Thermal expansion of niobium in the range 1500–2700 K by a transient interferometric technique

The linear thermal expansion of niobium has been measured in the temperature range 1500–2700 K by means of a transient (subsecond) interferometric technique. The basic method involves 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 is determined from the cumulative shift corresponding to each measured temperature. The results for niobium may be expressed by the relation (l-l ₀)/l ₀=5.4424×10^–3–8.8553×10^–6 T+1.2993×10^–8 T ² –4.4002×10^–12 T ³+6.3476×10^–16T⁴ where T is in K and l 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 not more than 2% at 2700 K.Paper presented at the Ninth International Thermal Expansion Symposium, December 8–10, 1986, Pittsburgh, Pennsylvania, U.S.A.     

Thermal properties of MoSi2 and SiC whisker-reinforced MoSi2

The heat capacity, thermal conductivity and coefficient of thermal expansion of MoSi₂ and 18 vol % SiC whisker-reinforced MoSi₂ were investigated as a function of temperature. The materials were prepared by hot isostatic pressing between 1650 and 1700 °C, the hold time at temperature being 4 h. The heat capacity of MoSi₂ showed an increase from about 0.44 Wsg^–11K^–1 at room temperature to 0.53 at 700 °C. Whisker reinforcement increased heat capacity by about 10%. Thermal conductivity exhibited a decreasing trend from 0.63 Wcm^–1 K^–1 at room temperature to 0.28 Wem^–1 K^–1 at 1400°C. Whiskers reduced conductivity by about 10%. The thermal expansion coefficient increased from 7.42 °C^–1 between room temperature and 200 °C to 9.13 °C^–1 between room temperature and 1200 °C. There was a 10% decrease resulting from the whiskers. The measured data are compared with literature values. The trends in the data and their potential implications for high-temperature aerospace applications of MoSi₂ are discussed.     

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.     

Interferometric technique for the subsecond measurement of thermal expansion at high temperatures: Applications to refractory metals

A high-speed interferometric technique has been developed at the National Institute of Standards and Technology to measure thermal expansion of metals between room temperature and temperatures primarily in the range 1500 K to near their melting points. The basic method involves resistively 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, with submillisecond resolution, 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 polarized beam from a He-Ne laser in the interferometer is split into two components, one which undergoes successive reflections from highly polished flats on opposite sides of the specimen and one which serves as the reference beam. The linear thermal expansion of the specimen is determined from the cumulative fringe shift corresponding to each measured temperature. The technique is capable of measuring linear thermal expansion with a maximum estimated uncertainty which ranges from about 1% at 2000 K to approximately 2% at 3600 K. Measurements have been performed on the refractory metals, niobium, molybdenum, tantalum, and tungsten, yielding thermal expansion data in the temperature range 1500 K up to near their respective melting points. Also, the technique has been used to follow the rapid dimensional changes that occur during solid-solid phase transformations; in particular, the transformation in iron has been studied.Invited paper presented at the Tenth International Thermal Expansion Symposium, June 6–7, 1989, Boulder, Colorado, U.S.A.     

Thermal expansion of irradiated polypropylene from 10–340 K

The coefficient of thermal expansion of gamma-irradiated polypropylene (PP) has been measured from 10–340 K by using the three-terminal capacitance technique. The samples were irradiated to 500 Mrad in air at room temperature with gamma rays from a⁶⁰Co source at a dose rate of 0.26 Mrad h^–1. The crystallinity of the sample was measured by X-ray diffraction technique. The crystallinity was found to decrease with radiation dose from 55% at 0 Mrad to 44.7% at 500 Mrad. The thermal expansion coefficient was found to be almost constant with radiation dose from 10–125 K and decreases with radiation dose from 125–340 K.     

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.     

Thermal expansion behavior and microstructure in bulk nanocrystalline selenium by thermomechanical analysis

Thermal expansion behavior of bulk nanocrystalline (NC) Se samples with a grain size range of 16–46 nm was studied by thermomechanical analysis (TMA) in the temperature range 290–373 K. Bulk NC Se samples were prepared by isothermally crystallizing the as-quenched bulk amorphous solid at 373–478 K. The glass transition and crystallization of the remaining amorphous Se in the partially crystallized samples were studied by TMA, and compared with the results of differential scanning calorimetry (DSC). The glass transition temperature, as determined from the thermal expansion behavior, was 308 K, 11 K lower than the value by DSC analysis. A structural densification phenomenon was observed in a grain growth process of an as-crystallized NC Se sample by TMA. It was found that the linear thermal expansion coefficient of the bulk NC Se sample increased with a reduction of grain size, from which the deduced thermal expansion coefficient of the interface decreased with the refinement of the grain size.     

