Positive Coefficient Of Thermal Expansion Research Articles

Presence of water at elevated temperatures, structural transition, and thermal expansion behavior in LaPO4:Eu

We report powder neutron diffraction studies in $\mathrm{L}{\mathrm{a}}_{0.95}\mathrm{P}{\mathrm{O}}_{4}:\mathrm{E}{\mathrm{u}}_{0.05}\phantom{\rule{4pt}{0ex}}(\mathrm{LaP}{\mathrm{O}}_{4}:\mathrm{Eu})$ at various temperatures up to 1163 K. From Rietveld refinement of the diffraction data, we identify the presence of water up to 567 K and an irreversible phase transition from hexagonal to monoclinic structure around 900 K involving the coexistence of phases over 700 to 1050 K. We observe from the neutron experiments that the thermal expansion in the hexagonal phase is much smaller than that in the monoclinic phase. We have performed first-principles lattice dynamics calculations in both the phases to identify the anharmonic phonons and thereby understand the thermal expansion behavior. The low-energy translational and librational modes of $\mathrm{P}{\mathrm{O}}_{4}$ tetrahedral units in the hexagonal phase show negative thermal expansion behavior, which is responsible for the overall smaller positive thermal expansion coefficient in the hexagonal phase in comparison to that in the monoclinic phase.

Microstructured Multicore Polymer Optical Fiber Temperature-insensitive Stress Sensor

We describe a novel microstructured multicore polymer optical fiber (m-MPOF) made of PMMA with air-holes running along the entire length of the fiber. In polymer, refractive index decreases with increasing temperature, a negative thermo-optic coefficient which results in the increase of coupling with increasing temperature thus reducing the beat length and causing a blue shift in transmission nulls, but with increase in temperature the spacing between cores will also increase which results in decreases of coupling and an increases the beat length, so a red shift in transmission nulls –a positive thermal expansion coefficient. In most part of the wavelength the thermo-optic effect dominates the thermal expansion effect, but at a particular wavelength both the effects cancel each other and have a zero change in the Neff with a change in temperature. So, as a result, both these effects get nullified at certain temperature making it a temperature insensitive fiber. Numerical calculations show the fiber is temperature insensitive for a range of 40℃ to 60℃ at a wavelength of 700 nm. The fiber is shown to be sensitive to stress at 700 nm with a sensitivity of 1.6 nm/Pa, which makes the said fiber temperature insensitive stress sensor.

A new design of dual-constituent triangular lattice metamaterial with unbounded thermal expansion

Triangular lattice metamaterials composed of bi-layer curved rib elements (called the Lehman–Lakes lattice) possess unbounded thermal expansion, high stiffness and impossibility of thermal buckling, which are highly desirable in many engineering structural applications subjected to large fluctuations in temperature. However, the requirement of such lattice metamaterial is that it must be a hinged joint in order to achieve the bending deformation upon heating freely, which directly leads to poor manufacturability, especially in small dimensions. In this study, a new design of dual-constituent triangular lattice metamaterial (DTLM) with good manufacturability is proposed to achieve the identical unbounded thermal expansion. In this lattice, a special bi-layer curved rib element where layer one is partially covered by layer two is presented, where the hinge joints are not necessary because the flexural rigidity in the single-layer part is much smaller than that in the bi-layer part, and the desirable thermal bending deformation can be achieved. A sample fabricated by additive manufacturing is given in order to show the good manufacturability; simultaneously, the multifunctional performance of the tailored DTLM with zero, large positive or negative coefficient of thermal expansion (CTE) can remain excellent, as well as the Lehman–Lakes lattice. Examples illustrate that the DTLM with zero CTE has about 34.2% improvement in stiffness and meanwhile has 17% reduction in weight compared with the Lehman–Lakes lattice. The stiffness of the DTLM has a moderate reduction when achieving the same large positive or negative CTE. In addition, the thermomechanical properties of the DTLM are given by the closed-form analytical solution and their effectiveness is verified by the detailed numerical simulation.

