Physica 83C (1976) 338-346 © North-Holland Publishing Company

THE MELTING TEMPERATURE OF PLATINUM MEASURED FROM CONTINUALLY MELTING AND FREEZING RIBBONS

J. BEZEMER and R. T. JONGERIUS Physical Laboratory Ri/ksuniversiteit Utrecht, The Netherlands

Received 5 June 1975 Revised 4 November 1975

The melting temperature of platinum can be measured by using pure platinum ribbons, heated by a modulated direct electric current. The modulation of the emitted radiation shows a sharply increasing distortion when the current is raised to a value whereby in each period the maximum of the temperature reaches the melting point. During a fraction of the period a small center dot of the ribbon melts, causing a rise in emissivity of the center. It has been found that the radiance tem- perature at which the melting starts can be measured with a sensitivity of 0.02 K. Furthermore, using an opto-electronic stabilization, platinum ribbons in free air can be kept within 0.2 K at a constant mean temperature close to the melting point for one hour or more. From measurements of the radiance temperature and the spectral emissivity the melting tem- perature of platinum on the IPTS-68 was found to be 2041.0 +-0.5 K.

1. Introduction

Several methods have been employed to determine the melting or freezing temperature of platinum. Some older measurements were performed with r.f. heated platinum ingots with a blackbody cavity, con- structed to realise the primary standard of light.

A recent determination with an indirectly heated ingot was carried out by Ouinn and Chandler [1, 2]. They found a freezing point of 2041.1 +-0.3 K on the IPTS-68, being 4 K lower than former measurements. Cezairliyan [3] described a method for the measure- ment of melting points based on the break of an electric circuit due to the melting of a thin wire. The wire was wound around a rapidly heated tube, used as a cavity radiator. The temperature was measured at the moment the wire broke, after about 0.8 s warm up time. With this technique he found 2045 +- 5 K for the melting point of platinum. Because of the interest in an accurate value for the platinum melting point for measurements in photometry and pyrometry, a new method has been developed. It avoids the need for the construction of a high temperature furnace and a blackbody radiator.

The experiments described here include accurate

measurements of platinum radiance temperatures. These measurements were performed with an optical standard pyrometer [4], calibrated according to the IPTS-68. A goldpoint blackbody radiator served as a reference, while higher temperatures were calibrated using radiance ratios produced by a beam splitter. The pyrometer contained three interchangeable interfer- ence falters with peak transmissions at 587,657 and 710 nm, for each of which a separate calibration was made.

2. Method

Platinum ribbons, 2 mm wide and 0.02 mm thick, made from platinum with only 10 ppm impurities, were heated to just below the melting point by a direct current of about 8 A. A modulation of this current with a frequency of 70 Hz and a variable amplitude up to 0.7 A was used to achieve tempera- ture amplitudes of O.5 to 5 K. By means of an increase in the direct current component, the ribbon tempera- ture could be raised to reach the melting temperature during a small phase interval at each period. Accord- ing to [5], the spectral emissivities at 650 nm of solid

338

J. Bezemer and R. T. Jongerius/The melting temperature of platinum 339

and liquid platinum are 0.33 and 038 , respectively. Thus as soon as a small amount of the surface of the ribbon melts, a sudden increase in emitted radiation can be detected. This increase was observed by measuring higher harmonics of the 70 Hz component in the emitted radiation. It was found that a change of the mean radiance temperature of less than 0.02 K was sufficient to produce a clearly detectable increase of the 210 Hz component of the radiation due to the change in emissivity. The standard optical pyrometer was used to measure the mean radiance temperature T R. The modulated emitted radiation was detected with a Si-photodiode. Its amplified output contained three components of special interest: the d.c. com- ponent Foe being a measure of the mean radiance, the 70 Hz component F70 (r.m.s. voltage) being a relative measure of the radiance amplitude and the 210 Hz component F210 being a measure of the change in emission of the central dot. The components Foe and F210 were used in an electronic feedback circuit to stabilize either the mean radiance or the 210 Hz radiance component. Fig. 1 shows T R as a function of F210 when Foe is slowly increased from 3.200 V up- ward and F70 is kept at 38 mV. The intersection of the "solid" curve and the "partially molten" curve determines the maximum value of TR at which no platinum is molten. Similar graphs at different tem- perature levels are found when other values of FT0, Le. other temperature amplitudes are chosen. The remainder of the distortion F210 at the "solid" curve

showed to be proportional to F70. By means of extra- polation of TR to zero values of both VT0 and F210, the radiance temperature at the melting point TR, m is found. This is shown in fig. 2, where T R is plotted versus V70 for a constant ratio of F210/VTO of 0.6 per cent.

