Oct 15, 2013 - frequency sine-wave generator which produces stable sinusoidal temperature .... coupled audio amplifier was used for this. However it had a.
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Apparatus for the measurement of thermal diffusivity featuring a low-frequency sine-wave generator and a digital phase meter
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1978 J. Phys. E: Sci. Instrum. 11 941 (http://iopscience.iop.org/0022-3735/11/9/019) View the table of contents for this issue, or go to the journal homepage for more
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J. Phys. E: Sci. Instrum., Vol. 11, 1978. Printed in Great Britain
Apparatus for the measurement of thermal diffusivity featuring a Iow-f req U en cy si ne-wave generator and a digital phase meter
1v Savvides and W Murray School of Physics, University of New South Wales, Kensington 2033, Australia Receiued 26 January 1578, in final ,form 28 April 1578
Abstract The apparatus enables the thermal diffusivity of a wide range of solids to be measured to an accuracy of i:2 % using the Angstrom method. It features a lowfrequency sine-wave generator which produces stable sinusoidal temperature conditions at the heater, and a digital phase meter which measures phase directly in degrees with a resolution of 0.1 '. A low-noise amplifier and an active bandpass filter are used to improve the signal-to-noise ratio whenever conditions are such that the signals from thermocouples or probes are weak. Results are reported of the thermal conductivity of samples of single-crystal silicon and germanium in the temperature range 300-700 K.
1 Intraduction The thermal conductivity of solids at high temperatures is often determined under dynamic conditions where the temperature at points along the length of a sample varies periodically. Normally, dynamic methods measure thermal diffusivity D which is defined as the ratio of thermal conductivity K to specific heat per unit volume. Sidles and Danielson (1954) and Abeles et a/(1960), using a modification of a method first proposed by Angstrom (1863), have shown that a high degree of accuracy in the thermal diffusivity is attainable at temperatures as high as 1270 K. The basic principle of this method is that if one end of a long bar-shaped sample is heated periodically and the other end is free to radiate to an ambient temperature, then the temperature along the sample also varies with the same period but with amplitude decaying exponentially to zero at the free end. As the temperature wave travels along the sample length with a finite velocity there is a phase relationship between any two points on this length. If the temperature wave is sinusoidal the solution to the heat equation is straightforward and the thermal diffusivity is given by
where 7 is the period of the wave, p is the phase difference and 6 is the ratio of the amplitudes at the two consecutive points along the sample separated by length L. In the absence of surface radiation losses, P = l n S. Radiation losses cause 0022-3735/78/0009-0941 $01.OO 8 1978 The Institute of Physics
/3 to decrease and In 6 to increase but the product ,8 In 6 remains constant and equation (1) is true as long as heat radiates from the surface of the sample into a black-body environment at ambient temperatures (Abeles ef a/ 1960). In order to determine thermal conductivity, values of specific heat and density are needed. However, the deteImination of these quantities is not difficult, and since they are not structure-sensitive it is not necessary to determine them for each sample of a solid. In this paper an apparatus is described for measuring the thermal diffusivity at high temperatures to i 2 % accuracy. The apparatus is capable of measuring the thermal diffusivity of a wide range of materials, such as single-crystal silicon which has a high diffusivity, and low-diffusivity materials such as Ge-Si alloys. A specially designed low-frequency sine-wave generator is employed to produce a very stable sinusoidal temperature wave at one end of a sample which is in contact with a heater of small heat capacity. The amplitude ratio is measured to an accuracy of kO.5%. Phase is measured directly in degrees with a resolution of 0.1" by a digital phase meter; a typical phase difference of 100" is determined to an accuracy of 50.29;. The overall accuracy is largely determined by the accuracy of measuring the thermocouple or probe szparation; this separation usually can be determined to I 0 . 5 accuracy.
