ON SOME FEATURES OF THERMAL RADIATION

V. A. SOKOLOV

(Presented by the scientific seminar of the Radio Engineering Faculty)

In a number of studies published recently by V. M. Kudryavtseva, G. I. Sinyapkina [1], and the author of the present article [2, 3], it has been shown that the so-called “candoluminescence” arising in certain oxides at high temperatures is not luminescent radiation, but thermal radiation, determined solely by the peculiarities of the temperature radiation of these substances. The investigation, for example, of the spectra of the high-temperature glow of zinc oxide made it possible to conclude that this type of glow fully obeys Kirchhoff’s law and, consequently, on the basis of the Vavilov–Wiedemann criterion cannot be luminescent. The same conclusion may also be drawn with respect to other metallic oxides that give an unusually bright blue or green glow at high temperatures. At the same time, according to the data of Nichols [4, 5] and others, similar oxides, when placed in a high-temperature (for example, oxygen–hydrogen) flame, radiate in the visible (blue) region many times more intensely than an absolutely black body, which, it would seem, can occur only in the presence of luminescence.

In a review on candoluminescence published in Advances in the Physical Sciences [3], we pointed to a possible explanation of this “paradox,” which, in our opinion, is connected with the fact that the black uranium oxide used as an absolutely black body, radiating very strongly in the infrared part of the spectrum, acquired in the flame a considerably lower temperature than the white¹ metallic oxide compared with it, which possesses great selectivity of blue glow and radiates little in the infrared region of the spectrum.

But at first glance such an explanation may seem insufficient. Indeed, for the region of the spectrum corresponding, for example, to the maximum of radiation \(\lambda_{\max}\), the latter increases in proportion to the fifth power of the absolute temperature of the body. Let us take the limiting case. Suppose that under the conditions of one and the same flame the temperature of one oxide is twice as high as the temperature of the other. It is clear,

that in this case, with identical absorption coefficients, the excess of the radiating power of the first body in comparison with the second cannot be more than 32-fold. At the same time, according to the data of Nichols and others, the radiation intensity of white oxide under the conditions of one and the same flame may exceed the radiation intensity of black oxide by a hundredfold and more.

In the present article we wish to draw attention to the fact that this “discrepancy” is entirely explicable on the basis of the laws of thermal radiation and is due, in particular, to the distinctive distribution of energy in the spectrum of the temperature radiation of solid bodies.

The point is that the law of the growth of radiation in proportion to the fifth power of the absolute temperature is valid only for the maximum of the radiation; in the general case, the growth of the emissive power of a body with temperature for any part of the spectrum cannot be described by the law \(\sim T^n\), and obeys only the general law

\[ \sim \frac{1}{e^{\frac{c_2}{\lambda T}} - 1}, \]

i.e., Planck’s law, according to which, in the visible part of the spectrum, the ratios between the ordinates of different temperature curves for specified wavelengths may be very large.

In Fig. 1 are shown the radiation curves of a black body for various temperatures. It is easy to see that the higher the temperature, the more steeply the corresponding curve rises on the left-hand side, i.e., on the side of the visible part of the spectrum. Taking for comparison two curves—one for a lower, the other for a higher temperature—we easily find for them such a value of \(\lambda\) for which the ratio of the ordinates of the corresponding curves would be extremely large. Moreover, this cannot occur in the infrared and especially in the far-infrared part of the spectrum, where the ratio between the ordinates of different isotherms gradually decreases, tending to unity.

Fig. 1

On the basis of what has been set forth, it is quite possible to explain the appearance of large ratios between the radiation intensities of white and black oxides as the result of a difference in temperatures.

As an illustration, let us calculate, for example, what the theoretical difference in temperatures between oxides excited by one and the same flame must be in order that the ratio between the intensities be of approximately the same order as in Nichols’s data. We shall do this concretely for the case of magnesium oxide, which according to Nichols radiates in the blue region of the spectrum \((\lambda = 0.45\mu)\) at a temperature of \(665^\circ\mathrm{C}\) 155.7 times more intensely than black oxide.

For this purpose we shall use Wien’s law

\[ E = c_1 \lambda^{-5} e^{-\frac{c_2}{\lambda T}}, \]

which is—

is a particular expression of Planck’s law for our case (for a relatively small value of \(\lambda\)).