To complete the determination of the melting tem- perature the spectral emissivity of the ribbon has to be known accurately. From the reproducing values of the radiance temperature near the melting point for different specimens it could be concluded that also the spectral emissivity reproduces. Nevertheless spectral emissivities from literature data [6, 7, 8] are not used since the measurements of the emissivity as a function of the temperature are in mutual disagreement and not sufficiently accurate. To find the emissivity near the melting point, the platinum ribbons were installed in a white, MgO coated, cylindrical enclosure that could be used as a photometer sphere. With four 100 W tungsten halogen lamps reflection measure- ments were made near the melting point. The pyrometer was used to measure the spectral radiances of the wall and the ribbon with and without illumina- tion of the house by the lamps. During these measure- ments the temperature of the ribbon was stabilized near its melting point by regulating the d.c. heating current to produce a constant small distortion (F210) in the radiation signal. From the increase of the radiance of the wall and the increase of the radiance of the ribbon due to the illumination, the spectral

1 8 3 3 0

1 8 3 2 9

1 8 3 2 8

1 8 3 2 7 .c_

K~ 1 8 3 2 . 6

1 8 3 2 5

1 8 3 2 , 4

0

I I I I

, / / t / t / t / p a r t i a l l y m o l t e n

} I 1

t I so l id t t i i I

I , I , I , I , I 0 5 .10 .15 2 0

~ 1 0 in m V

Fig. 1. Mean radiance temperature TR (657 nm) as a function of the distortion signal II210 at a modulation signal 1/70 of 38 mV.

~ ' i ' ] [ I ' I

1836 ! ~ t

1833 ~ ! ~ . I I , i , I

0 10 20 3 0 4 0

//70 in m V

Fig. 2. Extrapolation of the mean radiance temperature TR (657 nm) to zero modulation signal 1170. The modulation distortion V21O/VTO was kept at 0.6%.

340 J. Bezemer and R. T. Jongerius/The melting temperature o f platinum

reflectivity was found. Thanks to the fact that the ribbon had an almost specular reflection, not the whole cylinder needed to be illuminated very homo- geneously. However, the radiance from the part of the wall that mainly contributed to the radiance of the ribbon in the direction of observation had to be known accurately. To prevent serious influence from the hole in the cylinder through which the ribbon radiation was detected, the ribbon radiance was measured in a direction 30 degrees from the normal.

3. The apparatus

The platinum ribbons of 18 mm height were bent in an L shape and suspended by means of spotwelding to two stainless steel supporting rods. The lower rod could be moved to adjust the position of the vertical part of the ribbons.

The support was placed in the center of the cylin- drical enclosure which was 80 mm in diameter and 100 mm high. In the horizontal plane in the middle of the cylinder holes of 10 mm diameter were drilled to observe the ribbon and the wall (see fig. 3). The enclosure with the support could be rotated, so that the pyrometer could be aimed through hole a onto the ribbon and through hole b towards the wall near point e which was 60 degrees away from a. With a lens 15 mm outside of hole c the center of the ribbon was imaged onto the Si-diode detector which was con- nected to the outside of the cylinder. Hole d was used to scan the ribbon with a photomultiplier to deter- mine the position and the shape of the hottest dot on

d _a

c

Fig. 3. Si tuat ion o f the r ibbon in the pho tome te r house; a, c and d" axe holes to observe the r ibbon, hole b is used to measure the wall radiance at e.

the ribbon. The scanning was usedto adjust the verti- cal position of the support and to check the quality of the ribbon. Further positioning is carried out with a laserbeam through hole a. In its proper position, the ribbon reflects the beam to point e and makes it detec- table for the pyrometer at b.

The four halogen lamps for the illumination of the cylinder were installed near the top and the bottom cover, in such a way that no direct radiation could reach the front side of the ribbon, directed towards the pyrometer. Each lamp had a double wall envelope of ground glass with water cooling to prevent excessive current of air and to improve the homogeneity of the illumination.

