Development of a Laser Interferometric Dilatometer for Measurements of Thermal Expansion of Solids in the Temperature Range 300 to 1300 K

A laser interferometric dilatometer has been developed for measuring linear thermal expansion coefficients of reference materials for thermal expansion in the temperature range 300 to 1300 K. The dilatometer is based on an optical heterodyne interferometer capable of measuring length change with an uncertainty of 0.6 nm. Linear thermal expansion coefficients of silicon were measured in the temperature range 700 to 1100 K. The performance of the present dilatometer was tested by a comparison between the present data and the data measured with the previous version of the present dilatometer and the data recommended by the Committee on Data for Science and Technology (CODATA). The present data agree well with the recommended values over all the temperature range measured. On the other hand, the present values at lower temperatures are in poor agreement with the previous experimental data. The combined standard uncertainty in the present value at 900 K is estimated to be 1.1×10^–8 K^–1.     

Absolute thermal expansion measurements of single-crystal silicon in the range 300–1300 K with an interferometric dilatometer

The thermal expansion coefficient of single-crystal silicon has been measured in the range 300–1300 K using an interferometric dilatometer. The measurement system consists of a double-path optical heterodyne interferometer and a radiant image furnace with a quartz vacuum tube, which provides both accuracy and rapidity of measurement. The uncertainties in length and temperature determination are within 4 nm and 0.4 K, respectively. A high-purity dislocation-free FZ silicon single crystal was used in the study. Thermal expansion coefficients of silicon oriented in the [111] direction have been determined over the temperature range from 300 to 1300 K. The standard deviation of the measurement data from the best fitting for the fifth-order polynomial in temperature is 2.1×10^–8 K^–1. The present value for the thermal expansion coefficient agrees within 9×10^–8K^–1 with the interferometric measurement of polycrystalline pure silicon by Roberts (1981) between 300 and 800 K and within 1.2 × 10^–7 K^–1 with the single-crystal X-ray diffractometric measurement by Okada and Tokumaru (1984) between 300 and 1300 K.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Thermal expansion of Pyros from 20 to 1273 K

Pyros, which is a Ni-base alloy (82% Ni, 8% Cr, 4% W, 3% Mn, and 3% Fe), has been used extensively in France since 1926 as a temperature sensor and as a reference material for thermal expansion measurements. In this paper we present recent data on the expansion and expansivity of Pyros from 20 to 1273 K. Expansivity results, obtained by taking the derivative of a cubic-spline polynomial fitting performed to the L/L experimental data, show that Pyros is a stable material in the 20 to 1273 K temperature range. Furthermore, since the expansivity values are similar to those of steels, Pyros should be of special interest to laboratories which are concerned with expansion measurements on steels. Therefore, we suggest that Pyros be considered as a suitable reference material for thermal expansion measurements on steels, and until more accurate results are obtained, we propose our results as reference data between 20 and 1273 K.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

The Thermophysical Properties (Heat Capacity and Thermal Expansion) of Single-Crystal Silicon

Fragmentary investigations of the heat capacity and of the thermal expansion coefficient of single crystals of high-purity silicon are reported. The results of these investigations are compared with the entire body of data on these properties available to date. Generalized equations expressing the heat capacity and thermal expansion coefficient of silicon as functions of temperature are obtained for the temperature ranges of 298–1690 and 100–1400 K, respectively. The Debye temperature of crystalline silicon and the root-mean-square dynamic displacement of atoms from the equilibrium position in its crystal lattice are calculated using the available data on thermal expansion.     

Thermal expansion and density of 80.5% LiF-19.5% CaF2 eutectic

The thermal expansion of the 80.5% LiF-19.5% CaF₂ eutectic is measured in the temperature range from 300 to 850 K at an error of 1%. The measurement results are approximated by an equation whose coefficients were calculated by the least-squares method. The tabular data on the relative thermal expansion, as well as on the true and mean thermal expansion coefficients for the eutectic, are calculated in the temperature range from 300 K to the melting point of 1042 K. The eutectic density is determined by the method of hydrostatic weighing in distilled water. Based on the measurement results and thermal expansion data, the dependences of the eutectic density on temperature in the temperature range from 300 to 1042 K are calculated and presented in the form of tables. The error of calculation of the eutectic density is found to be equal to 0.039-0.194% depending on temperature.     

