FIGURE 1. Photomicrographs of the tungsten specimen before (upper photograph) and after (lower photograph) the entire set of experiments.

each quantity in terms of time, which then provided the input information for the determination of properties.

The pyrometer was calibrated before and after the entire set of experiments 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 also calibrated before and after the entire set of experiments. The details of the calibration procedures are given in an earlier publication [2].

The specimen was a tube fabricated from a tungsten rod by removing the center portion by an electroerosion technique. The outer surface of the specimen erosion technique. The outer surface of the specimen was polished to reduce heat loss due to thermal radiation. The nominal dimensions of the specimen were: length, 4 in (101 mm); outside diameter, 0.25 in (6.3 mm); and wall thickness, 0.02 in (0.5 mm).

Specimen characterization was made by the following methods: photomicrography, spectrochemical analysis, and residual resistivity ratio. Photomicrographs of the specimen (figure 1) indicate that considerable grain growth took place as the result of pulse heating to high temperatures. A list of the nature and composition of impurities in the specimen, at the end of the entire set of experiments as determined by

spectrochemical analysis,2 is given in table 1. Th residual resistivity ratio of the specimen (ratio o electrical resistivity at 273 K to that at 4 K), measure before the experiments, was 41.

The "effective" mass of the specimen was calculated from the total mass by the ratio of the geometric sur face area between voltage probes to total surface area Length measurements at room temperature were made with a micrometer microscope. The cross-sectiona area of the specimen was calculated from the mass density, and geometry. Density of the tungsten speci men was measured at 293 K to be 19.23 × 103 kg m-3 This compares favorably with a previously cited value of 19.3 × 103 kg m-3 [4].

3. Experimental Results

This section presents the thermophysical properties determined from the measured quantities. All values are based on the 1968 International Practical Temperature Scale [5]. In all computations, the geometrical quantities are based on their room temperature (298 K) dimensions. The experimental results are represented by polynomial functions in temperature obtained by least squares approximation of the individual points. The final values on properties at 100 degree temperature intervals computed using the functions are presented in table 2. Results obtained from individual experiments, by the method described previously [2], are given in the appendix (tables A-1. A-2, and A-3). The patterns of deviations of individual data points from the smooth functions for the properties are similar to those in the earlier work on tantalum [3].

2 Spectrochemical analysis of the tungsten specimen was made by the Lamp Metals and Components Department of the General Electric Company.

3.4. Normal Spectral Emittance

Normal spectral emittance was computed using data from three sets of two experiments, one in which the pyrometer was aimed at the surface of the specimen, and another in which it was aimed at the blackbody hole in the specimen. The target on the surface was a narrow flat surface ground along the specimen. The measurements were made at the effective wavelength of the pyrometer interference filter (650 nm; bandwidth 10 nm). The function for normal spectral emittance (standard deviation = 0.2%) that represents the results in the temperature range 2000 to 3000 K is: EN, λ= 0.3804-5.060 × 10-7 T (4)

where T is in K.

lere T is in K and c, in J mol-1K-1. In the computans of the heat capacity, the atomic weight of tungsten is taken as 183.85.

To determine the effect of thermal cycling on heat pacity, the results of four additional experiments vering the range 2000 to 3300 K were compared th those reported above. The average absolute fference between the two sets of results was less an 0.1 percent, which is smaller than the measureent resolution. This indicates that the measurements ere not sensitive to thermal cycling.

3.2. Electrical Resistivity

The electrical resistivity of tungsten was determined om the same experiments that were used to calculate e heat capacity. The function for electrical resistivity tandard deviation = 0.4%) that represents the results the temperature range 2000 to 3600 K is:

p=-14.08+ 3.515 × 10-2 T

(2)

4. Estimate of Errors

Estimates of errors in measured and computed quantities lead to the following estimates of errors in the properties over the temperature range 2000 to 3600 K.

Heat capacity: 2 percent at 2000 K, 3 percent at 3600 K.

Electrical resistivity: 1 percent

Hemispherical total emittance: 3 percent
Normal spectral emittance: 3 percent

Details regarding the estimates of errors and their combination in high-speed experiments using the present measurement system are given in a previous publication [2]. Specific items in the error analysis were recomputed whenever the present conditions differed from those in the earlier publication.

5. Discussion

Using eq (5) and the heat capacity results of this work, the quantity Ac was computed for temperatures above 2000 K. The results are tabulated in table 6. The uncertainty in the computed Ac may be as high as 1 J mol-1 K-1. This was obtained from the combined uncertainties in the coefficients in eq (5) and the measured heat capacities.

Although the mechanisms of vacancy generation become important at high temperatures, it was not possible to attribute the high values entirely to vacancies. To demonstrate this, a crude estimate of the contribution of vacancies to heat capacity was made using the method described in a previous publication [2]. The reported values for vacancy formation energy of tungsten are 3.3 eV [7] and 3.6 eV [8]. Results of quenching experiments on various refractory elements [7,9] have indicated that vacancy concentrations are probably in the range 0.01 to 0.1 percent at their melting points. Estimates corresponding to a vacancy concentration of 0.1 percent at the melting point and a vacancy formation energy of 3.3 eV are given in table 6. The results indicate that vacancy contribution would be small, less than 0.8 J mol-1 K-1 (upper limit) at 3600 K, and would not account for the high heat capacity values.

If the entire difference between measured and computed [using the first three terms in eq (5)] heat capacities is attributed to vacancies, values of 1.3 eV for energy and 12 percent for concentration at the melting point are obtained. Both of these values seem to be unrealistic for tungsten.

To give a simple expression for the heat capacity of tungsten over a wide temperature range, an empirical