dependency of the linear thermal expansion coefficient of amorphous ZrW2O8 with the annealing temperature, showing that it can be continuously tuned, in two stages, from about 7.5° to −9°C−1. These two stages are related to the relaxation of the amorphous phase and the onset of recrystallization, respectively.

Search for a novel zero thermal expansion material: dilatometry of the AgI-CuI system

AgI is a well-known superionic conductor possessing a negative thermal expansion (NTE) coefficient while CuI is a p-type semiconductor possessing a positive thermal expansion coefficient. Pellets of X-Ray Diffraction (XRD) characterized compositions in the AgI–CuI system namely, β AgI, γ AgI, Ag0.5Cu0.5I, Ag0.25Cu0.75I, Ag0.10Cu0.90I, Ag0.05Cu0.95I and γ CuI have been examined by quartz pushrod dilatometry measurements in order to look for a zero thermal expansion material. It is found that the systematic displacement of Ag by Cu gradually reduces the NTE anomaly in AgI. The composition Ag0.25Cu0.75I apparently exhibits near-zero thermal expansion. The results are discussed qualitatively in terms of relevant models.

Negative thermal expansion in silicalite-1 and zirconium silicalite-1 having MFI structure

In situ high temperature X-ray diffraction (HTXRD) studies on monoclinic silicalite-1 (S-1, silica polymorph of ZSM-5) and an orthorhombic metallosilicate molecular sieve, zirconium silicalite-1 (ZrS-1) with MFI structure (Si/Zr=50) have been carried out using a laboratory X-ray diffractometer with an Anton Parr HTK 1600 attachment. While the structure of the S-1 collapsed at 1123K forming α-cristobalite. S-1 and ZrS-1 showed a complex thermal expansion behavior in the temperature range 298–1023K, ZrS-1 was stable. Powder X-ray diffraction (PXRD) data taken in this region have shown strong negative lattice thermal expansion coefficient, αV=−6.75×10−6 and −17.92×10−6K−1 in the temperature range 298–1023K−1 for S-1 and ZrS-1 samples, respectively. The thermal expansion behavior of S-1 and ZrS-1 is anisotropic, with the relative strength of contraction along a axis is more than that along b and c axes. Three different thermal expansion regions could be identified in the overall temperature range (298–1023K) studied, corroborating with the three steps of weight loss in the TG curve of ZrS-1 sample. While the region between 298 and 423K, displays positive thermal expansion coefficient with αV=2.647×10−6 and 4.24×10−6K−1, the second region between 423 and 873K shows strong negative thermal expansion (NTE) coefficient αV=−7.602×10−6 and −15.04×10−6K−1, respectively, for S-1 and ZrS-1 samples. The region between 873 and 1023K, shows a very strong NTE coefficient with αV=−12.08×10−6 and −45.622×10−6K−1 for S-1 and ZrS-1, respectively, which is the highest in the whole temperature range studied. NTE seen over a temperature range 298–1023K could be associated with transverse vibrations of bridging oxygen atoms in the structure which results in an apparent shortening of the Si–O distances.

Thermal Expansion of Electrodeposited Nanoscale Multilayers of Invar with Copper

Nanoscaled, compositionally modulated multilayer alloys of NiFe in the Invar range and Cu were electroplated into an array of cylindrical microrecesses in polymethylmethacrylate 100 μm in diameter, 100 μm tall, with a center-to-center spacing of 300 μm. Deposition conditions were determined using a rotating Hull cell and linear sweep voltammetry. The presence of the nanoscale multilayers was confirmed by transmission electron microscopy and the thermal expansion of the multilayer microposts was measured over the range from 25 to 300°C. As deposited, the multilayer alloy exhibited a negative coefficient of thermal expansion (CTE); for a 4.5 nm thick Cu layer the CTE was -3.28 μm/m-°C up to 150°C and more negative for higher temperatures. To the best of the authors' knowledge this is the first observation of a room temperature, negative CTE in multilayered-Invar alloys. After thermal cycling, the alloy had a small positive CTE of 1.75 μm/m-°C up to 175°C, comparable to that of bulk Invar (1.00 μm/m-°C), and no increase of the CTE was observed for temperatures up to 275°C.

