Thermal Expansion Coefficients of Thin Crystal Films

The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.

PREPARATION OF HIGH THERMAL EXPANSION COEFFICIENT PORCELAINS FUSED TO METALS

Usually the thermal expansion coefficients (TEC) of metals are higher than that of porcelains. In order to match the TECs in the case of coating porcelains on metals, high TEC porcelains are needed. In this research, the high TEC phase leucite (KAlSi2 O6) in the high TEC porcelain was prepared by sol-gel method. The crystal size of leucite made by sol-gel is about 77nm through controlling the process parameters. The process from xerogel to leucite was investigated by means of DSC (differential scanning calorimetry), TG (thermogravimetry), XRD ( X-ray diffraction) and IR (infrared absorption spectrum). Leucite had been detected after the gel was treated at 900℃, this formation temperature is about 250℃ lower than that of melting method. The porcelain made from 50% of the leucite powder and 50% of low fused temperature frit has an average TEC of 19.2×10-6/℃ C from room temperature to 450℃, which is much higher than the common porcelains.

Effect of colouring green stage zirconia on the adhesion of veneering ceramics with different thermal expansion coefficients

This study evaluated the adhesion of zirconia core ceramics with their corresponding veneering ceramics, having different thermal expansion coefficients （TECs）, when zirconia ceramics were coloured at green stage. Zirconia blocks （N=240; 6 mm x 7 mm x 7 mm） were manufactured from two materials namely, ICE Zirconia （Group 1） and Prettau Zirconia （Group 2）. In their green stage, they were randomly divided into two groups. Half of the specimens were coloured with colouring liquid （shade A2）, Three different veneering ceramics with different TEC （ICE Ceramic, GC Initial Zr and IPS e.max Ceram） were fired on both coloured and non-coloured zirconia cores. Specimens of high noble alloys （Esteticor Plus） veneered with ceramic （VM 13） （n= 16） acted as the control group. Core-veneer interface of the specimens were subjected to shear force in the Universal Testing Machine （0.5 mm-min-1）. Neither the zirconia core material （P=0.318） nor colouring （P=0.188） significantly affected the results （three-way analysis of variance, Tukey＇s test）. But the results were significantly affected by the veneering ceramic （P=0.000）. Control group exhibited significantly higher mean bond strength values （45.7__.8） MPa than all other tested groups （（27.1__.4.1）-（39.7__.4.7） and （27.4__.5.6）-（35.9___4.7） MPa with and without colouring, respectively） （P^0.001）. While in zirconia-veneer test groups, predominantly mixed type of failures were observed with the veneering ceramic covering ~ 1/3 of the substrate surface, in the metal-ceramic group, veneering ceramic was left adhered 1/3 of the metal surface. Colouring zirconia did not impair adhesion of veneering ceramic, but veneering ceramic had a significant influence on the core-veneer adhesion. Metal-ceramic adhesion was more reliable than all zirconia-veneer ceramics tested.

The Approach of Compensation of Air Refractive Index in Thermal Expansion Coefficients Measurement Based on Laser Feedback Interferometry

We present the thermal expansion coefficient （TEC） measurement technology of compensating for the effect of variations in the refractive index based on a Nd： YA G laser feedback system, the beam frequency is shifted by a pair of aeousto-optic modulators and then the heterodyne phase measurement technique is used. The sample measured is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams hit perpendicularly and coaxially on each surface of the sample. The reference beams hit on the reference mirror and the high-refiectivity mirror, respectively. By the heterodyne configuration and computing, the influences of the vibration, distortion of the sample supporter and the effect of variations in the refractive index are measured and largely minimized. For validation, the TECs of aluminum samples are determined in the temperature range of 29-748K, confirming not only the precision within 5 × 10-7 K-1 and the accuracy within 0.4% from 298K to 448K but also the high sensitivity non-contact measurement of the lower reflectivity surface induced by the sample oxidization from 448 K to 748 K.

