JOURNAL OF RESEARCH of the National Bureau of Standards - A. Physics and Chemistry High-Speed (Subsecond) Measurement of Heat Heat Capacity, Electrical Resistivity, and Thermal Radiation Properties of Tantalum in the Range 1900 to 3200 K* A. Cezairliyan, J. L. McClure, and C. W. Beckett Institute for Materials Research, National Bureau of Standards, (September 11, 1970) Measurements of heat capacity, electrical resistivity, hemispherical total and normal spectral emittances of tantalum above 1900 K by a pulse heating technique are described. Duration of an individual experiment, in which the specimen is heated from room temperature to near its melting point, is less than one second. Temperature measurements are made with a photoelectric pyrometer. Experimental quantities are recorded with a digital data acquisition system. Time resolution of the entire system is 0.4 ms. Results on the above properties of tantalum in the range 1900 to 3200 K are reported and are compared with those in the literature. Estimated inaccuracy of measured properties in the above temperature range is 2 to 3 percent for heat capacity, 0.5 percent for electrical resistivity, 3 percent for hemispherical total emittance, and 2 percent for normal spectral emittance. Key words: Electrical resistivity; emittance; heat capacity: high-speed measurements; high tempera- 1. Introduction Conventional methods of measuring heat capacity, electrical resistivity, and other thermophysical properties at high temperatures employ "drop", steadystate, and quasi steady-state techniques in which the specimen is exposed to high temperatures for long periods of time, ranging from minutes to hours. Extension of these techniques to temperatures above 2000 K creates problems resulting from increased heat transfer, chemical reactions, evaporation, diffusion, loss of mechanical strength, etc. To overcome these limitations, this laboratory has recently developed a high speed measurement technique in which the specimen is heated and pertinent quantities required for the determination of properties are measured in short times. The duration of an individual experiment, in which the specimen is heated from room temperature to near its melting point, is less than 1 s. A millisecond resolution photoelectric pyrometer is used to measure the specimen temperature. The recordings of experimental quantities are made with a high-speed digital data acquisition system, which has a time resolution of 0.4 ms. The application of this technique to measurements on molybdenum has been published [1].1 General reviews on high-speed methods for the measurement of thermophysical properties of electrical conductors have been presented recently [2, 17]. This work was supported in part by the Propulsion Division of the U.S. Air Force Office of Scientific Research under contract ISSA-69-0001. Figures in brackets indicate the literature references at the end of this paper. In the present study the technique was used to determine the heat capacity and electrical resistivity of tantalum in the temperature range 1900 to 3200 K, and the hemispherical total and normal spectral emittances up to 3000 K. 2. Method The method employed in this study is based upon rapid resistive heating of the specimen by the passage of high currents and measuring the pertinent quantities with appropriate time resolution. The required quantities are the power imparted to the specimen and the temperature of the specimen, both as functions of time. Imparted power is obtained from measurements of current flowing through the specimen and the potential difference across the "effective" 2 specimen as a function of time. The relationship for heat capacity is obtained from power balances for the specimen during the pulse heating and the following free cooling periods. The expression for heat capacity, which was derived in an earlier publication [1], is where Cp = heat capacity in J mol-1 K-1 i= current through the specimen in A σ = Stephan-Boltzmann constant (5.6697 = A, effective specimen surface area in m2 To= room temperature in K n= amount of effective specimen in mol (dT dt)= heating rate in K s-1 1 The hemispherical total emittance, e, which appears in the radiation loss term of the heat capacity relation, is determined from data collected during the free cooling period. Derived from the power balance relationship during the cooling period and eq (1), the expression for e is (2) where L、= radiance from surface of specimen as observed by the pyrometer. L= blackbody radiance from sighting hole in specimen as observed by the pyrometer. In all the above equations, geometrical quantities are corrected for the presence of the sighting hole. and the quantities related to radiation from the sighting hole are corrected for scattered light and departure from blackbody conditions. 