Drastic tailorable thermal expansion chiral planar and cylindrical shell structures explored with finite element simulation

Design of materials and structures with quite low coefficient of thermal expansion (CTE), even zero or negative CTE is important for industrial application where drastic temperature changes are encountered. In this paper, making use of the bending of bi-material beam and the unique deformation mechanism of chiral lattice structures, five sets of chiral lattice composite structures with tailorable CTEs are proposed, where synergic effects of rigid node rotation and bi-material ligament bending deformation are responsible for giant range of structural deformation due to temperature change, from positive CTE to negative CTE through adjusting the geometrical parameters of composite bi-material chiral unit cell, and the relationship between unit cell geometric parameters and CTEs of the structure are studied systematically through finite element analysis. Finally, design of bi-material cylindrical shells consisting of anti-tetra chiral unit cells are proposed, and its axial CTEs with different number of the unit cells along the circumferential are studied systematically, demonstrating the robust range of CTEs can be generated through adjusting the geometrical parameters of chiral bi-material unit cells. The proposed chiral structures demonstrated promising application potentials in industrial fields, such as: aerospace and microelectronics, where extremely high structural accuracy is required during harsh working temperature environment.

Zero Thermal Expansion Polyarylamide Film with Reversible Conformational Change Structure

Interface failure due to thermal mismatch is one of the culprits that shorten life cycle of devices. In this work, we prepared a series of free-standing cross-linked polyarylamide films with tunable thermal responsive behaviors. By incorporating thermal contractile units, s-dibenzocyclooctadiene (DBCOD), which shrink as a result of thermally induced upconversion from twist boat to chair, negative, zero, and positive coefficients of thermal expansion (CTE) have been realized with the values of CTE ranging from −17.7 to 57.1 ppm/K (20–150 °C). This wide tunable CTE window allows the as-prepared cross-linked polyarylamide films to match desired thermal performance for specific applications. Zero-expansion polymer film without the need for inorganic dopants has also been obtained. Such a series of free-standing polyarylamide films with tunable thermal responses showed great potential for many practical applications.

A new design for enhanced stiffness of dual-constituent triangular lattice metamaterial with unbounded thermal expansion

Multifunctional lattice metamaterial with high stiffness and a wide range of tailorable coefficient of thermal expansion (CTE) is desirable in many engineering structural application subjected to large fluctuation in temperature. Dual-constituent triangular lattice metamaterial composed of completely bi-layer curved rib elements (called the Lehman-Lakes lattice) has unbounded thermal expansion; however, its stiffness has a substantial decrease due to the initial curvature of rib element. In this study, a new double-curve rib element is proposed, in which the two curve parts are asymmetric and the layer one is partially covered by layer two in every curve part. Then, the dual-constituent triangular chiral lattice metamaterial (DTCLM) composed of the newly designed rib elements is presented in order to improve its stiffness. When the used materials are considered to be invar and steel, compared with the Lehman-Lakes lattice, the new proposed DTCLM with zero CTE has about 2.9 times improvement in stiffness; when achieving the same large positive or negative CTE, the stiffness has also obvious improvement. Besides, the thermomechanical analysis of the new proposed DTCLM is given by the closed-form analytical solution. The effectiveness of the analytical models and the optimized results are verified by the detailed numerical simulation.

Analyzing Data on the Thermal Expansion Coefficient of Substances

The behavior of the entropy on the isotherm depends on the sign of the coefficient of thermal expansion (CTE). The boundaries of positive and negative CTEs are considered for water in the normal and supercooled state as a model for the behavior of other substances in structural transformations that ultimately ensure non-negative entropy values of matter.

Young's modulus and thermal expansion of tensioned graphene membranes

Tensioned graphene membranes are of interest both for fundamental physics and for applications ranging from water filtration to nanomechanical resonators. It is generally assumed that these membranes have a stretching modulus of about 340 N/m and a negative, temperature-independent thermal expansion coefficient due to transverse phonon modes. In this paper, we study the two-dimensional Young's modulus and thermal expansion of graphene as functions of temperature by using laser interferometry to detect the static displacement of the membrane in a cryostat. Surprisingly, we find that the modulus decreases strongly with increasing temperature, which leads to a positive temperature-dependent thermal expansion coefficient. We show that the thermally rippled membrane theory is not consistent with our data, while the effects of surface contaminants typically present on these membranes may explain the observed behavior. Our experiments undermine long-standing assumptions about tensioned two-dimensional membranes, but are consistent with puzzling behavior observed in previous experiments on graphene resonators.