Measurements of the thermal expansion coefficient of 1Cr18Ni9Ti stainless steel with a laser scanning microdisplacement detection technique

A laser scanning microdisplacement detection system has been developed to measure the thermal expansion coefficient of materials over the range from room temperature to 1200 K. The measurement apparatus consists of a dynamic heating device, a microdisplacement detection system, and a microcomputerbased high-speed data acquisition system. The specimen is dynamically heated from room temperature to 1200 K by passing a large electrical current through it. The thermal expansion of the specimen is detected by the laser detection system, which records the shift of Fraunhofer diffraction fringes with a photodetector. Measurements of the mean linear thermal expansion coefficient of 1Cr18Ni9Ti stainless steel in the range of 300–1200 K are described. The results are compared with other reported values of the thermal expansion coefficient. The maximum deviation between them is about 2.3% at the highest temperature, 1200 K.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Measurements of thermal expansion coefficient of phenolic foam at low temperatures

A dilatometer measuring thermal expansion coefficient at low temperatures is introduced. The thermal expansion coefficient of phenolic foam, a widely used thermal insulation material, was measured in the temperature range of 77-293 K by the dilatometer. The results showed that the thermal expansion coefficient of phenolic foam was very low in the tested temperature range with an error of about ±7.3%.     

Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739

An optical heterodyne interferometer has been combined with a helium flow cryostat to measure the linear thermal expansion coefficient of solids at cryogenic temperatures. The absolute accuracy in length measurement is within a few nanometres. Measurement results on a specimen of fused silica (SRM 739; by US NIST) in the temperature range 6–273 K are presented and compared with some literature data.     

Laser Interferometric Dilatometer Applicable to Temperature Range from 1300 to 2000 K

A laser interferometric dilatometer has been developed for measuring the thermal expansion of high-temperature solids in the temperature range 1300 to 2000 K. The dilatometer consists of a double-path optical heterodyne interferometer, a spectral-band radiation thermometer, and a vacuum chamber with carbon-composite heaters. The performance of the dilatometer has been assessed on the basis of measurements of linear thermal expansion coefficients for glassy carbon. The relative standard deviation of the measured values from those calculated from the fitting polynomial is 0.63% over the temperature range investigated. The combined standard uncertainties in the measured values are estimated to be less than 1.3% over this range. The process of sample relocation predominantly affects the reproducibility of the experimental results.     

Measurement of the thermal expansion coefficient of an all-sapphireoptical cavity

We present measurements of the frequency-temperature dependence of an all-sapphire Fabry-Perot optical cavity to be used as an optical frequency reference. Measurements were made by tracking the frequency of the cavity relative to a second high-stability cryogenic sapphire-spaced cavity-a technique with impressive resolution for measurements of the coefficient of thermal expansion (CTE). Measurements presented here cover the temperature range of 11 K to 26 K. We find that the CTE of the all-sapphire cavity for these temperatures is given by α_cavity=(7.7±0.9)×10^$ -¹³ T/sup (3.23±0.05/)     

Thermal expansion of tungsten in the range 1500–3600 K by a transient interferometric technique

The linear thermal expansion of tungsten has been measured in the temperature range 1500–3600 K by means of a transient (subsecond) interferometric technique. The tungsten selected for these measurements was the standard reference material SRM 737 (a standard for thermal expansion measurements at temperatures up to 1800 K). The basic method involved rapidly heating the specimen from room temperature up to and through the temperature range of interest in less than 1 s by passing an electrical current pulse through it and simultaneously measuring the specimen temperature by means of a high-speed photoelectric pyrometer and the shift in the fringe pattern produced by a Michelson-type interferometer. The linear thermal expansion was determined from the cumulative shift corresponding to each measured temperature. The results for tungsten may be expressed by the relation $$\begin{gathered} (l - l_0 )/l_0 = 1.3896 \times 10^{ - 3} - 8.2797 \times 10^{ - 7} T + 4.0557 \times 10^{ - 9} T^2 \hfill \\ - 1.2164 \times 10^{ - 12} T^3 + 1.7034 \times 10^{ - 16} T^4 \hfill \\ \end{gathered} $$ whereT is in K andl ₀ is the specimen length at 20°C. The maximum error in the reported values of thermal expansion is estimated to be about 1% at 2000 K and approximately 2% at 3600 K.     

Thermal Expansion and Some Characteristics of the Interatomic Bond Strength in Gallium and Indium Phosphides

A thermometric method is used to determine the thermal expansion coefficient of an InP melt in the temperature range of 1331–1426 K. A statistical treatment and a thermodynamic analysis of the thermal expansion coefficients for solid gallium and indium phosphides are performed using the relevant data on heat capacity. As a result, it is possible to recommend the most reliable values of the thermal expansion coefficient for these compounds in a wide temperature range. Based on these recommended data, the characteristic values of the Debye temperature and of the root-mean-square displacement of atoms from the equilibrium position are calculated, and the results are compared with the respective values obtained by other methods.     

