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.

A novel implementation algorithm of asymptotic homogenization for predicting the effective coefficient of thermal expansion of periodic composite materials

Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.

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.

Microstructure evolution,mechanical properties and tailoring of coefficient of thermal expansion for Cu/Mo/Cu clad sheets fabricated by hot rolling

The law of microstructure evolution and mechanical properties of hot roll bonded Cu/Mo/Cu clad sheets were systematically investigated and the theoretical prediction model of the coefficient of thermal expansion(CTE)of Cu/Mo/Cu clad sheets was established successfully.The results show that the deformation of Cu and Mo layers was gradually coherent with an increase in rolling reduction and temperature and excellent interface bonding was achieved under the condition of a large rolling reduction.The development of the microstructure and texture through the thickness of Cu and Mo layers was inhomogeneous.This phenomenon can be attributed to the friction between the roller and sheet surface and the uncoordinated deformation between Cu and Mo.The tensile strength of the clad sheets increased with increasing rolling reduction and the elongation was gradually decreased.The CTE of Cu/Mo/Cu clad sheets was related to the volume fraction of Mo.The finite element method can simulate the deformation and stress distribution during the thermal expansion process.The simulation result indicates that the terminal face of the clad sheets was sunken inward.

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.

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.

Analytical Model of Elastic Modulus and Coefficient of Thermal Expansion for 2.5D C/SiC Composite

To make better use of 2.5D C/SiC composites in industry, it is necessary to understand the mechanical properties. A finite element model＇of 2.5D composites is established, by considering the fiber undulation and the porosity in 2.5D C/SiC composites. The fiber direction of warp is defined by cosine function to simulate the undulation of warp, and based on uniform strain assumption, analytical model of the elastic modulus and coefficient of thermal expansion （CTE） for 2.5D C/SiC composites were established by using dual- scale model. The result is found to correlate reasonably well with the predicted results and experimental results. The parametric study also demonstrates the effects of the fiber volume fraction, distance of warp yarn, and porosity in micro-scale on the mechanical properties and the coefficients of thermal expansion.

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.

The Negative Thermal Expansion Property of NdMnO_(3) Based on Pores Effect and Phase Transition

A novel negative thermal expansion(NTE) material NdMnO_(3) was synthesized by solid-state method at 1 523 K. The crystal structure, phase transition, pores effect and negative expansion properties of NdMnO_(3) were investigated by variable temperature X-ray diffraction(XRD), scanning electron microscope(SEM) and variable temperature Raman spectra. The compound exhibits NTE properties in the orderly O' phase crystal structure. When the temperature is from 293 to 759 K, the ceramic NdMnO_(3) shows negative thermal expansion of-4.7×10^(-6)/K. As temperature increases, the ceramic NdMnO_(3) presents NTE property range from 759 to 1 007 K. The average linear expansion coefficient is-18.88×10^(-6)/K. The physical mechanism of NTE is discussed and clarified through experiments.

Modification of streamer-to-leader transition model based on radial thermal expansion in the sphere-plane gap discharge at high altitude

Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane gap discharge tests were carried out under the gap distance of 5 m at the Qinghai Ultra High Voltage(UHV)test base at an altitude of 2200 m.The experiments measured the physical parameters such as the discharge current,electric field intensity and instantaneous optical power.The duration of the dark period and the critical charge of streamer-toleader transition were obtained at high altitude.Based on radial thermal expansion of the streamer stem,we established a modified streamer-to-leader transition model of the sphere-plane gap discharge at high altitude,and calculated the stem temperature,stem radii and the duration of streamer-to-leader transition.Compared with the measured duration of sphere-plane electrode discharge at an altitude of 2200 m,the error rate of the modified model was 0.94%,while the classical model was 6.97%,demonstrating the effectiveness of the modified model.From the comparisons and analysis,several suggestions are proposed to improve the numerical model for further quantitative investigations of the leader inception.