A cellular metastructure incorporating coupled negative thermal expansion and negative Poisson's ratio

Current reported cellular metastructures can either achieve only tailorable thermal expansion or obtain only tunable Poisson's ratio. By contrast, here, we develop a kind of lightweight cellular metastructure which incorporates coupled tailorable thermal expansion and tunable Poisson's ratio. That is a wide range of positive, zero and especially negative values of both thermal expansion and Poisson's ratio can be simultaneously obtained. The ranges and constraints of the geometrical parameters are revealed, and the relative densities are only about 2%, indicating excellent lightweight character. Besides, analytical expressions for coefficient of thermal expansion (CTE) and Poisson's ratio (PR) are theoretically established and numerically simulated. Parameter analysis confirms that the range of tailorable CTE can be enhanced through rationally selecting large values of CTE ratio, first geometrical angle and height ratio. By adjusting the second and third geometrical angles, Poisson's ratio also can be tuned to be large negative, near zero and positive values. Particularly, the metastructure can give paired negative CTE and negative PR. Different combinations of paired characteristics including positive CTE + negative PR, positive CTE + positive PR and negative CTE + positive PR are also flexibly available. Moreover, CTE and PR are found to be highly coupled. To simultaneously obtain specific CTE and PR, design parameters should be selected with consideration of the coupling effect. The results here are expected to contribute feasibility to structures with both temperature and mechanical sensitivities.

Ultra-high-precision reflectors - design concepts, structural optimization and zero-expansion composites

The developing of satellite remote sensing technology demands high precision reflectors. This paper is devoted to the development of an ultra-high precision reflector, including the structural design and optimization, and even a kind of zero-expansion composite. A novel parabolic reflector without the traditional back surface is designed, simulated and analyzed. The relationships of some key parameters(surface error and weight) with other structural parameters are obtained. As the Kevlar fabric has negative CTE (Coefficient of Thermal Expansion) and CFRP has positive CTE, a Kevlar fabric-assisted carbon fiber composite is suggested. This composite exhibits the advantage of zero-expansion in 2D plane. Further, this zero-expansion laminate has been successfully manufactured. Finally, based on the design and analysis of the zero-expansion composite with CFRP and Kevlar fabric, an ultrahigh-precision reflector is successfully designed. The results of finite element method (FEM) show that the thermal distortion of the reflector meets the requirements of remote satellite, whose working radio frequency (RF) is 600[Formula: see text]GHz.

Thermal expansion coefficient measurement from electron diffraction of amorphous films in a TEM

We measured the linear thermal expansion coefficients of amorphous 5–30 nm thick SiN and 17 nm thick Formvar/Carbon (F/C) films using electron diffraction in a transmission electron microscope. Positive thermal expansion coefficient (TEC) was observed in SiN but negative coefficients in the F/C films. In case of amorphous carbon (aC) films, we could not measure TEC because the diffraction radii required several hours to stabilize at a fixed temperature.

Lightweight composite lattice cylindrical shells with novel character of tailorable thermal expansion

Composite lattice cylindrical shells widely utilized in aerospace engineering are susceptible to experience large temperature excursions, and generate undesirable thermal deformation. Here, we devise novel composite lattice cylindrical shells which can exclusively present a wide range of negative, positive and especially zero coefficient of thermal expansion (CTE) through structural design and rational arrangement of commonly available positive CTE composites. Theoretical analysis figures out the thermal deformation mechanism, and clearly establishes the important relationship that with adequate circumferential triangle units, the CTEs of the lattice cylindrical shells closely approach to the CTEs of the corresponding triangle and planar lattice composites. Finite element analysis firmly confirms the tailorable thermal expansion characteristics. Furthermore, in practical design of lattice cylindrical shells with commonly available composites, a wide range of tailorable thermal expansion up to −2200 to 2200 ppm/∘C, which is substantially larger than those of available engineering materials, can be easily achieved. Such wide range of CTEs and lightweight feature enable these composite lattice cylindrical shells to be potentially used in aerospace engineering.