Diameter-depended thermal expansion properties of Bi nanowire arrays

The lattice parameter of bismuth nanowires has been measured using the in situ high-temperature x-ray diffraction method. Single-crystalline Bi nanowire arrays with the diameters from 10nmto250nm have been fabricated within the porous anodic alumina membranes by a pulsed electrodeposition technique. Different temperature dependencies of lattice parameter and thermal expansion coefficient were found for Bi nanowires with different diameters, and there is a transition from positive thermal expansion coefficient at low temperature to negative one at high temperature, and the transition temperature shifts to high temperature with the increase in the diameter of Bi nanowires.

Thermal vibration of the rutile-type difluorides of first-row transition metals

The rutile-type structure is found in many dioxides. The rutile samples in this study, difluorides of the first-row transition-metals, MF2 (M = Mn, Fe, Co, Ni), are important materials from the view point of electronic and magnetic properties. Although almost rutile-type difluorides have the positive thermal expansion coefficient, FeF2 has a negative thermal expansion coefficient along the c axis in the high temperature region. In this study, we could obtain a detailed information about the thermal vibration of atoms by the analysis of EXAFS Debye–Waller factors. We discuss on the atomic momentum in the local structure of the difluorides. The EXAFS Debye–Waller factor is sensitive to short-range correlation of mutual atomic motions.The displacement correlation functions (DCF) for each neighbor atom were determined by using both the mean square relative displacement (MSRD) and the mean square displacement (MSD) by x-ray diffraction. It was proved that DCF/MSD in the second-nearest neighbor atoms of FeF2 is small, compared with other difluorides. This result suggests that in FeF2, the correlation between second-nearest neighbor atoms (Fe-Fe) is weak. Furthermore, we could estimate the force constant between absorbing and scattering atoms from the temperature dependence of EXAFS Debye–Waller factor. The value of the force constant suggests that in FeF6 octahedron in FeF2, two apical bonds are stronger than four equatorial bonds.

Zero Thermal Expansion in YbGaGe due to an Electronic Valence Transition.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Zero thermal expansion in YbGaGe due to an electronic valence transition.

Most materials expand upon heating. Although rare, some materials expand on cooling, and are said to exhibit negative thermal expansion (NTE); but the property is exhibited in only one crystallographic direction. Such materials include silicon and germanium at very low temperature (<100 K) and, at room temperature, glasses in the titania-silica family, Kevlar, carbon fibres, anisotropic Invar Fe-Ni alloys, ZrW2O3 (ref. 4) and certain molecular networks. NTE materials can be combined with materials demonstrating a positive thermal expansion coefficient to fabricate composites exhibiting an overall zero thermal expansion (ZTE). ZTE materials are useful because they do not undergo thermal shock on rapid heating or cooling. The need for such composites could be avoided if ZTE materials were available in a pure form. Here we show that an electrically conductive intermetallic compound, YbGaGe, can exhibit nearly ZTE--that is, negligible volume change between 100 and 400 K. We suggest that this response is due to a temperature-induced valence transition in the Yb atoms. ZTE materials are desirable to prevent or reduce resulting strain or internal stresses in systems subject to large temperature fluctuations, such as in space applications and thermomechanical actuators.

