ON THE NATURE OF THE ROTATIONAL STRUCTURE OF THE ALUMINUM OXIDATION SPECTRUM

L. V. ZHDANOVA

(Presented by Prof. V. A. Sokolov)

In the preceding work [1], on the basis of a study of the continuous, line, and vibrational spectra, an assumption was made concerning the thermal nature of the radiation from an aluminum flame. In the present work, for the purpose of further studying the structure and the nature of excitation of the aluminum oxidation spectrum, the rotational structure of the AlO molecule was investigated in the spectrum of an aluminum flame burning in oxygen.

For the AlO molecule (transition \({}^{2}\Sigma - {}^{2}\Sigma\)), according to [2], the distribution of intensities over the rotational lines of the bands is determined by the expression:

\[ I = C' (K' + K'' + 1) e^{-\frac{B'K'(K' + 1)hc}{kT}}, \tag{1} \]

where \(C'\) is a constant within the limits of the band, \(K'\) and \(K''\) are the quantum numbers corresponding to the total angular momentum exclusive of spin, and \(B = h/8\pi^{2}CI_{0}\) \((I_{0}\) is the moment of inertia of the molecule).

After taking logarithms and substituting numerical values of the constants [3], equation (1) takes the form:

\[ \lg \frac{I}{K' + K'' + 1} = C^{*} - 0.3738 \frac{K'(K' + 1)}{T}. \tag{2} \]

In the case of Boltzmann equilibrium, the dependence of \(\lg \dfrac{I}{K' + K'' + 1}\) on \(K'(K' + 1)\) is represented by a straight line, the slope of which makes it possible to find the temperature \(T_{\mathrm{vr}}\).

To obtain the spectra we used an ISP-67 spectrograph.

The rotational structure of the bands \(0—0\) \((4842.1\,\text{\AA})\) and \(1—0\) \((4648.2\,\text{\AA})\) was studied. The dispersion of the instrument in these regions was respectively \(1.8\,\text{\AA}/\text{mm}\) and \(1.92\,\text{\AA}/\text{mm}\). In the case of the \(0—0\) band, lines of the \(P\)-branch with \(K'' = 51—59\) and \(31—36\) were calculated; for the \(1—0\) band we were able to consider only lines of the \(P\)-branch with \(K'' = 58—64\).

The data obtained by us are presented in the figure, from which it is evident that the plot of the dependence of \(\lg \dfrac{I}{K' + K'' + 1}\) on \(K'(K' + 1)\) consists of two segments, which intersect when extended.

From the slopes of the straight lines the following values of the temperatures \(T_{\mathrm{rot}}\) were obtained:

\[ \begin{aligned} &\text{band } 0\!-\!0,\ \text{lines with } K''=31\!-\!36;\quad T_{\mathrm{rot}}=3400^\circ\mathrm{K};\\ &\text{band } 0\!-\!0,\ \text{lines with } K''=51\!-\!59;\quad T_{\mathrm{rot}}=9100^\circ\mathrm{K};\\ &\text{band } 1\!-\!0,\ \text{lines with } K''=58\!-\!64;\quad T_{\mathrm{rot}}=8000^\circ\mathrm{K}; \end{aligned} \]

The results can be explained if one assumes that in the aluminum flame there exist two different groups of electronically excited AlO molecules: one consisting of particles with a normal distribution of rotational energies, and the other consisting of particles possessing abnormally high rotational energies, produced as a result of an exothermic reaction. The emission of AlO molecules belonging to the second group thus has a luminescent nature. The “temperature” determined from the slope of the segment of the straight line corresponding to high \(K''\) is not a true one. \(T_{\mathrm{rot}}\), obtained from the slope of the straight line passing through the points corresponding to lower rotational levels, agrees with the adiabatic temperature of an aluminum flame \((3800^\circ\mathrm{K})\) [4] and with the vibrational temperature of AlO molecules in this flame [5].

Fig. 1. Dependence of \(\lg \dfrac{I}{K' + K'' + 1}\) on \(K'(K'+1)\) for the band \(0—0\) \((4842.1\ \text{Å})\).

Similar results, i.e., different \(T_{\mathrm{rot}}\) for different \(K''\), were obtained, for example, by Gaydon and Wolfhard, Broida, Hori, and others in determining temperatures from the rotational structure of OH, CH, CO, and CN in various flames, including flames burning at atmospheric pressure [6, 7, 8, 9].

The entire body of studies of the aluminum oxidation spectrum that we have carried out thus leads to the conclusion that two radiation zones exist in the aluminum flame itself:

1. The high-temperature zone (the combustion zone). The principal emitting particles—solid particles of the oxide being formed and aluminum atoms—are in thermal equilibrium with one another at a temperature \(T = 4900^\circ\mathrm{K}\). In addition, in this zone, as a result of incomplete dissociation, AlO molecules exist. Formed in the exothermic reaction, they possess large rotational energies and do not obey Boltzmann’s law, giving luminescent radiation.

2. The zone of lower temperature (the afterburning zone) gives purely thermal emission. The principal emitting particles of this zone—AlO molecules—are in thermal equilibrium with one another, and there is equilibrium between their vibrational and rotational degrees of freedom. Aluminum atoms in this zone are not excited; the thermal radiation of solid particles in this zone is not significant in comparison with the high-temperature zone of the flame.

REFERENCES

1. L. V. Zhdanova, V. A. Sokolov. Journal of Applied Spectroscopy, 1, 272, 964.

2. G. Herzberg. Spectra and Structure of Diatomic Molecules. IL, 1949.

3. W. Pomeroy. Phys. Rev., 29, 59, 1957.

4. A. Grosse, J. Conway. Ind. Eng. Chem. Wash., 50, 663, 1958.

5. L. V. Zhdanova, V. A. Sokolov. Journal of Applied Spectroscopy (in press).

6. A. G. Gaydon, H. G. Wolfhard, Proc. Roy. Soc., A194, 169, 1948.

7. W. R. Kane, H. P. Broida, J. Chem. Phys., 21, 347, 1953.

8. H. P. Broida, J. Chem. Phys., 21, 340, 1953.

9. T. Hori, Proc. Proc. Phys.-math. Soc. Japan, 25, 595, 1943.