Auxetic and Negative Thermal Expansion Structure Based on Interconnected Array of Rings and Sliding Rods

An exploration by analytical method has been made herein for a mechanism‐based structure that involves a two‐dimensional array of rings and a three‐dimensional array of double‐rings, with short fixed rods and long sliding rods attached at the outer and inner surfaces of the rings, respectively. Based on the theory of thin rings, effective Poisson's ratio and effective coefficient of thermal expansion (CTE) models have been obtained for single‐ring structures, pole‐loaded double‐ring structures, and equator‐loaded double‐ring structures. Results establish a very strong correlation between these effective properties with the ring radius and rod lengths. In addition, the analysis of four of the double‐ring structures reveals that the sign of Poisson's ratio is dependent on the direction of loading. An example application is demonstrated herein in which positive thermal expansion rings, used in conjunction with rigid rods, enable the design of an overall zero thermal expansion structure (i.e., minimal thermal stress) with tunable negative thermal expansion internal microstructure for use as sieve. Finally, it is herein shown that, by judicious positioning of the short fixed rods and/or long sliding rods, one may possibly obtain various combinations of positive and negative CTEs with positive and negative Poisson's ratio.

Three-dimensional metamaterials with a negative Poisson's ratio and a non-positive coefficient of thermal expansion

Four types of three-dimensional (3-D) metallic metamaterials with tailorable thermo-mechanical properties are designed. For the first three types, the structure-property relations are studied by adjusting design parameters including two length parameters, one angle parameter and two material combinations. For the fourth type, one additional angle parameter is involved. It is shown that each of the four types of metamaterials designed exhibits the cubic symmetry and thus needs three independent elastic constants to characterize its elastic behavior and one coefficient of thermal expansion to describe its isotropic thermal expansion. The effects of the design parameters on the effective Poisson's ratio (PR), coefficient of thermal expansion (CTE), Young's modulus, shear modulus and the relative density are systematically investigated for each of the four types of designed metamaterials by using unit cell-based finite element simulations that incorporate periodic boundary conditions. It is found that 3-D metallic metamaterials with positive, near-zero or negative PR and CTE can be obtained by tailoring the bi-material lattice structures and material combinations. Also, it is revealed that metamaterial # 1 can achieve both a negative PR and a non-positive CTE while maintaining a high stiffness and a low relative density (and thus a lightweight). The good tunability of thermo-mechanical properties of the four types of metamaterials provides an avenue of enabling the expansion of Ashby's material chart to produce more material options for engineering applications.

Effects of Al particles and thin layer on thermal expansion and conductivity of Al–Y2Mo3O12 cermets**Project supported by the National Natural Science Foundation of China (Grant Nos. 10974183 and 11104252), the Doctoral Fund of the Ministry of Education of China (Grant No. 20114101110003), the Fund for Science & Technology Innovation Team of Zhengzhou, China (Grant No. 112PCXTD337), the Industrial Science and

Low thermal expansion composites are difficult to obtain by using Al with larger positive thermal expansion coefficient (TEC) and the materials with smaller negative TECs. In this investigation, Y2Mo3O12 with larger negative TEC is used to combine with Al to obtain a low thermal expansion composite with high conductivity. The TEC of Al is reduced by 19% for a ratio Al:Y2Mo3O12 of 0.3118. When the mass ratio of Al:Y2Mo3O12 increases to 2.0000, the conductivity of the composite increases so much that a transformation from capacitance to pure resistance appears. The results suggest that Y2Mo3O12 plays a dominant role in the composite for low content of Al (presenting isolate particles), while the content of Al increases enough to contact each other, the composite presents mainly the property of Al. For the effect of high content Al, it is considered that Al is squeezed out of the cermets during the uniaxial pressure process to form a thin layer on the surface.

Tailorable Thermal Expansion of Lightweight and Robust Dual-Constituent Triangular Lattice Material

Current studies on tailoring the coefficient of thermal expansion (CTE) of materials focused on either exploring the composition of the bulk material or the design of composites which strongly depend on a few negative CTE materials or fibers. In this work, an approach to achieve a wide range of tailorable CTEs through a dual-constituent triangular lattice material is studied. Theoretical analyses explicitly reveal that through rational arrangement of commonly available positive CTE constituents, tailorable CTEs, including negative, zero, and large positive CTEs can be easily achieved. We experimentally demonstrate this approach through CTE measurements of the specimens, which were exclusively fabricated from common alloys. The triangular lattice material fabricated from positive CTE alloys is shown to yield large positive (41.6 ppm/°C), near-zero (1.9 ppm/°C), and negative (−32.9 ppm/°C) CTEs. An analysis of the collapse strength and stiffness ensures the robust mechanical properties. Moreover, hierarchal triangular lattice material is proposed, and with certain constituents, wide range of tailorable CTEs can be easily obtained through the rationally hierarchal structure design. The triangular lattice material presented here integrates tailorable CTEs, lightweight characteristic, and robust mechanical properties, and is very promising for engineering applications where precise control of thermally induced expansion is in urgently needed.