The electronic part of the apparatus is outlined in fig. 4. The stabilization of the mean temperature of the central part of the ribbon was achieved by feed- back of the difference between the photodiode signal V~c and a manually controlled voltage V 0. With this stabilization slow temperature fluctuations from draught could be reduced by a factor of 500 to 0.04 K. When only radiation heat losses are concerned, the relaxation time constant of the ribbon for small tem- perature deviation from the temperature T is

r = Cpal8r3 to, (1)

where Cp is the specific heat (heat per degree per unit volume), d is the thickness of the ribbon, e t is the total emissivity and o is the Stefan-Boltzmann constant. For our ribbons this yields r = 0.09 s. Experimentally a lower value due to heat convection was found, viz. r = 0.06 s. Due to this time constant, temperature fluctuations above 2.5 Hz are attenuated proportionally to the frequency, with 2.5 Hz as 3 dB value. For good stabilization a high amplification in

"1he feedback loop at this frequency is required. However, the bandwidth and the amplification were limited by the condition that the 70 Hz modulation amplitude and higher frequency signals should not be suppressed too strongly, whereas oscillations are gener- ated by very sharp low pass f'flters in consequence of phase shifts. With an amplification of unity at 70 I-Iz, the open loop gain was 500 up to 2.5 Hz. The phase shift due to •tering (including the phase shift from 0 to 90 degrees produced by the ribbon) was 70 degrees at 2.5 Hz and 120 degrees at 70 Hz. The maximum phase shift was 160 degrees at 20 Hz. A

J. Bezemer and R. T. Jongerius/The melting temperature o f platinum 341

dc reference manual voltage //O

control

~ differential amplifier & ,filter

lock- in " J~, amplifier F

? 210 HZ 1. ]Si-phOtO selective ~1--1 diode and amplifier [ [amplifier

. Y heating current amplifier

oscilloscope L F

frequency divider 70 Hz

~1___f alternating voltage 210 Hz

1 1 . ~ scanning ribbon photo

multiplier ]~ 210 Hz selective amplifier

Jq °scill°sc°pe I

Fig. 4. Principle of the detection and stabilization apparatus.

second feedback loop, stabilizing the distortion, made it possible to prevent slow temperature drift from or towards the melting point. This was effected by lowering the d.c. voltage V 0 proportional to the increase of the distortion signal, amplified by a lock-in amplifier. Its output only contained d.c. and low fre- quency voltages up to 0.02 Hz. The correct phase of the distortion 210 Hz component with respect to the phase of the 70 Hz component could be monitored on an oscilloscope and measured with the lock-in amplifier.

4. Measurements

Two series of 10 measurements have been per- formed, measuring radiance temperatures and spectral radiances with the pyrometer at 587 and 657 nm. In these measurements corrections for spectral distri- bution have been applied as described in [4]. The spectral distribution of the radiation of platinum was computed for a spectral emissivity that depended parabolically on the wavelength as followed from measurements at the three wavelengths of the pyrometer, 587, 657 and 710 nm. The spectral distri. bution of the radiation from the wall was approximated

by a distribution temperature of 3300 K. With each of the twenty measurements all quantities were deter- mined two or more times to correct for the slow reduo tion of the radiance of the wall of the enclosure (1% per hour) due to deposition of evaporated platinum on the top cover of the cylinder. During the period of the measurements the MgO coating was refreshed five times. Each measurement was performed with a new ribbon. To complete the twenty measurements, about twice as many ribbons were needed. Some ribbons were lost because they melted during the adjustment of the position. Other ribbons were not used because the hottest part of the ribbon shifted away from the measuring area and no stable distortion signal could be obtained.

The spectral emissivity at the melting point in a direction at 30 degrees from the normal has been determined from the reflectance according to

e-- 1 - Ri - R - - + %, (2) Wi-W

where R and W are the relative spectral radiances of the ribbon center and the wall of the photometer house. The index i is added to the quantities measured during the illumination with the lamps. Measurements

342 J. Bezemer and R. T. Jongerius/The melting temperature of platinum

were carried out at a mean temperature some degrees below the melting point. For this reason the correc- tion term C e of +0.37 × 10 -4 per K temperature difference had to be applied. Typical relative values for the spectral radiances as measured at 2.7 K below the melting point are shown in table I. The attainable ratio of Wi[R becomes larger at smaller wavelengths, causing smaller errors in the measured spectral emissivity. For this reason it was advantageous to perform measurements not only at the main wave- length of the pyrometer (657 nm) but also at 587 nm.

