Masahiro Okaji

Linear Thermal Expansion Coefficient of Silicon from 293 to 1000 K

As a part of the program to establish a thermal expansion standard, the linear thermal expansion coefficients of single-crystal silicon have been determined in the temperature range 293 to 1000 K using a dilatometer which consists of a heterodyne laser Michelson interferometer and gold versus platinum thermocouple. The relative standard deviation of the measured values from those calculated from the best least-squares fit was 0.21%. The relative expanded uncertainty in the measurement was estimated to be 1.1 to 1.5% in the temperature range, based upon an analysis of thirteen standard uncertainties. The present data are compared with the data previously obtained by similar dilatometers and the standard reference data for the thermal expansion coefficient of silicon, recommended by the Committee on Data for Science and Technology (CODATA). The present data are in good agreement with the most recently reported data but not with the earlier high-temperature data used to evaluate the standard reference data, which suggests a need for the reevaluation of the standard reference data for the thermal expansion coefficient of silicon at temperatures above 600 K.

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.

Anisotropic thermal-diffusivity measurements by a new laser-spot-heating technique

A new technique to measure thermal diffusivities of solid materials, including their anisotropic behaviours, has been developed. The technique is based on periodic heating: an intensity-modulated laser beam is focused to make a small heat spot on the front side of a thin-plate specimen and the excited temperature waves are detected by a thin thermocouple attached onto its rear side. The phase lag of temperature waves is monitored as a function of the distance between the heated spot and the sensing point. The accuracy and the applicability of the present technique were well verified by using two kinds of isotropic reference samples, an austenitic stainless steel and pure copper. The typical uncertainty is estimated to be 5% at room temperature. This technique was applied to evaluate the highly anisotropic thermal diffusivity of highly oriented pyrolytic graphite (HOPG). Its anisotropy, Dab/Dc (the ratio of the in-plane thermal diffusivity to the out-of-plane one), was observed to be about 220.

A calibration method for measuring thermal expansions with a push-rod dilatometer

The calibration method for measuring the linear thermal expansion coefficient (LTEC) with a push-rod dilatometer was examined by considering a simple model. To verify the validity of the calibration method, measurements of LTECs for samples of fused silica (SRM 739) and a sample of a single crystal of silicon were carried out with a push-rod dilatometer in the temperature range from room temperature to 973 K. Measurements of melting points of pure metals for temperature calibration, measurement of the sensitivity of a displacement measurement device with a laser interferometer and evaluation of the influence of fluctuations in room temperature on the measured displacement results were also carried out. As a result, the calibrated results of the LTEC for the silicon sample corresponded to the reference value for silicon to within a deviation of ±2% over the measurement temperature range and the validity of the analysis for the push-rod dilatometer was confirmed.

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.

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.

Anomalous thermal expansion behaviors in Sm-Ba-Cu-O superconductors

Abstract Linear thermal expansion coefficients α of c-axis oriented Ag-added Sm-Ba-Cu-O superconductors have been measured in the range of 10 — 300 K. The α showed a large bump along the c-axis and a large dent along the ab-plane around 170 – 260 K for the 2 wt% and 5 wt% Ag 2 O specimens, but these anomalies essentially disappeared with thermal cycles between room and cryogenic temperatures. In contrast, there were no significant anomalies for the 10 wt% and 20 wt% Ag 2 O specimens. These results suggest that the addition of Ag 2 O should moderate deformation and help to increase mechanical strength.

Ultraprecise thermal expansion measurements of partially stabilized zirconia gauge blocks with an interferometric dilatometer

Linear thermal expansion coefficients (LTECs) of two kinds of partially stabilized zirconica (PSZ) gauge blocks were measured in the range from -10 to 60 degrees C with an optical heterodyne interferometric dilatometer. The dilatometer provides an order of 1 X 10-9 K-1 uncertainty and reproducibility in LTEC measurement. LTEC of (9.230 +/- 0.012) X 10-6 K-1 were obtained for four 2 percent Al2O3- PSZ gauge blocks, and (9.383 +/- 0.001) X K-1 for one 99.9 percent PSZ gauge block. These differences are discussed, together with the compositions and production lots.