Showing papers on "Absorption spectroscopy published in 1979"

Extended X-Ray—Absorption Fine Structure of Small Cu and Ni Clusters: Binding-Energy and Bond-Length Changes with Cluster Size

Abstract: Extended x-ray-absorption fine-structure measurements have been made on metal clusters of Cu and Ni which were formed by vapor deposition on amorphous carbon substrates. Small clusters of both elements show a substantial contraction of the nearest-neighbor metal-metal distance and an increase in binding energy for the onset of the $K$ absorption edge. The results are explained by the increasing surface-to-volume ratio as the cluster size decreases resulting in a more free-atom---like configuration of the metal atoms.

Effect of chemical environment on magnitude of x‐ray absorption resonance at LIII edges. Studies on metallic elements, compounds, and catalysts

Abstract: We report spectra isolating the LIII x‐ray absorption threshold resonance of the elements iridium, platinum, and gold in the pure metallic state and in a variety of compounds. When normalized spectra obtained on the metals are subtracted from those obtained on the compounds, the resulting difference spectra are related to differences in the electronic structure of the absorber atom in the two types of environment. The change in area of a threshold resonance line obtained from such a difference spectrum can be related to the ionicity of the bonds of the absorber atom in its compounds. Measurements on supported platinum and iridium catalysts provide information on electronic changes in the metal due to the small size of the metal clusters or to interaction with the support material. Information on electronic changes due to interaction of the catalysts with gas molecules may also be obtained.

Temperature dependence of the optical properties of silicon

Abstract: The spectral dependence of the absorption coefficient of silicon for photon energies up to 2.7 eV was determined for several temperatures in the range 298–473 K. The effect of a temperature increase appears as a red shift of the absorption spectrum. The magnitude of the shift is larger than that of the fundamental energy gap, increases with increasing photon energy in the range 1.1–1.7 eV, and is constant for energies greater than 1.7 eV. A phenomenological expression deduced by analysis of the data may be used to calculate α (E) at elevated temperature, given α (E) at room temperature. The reflectance was also measured at 299, 413, and 516 K in the photon energy range 2.5–3.8 eV.

X-ray filter assembly for fluorescence measurements of x-ray absorption fine structure.

Abstract: Fluorescence detection, in principle, permits the detection of the extended x-ray absorption fine structure (EXAFS) of more dilute atoms than can be obtained in absorption. To take advantage of this it is necessary, in practice, to eliminate the background that normally accompanies the fluorescence signal. We describe an x-ray filter assembly that accomplishes this purpose. The unique characteristic of the assembly is a slit system that minimizes the fluorescence background from the filter. The theory of the slit assembly is presented and is found to agree with measurements made on the Fe EXAFS of a dilute sample. The filter assembly has a better effective counting rate in this case than that of a crystal monochromator design.

Absorption coefficient of silicon for solar cell calculations

Abstract: The optical absorption coefficient is an important parameter in calculating the performance characteristics of solar cells. For silicon solar cells it is desirable to know the absorption coefficient over the range of 1.1–4.0 eV and over a wide range of temperature, particularly when evaluating the concentration type systems. An analytical (empirical) expression has been developed for this purpose. We have interpreted the available experimental data in terms of three bands of silicon. With our fit, the experimental data can be explained to within an accuracy of 20% and its validity extends from 1.1 to 4.0 eV and over the temperature range of 20–500°K.

Temperature and isotope effects on the shape of the optical absorption spectrum of solvated electrons in water

Abstract: The optical absorption spectra of solvated electrons in H/sub 2/O and D/sub 2/O have been measured at 274, 298, 340, and 380 K. All the spectra were fitted very well with the Gaussian and Lorentzian shape functions at the low- and high-energy sides of the absorption maximum, respectively, excluding the high-energy tail. The spectrum does not shift uniformly with temperature. The temperature coefficient of absorption decreases rapidly with increasing energy on the low-energy side of the absorption maximum, while it changes only slightly on the high-energy side. When the temperature increases the Lorentzian width remains constant, the Gaussian width varies proportionally to T/sup 1/2/, and the spectrum becomes more symmetrical. On going from H/sub 2/O to D/sub 2/O we found that the spectrum at a given A/A/sub max/ shows a shift of +0.05 eV in the low-energy wing. The shift decreases with increasing energy, reaching 0.03 eV at the absorption maximum. On the high-energy side of the band the shift becomes negative at h..nu.. > 2.2 eV. The shift on the low-energy side seems to be related to the difference of the zero-point energies of the inter- and intramolecular vibrations. The wavelength dependence of the temperature and isotope effects ismore » consistent with the model that different types of excitation occur on the low- and high-energy sides of the absorption band. The temperature and isotopic dependence of the low-energy side are consistent with its width being due to phonon interactions.« less

