Thermal Expansion Coefficient Temperature Research Articles

Investigation of the effects of rare earth element doping on the thermophysical properties of Gd2Zr2O7 by first principles

Gd2Zr2O7 is one of the most promising new generation of ceramic materials for high temperature thermal barrier coatings. However, it still has great potential of improving thermal and mechanical properties and contributing tobetter thermal cycling performance of the coating. Doping rare earth elements in Gd2Zr2O7 is an effective method to enhance its thermal and mechanical properties. In this paper, the first principles is used to calculate the thermophysical properties of doped Gd2Zr2O7 with 16 rare earth elements, including modulus of elasticity, Debye temperature, minimum high-temperature thermal conductivity, high temperature thermal expansion coefficient, and fracture toughness, by which all doped Gd2Zr2O7 ceramics were ranked using the entropy method. The results show that doping with Pr, Sm, Yb, and Nd showed superior comprehensive performance. Specially, (Gd0.875Pr0.125)2Zr2O7 has the lowest Young's modulus of 244 MPa, Pugh ratio of 0.53, Debye temperature of 523.4 K, thermal conductivity of 1.27 W/(m·K), and the largest coefficient of thermal expansion of 9.19 × 10−6 K−1, and (Gd0.875Ho0.125)2Zr2O7 has the highest fracture toughness of 2.21 MPa·m1/2.

Temperature-Dependent Elastic Properties of B4C from First-Principles Calculations and Phonon Modeling

Boron carbide plays a crucial role in various extreme environment applications, including thermal barrier coatings, aerospace applications, and neutron absorbers, because of its high thermal and chemical stability. In this study, the temperature-dependent elastic stiffness constants, thermal expansion coefficient, Helmholtz free energy, entropy, and heat capacity at a constant volume (Cv) of rhombohedral B4C have been predicted using a quasi-harmonic approach. A combination of volume-dependent first-principles calculations (density functional theory) and first-principles phonon calculations in the supercell framework has been performed. Good agreement between the elastic constants and structural parameters from static calculations is observed. The calculated thermodynamic properties from phonon calculations show trends that align with the literature. As the temperature rises, the predicted free energy follows a decreasing trend, while entropy and Cv follow increasing trends with temperature. Comparisons between the predicted room temperature thermal expansion coefficient (TEC) (7.54×10−6 K−1) and bulk modulus (228 GPa) from the quasi-harmonic approach and literature results from experiments and models are performed, revealing that the calculated TEC and bulk modulus fall within the established range from the limited set of data from the literature (TEC = 5.73–9.50 ×10−6 K−1, B = 221–246 GPa). Temperature-dependent Cijs are predicted, enabling stress analysis at elevated temperatures. Overall, the outcomes of this study can be used when performing mechanical and thermal stress analysis (e.g., space shielding applications) and optimizing the design of boron carbide materials for elevated temperature applications.

Design and application testing of imaging probe for strain measurement

To address the challenge of obtaining key device strain parameters within narrow spaces, this paper presents the design of a small-sized optical imaging probe with an independent optical system based on the basic principle of digital image correlation (DIC). To validate the strain measurement accuracy of the probe, a high-temperature heating system was built under in a laboratory setting, and experimental tests involving room temperature strain measurement and high temperature thermal expansion coefficient measurement were conducted. The findings demonstrate the potential of the developed probe for strain measurement in critical components situated in restricted spaces.

Novel ultralow-permittivity BaMg2Al6Si9O30-based microwave dielectric ceramics with self near-zero temperature coefficient of resonant frequency and thermal expansion