Measurement Method of Compressibility and Thermal Expansion Coefficients for Density Standard Liquid at 2329 kg/m^3 based on Hydrostatic Suspension Principle

The accurate measurement on the compressibility and thermal expansion coefficients of density standard liquid at 2329kg/m3（DSL-2329） plays an important role in the quality control for silicon single crystal manufacturing. A new method is developed based on hydrostatic suspension principle in order to determine the two coefficients with high measurement accuracy. Two silicon single crystal samples with known density are immersed into a sealed vessel full of DSL-2329. The density of liquid is adjusted with varying liquid temperature and static pressure, so that the hydrostatic suspension of two silicon single crystal samples is achieved. The compression and thermal expansion coefficients are then calculated by using the data of temperature and static pressure at the suspension state. One silicon single crystal sample can be suspended at different state, as long as the liquid temperature and static pressure function linearly according to a certain mathematical relationship. A hydrostatic suspension experimental system is devised with the maximal temperature control error ±50 μK; Silicon single crystal samples can be suspended by adapting the pressure following the PID method. By using the method based on hydrostatic suspension principle, the two key coefficients can be measured at the same time, and measurement precision can be improved due to avoiding the influence of liquid surface tension. This method was further validated experimentally, where the mixture of 1, 2, 3-tribromopropane and 1,2-dibromoethane is used as DSL-2329. The compressibility and thermal expansion coefficients were measured, as 8.5′10–4 K–1 and 5.4′10–10 Pa–1, respectively.

Numerical investigation of multi-beam laser heterodyne measurement with ultra-precision for linear expansion coefficient of metal based on oscillating mirror modulation

This paper proposes a novel method of multi-beam laser heterodyne measurement for metal linear expansion coefficient. Based on the Doppler effect and heterodyne technology, the information is loaded of length variation to the frequency difference of the multi-beam laser heterodyne signal by the frequency modulation of the oscillating mirror, this method can obtain many values of length variation caused by temperature variation after the multi-beam laser heterodyne signal demodulation simultaneously. Processing these values by weighted-average, it can obtain length variation accurately, and eventually obtain the value of linear expansion coefficient of metal by the calculation. This novel method is used to simulate measurement for linear expansion coefficient of metal rod under different temperatures by MATLAB, the obtained result shows that the relative measurement error of this method is just 0.4%.

Anisotropy of Expansion Coefficient and Slag Resistance of Spinel Carbon Bricks

Effects of the pressure direction on the thermal expansion and slag corrosion resistance were investigated and anisotropic microstructures of flaky graphite in spinel carbon bricks were examined. The experimental results show that slag corrosion velocities in the direction parallel to the pressure direction display a decrease of 34% compared to those in the vertical direction. Meantime, the linear expansion coefficient in the direction parallel to the pressure direction is 2.45 times as large as that in the vertical pressure direction. Slag corrosion velocities of spinel carbon bricks soaked in the AOD melting slag display a 46%-47% decrease compared to those of magnesia carbon bricks. The microstructure observation shows that spinel carbon bricks have a high degree of preferred orientation.

Effects of heat treatment temperature on crystallization and thermal expansion coefficient of Li_2O-Al_2O_3-SiO_2

The basic glass of Li2O-Al2O3-SiO2 system using P2O5 as nucleator was prepared by means of conventional melt quenching technology, and the heat-treatment process was determined by using differential thermal analysis. The crystalline phases and the microstructure of the glass-ceramics were investigated by using X-ray diffraction and scanning electron microscopy. The results show that the glass based on Li2O-Al2O3-SiO2 oxides using P2O5 as nucleator can be prepared at lower melt temperature of 1 450 ℃ and the glass-ceramics with lower thermal expansion coefficient of 21.6×10-7 ℃-1 can also be obtained at 750 ℃. The glass-ceramics contain a few crystal phases in which the main crystal phase is β-quartz solid solution and the second crystal phase is β-spodumene solid solution. When the heat treatment temperature is not higher than 650 ℃, the transparent glass-ceramics containing β-quartz solid solution can be prepared. β-quartz solid solution changes into β-spodumene solid solution at about 750 ℃. And the appearance of the glass-ceramics changes from translucent, part opaque to complete opaque with increasing （temperature.）

High Performance ZrNbAl Alloy with Low Thermal Expansion Coefficient

Thermal expansion is a common phenomenon in both metals and alloys, which is important for metallic material applications in modern industry, especially in nuclear and aerospace industries. A lower thermal expansion coefficient may cause lower thermal stress and higher accuracy. A new Zr-based alloy is developed and presented.The XRD diffraction results demonstrate that only a close-packed hexagonal phase（α or α＇ phase） exists in the microstructure. The thermal expansion and mechanical properties are studied. According to the experimental results, the new Zr-based alloy presents a low thermal expansion coefficient and good mechanical properties.Also,its thermal expansion coefficient is stable through solution treatment.