Anharmonicity in mineral physics: A physical interpretation

Mineral physicists often refer to the quasi‐harmonic approximation. This approximation accepts the intrinsically anharmonic effects of positive thermal expansion coefficient, α, and pressure‐dependent bulk modulus, KT. However, for insulators at high temperatures, the classical specific heat, CV, and the product αKT are assumed to be independent of temperature at constant volume. Departures from this approximation are termed anharmonicity. We interpret this distinction using derivatives of the atomic potential function, ϕ(r), with atomic spacing, r. CV and KT are reasonably explained by harmonic bonds, that is, ϕ ∝ (r − a)2, where a is the equilibrium value of r, so that ϕ″ = d2ϕ/dr2 is the only derivative considered. Thermal pressure or expansion and pressure dependence of KT depend on ϕ‴ (referred to as first‐order anharmonic effects). Temperature dependence of CV requires ϕiv and is a second‐order anharmonic effect. The temperature variation of αKT arises from ϕv, a third‐order effect. By calculating the Grüneisen parameter, γ, as the ratio of thermal pressure to thermal energy, we relate its anharmonicity to a ratio of derivatives of ϕ. For all commonly used finite strain theories, this gives a temperature variation of γ at high temperature and constant volume systematically less than that of CV. Anharmonicity of CV, which has been more comprehensively studied, may be a few percent at 2000 K, but decreases strongly with compression, so that anharmonicity of both γ and CV is negligible (less than 1% in the case of γ under deep‐Earth conditions).

Effects of Fiber Orientation and Elastic Constants on Coefficients of Thermal Expansion in Laminates

Effects of the fiber orientation and elastic properties of composites on the coefficient of thermal expansion (CTE) of balanced and symmetric angle-ply laminates were investigated. Criteria for achieving negative CTEs were derived for [ - / ] ns laminates. For this type of laminate, it is possible to produce negative CTEs with composites possessing positive CTEs. It was found that the ratio of the in-plane shear modulus G 12 to Young's modulus E 1 has the dominant effect on the laminate CTEs. A carbon/epoxy composite was used to demonstrate how to tailor the angle-ply laminate to maximize the magnitude of positive and negative CTEs.

Molecular dynamics study of cristobalite silica using a charge transfer three-body potential: Phase transformation and structural disorder

Structural and dynamic properties of cristobalite silica have been studied using molecular dynamics simulations based on a charge transfer three-body potential model. In this potential model, the directional covalent bonding of SiO2 is characterized by a charge transfer function of the interatomic distance between Si and O atoms, and in the form of Si–O–Si and O–Si–O three-body interactions. The dynamic properties such as infrared spectra and density of states at room and elevated temperatures are in excellent agreement with experiments, and are also consistent with the recently proposed rigid unit modes model. The α- and β-cristobalite crystallographic structures are well reproduced in this model, and the transition between these modifications occurs reversibly and reproducibly in simulations, both as a result of changes in pressure and temperature. The thermally induced transition results in a significantly more disordered β-cristobalite than the pressure-induced β-cristobalite at room temperature. While simulated α-cristobalite exhibits a positive thermal expansion coefficient, it is almost zero for β-cristobalite up to 2000 K and slightly negative at higher temperatures, confirming results from recent x-ray diffraction experiments and other simulations with potential models based on ab initio calculations.

Thermoelastic anisotropy of a natural fiber

In order to develop structure–property relationships in composite systems, it is often necessary to know the properties of the fiber and matrix constituents. Much research indicates that natural-fibers exhibit a complicated anisotropic structure. Unfortunately, the property anisotropy of most natural fibers has been left undetermined. In this study, dynamic mechanical and thermal mechanical techniques have been employed to measure the elastic and thermal expansion characteristics of a model composite system containing jute fibers over a broad temperature range. The results of these measurements were in turn incorporated into a number of pertinent micro-mechanical models to estimate the thermoelastic properties of the natural fibers. The jute fibers investigated in this study exhibited considerable elastic and thermal expansion anisotropy. The longitudinal Young’s modulus of the fibers has been determined to exceed the transverse fiber modulus by as much as an order of magnitude in certain temperature regimes. The fibers exhibit negative thermal expansion coefficients along their lengths; however, large positive thermal expansion coefficients, similar in magnitude to many polymeric materials, have been estimated in the transverse directions.

Athermal polarisation-independent arrayed- waveguide grating (AWG) multiplexer using an all-polymer approach

An athermal arrayed-waveguide grating (AWG) multiplexer relying on an all-polymer approach is reported. By properly adjusting the positive coefficient of thermal expansion of the polymer substrate and the negative thermo-optic coefficient of the polymer waveguide, athermal and polarisation-independent AWG devices are demonstrated.