Measurement of Melting Point and Radiance Temperature (at Melting Point and at 653 nm) of Hafnium-3 (wt. %) Zirconium by a Pulse Heating Method

A subsecond duration pulse heating method is used to measure the melting point and radiance temperature (at 653 nm) at the melting point of hafnium containing 3.12 weight percent zirconium. The results yield a value of 2471 K for the melting point on the International Practical Temperature Scale of 1968. The radiance temperature (at 653 nm) of this material at its melting point is 2236 K, and the corresponding normal spectral emittance is 0.39. Estimated inaccuracies are: 10 K in the melting point and in the radiance temperature, and 5 percent in the normal spectral emittance.


. Introduction
A subsecond-duration pulse heating technique was used earlier to measure the melting point and the radiance temperature 1 at the melLing point of several refractory metals [1 -7] . 2 In the present study, the same technique is used foJ' similar meaSUlements on hafnium containing 3.12 weight percent zirconium.
The method is based on rapid resistive self-heating of the specimen from loom temperature to high temperatures (above 1500 K) in less than one second by the passage of an electrical current pulse through it; and on measuring, with millisecond resolution, such experimental quantities as current through the specimen, potential drop across the specimen, and the specimen temperature. Temperature is measured with a high-speed photoelectric pyrometer [8], which permits 1200 evaluations of specimen temperature per second. Details regarding the construction and operation of the measurement system, the methods of measuring experimental quantities, and other pertinent information, such as the formulation of relations for properties, elTor analysis, etc. are given in earlier publications [9,10].

Measurements
The material used in this study was a hafnium 'This work was supported in part by tho U.S. Air Force Office of Scientific Research.
I Radiance temperature (sometimes referred to as brightness temperature) is the apparent temperature of the specimen surface correspo nding to the effeclive wavelength of the measuring pyrometer. 2  The total amount of all other detected clements was less than 70 ppm, each element being below 10 ppm limit. Measuremen ts were performed on two specimens in the form of tubes and nine specimens in the form of strips. The tubes, used to determine the ~elting point, were fabricated from rods by removmg the center portion using an electro-erosion technique. A small rectangular hole (1 x 0.5 mm) was fabricated in the wall at the middle of the specimen to approximate blackbody conditions for the pyrometric temperature measurements. Prior to the experiments, the tubular specimens were heat treated by subjecting them to 10 heating pulses [up to 1700 K] in a vacuum environment of 1.3 x 10 3 N'm-2 (,,-,10-5 torr). The nominal dimensions of the tubes were: length, 89 mm; outside diameter, 6.4 mm; wall thickness, 0.5 mIn.
The strips were used to measure the J'adian~e Lelllperature at the melting point. Before the expel'JInents, the surface of the specimens was treated using abra-'live; three different grades of abrasive were used yielding specimens with three d.ifferen t su rface roughnesses (ranging from approxImately 0.2 !-I1ll to 0.5 !-1m in RMS). The nominal dimensions of the strips were: length, 76 mm; width, 3.2 mIn; thickness, 1.6 mm.
The experiments on the tubular specimens were conducted in a vacuum environment of approximately 1. 3 x 10 3 N'm -2 ('" 10 -5 torr), while all the experiments on strip specimens were conduced in an argon environment at atmospheric pressure. The heating rates for the tubular specimens were approximately 8000 K'S-l (specimen I) and 6000 K'S-l (specimen II) corresponding to specimen heating periods (from room temperature to melting point) of approximately 300 ms and 400 ms, respectively. The heating rates for the strips near the melting point varied from 2000 K'S-l to 4800 K'S-l, and the corresponding heating periods varied from 800 ms to 350 ms.
The high-speed pyrometer was calibrated before the entire set of experiments, using a tungsten filament standard lamp, which in turn was calibrated against the NBS "Temperature Standard." All temperatures reported in this paper, except where explicitly noted, are based on the International Practical Temperature Scale of 1968 [11].