Study on Thermal Expansion Coefficient of Sealing Materials for Ceramic Metal Halide Lamps

With Al2O3, Dy2O3, and SiO2 as starting materials, the basic glass of Al2O3-Dy2O3-SiO2 system was prepared by conventional melting technology, and their thermal expansion coefficients （TECs） at different anneal time were investigated. TECs of the basic glass, which were heat-treated under different temperature, were also investigated. The result showed that TECs of the basic glass gradually approached a fixed value as the anneal time was extended, which suggested that most of the inner stress had been eliminated. After heat treatment, the contents of Dy2O3, Dy2Si2O7, and a new crystal increased up to 1200 ℃ and decreased below 1250 ℃, which was consistent with the TEC change of crystallized samples. This suggests that the crystal has a direct effect on TECs of the crystallized samples.

Determination Method of Thermal Expansion Coefficient of Cordierite

Cordierite ceramics were prepared by using talc, bauxite and kaolin clay as starting materials. According to the detected resuh of XRD step-scanning from 25° to 35° by a high temperature X-ray diffractometer, 20 and d values of five peaks of cordierite crystal were ascer- rained. Then the least squares technique was used to cal- culate the crystal parameters ： at 25 ℃ , a = b = O. 981 8 nm, c =0. 927 4 nm, V=O. 774 3 nm3 ; at 600 ℃ , a =b =O. 982 0 nm, c=0.9252 nm, V=O. 773 5 nm3. The crystal volumetric coefficient of thermal expansion （CTE） and linear CTE along a and c axes were calcu- lated, αv = 2. 33 × 10-6℃-1, αa = αb, = 3. 27 × 10-6℃ -1 , αc = -4.19 ×10-6℃ -1. The average CTE of cordierite crystal is as low as O. 78 × 10-6℃ -1

Superplastic forming of Ti6Al4V alloy using ZrO_(2)-TiO_(2) ceramic die with adjustable linear thermal expansion coefficient

Firstly,the relation between the coefficient of thermal expansion(CTE)and the volume fraction of TiO_(2) was investigated, and also the influence of relative density of ceramic on the CTE was studied.The results show that the volume fraction of TiO_(2) and the relative density both make influence on the CTE of ZrO_(2)-TiO_(2) ceramic.According to the results,the ZrO_(2)-TiO_(2)(volume fraction of TiO_(2) is 27%)ceramic die with the similar CTE(8.92×10^(-6) ℃^(-1))to Ti6Al4V was fabricated.Secondly,to evaluate the dimensional accuracy of the workpiece superplastically formed,the Ti6Al4V impression experiment was performed.The result shows that the dimensional inaccuracy of workpiece is 0.003.Thirdly,in order to evaluate the practicability,the experiment of superplastic forming Ti6Al4V using ZrO_(2)-TiO_(2) cylinder ceramic die was carried out.The Ti6Al4V cylinder shows good shape retention and surface quality,and high dimensional accuracy.The ceramic dies seem to be adequate for superplastic forming the high accuracy Ti6Al4V, and the trials have confirmed the potential of the ZrO_(2)-TiO_(2) ceramic die.

Determination of the Thermal Expansion Coefficient of Concrete at Early Ages by Using Temperature-stress Testing Machine

By using the uptodate temperatuer-stress testing machine, the thermal expansion coefficient of concrete at early ages was studied and indicative conclusions were achieved ： temperature rising due to hydration heat is not directly correlated with cracking, but the temperature and stress evolation process should be taken into consideration in the same time. Proper chemical admixtures and mineral cornpasitions can improve the mechanical properties of concrete such as thermal expansion coefficient, which is very indicative in practice.