The extrapolation of the mean radiance tempera- ture to zero temperature amplitude as shown in fig. 2 was carried out only in preliminary measurements to verify linearity. In the final measurements, linear extrapolation was performed by using only two measurements at different temperature amplitudes. To facilitate measurements, relative values of the spectral radiance R instead of radiance temperatures were measured and extrapolated to zero temperature amplitude, yielding R 0. At only one of the two tem- perature amplitudes, indicated by the index x, also the apparent radiance temperature T~, x was measured. The radiance temperature at the melting point, TR, m, was found from

was added. Another correction, Cg, had to be included for the temperature gradient across the ribbon. Tem-

• perature distributions have been found similar to those of tungsten strip lamps [9]. While the tempera- ture gradient along the ribbon in vertical direction was negligible, in the horizontal direction a parabolic temperature distribution was observed, due to low temperatures at the edges of the ribbon. It was tried to improve the temperature distribution by finishing the edges by means of spark erosion. Also wider ribbons were examined, In both cases no signifi- cant improvement was obtained. For the width of the measured area of 0.30 mm situated within 0.10 mm on the middle of the ribbon, a correction equivalent to 0.20 K was computed. The error in this value is supposed to be less than 0.10 K.

Finally, the melting temperature of platinum T m is found from

1 _ 1 + X l n e . (4) T m TR,m C2

The results of the measurements are given in table II. The standard deviations in single results of e at 587

1 _ 1 +~__lnR__sx+ X_.~(l_e) W x _ C (3)

TR,m 7R,x c2 R0 c2 Rx g"

In this formula ;~ is the wavelength and c 2 is the second radiation constant of Planck's law. The first and the second term on the right express the extra- polation in terms of radiance temperature. The apparent radiance temperature TR, x s '_t~ll differed from the mean radiance temperature T R as mentioned before due to reflected light from the wall of the enclosure, illuminated by the ribbon itself. For this difference the third term, equivalent to about 1 K,

Table I Ratios of typical spectral radiances of the ribbon and the enclosure with the resulting emissivity according to formula 2

Wavelength Ri/R Wi/R W/R C e e (nm)

587 1.4951 0.7365 0.0086 0.0001 ~ 0.3199 657 1.3140 0.4581 0.0083 0.0001 0.3020

Table II Emissivity, radiance temperature and temperature of platinum ribbon at the melting point. Results from two series of ten measurements, mean values and standard deviations in single results

587 nm 657 nm

e TR, m T m e TR, m T m

(K) (K) (K) (K)

0.3183 1863.54 2041.22 0.3031 1836.39 2040.64 0.3186 1863.78 2041.30 0.3044 1836.43 2039.89 0.3154 1863.79 ~ 2043.04 0.3008 1835.84 2041.45 0.3175 1863.76 2041.86 0.3042 1836.27 2039.83 0,3175 1863.69 2041.79 0.3025 1836.20 2040.80 0.3192 1864.14 2041.42 0.3031 1836.20 2040.40 0.3199 1863.69 2040.50 0,3020 1836.35 2041.31 0.3199 1864.11 2041.05 0.3014 1836.41 2041.76 0.3221 1863.71 2039.36 0.3041 1836.38 2040.01 0.3190 1863.59 2040.90 0.3012 1836.63 2042.17

0.3187 1863.78 2041.24 0.3027 1836.31 2040.83

±0.0018 ±0.20 ±0.95 ±0.0013 ±0.21 ±0.82

Z Bezemer and R. Z Jongerius/The melting temperature of platinum 343

and 657 nm are equivalent to temperature differences at the melting point of 0.95 K and 0.83 K, respectively.

5. Discussions concerning the method

One aspect of the measurements not mentioned so far is the considerable deviation of the direction of observation of the ribbon surface from the normal. It causes a change in emissivity and the detected radia- tion becomes polarized. The emissivity for radiation polarized parallel to the plane of observation increases by 0.038, while the emissivity for radiation polarized normal to the plane of observation decreases by 0.035. This follows from the estimated values n = 2 and k = 4 for the complex index of refraction n - ik [ 10]. But since the changes in reflectance are equally but in opposite sense according to Kirchhoff's radiation law, the total influence on the resulting melting tempera- ture cancels out.

