Abstract
The effects of pressure and temperature on the absorption coefficient of ammonia (NH3) gas self-perturbed and perturbed by nitrogen (N2) gas have been measured. We varied the gas pressure from 10 to 160 Torr and the temperature from 235 to 296 K in order to study the absorption coefficient at the center and the wings of lines in the band of NH3. These measurements were made using a high resolution (0.0038 cm−1) Bruker Fourier-transform spectrometer. These spectra have been analyzed using the method of multipressure technique permitting to succeed to an evolution of the absorption coefficient with the pressure and the quantum numbers and of the NH3 molecule. The results show that the absorption coefficient varies as a quadratic function of the pressure at the center of a given line. However, it has a linear evolution in the wings of the line. Moreover, the absorption coefficients are inversely proportional to temperature in the wings when NH3 lines are broadened by N2. The retrieved values of these coefficients were used to derive the temperature dependence of N2 broadening NH3 lines. The absorption coefficients were shown to fit closely the well-known exponential law.
1. Introduction
The infrared spectroscopic investigations of the atmospheres of stars, planets, and their satellites, using infrared spectroscopy, not only provide valuable information about the chemical elements that they consist of, but also about the horizontal and the vertical distribution of their minor constituents. Due to the complexity of the line profiles used to model the spectral shapes (absorption, broadening, intensity), it is necessary to determine experimentally the line parameters of the spectra in order to test the models being used.
Several studies in the literature have investigated the spectral properties of NH3 in several infrared bands. Aroui et al. [1] have studied the self-broadening and line intensities, Nouri et al. [2] have studied the temperature dependence of pressure broadening, and other authors [3, 4] were interested in the absorption coefficient at the line centers of NH3. Experimentally absorption coefficients for broadband ArF excimer radiation laser were determined for NH3 at temperatures up to 3500 K [5]. Measurements of the NH3 absorption coefficients at CO2 laser wavelengths have been done by Zelinger et al. [5] using photoacoustic spectroscopy. NH3 absorption coefficients were also measured by Allario and Seals [6] using several transitions of a CO2 laser for small concentrations of NH3 perturbed by N2. The influence of CO2 Laser line width on the measured absorption coefficients of atmospheric ammonia has been studied by Voitsekhovskaya et al. [7].
The focus of the present study is to present absorption line profile measurements of NH3 in the 6 μm region ( branch of the band). In this range, we resolved the spectra for different and quantum numbers. We have determined the absorption coefficients in the centers and in the wings of NH3 lines self-perturbed and perturbed by N2 at various pressures (10–160 Torr). The measurements were made for different gas temperatures 235, 245, 268, and 296 K. The analysis was made as a function of and quantum numbers, and the results were compared to the previous investigations.
2. Experimental
The measurements were made using a high-resolution Bruker Fourier transform spectrometer (Bruker IFS 120 HR) [8, 9]. This spectrometer is equipped with different components: a Globar source, a KBr beam splitter, a filter eliminating infrared radiation above 2500 cm−1, and a photovoltaic HgCdTe detector cooled at 77 K by liquid nitrogen.
The spectral resolution was about 0.0038 cm−1 after apodization with a triangular function. This value is equal to the half-width at half maximum of the apparatus function approximated in the calculations by a Gaussian shape. This approximation has a negligible contribution to systematic errors since the pressure-broadened lines were much larger [2, 10]. Ammonia gas in natural abundances was provided by Air Liquid France with stated purity of 98.5%. The spectra were measured at different pressures covering the lines of the branch of the band of ammonia. NH3 and N2 gases were contained in a metallic cell with a 2.5 cm path length for NH3 self-perturbed, and in a Pyrex glass cell with a 15 cm path length for NH3 perturbed by N2. Both of the absorption cells are sealed by CaF2 windows.