Density and thermal expansion coefficients of liquid and austenite phase in lamellar cast iron

Volume change related defects formation mechanisms are an important detracting phenomenon in production of complex shaped cast components.Among different technical alloys,cast iron behaves in a complex manner due to the combined volume change of the formed phases.The liquid and the austenitic phase are contracting while the graphite phase is expanding during the solidification.The complex volume change in combination with complex casting shapes causes a considerable deviation from isotropy in the solidification domain.The mentioned difficulties are considered the main reason why an extensive research work is condensed in the literature within this topic.The multitude of reported experimental set up and the various efforts to interpret the volume change phenomena in terms of density and thermal expansion coefficients makes the results difficult to compare from different sources.With these difficulties in mind,the present paper presents a broad experimental series and measures unidirectional linear deformation of an industrially spread lamellar cast iron alloy system(Fe-C-2Si)using the push-rod based dilatometer technique.The measurements are divided into two major groups with respect to the liquid iron deformation over the liquidus temperature line,and the austenite deformation below the solidus temperature line.The obtained results are interpreted as thermal expansion coefficients,density variation slopes,and density data at the liquids and solidus temperature.The obtained results are compared with literature data and with calculated values by the Thermo Calc software.

Micromechanical Analysis of Thermal Expansion Coefficients

Thermal expansion coefficients play an important role in the design and analysis of composite structures. A detailed analysis of thermo-mechanical distortion can be performed on microscopic level of a structure. However, for a design and analysis of large structures, the knowledge of effective material properties is essential. Thus, either a theoretical prediction or a numerical estimation of the effective properties is indispensable. In some simple cases, exact analytical solutions for the effective properties can be derived. Moreover, bounds on the effective values exist. However, in dealing with complex heterogeneous composites, numerical methods are becoming increasingly important and more widely used, because of the limiting applicability of the existing (semi-)analytical approaches. In this study, finite-element methods for the calculation of effective thermal expansion coefficients of composites with arbitrary geometrical inclusion configurations are discussed and applied to a heterogeneous lightning protection coating made from Dexmet&#174 copper foil 3CU7-100FA and HexPly&#174 epoxy resin M21. A short overview of some often used (semi-)analytical formulas for effective thermal expansion coefficients of heterogeneous composites is given in addition.

Properties of Ultra-low Thermal Expansion LAS Transparent Glass-ceramics Prepared by Spodumene

The glass-ceramics were prepared with the spodumene mineral as the main raw material,and the effects of ZrO_(2)replacing TiO_(2)on the samples were systematically investigated.The results show that the substitution of ZrO_(2)for TiO_(2)is not conductive to precipitate𝛽β-quartz solid solution phase,but can improve the transparency and flexural strength of glass-ceramics.And the glass-ceramic with the highest visible light transmittance(87%)and flexural strength(231.80 MPa)exhibits an ultra-low thermal expansion of-0.028×10^(-7)K^(-1)in the region of 30-700℃.

Coefficient of Thermal Expansion of Liquid Helium Ⅱ

We can write the coefficient of thermal expansion of liquid helium in terms of the isothermal compressibility.Together they are connected by some terms which are microscopic or quantum mechanical in nature.Here we give the necessary derivation.

Rolling Decision Model of Thermal Power Retrofit and Generation Expansion Planning Considering Carbon Emissions and Power Balance Risk

With the increasing urgency of the carbon emission reduction task,the generation expansion planning process needs to add carbon emission risk constraints,in addition to considering the level of power adequacy.However,methods for quantifying and assessing carbon emissions and operational risks are lacking.It results in excessive carbon emissions and frequent load-shedding on some days,although meeting annual carbon emission reduction targets.First,in response to the above problems,carbon emission and power balance risk assessment indicators and assessment methods,were proposed to quantify electricity abundance and carbon emission risk level of power planning scenarios,considering power supply regulation and renewable energy fluctuation characteristics.Secondly,building on traditional two-tier models for low-carbon power planning,including investment decisions and operational simulations,considering carbon emissions and power balance risks in lower-tier operational simulations,a two-tier rolling model for thermal power retrofit and generation expansion planning was established.The model includes an investment tier and operation assessment tier and makes year-by-year decisions on the number of thermal power units to be retrofitted and the type and capacity of units to be commissioned.Finally,the rationality and validity of the model were verified through an example analysis,a small-scale power supply system in a certain region is taken as an example.The model can significantly reduce the number of days of carbon emissions risk and ensure that the power balance risk is within the safe limit.

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