This cancellation also holds for influences caused by the surface conditions of the ribbon (crystal orientation, surface roughness) and for the residual polarization sensitivity of the pyrometer (less than 0.5%), since the spectral emissivity and the radiance temperature both are found from the same ribbons in the same position using the same apparatus. Only a secondary effect of the surface roughness gives rise to a measuring error as mentioned later on.

An important question about the method is whether the observed temperature at which the surface melts is equal to or perhaps lower than the melting temperature of bulk material, or more precisely the melting temperature at a solid liquid interface. In fact a slightly higher temperature exists at the inside of the ribbon with respect to the surface temperature (about 0.01 K) due to the electrical heat production, while it appears that there is a preference for melting at the surface.

An elegant experiment would be to melt the ribbon gradually up to a substantial part of the thickness and to observe whether the spectral radiance of the ribbon changes while it is illuminated homogeneously by the wall of the enclosure having a spectral radiance tem- perature of 2041 K. Then only eventual true tempera- ture increases could be observed. But this experiment requires a six times higher radiance of the wall than can be reached with the present apparatus. Also

measurements of the emissivity at several melting depths are not possible with sufficiently high precision due to lack of stability during the successive measure- ments.

However, from two experiments, comprising only spectral radiance measurements, evidence was found to conclude that the melting temperatures at the surface and in the bulk material differed less than 0.1 K. With these experiments it was supposed that the solid liquid interface is composed of only a few atomic layers. This is very thin with respect to the surface layer of optical interaction. The absorption of an electromagnetic wave is described by the decrease of the amplitude according to

E = E 0 exp (-21rkx/;k), (5)

where k is the imaginary part of the index of refrac- tion, x is the absorption depth and ?~ is the wavelength in vacuum.

The first experiment consisted of the determina- tion of the depth of melting at moderately distorted signals in the range as shown in fig. 1. Besides the regulating detector a second Si-photodiode detector with a high-power optical magnification was installed. Its small circular measuring area of 0.06 mm in diameter made it possible to measure the radiance of the ribbon in more detail than with the regulating detector, which observed an area of one square mm. The distortion of the modulated signal appeared to be about fifty times larger with the second detector, indi- cating that only a small spot is melting. The detector output, as produced by a transient recorder, is shown in fig. 5. Figs. 5a through 5d show the signals from a ribbon with a 3 K temperature amplitude from zero to moderate distortion signals of the regulating detec- tor. When the d.c. heating current is increased further, signals as presented in figs. 5e through 5h are found. At 5g and 5h during the whole period liquid platinum is present. Fig. 5c was recorded at a distortion voltage V21 o of about 0.20 mV (fig. 1). At this distortion voltage, peaks of 2 to 5% of the total d.c. signal of the second detector were found. From this high increase of the emissivity, it can be concluded that the surface layer of optical interaction melts to at least a consider. able depth. The spectral radiance of liquid platinum was measured and compared with the spectral radiance at the peaks. Several ribbons were heated until the

344 J. Bezemer and R. T. Jongerius/The melting temperature of platinum

T signal

-°:,7 A A l/

g n

Fig. 5. Spectral radiance of a central spot of a ribbon as measured with a Si-photodiode. The respective curves repre- sent the 70 Hz modulated signals, distorted by melting, at increasing modulated heating currents. The distance between the two horizontal lines represents on the linear scale the initial temperature amplitude of 3 K, equivalent to 1.2% of the total signal.

total cross section melted and the liquid platinum flowed away. With the transient recorder in the pre- trigger mode, the radiance during the last milliseconds of the melting was recorded. The emissivity of liquid platinum did not exceed 1.15 times the emissivity of the solid platinum at the melting point (for the spectral sensitivity of the Si-photodiode at about 950 nm). So up to about one third of the detected radiation at the peaks can be considered to be contributed by the liquid platinum. Taking the optical absorption factor k to be 4, the molten layer had to be at least 20 nm thick. At this quantity of molten platinum, the mean radiance temperature as measured with the pyrometer was only 0.3 K above the value at the start of melting (fig. 1). This radiance temperature difference equals the sum of the estimated contributions from the increase of emissivity at the peak (0.2 K) and the increase of the mean true temperature of solid plati- num below the melting temperature (0.1 K). So it can be concluded that the melting temperature changes less than 0.1 K when the thickness of the molten layer increases up to many atomic layers.