Optical absorptions of light and heavy water by laser optoacoustic spectroscopy

Abstract: A pulsed dye-laser optoacoustic spectroscopy technique has been used to measure the absorption spectra of light and heavy water at 21.5 degrees C in the visible region. Basic principles of pulsed optoacoustic spectroscopy technique and the procedure for absolute calibration are discussed with reference to its application in water. Experimental details of the application of optoacoustic spectroscopy to water are given. Our absorption coefficients, of accuracies about +/- 10%, are believed to be the most reliable so far. Light water has a broad absorption minimum near 475 nm where the absorption coefficient is 1.8 x 10(-4) cm(-1). Heavy water exhibits a totally different absorption spectrum and has a broad absorption minimum near 600 nm where the absorption coefficient is 1.9 x 10(-4) cm(-1). Previous measurements of the optical spectra of water were done mostly by long-path transmission measurements, and they display disagreement by factors as large as 10 near the green absorption minimum of light water. We give a critical comparison of our optoacoustic absorption spectra with other existing data.

The B1Πu–X1Σg+ band system of the 7Li2 molecule

Abstract: The absorption and laser induced fluorescence spectra of the B1Πu–X1Σg+ band system of the 7Li2 molecule has been photographed at high resolution (360 000) and high dispersion (0.4 A/mm). Over 14 000 spectral lines have been assigned to this band system for a wide range of rotational quantum numbers (J=0−80) and vibrational quantum numbers (v′=0−13 and v″=0−18). Using a Dunham type analysis, we have obtained the molecular constants for both states and have fitted 8358 nonoverlapping lines with an rms error of 0.012 cm−1. The B1Πu lambda doubling constants, including the centrifugal distortion lambda doublet constant, have been determined. Quantum mechanical potential curves have been generated for this system using a novel variational procedure and Franck–Condon factors for different rotational quantum numbers have been determined over the range of vibrational levels observed. Excellent agreement has been achieved for the centrifugal distortion terms Dv, Hv, and LV which were obtained from the least squar...

Results of a homogeneous survey of absorption lines in QSOs of small and intermediate emission redshift.

Abstract: Results are presented for a spectroscopic survey of an intermediate (1.20z/sub em/ have velocity dispersion very similar to that expected if the absorbing material and the QSO are members of clusters of galaxies, and we interpret systems with vertical-bar z/sub em/-z/sub abs/ vertical-bar< or approx. =3000 km s/sup -1/ as predominantly associated with galaxy clusters. The remaining absorption is due to material ejected by QSO. We suggest that broad-line absorption systems are recently ejected gas which eventually evolves into multiple sharp-line systems, two examples of which are found in our survey. It is suggested that the distribution of C IV and Mg II absorption systems in redshift can be explained by assuming that the absorbing gas in intervening clusters of galaxies is the same as the gas in clusters which contain QSOs, with the exception that the QSO--containing cluster gas has higher ionization.

Significance of absorption features in Io's IR reflectance spectrum

Abstract: This paper shows that the presence of SO2 may have important implications for Io's atmosphere and transient phenomena. It is suggested that any abundant metal-containing compounds, such as halides or sulfides, are spectrally bland in the wavelength region from 2.0 to 5.0 microns.

An absorption feature in the spectrum of the pulsed hard X-ray flux from 4U0115 + 63

Abstract: A spectral feature, apparently an absorption line, has been observed at an energy of 20.1 + or - 0.5 keV in the pulsed flux of the 3.61-s X-ray pulsar 4U 0115+63 by using the UCSD/MIT instrument on HEAO 1. The line strength, expressed as equivalent width, is 3.1 + or - 0.5 keV. Although essentially unresolved, the feature has a depth more than 60% of the continuum flux. If the feature arises by cyclotron resonance absorption near the magnetic poles of the neutron star, it implies a magnetic field of between approximately 1.8 and 2.5 x 10 to the 12th G, depending on the gravitational redshift (no more than about 5-40%).

Picosecond transient spectroscopy of molecules in solution

Abstract: The transient absorption spectra of a number of compounds in solution at room temperature have been measured with picosecond‐scale time resolution and unprecedented accuracy and reliability. It is found that the spectra of benzophenone, xanthone, 9‐fluorenone, p‐benzoquinone, acridine, quinoxaline, t‐stilbene all show significant evolution following excitation with the 353 nm third harmonic of a mode‐locked Nd:glass laser. These spectral changes provide evidence for previously unrecognized photophysical behavior in the systems studied, including vibrationally nonthermalized triplet states in benzophenone which persist for tens of picoseconds, and formerly unobserved singlet absorptions in acridine, quinoxaline, fluorenone, and benzoquinone. The inadequacy of single wavelength probing techniques in deducing the dynamics of complex molecular systems such as these is demonstrated by the large extent to which spectra of different states overlap. In many cases a reinterpretation of previous single wavelength results is required because of the presence of vibrationally and electronically unrelaxed species. The apparatus used here to obtain the high quality visible transient spectra is described and its performance characterized.