Novel BaMg2Al6Si9O30-based ceramics were prepared using the traditional solid-phase reaction method, and this paper presents the fabrication procedure, crystal structure, microstructure, microwave dielectric properties and temperature coefficient of thermal expansion of BaMg2Al6Si9O30-based ceramics. BaMg2Al6Si9O30-based ceramics were found to possess a hexagonal crystal structure with the P6/mcc space group. The BaAl2Si2O8 and BaMg2Al6Si9O30 phases coexisted in BaMg2Al6Si9O30 ceramic given that raw MgO material reacted easily with water vapour in the air, and the BaMg2Al6Si9O30 single-phase ceramic could be synthesized with calcined raw MgO material. The BaMg2Al6Si9O30 single-phase ceramic exhibited ultralow εr (5.68 at 14.05 GHz), moderate Q×f value (28534 GHz at 14.05 GHz), a self near-zero τf value (7.35 ppm/°C), a near-zero average temperature coefficient of thermal expansion (+1.89 ppm/°C) at 30 °C1000 °C and a rare negative temperature coefficient of thermal expansion (9.43 ppm/°C) at 655 °C710 °C. The rare near-zero and negative thermal expansions of the BaMg2Al6Si9O30 single-phase ceramic were mainly related to the strong Si/Al-O bonds with high relative covalency and 2 coordinate O(1) allowing longitudinal vibrations.

Constructive approach to reduce the influence of temperature on spring suspension eigenfrequencies

PurposeOne of the problems encountered by developers of inertial systems, such as gyroscopes and accelerometers, is the critical dependence of the eigenfrequencies of elastic suspensions (ES) on temperature when using substrates for sensors made of dielectric materials, such as borosilicate glass. The internal stresses arising in the ES caused by the difference in the temperature coefficients of linear expansion (TCLE) lead to deformation of the sensor and complication of the electronic part of the sensor. The purpose of this paper is to approach for in-plane and out-of-plane ES are considered that allow for minimization of the influence of internal stresses on eigenfrequencies.Design/methodology/approachAnalytical, finite element and experimental results are considered. The temperature coefficient of thermal expansion, the Young’s modulus and the Poisson ratio are given as a function of temperature. The shape of the spring elements (SEs) and the construction of the elastic suspension are the main topics of focus in this study. The authors’ out-of-plane ES based on a meander-like spring element implemented via finite element modeling show good agreement with the experimental results.FindingsMeander-like SEs have been developed that have lower temperature errors in comparison with traditional types of SEs. The main contribution to the change in the eigenfrequency from temperature is made by internal stresses that arose from the deformation of the bonded materials with different TCLE. The change of eigenfrequency from the temperatures that were calculated by finite element method did not exceed 0.15%, however, in practice, the scatter of the obtained characteristics for different samples showed a change of up to 0.3%.Originality/valueThis study shows a way to design and optimize the structure and theoretical background for the development of the microelectromechanical systems (MEMS) inertial module combining the functions of gyroscope and accelerometer. The obtained results will improve and expand the manufacturing technology of MEMS gyroscopes and accelerometers.

77 new thermodynamic identities among crystalline elastic material properties leading to a shear modulus constitutive law in isotropic solids

Thermodynamics of crystalline materials is analyzed using strain volumes, an incremental tensorial state variable which is the volume per unit mass multiplied by the incremental strain. It is shown that the derivatives of the strain volume variables with respect to the stresses are reduced to conventional well known isothermal, elastic, and crystallographic compliances and crystallographic thermal expansion coefficients. The formulism is extended to all third order derivatives which establish 77 new thermodynamic identities: 27 are thermal and 50 are among selected stress components of elastic compliances. The stress dependence of heat capacity is typically coupled into the crystallographic thermal expansion coefficient's temperature dependence; the temperature dependence of the elastic compliances is related to the stress dependence of the thermal expansion coefficients; stress dependent relationships among elastic compliances are also found. This paper emphasizes internal self-consistency. General triclinic identity relations which are of academic interest are applied to specific higher symmetries including orthorhombic, tetragonal, and cubic; identities in higher symmetry crystals are very useful. A new generalized, constitutive law is found and applied to isotropic polycrystalline materials; the concept is based on shear thermal expansion coefficients. The constitutive modulus relation describes thermal and pressure properties only through an isochoric modulus.

Effect of Thermal and Structural Disorder on the Electronic Structure of Hybrid Perovskite Semiconductor CH3NH3PbI3.