Melting Point
Temperature of the tubular specimens was measured near and during the initial melting period, until the specimen collapsed. Typical results for the variation of the specimen temperature as a function of time (for specimen I) are shown in figure 1. The plateau in temperature indicates the region of solid and liquid equilibria. The complete results for the tubular specimens are presented in table 1. The value of the melting point was obtained by averaging temperature points on the plateau for each specimen. The duration of the plateau of specimen II is shorter than that of specimen I because of an early collapse of the second specimen. To determine the trend of measured temperatures at the plateau, temperatures for specimen I were fitted to a linear function in time  using the least squares method. The slope of the linear function was -23 K·s-1, which corresponds to a maximum temperature difference of less than 0.4 K between the beginning and the end of the plateau. This procedure gave a standard deviation of 0.4 K, the same as that obtained by averaging the temperatures. The average melting point of the specimens is 2471.2 K with an average absolute deviation from the mean of 0.1 K. It may be concluded that the melting point of hafnium-3 (wt. %) zirconium measured in this work is 2471 K.

Radiance Temperature at the Melting Point
Radiance temperature measurements were performed on strips at 653 nm which corresponds to the effective wavelength of the pyrometer's interference filter. The bandwidth of the filter was 10 nm. The circular area viewed by the pyrometer was 0.2 mm in diameter.
Radiance temperature of hafnium-3 (wt. %) zirconium at its melting point for the nine experiments (corresponding to nine specimens) and other pertinent results are reported in table 2 .. The va~'ia tion of radiance temperature as a functlOn of tIme near and at the melting point is shown in figure 2 for a typical experiment (specimen II).
A single value for the radiance temperature at the plateau for each specimen was obtained by averagina the temperatures at the plateau. The number of te~peratures used for averaging ranged from 22 to 55, depending both on the heating rate and on the behavior of the specimen during melting. The standard deviation of an individual temperature from the average was in the range 0.1 to 0.5 K for ~ll. the experimen~s . Similar values. (for standard .devIatI,:m) were obtamed when data 111 the premeltmg perIod were fitted to a quadratic function in time. This indicates that during melting no undesirable e.ffects took place, such as vibration of the .specImen, development of hot spots. in the speClme~. and random changes in the speCImen surface condItlOns.
To determine the trend of measured temperatures at the plateau, temperatures for each experiment were fitted to a linear function in time using the least squares method. The detailed results are reported in table 2. The temperature difference between the beginning and the end of the plateau (corresponding to the slope in the plateau) is in the I:ange 0-0.7 K. The standard deviation of an indiVIdual  temperatur~ from the linear function was approximately the same as the standard deviation obtained by direct averaging of the temperatures. The average radiance temperature at the melting point for the nine specimens was 2236.4 K with an average absolute deviation of 0.6 K and a maximum absolute deviation of 1.3 K. The results are presented in figure 3. It may be concluded that the radiance temperature (at 653 nm) of hafnium-3 (wt. %) lIirconium at its melting point is 2236 K.
The normal spectral emittance at the melting point was determined using the results of the radiance temperature (obtained from the measurements on strip specimens) and the melting point (obtained from the measurements on tubular specimens). The results yield a value of 0.39 for the normal spectral  emittance (at 653 nm) at the melting point of hafnium-3(wt. %) zirconium. No effect was noticed with the variation in initial roughness.

Estimate of Errors
Sources and estimates of errors in experiments similar to the ones conducted in this study are given in detail in earlier publications [1,9]. Specific items in the error analysis were recomputed whenever the present conditions differed from those in the earlier publications. The resultant estimated maximum errors in the reported values are: 10 K in the melting point and in the radiance temperature at the melting point, and 5 percent in the normal spcctl'fil em ittance.

Discussion
The values of the melting point of hafnium reported in the literature are given in table 3. The values cannot be easily compared to one another or to the present value because of the differences in zirconium content of the hafnium used by the various investigators. Ackermann and Rauh [19] have estimated that the melting point of 100 percent pure hafnium should be approximately 2495 K. If the present value were corrected for the zirconium content of the hafnium, it would be somewhat higher than the estimate of Ackermann and Rauh.
No values for the normal spectral emittance of hafnium at its melting point were found in the literature. Peletskii and Druzhinin [20] have reported a value of 0.39 (at 0.65 Mm) at 2150 K for the /3-phase hafnium, which is id en tical to the value of the present work.  [21] reported a revision of this value which ,,,hen corrected to IPTS-68 is 2467 ± ].')1(.