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.     

A laser interferometric dilatometer for low-expansion materials

The development of a high-precision dilatometer based on interferometry presents a number of challenges. This paper describes a laser interferometric dilatometer developed for high-precision thermal expansion measurements in the materials laboratory. The Sandia dilatometer uses dual-beam laser interferometry with a computer-controlled optical alignment feature to achieve high-precision length change measurements. This device has been modified to expand its measurement capabilities in a number of areas. A new thermal chamber has been incorporated which provides a range of measurement from 90 to 500 K while minimizing thermal effects on the optical portion of the instrument. A new specimen holder has been developed to cover this temperature range while accommodating a wider variety of specimen types. In particular, thin (1-mm) composities may be employed in the holder, which uses a single specimen, with only modest shape and preparation requirements, to provide absolute length change measurements. Tilt errors limit the overall performance of dilatometers based on dual-beam interferometry. Significant improvements in precision were demonstrated by incorporating a unique optical system which independently measures specimen holder tilt; tilt errors were corrected and a length change resolution near 0.4strain was achieved. Expansion coefficient data obtained with the device agreed with established results on fused silica and stainless steel. New expansion data were obtained from 90 to 293 K on stainless steel, NBS Standard Reference Material 738.Invited paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

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 and Electrical Properties of Gadolinium Sulfides at High Temperatures

A study is made into the temperature dependence of the thermal conductivity, electrical conductivity, thermoelectromotive force, thermal expansion coefficient, and heat capacity in the temperature range from 300 to 1200 K for polycrystalline gadolinium sulfides GdS _y (y= 1.495–1.487) produced both by recrystallization pressing and by crystallization from a melt. The role of the mechanisms of heat and charge transfer is estimated depending on the composition. The reasons for changes in their electrical and thermal properties are analyzed. The thermoelectric efficiency is calculated. It is demonstrated that Z 0.6 × 10^–3K^–1at T 1000 K.     

Thermophysical Properties of 75Ni–15Mo–10Re Alloy

The true heat capacity, thermal expansion, thermal conductivity, electrical resistance, and density of NMR-75 alloy (75 wt % Ni, 15 wt % Mo, and 10 wt % Re) are investigated in a temperature range of 300–1300 K. The enthalpy, mean coefficient of thermal expansion, thermal diffusivity, and Lorentz number are calculated from the obtained experimental data. The measurement results show that a reversible structural transformation occurs in the alloy in a temperature range of 750–960 K. In accordance with the phase diagram, the ternary system of the alloy consists of an a-solid molybdenum–nickel solution, which is in equilibrium with a -solid rhenium–nickel solution and a Ni₄Mo intermetallic compound. On heating the alloy in a temperature range of 750–960 K, the intermetallic compound transforms into the -solid molybdenum–nickel solution with the absorption of heat, while the ordered structure transforms into a disordered one. The thermal effect Q = 6 kJ/kg and the activation energy of alloy disordering E = 2.2 eV are estimated. The transformation proper is regarded as a second-order transition.     

Thermophysical Properties of Sulfides of Lanthanum, Praseodymium, Gadolinium, and Dysprosium

The temperature dependence of the thermal conductivity, electrical conductivity, thermoelectromotive force, and thermal expansion coefficient for sulfides of lanthanum, gadolinium, praseodymium and dysprosium of the composition Ln_{3 – x} V _x S₄ is investigated in the temperature range from 300 to 1200 K. It is shown that the transfer phenomena and thermoelectrical properties of the investigated compositions depend on the concentration of current carriers, cation vacancies, and mobility. Gadolinium sulfide is found to have the highest thermoelectrical efficiency. The scattering from ions of rare-earth elements has a noticeable effect on the magnitude and temperature dependence of the lattice thermal conductivity and electrical resistance.     