In this Letter, we investigate the temperature dependence of the optical properties of methylammonium lead iodide (MAPbI3 = CH3NH3PbI3) from room temperature to 6 K. In both the tetragonal (T > 163 K) and the orthorhombic (T < 163 K) phases of MAPbI3, the band gap (from both absorption and photoluminescence (PL) measurements) decreases with decrease in temperature, in contrast to what is normally seen for many inorganic semiconductors, such as Si, GaAs, GaN, etc. We show that in the perovskites reported here, the temperature coefficient of thermal expansion is large and accounts for the positive temperature coefficient of the band gap. A detailed analysis of the exciton line width allows us to distinguish between static and dynamic disorder. The low-energy tail of the exciton absorption is reminiscent of Urbach absorption. The Urbach energy is a measure of the disorder, which is modeled using thermal and static disorder for both the phases separately. The static disorder component, manifested in the exciton line width at low temperature, is small. Above 60 K, thermal disorder increases the line width. Both these features are a measure of the high crystal quality and low disorder of the perovskite films even though they are produced from solution.

The thermal and electrical properties of the promising semiconductor MXene Hf2CO2.

With the growing interest in low dimensional materials, MXenes have also attracted considerable attention recently. In this work, the thermal and electrical properties of oxygen-functionalized M2CO2 (M = Ti, Zr, Hf) MXenes are investigated using first-principles calculations. Hf2CO2 is determined to exhibit a thermal conductivity better than MoS2 and phosphorene. The room-temperature thermal conductivity along the armchair direction is determined to be 86.25~131.2 Wm−1 K−1 with a flake length of 5~100 μm. The room temperature thermal expansion coefficient of Hf2CO2 is 6.094 × 10−6 K−1, which is lower than that of most metals. Moreover, Hf2CO2 is determined to be a semiconductor with a band gap of 1.657 eV and to have high and anisotropic carrier mobility. At room temperature, the Hf2CO2 hole mobility in the armchair direction (in the zigzag direction) is determined to be as high as 13.5 × 103 cm2V−1s−1 (17.6 × 103 cm2V−1s−1). Thus, broader utilization of Hf2CO2, such as the material for nanoelectronics, is likely. The corresponding thermal and electrical properties of Ti2CO2 and Zr2CO2 are also provided. Notably, Ti2CO2 presents relatively lower thermal conductivity but much higher carrier mobility than Hf2CO2. According to the present results, the design and application of MXene based devices are expected to be promising.

Influence of mechanical activation on MgO-Al2O3-SiO2 system in the presence of TeO2 additive

Cordierite 2MgO+2Al2O3+5SiO2 is frequently used ceramic material, that is commonly used as a carrier of electrical components due to its low dielectric constant (~ 5), and low temperature thermal expansion coefficient (20·10-7 oC-1). In order to accelerate the process of sintering, 5.00 mass% TeO2 was added to the starting mixtures. System was tested in two parallel mixtures, one with no additives, and the other one with TeO2. The mechanical activation of the both mixtures was performed in a highenergy ball mill in time intervals from 0 to 40 min with ball to powder mass ratio 1:40. The particle size analysis (PSA) was employed in order to determine the changes in the particle size of the mechanically treated powders. The phase composition of the starting powders as well as microstructures was analyzed by the means of X-ray diffraction method and SEM.

Performance of Axially Restrained Hollow and Concrete Filled Oval Steel Columns Subjected to Hydrocarbon Fire

This paper represents the outcomes of the first research in the world involving experimental and validated theoretical study to investigate the performance of axially restrained steel columns with hollow and concrete filled elliptical sections subjected to fire. The test programme involved 9 hollow and concrete filled columns with 200 × 100 × 8 mm oval section yielding a slenderness λ=51 and tested under the severe hydrocarbon fire curve. The 1800 mm columns were tested under loading ratios = 0.2, 0.4 and 0.6 of the ultimate strength. The paper presents the obtained experimental results including measured axial and lateral displacements, restraint forces and failure time. A three-dimensional model was built using the finite element method (FEM) and was validated using the obtained tests results. By using variable with temperature thermal expansion coefficient and the EC3 thermal parameters, the finite element model demonstrated an excellent agreement with test results of failure temperatures, failure modes, axial displacements and generated axial forces. The verified finite element model was used to conduct a parametric analysis involving a range of parameters of loading level and slenderness. The study has shown that the concrete filled sections have demonstrated an improved fire resistance when compared to the hollow sections under low loading ratios. The research indicates that imposing axial restraint has reduced the fire resistance of columns by approximately one third on the time domain. The study has also shown a non-linear relationship between the loading ratio and slenderness of elliptical columns and that the load ratio has more effect on fire resistance of columns with high slenderness.