Tunable air-suspended polymer grating couplers

We present thermal tuning of air-suspended SU-8 polymer waveguide grating couplers for TE-polarized light. Numerical simulations have been performed to estimate the wavelength shift caused by the change of temperature. Due to the small positive thermal expansion and large negative thermo-optic coefficient of SU-8, a shift toward shorter wavelengths is expected. In the experimental evaluation, a negative wavelength shift from 1542 nm at 20°C toward 1527 nm at 56°C is obtained with approximately −0.42 nm K−1 matching the theoretical considerations.

Structural Contraction of Zeolitic Imidazolate Frameworks: Membrane Application on Porous Metallic Hollow Fibers for Gas Separation.

Positive thermal expansion coefficients (TECs) of 52 × 10-6 and 35 × 10-6 K-1 were experimentally calculated in the -116 to 250 °C range for the III-phases of zeolitic imidazolate frameworks (ZIF) ZIF-9(Co) and ZIF-7(Zn), respectively, by means of the unit cell dimensions and volume of the materials in the monoclinic crystal system calculated from the XRD patterns. The unit cell dimensions and volume showed a significant expansion phenomenon as the temperature increased, by as much as 5.5% for ZIF-9-III in the studied range. To exploit the advantages of such thermal behavior, a new approach to the fabrication of ZIF-9-III membranes on thin, flexible, and highly porous nickel hollow fiber (Ni HF) supports by a versatile and easy-controllable microfluidic setup is herein reported. These Ni HF supports result from the sintering of 25-μm Ni particles and display very positive mechanical properties and bending resistance. As compared to the traditional polymer-based HF membranes, the ZIF metal-supported membrane exhibited good durability and robustness throughout its operation in a wide temperature range and after heating and cooling cycles. These benefits derive from (1) the pore-plugging membrane configuration resulting from the high porosity of the support and (2) the similarity between the TECs of the ZIF and the metallic support, both positive, which enhances their mutual compatibility. An increase in the H2/CO2 separation selectivity at low temperatures (as high as 22.2 at -10 °C, along with 102 GPU permeance of H2) was achieved, in agreement with the structural variations observed in the ZIF material.

Metamaterials with negative Poisson’s ratio and non-positive thermal expansion

Four metallic metamaterials with tailorable mechanical properties are designed using bi-material star-shaped re-entrant planar lattice structures, which do not involve pins, adhesive, welding or pressure-fit joints and can be fabricated through laser-based additive manufacturing. Three length parameters, one angle parameter and three material combinations are used as adjustable design parameters to explore structure-property relations. For each of the four designed metamaterials, the effects of the design parameters on the Poisson’s ratio (PR), coefficient of thermal expansion (CTE), Young’s modulus and relative density are systematically investigated using unit cell-based finite element simulations that incorporate periodic boundary conditions. It is found that the bi-material lattice structures can be tailored to obtain 3-D printable metallic metamaterials with positive, near-zero or negative PR and CTE together with an uncompromised Young’s modulus. In particular, it is shown that metamaterial # 1 can exhibit both a negative PR and a non-positive CTE simultaneously. These metallic metamaterials can find applications in structures or devices such as antennas and precision instruments to reduce thermomechanical stresses and extend service lives.

Synthesis of Freestanding Graphene on SiC by a Rapid-Cooling Technique.

Graphene has a negative thermal expansion coefficient; that is, when heated, the graphene lattice shrinks. On the other hand, the substrates typically used for graphene growth, such as silicon carbide, have a positive thermal expansion coefficient. Hence, on cooling graphene on SiC, graphene expands but SiC shrinks. This mismatch will physically break the atomic bonds between graphene and SiC. We have demonstrated that a graphenelike buffer layer on SiC can be converted to a quasifreestanding monolayer graphene by a rapid-cooling treatment. The decoupling of graphene from the SiC substrate was actually effective for reducing the electric carrier scattering due to interfacial phonons. In addition, the rapidly cooled graphene obtained in this way was of high-quality, strain-free, thermally stable, and strongly hole doped. This simple, classical, but quite novel technique for obtaining quasifreestanding graphene could open a new path towards a viable graphene-based semiconductor industry.