The pressures of the gases were measured accurately using three calibrated capacitive MKS Baratron transducers with full-scale readings of 10, 100, and 1000 mbar. The accuracy of these manometers is 0.5% of the readout. Ammonia sample pressures were allowed to stabilize for sufficient time before the spectrum of the sample was finally recorded.
For NH3 self-perturbed, the pressure was varied from 5 to 120 mbar, whereas for NH3 perturbed by N2 we varied the gas pressure from 10 to 160 Torr. For the present experiments, the temperatures varies from 235 to 296 K. Each temperature was monitored by three calibrated thermocouples (Pt-100).
The measured intensity of the incident light () and the transmitted light () at wave-number were converted to transmission spectra using Lambert-Beer’s law
Table 1 summarizes the experimental parameters. The spectral region for this study is between 1470 and 1600 cm−1. Figure 1 shows short transmittance spectra of NH3 around 1550 cm−1 exhibiting some prominent lines of the branch. These spectra were recorded at K. At low pressure, the lines are separated, but when the pressure increases the lines widen and begin to overlap.
3. Fitting Procedures
The absorption coefficient of an isolated line of the band is obtained by comparing the recorded line with a synthetic line. The adjustment is performed using the Rosenkranz profile given [11, 12] by where is the NH3 pressure, is the partial pressure of the perturbing gas, represents the line , its intensity, its wave number including the collisional shift , the unperturbed or zero pressure wave number), its broadening coefficient, and its mixing parameter.
The modelled transmission is the result of a convolution of with a Doppler profile () and the apparatus function of the spectrometer () [10]. where represents the length of the absorption cell.
The differences between the experimental and calculated spectra were minimized by adjusting the parameters , , , and using a nonlinear least-squares multipressure fitting technique where all spectra at various pressures are successively adjusted using (3). An example of multipressure fit in the case of line for four NH3 pressures (30, 60, 91, and 120 mbar) is shown in Figure 2. Residual (measured minus calculated) spectra are shown in the lower part of graphs.
As illustrated by this figure, the theoretical model given by (3) proves sufficiently accurate to fit very well the observed spectral lines without accounting for Dicke narrowing and/or speed dependence and demonstrates at the same time that the line coupling cannot be neglected.
4. Results Analysis
4.1. Line Center Absorption Coefficients
We have made measurements of the absorption coefficients for 60 isolated lines of NH3 in the spectral region between 1470 and 1600 cm−1. For illustration, the evolution of the absorption coefficient à K for the line at various pressures of NH3 is shown in Figure 3(a).
In the low-pressure regime, we notice that the absorption coefficient of a given line varies as a quadratic function of pressure as given by the following equation: where is a constant value depending on the individual line.
This figure shows that at high-pressure region, the absorption coefficient tends towards a constant value and hence becomes independent of pressure.
These results are in agreement with those published in [4], where the author studied some lines of the band of NH3.
The inverse of the absorption coefficient as a function of the square of the NH3 pressure is plotted in Figure 3(b) for the line. Indeed, one can see that these two parameters vary linearly. The slope of the obtained straight line is related to the line intensity and self-broadening coefficient of the considered line [4].
Results obtained for NH3 perturbed by N2, show that the peak absorption coefficient, for the 60 lines studied in this work, is decreasing with the N2 pressure. Figure 4 illustrates the variation of the line center absorption coefficients versus the N2 pressure for the lines at K. This figure also shows that the absorption coefficient decreases with the pressure of the perturbing gas. Moreover, it illustrates that decreases with quantum number for a given . For example, the of line is greater than that of line.
Figure 5 represents the evolution of the absorption coefficient with the quantum number in the case of NH3–NH3 gas mixture at K and Torr. The coefficient has a maximum at for the lines and decreases monotonically for with increasing .
According to the literature [10, 13], the line intensity depends on the statistical weight factor , which is related to the quantum numbers and . The intensities of the transition having a statistical weight (i.e., for , ) are generally higher than of those lines having a statistical weight for . As illustrated by Table 4, one can conclude that the absorption coefficients and the line intensities vary in the same way as a function of the quantum numbers.