High Temperature Thermal Expansion and Elastic Modulus of Steels Used in Mill Rolls

The high temperature thermal expansion coefficient (TEC) and elastic modulus of five steels used in mill rolls production were investigated by dilatometer and impulse excitation techniques (IET). The measurements were provided at heating from room temperature till temperatures of about 1000 °C and subsequent cooling. The obtained data were attributed to the properties of predominating phases (austenite, martensite, pearlite, and bainite). The TEC and elastic modulus of corresponding phases were similar for all investigated steels despite the difference in their chemical composition. The steels with a chromium content of 2.95 wt.% and more show enhanced ability to quench hardening. This is an important prerequisite for production of high quality mill rolls.

Repeat sequence proteins as matrices for nanocomposites

Recombinant protein–inorganic nanocomposites comprised of exfoliated Na + montmorillonite (MMT) in a recombinant protein matrix based on silk-like and elastin-like amino acid motifs (silk elastin-like protein (SELP)) were formed via a solution blending process. Charged residues along the protein backbone are shown to dominate long-range interactions, whereas the SELP repeat sequence leads to local protein/MMT compatibility. Up to a 50% increase in room temperature modulus and a comparable decrease in high temperature coefficient of thermal expansion occur for cast films containing 2–10 wt.% MMT.

Environmental stability and cryogenic thermal cycling of low-temperature plasma-deposited silicon nitride thin films

Stress in low-temperature plasma-enhanced chemical vapor deposited silicon nitride (SiNx) thin films subject to cryogenic thermal cycling (100–323K) has been measured. It is observed that the SiNx deposition temperature strongly influences the thin film characteristics. For films deposited between 200 and 300°C, the thermal expansion coefficient is similar to that of silicon over the 180–323K temperature range. The room temperature thermal expansion coefficient of SiNx films is found to decrease sublinearly from 5.2×10−6to2.6×10−6K−1 as the temperature of the deposition process is increased from 50to300°C. The negative correlation between deposition temperature and thin film thermal expansion coefficient, and the positive correlation between deposition temperature and the thin film Young’s modulus inferred from nanoindentation are postulated to be associated with the local bonding environment within the thin film. The stress state of SiNx films deposited above 150°C is stable under atmospheric conditions, in contrast to SiNx films deposited below 100°C, which under atmospheric storage conditions become more tensile with time due to oxidation. In addition, SiNx thin films deposited below 100°C exhibit higher tensile stress values in vacuum than at atmospheric pressure, and vacuum annealing at 50°C of films deposited below 100°C introduces further tensile stress changes. These stress changes have been shown to be fully reversible upon reexposure to high purity nitrogen, helium, argon, oxygen, or laboratory atmosphere, and are likely to be associated with thin film porosity.

Temperature dependences of thermal expansion and saturation magnetization in Fe(67.0%)-Ni(32.5%)-Co(0.5%) Invar alloy with nanocrystalline structure

The effect of the nanocrystalline structure of Fe(67.0%)-Ni(32.5%)-Co(0.5%) Invar alloy on its thermal expansion is considered. It is found that the structure with grain mean sizes of about 100 nm increases its temperature coefficient of thermal expansion in the range of “invarness,” i.e., in the temperature range where the alloy offers the Invar properties. Reasons for this behavior are analyzed by taking the temperature dependence of the saturation magnetization.

Thermal expansion, vitrification temperature, and corrosion behavior of lead-borosilicate glasses

Data on the values of the temperature coefficient of thermal expansion (isodilates) and vitrification isotherms are presented. The chemical resistance (isochores of alkali- and acid-resistance) of lead-borosilicate glasses is studied. The behavior of the properties is studied in the ternary SiO2-B203-PbO system.