Taking logarithms, we have:

\[ \lg E=\lg C_1-5\lg\lambda-\frac{C_2}{\lambda T}\lg e. \]

Let \(\lambda=0.45\mu=4.5\cdot10^{-5}\ \text{cm}\). Since we are interested in the difference between the logarithms of the emissive powers at different temperatures and at the same \(\lambda\), it is necessary to calculate on the right-hand side only the last term, \(-\dfrac{C_2}{\lambda T}\lg e\), since the first two are constants.

We shall assume that the temperature of black oxide is \(665^\circ\text{C}=938^\circ\) absolute.

Substituting the values of \(\lambda\), \(T\), and the constants \((C_2=1.43\ \text{cm deg.},\ \lg e=0.43)\) and denoting \(\lg E_1-\lg C_1+5\lg\lambda=-\dfrac{C_2}{\lambda T}\lg e\) by \(\lg E'_1\), we have:

\[ \lg E'_1 = -\frac{1.43\cdot0.43}{T\cdot4.5\cdot10^{-5}} = -\frac{13.6\cdot10^3}{T} = -\frac{13.6\cdot10^3}{0.938\cdot10^3} = -14.50. \]

Let us now suppose that MgO, being in the same flame, for the reasons set forth above has a higher temperature than black oxide. The absorption coefficient of MgO at high temperature for \(\lambda=0.45\mu\), according to its value as measured by Liebmann [6], is close to unity. This gives us the right to apply the same formula (for black radiation) to MgO as well in this region of the spectrum.

The radiation of MgO under flame conditions may exceed, according to Nichols, the radiation of black oxide by a factor of 155.7. From this let us find how much higher the temperature of MgO must be if the temperature of the black oxide is \(T_1=665^\circ\text{C}\).

Since \(\lg 155.7=2.192\), and since for \(T_1=665^\circ\text{C}=938^\circ\) absolute we obtained \(\lg E'_1=14.50\), then \(\lg E'_2\) for the case sought must be greater by 2.192:

\[ \lg E'_2=\lg E'_1+\lg155.7=-14.50+2.192=-12.408,\ \text{i.e.} \]

\[ \lg E'_2=-\frac{13.6\cdot10^3}{T_2}=-12.408. \]

Hence the required temperature is

\[ T_2=\frac{13.6\cdot10^3}{12.408}=1.096\cdot10^3= \]

\[ =1096^\circ\ \text{absolute}=823^\circ\text{C}. \]

This is the temperature at which, according to our assumptions, MgO is found in the flame in the case where in the same flame black oxide has the temperature \(T_1=938^\circ\) absolute \(=665^\circ\text{C}\).

The difference in temperatures would be \(823-665=158^\circ\), which is entirely possible, since for other oxides there were experi-

experimentally established differences in temperatures, and of a considerably larger order (thus, for example, in one and the same flame, at \(T_1 = 1350^\circ\) abs., thorium oxide assumes a temperature \(T_2 = 1800^\circ\) abs. [7]).

REFERENCES

1. V. M. Kudryavtseva and G. I. Sinyakina, Temperature radiation of zinc oxide, Dokl. Akad. Nauk SSSR, vol. 59, no. 8, 1948.

2. V. A. Sokolov, On the thermal character of luminescence during the oxidation of zinc. Dokl. Akad. Nauk SSSR, vol. 66, no. 1, 1949.

3. V. A. Sokolov, Candoluminescence, Uspekhi Fizicheskikh Nauk, vol. 47, issue 4, 1952.

4. E. L. Nichols, H. L. Howes and D. T. Wilber, Cathodo-luminescence and the luminescence of incandescent solids, Washington, 1948.

5. L. T. Minchin, Luminescence of oxides under flame excitation, Trans. Farad. Soc., vol. 35, part 1, 1939.

6. G. Liebmann, Die Temperaturstrahlung der ungefärbten Oxyde im Sichtbaren, Zts. f. Phys., bd. 63, 1930.

7. Ribaud, Optical Pyrometry, GTTI, 1934.

1. As a rule, oxides possessing the mentioned feature of thermal radiation have, under ordinary conditions, a white color. ↩