Influence of average radii of RE3+ ions on phase structures and thermal expansion coefficients of high-entropy pyrosilicates

High-entropy pyrosilicate element selection is relatively blind, and the thermal expansion coefficient (CTE) of traditional β-type pyrosilicate is not adjustable, making it difficult to meet the requirements of various types of ceramic matrix composites (CMCs). The following study aimed to develop a universal rule for high-entropy pyrosilicate element selection and to achieve directional control of the thermal expansion coefficient of high-entropy pyrosilicate. The current study investigates a high-entropy design method for obtaining pyrosilicates with stable β-phase and γ-phase by introducing various rare-earth (RE) cations. The solid-phase method was used to create 12 different types of high-entropy pyrosilicates with 4–6 components. The high-entropy pyrosilicates gradually transformed from β-phase to γ-phase with an increase in the average radius of RE^(3+) ions ( r¯(RE^(3+))). The nine pyrosilicates with a small r¯(RE^(3+)) preserve β-phase or γ-phase stability at room temperature to the maximum of 1400 ℃. The intrinsic relationship between the thermal expansion coefficient, phase structure, and RE–O bond length has also been found. This study provides the theoretical background for designing high-entropy pyrosilicates from the perspective of r¯(RE^(3+)). The theoretical guidance makes it easier to synthesize high-entropy pyrosilicates with stable β-phase or γ-phase for the use in environmental barrier coatings (EBCs). The thermal expansion coefficient of γ-type high-entropy pyrosilicate can be altered through component design to match various types of CMCs.

Mechanically Strong and Flame‑Retardant PBO/BN/MXene Nanocomposite Paper with Low Thermal Expansion Coefficient,for Efficient EMI Shielding and Heat Dissipation

As portable and wearable electronic devices are rapidly developing,there is an urgent need for flexible and robust thermally conductive electromagnetic interference shielding materials to address the associated electromagnetic pollution and overheating issues.Herein,multifunctional poly(p-phenyl-2,6-phenylene bisoxazole)nanofiber/boron nitride nanosheet/Ti_(3)C_(2)T_(x)MXene nanosheet(PBO/BN/MXene)composite papers are prepared by a gel microparticle-mediated ordered assembly process with the aid of vacuum-assisted filtration.Nacre-like“brick and mortar”structure,segregated structure and sandwich structure are integrated into the composite paper,so that efficient thermally and electrically conductive networks have been established.When the BN and MXene contents are 29.2 wt%and 41.7 wt%,the 13μm thick composite paper exhibits an EMI shielding performance of 31.8 dB and a thermal conductivity of 26.1 W/mK,markedly superior to those of the control samples without the ordered structures.Meanwhile,because of the unique architecture and inherent advantages of the building blocks,the composite paper exhibits extremely low coefficient of thermal expansion(~1.43 ppm/K),excellent mechanical properties,and outstanding thermal stability and flame retardance,making it highly advantageous for practical applications in electronic devices.This work offers a promising approach for fabricating high-performance multifunctional composites by constructing efficient filler networks.

Influence of Chemical Composition on Phase Transformation Temperature and Thermal Expansion Coefficient of Hot Work Die Steel

On the basis of the uniform design method, six kinds of martensitic hot work die steels were designed. The phase transformation temperatures including Ac1 , Ac3 , and Ms were measured by DIL805A quenching dilatometer. The influences of the main elements on phase transformation temperatures were analyzed by quadratic stepwise regression analysis, and three corresponding equations were obtained. These equations, in which the interactions of the elements were considered, showed more effectiveness than the traditional ones. In addition, the thermal expansion coefficients of these steels in annealed state and quenched state were also obtained during the tests. The influences of chemical composition and temperature on the thermal expansion coefficient were analyzed; the equations obtained were verified by using several kinds of steels. The predicted values were in accordance with the results of the experiments.