Infrared optical absorption of Hg1−xCdxTe

Abstract: The absorption near the fundamental absorption edge of Hg1−xCdxTe was measured over the composition range 0.205⩽x⩽0.220 at temperatures from 80 to 300 K. The dispersion of the index of refraction of Hg1−xCdxTe was obtained from the interference pattern. It was found that the absorption tail obeys a modified Urbach’s rule and is expressed by α=α0 exp[σ (E−E0)/(T+T0)] for 20⩽α (cm−1) ⩽1000. The fitting parameters α0, σ, T0, and E0 vary regularly with x. The expression is used to obtain the absorption coefficient and the temperature coefficient of the gap as a function of x and T. Evidence is presented to show that these parameters may be extrapolated to calculate the absorption beyond the measured composition range.

Micellar Solubilization of Proteins in Aprotic Solvents and their Spectroscopic Characterisation

Abstract: The quaternary ammonium salt methyl-trioctylammonium chloride enables the transfer of α-chymotrypsin, trypsin, pepsin and glucagone from water to cyclohexane. Reversed micelles, whose polar core solubilizes both protein and water, are probably formed in the apolar phase. The influence of various parameters on the phase transfer (concentration, pH, solvent, temperature, etc.) has been investigated. Absorption, fluorescence and circular dichroism studies of the biopolymers in the cyclohexane system have been carried out. For trypsin and chymotrypsin, the CD. signal in the 200 nm region is very similar in water and in cyclohexane, which suggests that the polypeptide folding is not substantially different in the two phases. The fluorescence quantum yield is always much larger in the cyclohexane phase than in water. The longer wavelength region of the UV. absorption spectrum is slightly red-shifted relative to water, and a band at 225 nm, probably arising from the aromatic chromophore, is apparent in the organic phase. Reasons for these spectral perturbations are discussed. The enzymes transferred from water into cyclohexane phases can be continuously retransferred into a second water phase. The possible relevance of this ‘double transfer’ as a model for the vectorial transport of biopolymers or a separation technique is discussed.

Two-Photon Absorption in Zinc-Blende Semiconductors

Abstract: Two-photon absorption can become the dominant loss mechanism for semiconductors subjected to sufficiently intense laser light in the frequency range Svp&E, &28p, where +p is the laser frequency and E, is the energy gap. The proper understanding of this effect can yield information not accessible to one-photon transitions, and is important for the operation of a number of devices such as \"inducible absorbers, \" twophoton-pumped and spin-flip Raman lasers, and infrared detectors. There has been a long-standing discrepancy, in some cases of more than an order of magnitude, between reports of the measured frequency dependence of the two-photon absorption coefficient and the theoretically predicted values, in particular for two-photon energies much greater than E, (see, for example, Basov et al. ,' Lee and Fan, ' and Doviak et al. ') We show in the present work that a simple three-band model calculation provides a single comprehensive description of both the magnitude and the frequency dependence of the two-photon absorption coefficient for a wide range of III-V and II-VI zinc-blende semiconductors. For a given photon energy the magnitude of the coefficient d(An) Kal dt 28&p (2)

The 4-8 micron spectrum of the infrared source W33 A

Abstract: The spectrum of the highly obscured infrared source W33 A from 4.5 to 8 microns is measured in order to investigate the intervening cold, dense interstellar material. Spectrophotometry at a relative spectral resolution of about 0.015 by an airborne filter-wheel infrared spectrometer reveals strong absorption features at 4.61, 5.99 and 6.78 microns. The absorption at 4.61 microns is attributed primarily to the fundamental vibration-rotation band of CO at a column density (at least 10 to the 19th/sq cm) which is 10% of the carbon inferred from silicate abundances. The strengths and line widths of the absorption agt 5.99 and 6.78 microns are interpreted as evidence of absorption in the resonance bands of carbonyl, carbon-carbon double, methyl and methylene bonds of hydrocarbons associated with interstellar dust.