3. Apparatus A functional diagram of the measurement system used in this study is shown in figure 1. The details of the system were described in an earlier publication [1] The specimen was a tube approximately 100 mm long with a small rectangular hole fabricated in the wall at the middle of its length to approximate blackbody conditions. The knife-edge probes, which were used for potential measurements, were made of tantalum and were placed 50 mm apart on the middle por tion of the specimen. The portion between the probes. defined as “effective“ specimen, was free from signif. cant temperature gradients for the duration of ar experiment. The specimen and the associated com ponents were contained in a vacuum chamber. The specimen temperature was measured with a (3) high-speed photoelectric pyrometer [12], which per mits 1200 evaluations of the specimen temperature per second. The pyrometer alternately compares the radiance from the blackbody hole in the specimen to that of a reference lamp. Equation (2) is used to compute values for eat selected temperatures, which are used to obtain a function for e in terms of temperature. Then, e values from this function are substituted in eq (1) to obtain heat capacity over the entire temperature range. Data from the heating period is also used to calculate the electrical resistivity with the aid of the equation and temperature were recorded with a high-speed Electrical signals corresponding to voltage, current. digital data acquisition system, which consists of a multiplexer, analog-to-digital converter, and a core memory together with various control and interfacin equipment. At the end of each experiment, the data were retrieved and recorded in printed numeric form and on punched paper tape via a teletypewriter. During this retrieval period, data were also sent to a time(4) sharing computer for immediate processing. Electrical signals corresponding to voltage, current. and temperature were also monitored simultaneously with oscilloscopes. 4. Measurements Measurements were made on four tantalum specimens. The first two specimens were used for experiments in the temperature interval 1900 to 3000 K To optimize the operation of the pyrometer, this tem perature interval was divided into three ranges with three experiments per range. These nine experiments are referred to as a series. The temperature ranges were low, 1900 to 2250 K; medium, 2100 to 2600 K. Two complete series of experiments were conducted on the first specimen (Ta-1). During the second series, wo additional experiments were conducted, one in the ow range and one in the high range, to measure the surface radiance of the specimen. Before the start of he first series of experiments, the specimen (Ta−1) vas subjected to approximately 30 heating pulses (in he range 2200 to 3000 K) to anneal the specimen and o determine the optimum heating rate for each temperature range. At the end of the first series of experiments and before the start of the second series, the specimen was pulse heated 15 times to 3000 K. One experiment per temperature range was conducted on the second specimen (Ta-2) without any prior heating Dulses. To obtain heat capacity and electrical resistivity In the temperature range 2950 to 3200 K, two other specimens, (Ta-3) and (Ta-4), were used. The duration of the current pulses ranged from 280 to 520 ms depending on the temperature. The average heating rate of the specimen was 5700 and 3700 K s-1 at 2000 and 3200 K, respectively. At these temperatures, radiative heat losses from the specimen amounted to approximately 3 and 22 percent of the input power, respectively. All of the experiments were conducted with the specimen in a vacuum environment of approximately 10-4 torr. The data on voltage, current, and temperature were used to obtain third degree polynomial functions for each quantity in terms of time, which then provided the input information for the equations of section 2. During the entire set of experiments, the pyrometer was calibrated five times against a tungsten filament standard lamp, which in turn was calibrated against the NBS Temperature Standard. The digital recording system including the differential amplifiers was calibrated three times during the experiments. The details of the calibration procedures are given in an earlier publication [1]. Prior to the start of the experiments, the optical system of the pyrometer was modified to reduce the effect of light scattered from the area around the sighting hole in the specimen. In the present system this effect is approximately one percent. The blackbody quality of the specimen sighting hole was estimated to be 0.99 using DeVos' [13] method. The temperature data from the pyrometer were corrected for both scattered light and departure from blackbody conditions. The details of the methods employed for these corrections are given in an earlier publication [1]. The nominal dimensions of the tubular tantalum specimens