Also from an other phenomenon the consistency of the melting temperature can be shown. Sometimes at places close to molten areas and in particular at the opposite surface of molten areas no melting was observed although the temperature stayed near the melting point for some time during the period. So the spectral radiance of solid platinum close to a surface of liquid platinum can be found. Spectral radiances of both sides of several ribbons were measured using the second detector for one side and a third Si-photodiode detector for the other side. This third detector had a measuring area on the ribbon of 0.3 mm in diameter. Both detectors were adjusted with respect to one another, while the ribbon was removed. Then an image of the limiting opening of the third detector, formed at the fleldstop of the second detector, could be observed. There was a preferance for melting at the side of the second detector, at the "inside" of the L shaped ribbon. So the melting was observed from a small surface area at one side of the ribbon with the second detector and the radiance of the non molten platinum was measured at a larger surface area opposite of it at the other side with the third detector. With many ribbons sooner or later melting was observed at both sides. But with three out of ten ribbons successful measurements were obtained. In fig. 6 the recorded detector signals for one ribbon are presented. The figs. 6a through 6d show the modulation

l , o tg2 ,oes

Fig. 6. Spectral radiances of small central spots of a ribbon at opposite surfaces, measured with two Si-photodiodes. The curves a through d represent modulated signals with increas- ing distortion due to melting, measured at one side of the ribbon. The curves e tltrough h represent the corresponding signals from the other side, showing the maximal radiance of solid platinum near the melting temperature. For scale dimensions see fig. 5.

Z Bezemer and R. T. Jongerius/The melting temperature o f platinum 345

signals of the second detector at different distortions and the figs. 6e through 6h show the corresponding signals of the third detector. With an initial tempera- ture amplitude of 3 K, the d.c. heating was increased until during about half the period some platinum was molten. Neglecting the variation of the emitted energy during the period, in the case illustrated by fig. 6h each period about equal amounts of heat are available for the 3 K temperature increase and for the melting of platinum. This can be deduced from the phase shift of about 90 ° between the temperature modula- tion and the supplied energy modulation. From this heat balance it follows that the average thickness of the molten layer of platinum in the observed region is 100 nm. With the increase of melting as shown in the figs. 6e through 6h, the top temperature increased by 0.2 +-0.1 K. This increase is due to the disappearance of the temperature gradient in the observed region, leading to an estimated increase of the mean tempera- ture in this area of 0.2 -+ 0.1 K during melting. So also with this experiment no difference within an error of 0.2 K between the surface and the bulk melting tem- perature was found.

The purity of the platinum was stated by the manufacturer to be 99.999% pure. To check this, an analysis by means of X-ray fluorescence was made. No impurities were found. The minimal detectable amount was 2 to 3 ppm for most of the probable impurities. The influence of the impurities on the melting temperature is of the order of magnitude of - 0 . 0 2 K. This value was found from a rough estima- tion of an "over-all" mean value of - 2 mK per ppm, found from phase diagrams for binary alloys of platinum and several other elements. With the present method no contamination of the platinum occurred, since no vessel was needed for the melting. No special surface effects are expected from the impurities. At small quantities, most elements are in homogeneous solid solution. Insoluble impurities at the surface (if any) might change the emissivity but not the final measured melting temperature. To investigate influ- ence from eventual absorption of oxygen, radiance temperatures of several ribbons at the melting point were measured, both in air and in an argon atmos- phere. Since no radiance temperature differences (within 0.1 K) were observed, it is unlikely that the melting point is influenced by solved oxygen.

6. Accuracy

The errors in the measurements are subdivided into random errors and systematic errors. The random errors are supposed to affect each single measurement but not the mean of a large number of measurements, while the systematic errors are supposed to have about equal influence on each measurement of the series of measurements concerned. The random errors are expressed in standard deviations, the systematic errors at first are expressed in maximal errors.