(Ho_(0.25)Lu_(0.25)Yb_(0.25)Eu_(0.25))_(2)SiO_(5) high-entropy ceramic with low thermal conductivity,tunable thermal expansion coefficient,and excellent resistance to CMAS corrosion

Low thermal conductivity,compatible thermal expansion coefficient,and good calcium–magnesium–aluminosilicate(CMAS)corrosion resistance are critical requirements of environmental barrier coatings for silicon-based ceramics.Rare earth silicates have been recognized as one of the most promising environmental barrier coating candidates for good water vapor corrosion resistance.However,the relatively high thermal conductivity and high thermal expansion coefficient limit the practical application.Inspired by the high entropy effect,a novel rare earth monosilicate solid solution(Ho_(0.25)Lu_(0.25)Yb_(0.25)Eu_(0.25))_(2)SiO_(5)was designed to improve the overall performance.The as-synthesized(Ho_(0.25)Lu_(0.25)Yb_(0.25)Eu_(0.25))_(2)SiO_(5)shows very low thermal conductivity(1.07 W·m-1·K-1 at 600℃).Point defects including mass mismatch and oxygen vacancies mainly contribute to the good thermal insulation properties.The thermal expansion coefficient of(Ho_(0.25)Lu_(0.25)Yb_(0.25)Eu_(0.25))_(2)SiO_(5)can be decreased to(4.0–5.9)×10^(-6)K^(-1)due to severe lattice distortion and chemical bonding variation,which matches well with that of SiC((4.5–5.5)×10^(-6)K^(-1)).In addition,(Ho_(0.25)Lu_(0.25)Yb_(0.25)Eu_(0.25))_(2)SiO_(5)presents good resistance to CMAS corrosion.The improved performance of(Ho_(0.25)Lu_(0.25)Yb_(0.25)Eu_(0.25))_(2)SiO_(5)highlights it as a promising environmental barrier coating candidate.

ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.

Size-and temperature-dependent Young's modulus and size-dependent thermal expansion coefficient of nanowires

Nanowires(NWs) exhibit size-dependent mechanical properties due to the high surface/volume ratio, in which temperature also plays an important role. The surface eigenstress model is further developed here to quantitatively predict the size-dependent mechanical properties of NWs and results in analytic formulas. Molecular dynamics(MD) simulations are conducted to study the size-dependent mechanical of [100], [110] and [111] Ni and Si nanowires within the temperature range of 100–400 K and the MD results verify perfectly the newly developed surface eigenstress model.

New class of high-entropy pseudobrookite titanate with excellent thermal stability,low thermal expansion coefficient,and low thermal conductivity

As a type of titanate,the pseudobrookite(MTi_(2)O_(5)/M_(2)TiO_(5))exhibits a low thermal expansion coefficient and thermal conductivity,as well as excellent dielectric and solar spectrum absorption properties.However,the pseudobrookite is unstable and prone to decomposing below 1200℃,which limits the practical application of the pseudobrookite.In this paper,the high-entropy pseudobrookite ceramic is synthesized for the first time.The pure high-entropy(Mg,Co,Ni,Zn)Ti_(2)O_(5) with the pseudobrookite structure and the biphasic high-entropy ceramic composed of the highentropy pseudobrookite(Cr,Mn,Fe,Al,Ga)_(2)TiO_(5) and the high-entropy spinel(Cr,Mn,Fe,Al,Ga,Ti)_(3)O_(4) are successfully prepared by the in-situ solid-phase reaction method.The comparison between the theoretical crystal structure of the pseudobrookite and the aberration-corrected scanning transmission electron microscopy(AC-STEM)images of high-entropy(Mg,Co,Ni,Zn)Ti_(2)O_(5) shows that the metal ions(M and Ti ions)are disorderly distributed at the A site and the B site in high-entropy(Mg,Co,Ni,Zn)Ti_(2)O_(5),leading to an unprecedentedly high configurational entropy of high-entropy(Mg,Co,Ni,Zn)Ti_(2)O_(5).The bulk high-entropy(Mg,Co,Ni,Zn)Ti_(2)O_(5) ceramics exhibit a low thermal expansion coefficient of 6.35×10^(−6) K^(−1) in the temperature range of 25-1400℃ and thermal conductivity of 1.840 W·m^(−1)·K^(−1) at room temperature,as well as the excellent thermal stability at 200,600,and 1400℃.Owing to these outstanding properties,high-entropy(Mg,Co,Ni,Zn)Ti_(2)O_(5) is expected to be the promising candidate for high-temperature thermal insulation.This work has further extended the family of different crystal structures of high-entropy ceramics reported to date.