were: length = 4 in (101 mm), outside diameter=0.25 in (6.3 mm), and wall thickness = 0.02 in (0.5 mm). The outer surface of each specimen was polished to reduce heat loss due to thermal radiation. Specimen characterization was made on one specimen (Ta-1) by the following methods: photomicrography, chemical analysis, and residual resistivity ratio. Photomicrographs of the specimen before and after the entire set of experiments are shown in figure 2. It may be seen that considerable grain growth has taken place as the result of pulse heating the specimen to high temperatures. Chemical analyses were made of the specimen before and after the entire set of experiments. Comparison of results does not indicate any detectable change in impurity content. A list of the nature and composition of impurities in the specimen is given in table 1. tive" mass of the specimen was calculated from the total mass by ratio of the geometric surface area between voltage probes to total surface area. Length measurements at room temperature were made with a micrometer microscope to the nearest 0.03 mm. The thickness of the cylinder wall was calculated from the mass, surface areas, and density. Density of tantalum at 298 K was obtained by the water displacement method in a pycnometer. The results of three determinations gave a value of 16.65 × 103 kg m-3 with an average deviation of 0.03 percent. This compares favorably with the reported value of 16.6 × 103 kg m-3 [16]. TABLE 1. Impurities in tantalum specimen Based on ambient temperature (298 K) dimensions. "Extrapolated from higher temperature results. 5.1. Normal Spectral Emittance To calculate the normal spectral emittance, tw experiments were performed to measure the surface radiance of the Ta-1 specimen during the second heating series. The measurements were made at the effective wavelength of the pyrometer interference filter (650 nm; bandwidth 10 nm). The normal spectra emittance was calculated using the radiance dat from each surface experiment together with the date from a previous or later regular blackbody experiment The hemispherical total emittance of the Ta-1 specimen was computed with the aid of eq (2) using temperature data taken during both heating and initial free cooling periods in an experiment. A third degree polynomial function for heat capacity in terms of temperature for each heating series on Ta-1 was obtained by least squares approximation of results from individual experiments. The standard deviation of the points from the function for the first and second heating series were 0.19 and 0.17 percent, respectively. A similar function was also obtained for the combined results of experiments in the first and second series with a standard deviation of 0.18 percent. A linear function for hemispherical total emittance for each heating series was obtained by least squares approximation of the individual values. The standard deviation of the points from the function for the first and second heating series were 0.7 and 0.5 percent, respectively. The functions that are valid in the temperature range 2300 to 3000 K are: €= 0.2197 +4.146 × 10−3T Figure 5 shows the deviations of the experimental results from the smooth function for the combined heating series. The figure also shows the deviation of the function for each individual heating series from the heat capacity function for the combined series. Compared to the function for the combined series, the average difference between the functions for the first and second heating series is about 0.1 percent, which is smaller than the measurement resolution. Therefore, it may be concluded that the measured heat capacity shows no significant difference between the two heating series. The function for the combined series that is valid in the temperature range 1900 to 3000 K is: cp=-6.549 +4.583 × 10-2T - 2.013 × 10-572 +3.325 × 10-973 (9) where T is in K and c, in J mol K-'. Heat capacity up to 3000 K computed using the above equation is given in table 2. In the computations of heat capacity. the atomic weight of tantalum was taken as 180.95 [15]. Without any prior heating pulses, three experiments were conducted on a second tantalum specimen (Ta-2). Figure 6 shows the difference in measured heat capacity between Ta-1 and Ta-2. The base line in figure 6 represents the smooth function for heat (first series) (7) capacity of Ta-1 given by eq (9). The maximum deviation between the heat capacity results of the two specimens occurs at the lowest temperature and is less than 1 percent. The tendency for the heat capacity of Ta-2 to approach that of Ta-1 as the temperature increases may be due to annealing effects as the temperature range for the Ta-2 specimen was increased. € = 0.1991 +4.687 × 10-57 second series) (8) Hemispherical total emittance computed using eq (8) s given in table 2. The experimental results are presented in figure 4. |