The main sources or error are: 1) inhomogeneity of the wall radiance in combination

with roughness and wrong orientation of the ribbon; 2) fluctuations in the measured radiances of the ribbon; 3) the calibration error of the pyrometer and 4) the error in the measured radiance temperature of

the ribbon from the temperature gradient and the spectral radiation distribution. The first error source was analyzed by measuring

radiance gradients of the wall for several coatings, pre- pared in the same way as the coatings used for the emissivity measurements. Furthermore, it was ex- amined which region of the wall could contribute to the measured radiance, reflected by the ribbon. This was found by aiming a narrow light beam from the pyrometer entrance solid angle onto the ribbon. The reflected light formed a light spot of about 10 mm in diameter on the wall, indicating the area of interest. From repeated adjustments of a ribbon as pointed out in section 3, a reproducibility of the place of the spot on the wall within 5 mm was estimated. Combining some possible deviations in position of the light spot with measured radiance gradients of the wall, errors for the hypothetical cases were computed by approxi- mation. Supposing no special preference exists for the direction of the deviations of the position, a random error can be expected from the linear component of the radiance gradient. The quadratic component, how- ever, causes errors of the same sign for each deviation in adjustment. Since for several emissivity measure- ments the same coating was used, for the quadratic gradient a systematic error was taken into account. The results of the computations yielded a random error of 1.0 K in a single measurement and a maximal systematic error of 0.2 K. The magnitude of the random error agrees with the deviations in the emis- sivity measurements in table II columns 1 and 4. The

346 J. Bezemer and R. T. Jongerius/The melting temperature o f platinum

second source of error is mainly important for the determination of the emissivity according to formula 2. A random error equivalent to 0.40 K was found as a mean value for both wavelengths. From the calibra- tion of the pyrometer with respect to the IPTS-68 a maximal systematic error of 0.40 K was contributed. The additional systematic error in the determination of the radiance temperature of the ribbon was 0.10 K.

Taking the two random errors for the determina- tion of the emissivity together, for each measurement a standard deviation of i. 1 K is found. This is in agree- ment with the standard deviation of the measurements (see table II columns 3 and 6). Since ten measure- ments in each series were made, the standard deviation of the arithmetic mean for each series is 0.3 5 K. The total maximal error from systematic errors is 0.70 K.

To express this error in terms of probability it can be taken equivalent to a standard deviation of 0.40 K, when a constant probability between the error limits is assumed [11]. Together with the random error, the standard deviation for the result of one series is 0.53 K and for both series combined 0.47 K. Summarizing, for the melting temperature of platinum from twenty measurements,

Tm= 2041.0+0.5 K.

7. Conclusions

With the method presented here, accurate measure- ments of melting points can be made with a simple apparatus. The melting point of platinum as found

here corresponds with the value found by Quinn and Chandler, differing considerably from older measure- ments. The radiance temperature of different ribbons, which had no special surface treatment after rolling, showed surprising consistency. Platinum ribbons with a temperature stabilization as described here could be used very well for temperature calibrations.

Acknowledgements

The authors thank Professor A. M. Hoogenboom for the useful suggestions and the stimulating dis- cussions on the subject. Mr. H. A. Schoonderwoerd and Mr. A. Slomp are thanked for their help with the measurements.

References

[1] T. J. Quinn and T. R. D. Chandler, Metrologia 7 (1971) 132.

[2] T. J. Quinn, Metrologia 10 (1974) 115. [3] A. Cezairliyan, J. Res. Nat. Bur. Stand. 74C (1970) 87. [4] J. Bezemer, Metrologia 10 (1974) 47. [5] Handbook of Chemistry and Physics, R. C. Weast, ed.

(Chemical Rubber Publ. Co., Cleveland, 1968). [6] R. E. Stephens, J.O.S.A. 29 (1939) 158. [7] G. L. Abbott, Nasa SP-31 (1963) 293. [8] A. H. Madjid, R. L. Stover and J. M. Martinez, Phys.

Con. Matter 17 (1974) 125. [9] G. P. Brouwer, Philips Res. Repts 18 (1963) 361.

[10] Handbuch der Experimentalphysik, W. Wien und F. Harms, (Akad. Verlagges., Leipzig, 1928) Band 18.

[11] C. F. Dietrich, Uncertainty, Calibration and Probability (A. Hilger, London, 1973).