Thermophysical properties of ceramic matrix composites produced by polymer pyrolysis

A unidirectional composite and a series of bidirectionally reinforced composites were fabricated using carbon fibre reinforcement in a silicon carbide matrix, which was produced by the pyrolysis of a polymer precursor. The thermal expansion over the temperature range 20–1000 °C has been measured and the thermal diffusivity measured over the temperature range 200–1200 °C. Thermal diffusivity data was converted to conductivity data using measured density and literature specific heat data. Metallographic examination has been carried out on the composites and the results are discussed in terms of the observed microstructural features.     

A dynamic technique for measurements of thermophysical properties at high temperatures

A technique is described for the dynamic measurement of selected thermophysical properties of electrically conducting solids in the range 1500 K to the melting temperature of the specimen. The technique is based on rapid resistive selfheating of the specimen from room temperature to any desired high temperature in less than 1 s by the passage of an electrical current pulse through it and on measuring the pertinent quantities, such as current, voltage, and temperature, with millisecond resolution. The technique was applied to the measurement of heat capacity, electrical resistivity, hemispherical total emissivity, normal spectral emissivity, thermal expansion, temperature and energy of solid-solid phase transformations, melting temperature, and heat of fusion. Two possible options for the extension of the technique to measurements above the melting temperature of the specimen are briefly discussed. These options are: (1) submillisecond heating of the specimen and performance of the measurements with microsecond resolution, and (2) performance of the experiments in a near-zero-gravity environment with millisecond resolution.Paper presented at the Japan-United States Joint Seminar on Thermophysical Properties, October 24–26, 1983, Tokyo, Japan.     

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.     

Automated low-temperature dilatometer

We have developed a small automated lowtemperature dilatometer for investigation of the thermal coefficient of linear expansion for solid materials in the temperature range 4–300 K. The metrological characteristics of the apparatus allow us to solve an auxiliary range of research and applied problems. The economical use of liquid coolants in the cryostat substantially reduces operating expenses.Translated from Izmeritel'naya Tekhnika, No. 10, pp. 48–50, October, 1994.     

High thermal expansion KAlSiO4 ceramic

Orthorhombic kalsilite (KAlSiO₄) was prepared by solid-state reaction from K₂CO₃, Al₂O₃, and SiO₂. The axial thermal expansion coefficients of the orthorhombic kalsilite were 1.6×10^–5°C^–1 for the a-axis, 1.6×10^–5°C^–1 for the b-axis, 2.8×10^–5°C^–1 for the c-axis, and 2.0×10^–5°C^–1 for the average from room temperature to 1000°C. A high thermal expansion ceramic consisting of the orthorhombic kalsilite was prepared by sintering. The densification was promoted by adding Li₂CO₃. The KAlSiO₄ ceramic sintered at 1200°C for 2 h with 5 wt% Li₂CO₃ had a bending strength of 65 MPa and linear thermal expansion coefficient of 2.2×10^–5 °C^–1 from room temperature to 600°C.     

Thermal diffusivity of solids with a low expansion coefficient: A dilatometric technique

A dilatometric method is presented, suitable to obtain both thermal diffusivity and conductivity of low-conducting solids with a low expansion coefficient. The repeatibility of the measurements of thermal conductivity is 3%, whereas that for diffusivity is 5 %. Data for fused silica at room temperature are given, consistent with those reported in the literature. Since the method is based on detecting the thermal expansion of a copper disk in thermal contact with the specimen, its range of applicability is linked to the sensitivity by which the dilation of copper can be measured: no difficulty arises between liquid nitrogen and 1000°C.     

Measurement of Thermal Diffusivity at Low Temperatures Using an Optical Reflectivity Technique

An experimental arrangement has been developed for measuring the transient temperature responses and the thermal diffusivities of foil materials in the range of 10 to 300K by using the optical reflectivity technique. The cryogenic system with optical windows is designed to provide temperatures from 10 to 300 K. The front surface of a foil specimen is heated by a pulsed Nd:YAG laser. In situ measurement of the reflectivity of a continuous-wave He–Ne laser at the rear surface is conducted on the microsecond time scale. Using the temperature dependence of reflectivity, the transient temperature response is deduced. The thermal diffusivity is obtained by fitting Parker's formulae to the experimental data on temperature rise. Stainless-steel foils are chosen as samples and are studied in the region from 10 to 300 K. The accuracy is examined by comparing the present results with the theoretical temperature responses and thermal diffusivity data from the literature. Good agreement is observed.