4.2. Line Wing Absorption Coefficients
According to our analysis, we observe a quadratic dependence of the absorption coefficient as a function of pressure of the NH3 gas that can be modeled as follows [14]: is the normalized absorption coefficient depending on the temperature and the wave number of the line; is the NH3 pressure. Table 2 gives the self-absorption coefficient of the two wings of and lines as a function of the square of NH3 pressure () at K. Figure 6 shows the variation of self-absorption coefficient of the right wings of and lines as a function of the square of NH3 pressure (). One can see that the wing absorption coefficients increase linearly with pressure.
All the self-absorption coefficients measured for the pressure and temperature ranges considered in this study validate the above quadratic pressure dependence given by (5).
For NH3–N2 gas mixtures, a sample of the absorption coefficient for the two wings of the line as a function of N2 pressure () at K is given by Table 3. This table reveals an increasing of with . So the coefficient can be described by the following equation [15]: where is the normalized absorption coefficient.
The and parameters were determined using (6) and the absorption coefficient values for the right and left wings of the each line considered in this work. The results at K are given in Table 4 for 32 ro-vibrational antisymmetric lines in the branch of the band along with the estimated errors given in parentheses. These errors correspond to the statistical errors expressed as one-time standard deviation for all spectroscopic parameters determined in this work. As expected, the errors vary widely with the lines. The stronger and less blended ones are better determined. For the lines which are too weak or too strongly blended, no reliable fit could be obtained. For this reason, some lines have been disregarded. The assignments of the lines considered in this table are taken from [16]. Within the experimental errors, as seen by Table 4, the values of and are practically identical for the two wings.
Figure 7 shows the variation of the absorption coefficient with the N2 pressure for the two wings of the line for NH3–N2 mixtures at K. As shown by this figure, the variation of the absorption coefficient divided by the NH3 pressure () with the N2 pressure is linear. Also, we observe that the values of and parameters are practically the same for the left and right wings of the lines.
4.3. Temperature Dependence
Spectra of the band of NH3 perturbed by N2 were recorded at four temperatures 235, 245, 268, and 296 K for different pressures of nitrogen (). For these spectra, the pressure of NH3 was fixed. Variation of the absorption coefficient at the line center as a function of for the line for and 265 K is shown by Figure 8 which illustrates a decreasing of the absorption coefficient with temperature.
According to Shi and Zhang and Bauer et al. [17, 18], the temperature dependence of absorption coefficient could be presented by the simple power law: where is the temperature exponent and is the reference temperature. In our case K.
From the measured values of the absorption coefficients for the considered temperatures, one can determine the values of the exponent A as the slope of least square fits from the graphs of as a function of . The straight lines obtained for all the transitions considered in this work validate (7) within the indicated temperature range. Figure 9 illustrates the variation of as a function of for the line. The variation is linear; the slope of the line obtained from a linear regression gives a temperature exponent .
This dependence is in agreement with the work performed by Bauer et al. [18] in their study of the temperature dependence of the absorption coefficient of H2O transitions.
5. Conclusion
Using spectra recorded using a Fourier transform spectrometer and a multispectrum fitting technique, we have determined the absorption coefficients at the center and in the wings of 60 lines pertaining to the branch of the band of NH3 as a function of NH3 and N2 pressures for different temperatures. The present results are in agreement with other recent measurements. In the low-pressure region, the self-absorption coefficient at the center of a given line varies with pressure as a quadratic function. At higher pressures, this coefficient tends to become constant. For NH3–N2 mixture, the values of the absorption coefficients exhibit a decreasing with N2 pressure.
In the wings of the lines, these coefficients show an increasing with the square of NH3 pressure, while for NH3-N2 gas mixtures they increase with N2 pressure.
For this gas mixture, we have studied the temperature dependence of absorption coefficient which fits closely an exponential low. The temperature exponents of this law were derived for the line.