Thermal Expansion of Gallium and Indium Phosphides: Thermodynamic Evaluation

The thermal expansion coefficient of molten InP was measured between 1331 and 1426 K. The available thermal expansion data for solid InP and GaP were critically evaluated and optimized with the use of heat capacity data. The most reliable data over a wide temperature range were recommended and were used to calculate the Debye characteristic temperature. The results were compared with the data obtained by other methods.     

SiC换热器材料热物理性质的研究

本文采用ＴＬＰ－１８型激光热常数仪和岛津ＴＭＡ－３０热分析仪研究了温度对等静压ＳｉＣ换热器材料的导热系数和热膨胀系数的影响，并对影响ＳｉＣ抗热震性能的各因素进行了分析。     

Reference Correlation for the Viscosity of Liquid Cyclopentane from 220 to 310 K at Pressures to 25 MPa

A correlation in terms of temperature and molar volume is recommended for the viscosity of liquid cyclopentane as a reference for low-temperature, high-pressure viscosity measurements. The temperature range covered is from 220 to 310 K and the pressure range from atmospheric up to 25 MPa. The standard deviation of the proposed correlation, within a 95% confidence limit, is 1%.     

Thermophysical Properties of Gaseous Tungsten Hexafluoride from Speed-of-Sound Measurements

The speed of sound was measured in gaseous WF₆ using a highly precise acoustic resonance technique. The data span the temperature range from 290 to 420 K and the pressure range from 50 kPa to the lesser of 300 kPa or 80% of the sample's vapor pressure. At 360 K and higher temperatures, the data were corrected for a slow chemical reaction of the WF₆ within the apparatus. The speed-of-sound data have a relative standard uncertainty of 0.005%. The data were analyzed to obtain the ideal-gas heat capacity as a function of the temperature with a relative standard uncertainty of 0.1%. These heat capacities are in reasonable agreement with those determined from spectroscopic data. The speed-of-sound data were fitted by virial equations of state to obtain the temperature dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials and the second based on a hard-core Lennard–Jones intermolecular potential. The resulting virial equations reproduced the sound-speed data to within ±0.005% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less. The hard-core Lennard–Jones potential was used to estimate the viscosity and the thermal conductivity of dilute WF₆. The predicted viscosities agree with published data to within 5% and can be extrapolated reliably to higher temperatures.     

Negative thermal expansion coefficient of graphene measured by Raman spectroscopy

The thermal expansion coefficient (TEC) of single-layer graphene is estimated with temperature-dependent Raman spectroscopy in the temperature range between 200 and 400 K. It is found to be strongly dependent on temperature but remains negative in the whole temperature range with a room temperature value of (-8.0 ± 0.7) × 10(-6) K(-1). The strain caused by the TEC mismatch between graphene and the substrate plays a crucial role in determining the physical properties of graphene, and hence its effect must be accounted for in the interpretation of experimental data taken at cryogenic or elevated temperatures.     

Hybridization of carbon–glass epoxy composites: An approach to achieve low coefficient of thermal expansion at cryogenic temperatures

The paper is based on a study to develop carbon–glass epoxy hybrid composites with desirable thermal properties for applications at cryogenic temperatures. It analyzes the coefficient of thermal expansion of carbon–epoxy and glass–epoxy composite materials and compares it with the properties of carbon–glass epoxy hybrid composites in the temperature range 300 K to 125 K. Urethane modified epoxy matrix system is used to make the composite specimens suitable for use even for temperatures as low as 20 K. It is noted that the lay-up with 80% of carbon fibers in the total volume fraction of fibers oriented at 30° and 20% of glass fibers oriented at 0° yields near to zero coefficient of thermal expansion as the temperature is lowered from ambient to 125 K.     

光干涉法高精度材料线膨胀系数测量

中国计量科学研究院研制的高精度材料线膨胀系数测量装置,满足温度范围为5～40 ℃、被测件长度在20～1 000 mm之间的线膨胀系数测量。采用激光干涉法测量被测件长度变化量,用高精度温度传感器测量温度值。设计了热平衡式干涉镜,利用空气折射率修正和零位误差补偿技术,保证在5～40 ℃变温范围内激光干涉仪的测量精度。以500 mm标准量块作为测量对象,线膨胀系数测量结果与德国物理技术研究院(PTB)测量结果的相对偏差为0.2%。材料线膨胀系数测量不确定度达到3×10^-8K^-1。     

The Thermal and Elastic Properties of Zinc Oxide-Based Ceramics at High Temperatures

The thermal conductivity, thermal expansion coefficient (TEC), and the propagation velocity of longitudinal and transverse ultrasonic waves in ZnO-based ceramics are investigated in the temperature range from 300 to 1200 K with a porosity from 1.5 to 21%. The Young, shear, and bulk moduli and the Poisson ratio are calculated from the data on the propagation velocities of ultrasonic waves. Formulas are suggested to calculate the investigated parameters as a function of temperature and porosity.