Measurement and calculation of the thermal expansion coefficient of diamond

Abstract Measurements of the thermal expansion coefficient and pecific heat from room temperature to 850 K on 300 μm polycrystalline diamond samples are described. The extrapolated room temperature thermal expansion coefficient is similar to single crystal diamond (0.7 × 10 −6 ±0.3 × 10 −6 K −1 ). At 313 K the measured specific heat is 7.05 J mol −1 K −1 which agrees with the recommended single crystal data. With increasing temperature the thermal expansion coefficient is clearly higher than the recommended values for single crystal diamond. Also, the specific heat is larger than recommended values for single crystal diamond above room temperature. The temperature dependence of specific heat provides the main contribution to temperature dependence of the thermal expansion coefficient. Calculation of the thermal expansion coefficient from measured specific heat provides a better fit to our measurements between 500 and 700 K than the recommended data.

Nonlinear thermoacoustics and electrostriction explanations of acoustic signatures in 4 °C water caused by laser pulses and proton beams

Experiments in water with proton beams [Hunter et al., J. Acoust. Soc. Am. 69, 1557–1562 (1981)] and with laser pulses [Hunter, Jones, and Malbrough, J. Acoust. Soc. Am. 1563–1567 (1981)] give pressure signatures superimposed of a bipolar signal (reversing polarity at 4 °C) and an anomalous tripolar signal that at onset is (1) negative (proton beams) or (2) positive (laser pulses). The explanation for (1) is that charge added by a proton beam causes a surrounding short‐lived electric field that, via electrostriction, initially accelerates fluid inwards and temporarily lowers pressure in an annular region and raises it in the core. Such causes a minus‐plus‐minus‐plus shaped signature varying inversely with electrical conductivity. The explanation for (2) ensues from a formulation that uses the thermal expansion coefficient's temperature dependence. Such yields an additional source term (nonzero at 4 °C and proportional to negative of second time derivative of square of heat added per unit volume) to inhomogeneous wave equation, resulting in initially positive signature. Pulse durations and charge relaxation times are assumed short compared to acoustic transit time across diameter, so all signature time scales are of order of latter. Rough numerical estimates are not inconsistent with reported crossovers in initial polarity at 6° and 3 °C, respectively. The small second positive peak in the tripolar signal and the precursors in the laser beam experiments are still not understood. [Work supported by ONR.]

Low temperature thermal expansion and specific heat of PrNi 5

Experimental data on the low temperature thermal expansion coefficient α and specific heat c p of PrNi 5 between 1.5 and 12 K are presented. The thermal expansion is very anisotropic at these temperatures. At 12 K, α ‖ and α ⊥ are both of the order of 1.5 × 10 −5K −1, but of opposite sign. Both α and c p show anomalous behaviour below 10K and several possibilities of the nature of these anomalies are discussed.

Collision probability calculations of multiplication factors for lattices

A multigroup version of the method of successive generations is used to determine the multiplication factors of unmoderated and unreflected periodic lattices of identical fissile components. The lattice components must be one-dimensional (i.e. spheres, infinitely long cylinders or infinite slabs). Lattices of nearly one-dimensional components (cubes or long cylinders) may, however, be approximately treated. The lattice components may be arranged in a linear, planar or cuboidal manner; the permissible component arrangements being limited by the lattice component geometry. The computation traces successive neutron collisions in the lattice, starting from a uniform neutron-source density distribution in each lattice component. The initial source density energy distribution is specified in a 16-group format which is obtained from S 4 transport equation solutions. The method satisfactory predicts the critical pitch of two experimentally measured lattices and, to this degree of confidence, is used to compute the critical parameters of other similar lattices. The method is also used to find the reactivity temperature coefficient of thermal expansion for several just-critical arrays. This coefficient is found to be positive for large arrays of small elements which have a high interaction factor.

Theory of thermal expansion of a graphite crystal in the semi-continuum model

A new theory of the principal thermal expansion coefficients of a graphite crystal is derived using the lattice dynamics obtained by Komatsu. The theory is compared with new data on the low temperature thermal expansion coefficients of very highly oriented pyrolytic graphite and high temperature X-ray data. Values of some of the lattice anharmonic coefficients are estimated.