Optical absorption and radiative heat transport in olivine at high temperature

Abstract: Results are presented of measurements of the optical absorption spectra (300-8000 nm) of olivine as a function of temperature (300-1700 K) under conditions of controlled and known oxygen fugacity within the stability field of the samples. The absorption spectra are used to calculate the temperature-dependent radiative transfer coefficient of olivine and to numerically study the accuracy of the method. The present absorption measurements in olivine under oxidizing conditions known to be within the olivine stability field indicate that the effective radiative conductivity K(R) is lower than that obtained in previous studies under different experimental conditions. The lower value of K(R) makes it more likely that some of the earth's internal heat is removed by convection and less likely that thermal models involving conduction and radiation alone will satisfactorily explain thermal conditions in the earth's mantle.

Synchrotron Radiation: Techniques and Applications

Abstract: 1. Introduction - Properties of Synchrotron Radiation.- 1.1 Historical Development.- 1.2 Quantitative Properties.- 1.2.1 Equations for Ideal Orbits.- 1.2.2 Considerations for Real Orbits.- a) Coherence.- b) Periodic Wigglers.- c) Synchrotron Accelerators.- d) Beam Cross Section and Divergency.- 1.2.3 Time Structure.- 1.3 Comparison with other Sources.- 1.3.1 Infrared and Visible Range.- 1.3.2 Vacuum Ultraviolet Range.- 1.3.3 X-rays.- 1.4 Acknowledgments.- References.- 2. The Synchrotron Radiation Source.- 2.1 Fundamental Concepts.- 2.1.1 Orbit Dynamics.- a) Betatron Oscillations.- b) Betatron Oscillations of Off-energy Particles.- c) Phase Focusing and Synchrotron Oscillations.- 2.1.2 Radiation Damping.- 2.1.3 Beam Lifetime.- 2.1.4 Beam Cross Section.- 2.2 Design Considerations.- 2.2.1 Magnetic Field and Energy.- 2.2.2 Lattice.- 2.2.3 Injector.- 2.2.4 Accelerating System.- 2.2.5 Energy Shifter Wigglers.- 2.2.6 Multipole Wigglers (Undulator).- 2.3. Design Examples.- 2.3.1 Aladdin.- a) Lattice.- b) Vacuum System.- c) Accelerating System.- d) Injector.- e) Computer Control.- 2.3.2 The National Synchrotron Light Source (NSLS).- References.- 3. Instrumentation for Spectroscopy and other Applications.- 3.1 Layout and Operation of Laboratories.- 3.1.1 VUV Laboratory at a Small Storage Ring.- 3.1.2 VUV and X-Ray Laboratory at a Large Storage Ring.- 3.1.3 Beam Line Optics.- a) General Considerations.- b) The Phase Space Method.- c) Magic Mirrors.- 3.2 Optical Components.- 3.2.1 Mirrors and Reflective Coatings.- a) General Remarks.- b) Reflectivity in the Vacuum Ultraviolett.- c) Coating Materials and Multilayer Coatings.- d)Sattering and Stray Light.- e) Mirror Substrate Materials.- f) Imaging in VUV.- 3.2.2 Dispersive Elements.- a) Reflection Grating Dispersors.- b) Spherical Concave Gratings.- c) Aspherical Concave Gratings.- d) Efficiency and Blaze.- e) Holographic Gratings.- f) Zone Plates and Transmission Gratings.- g) Crystals for Monochromators.- 3.2.3 Filters and Polarizers.- a) Filters and higher Order Problems.- b) Polarizers.- 3.3 VUV Monochromators.- 3.3.1 General Considerations.- 3.3.2 Normal Incidence Monochromators.- 3.3.3 Grazing Incidence Monochromators.- a) Plane Grating Monochromators.- b) Rowland Mountings.- c) Non-Rowland Monochromators.- 3.3.4 New Concepts.- 3.4 X-Ray Monochromators.- 3.4.1 Plane Crystal Instruments.- 3.4.2 Higher Order Rejection.- 3.4.3 Bent Crystal Monochromators.- 3.5 Photon Detectors.- 3.5.1 Detectors for the Vacuum Ultraviolet.- 3.5.2 X-Ray Detectors.- 3.6 Typical Experimental Arrangements.- 3.6.1 Experiments in the Vacuum Ultraviolet.- a) Absorption Reflection, Ellipsometry.- b) Luminescence, Fluorescence.- c) Photoionisation, Fotofragmentation.- d) Photoemission.- e) Radiometry.- f) Microscopy.- 3.6.2 Experiments in the X-Ray Range.- a) Single Crystal Diffraction.- b) Small Angle Diffraction.- c) Small Angle Scattering.- d) Mossbauer Scattering.- e) Energy Dispersive Diffraction.- f) Interferometry.- g) Absorption (EXAFS).- h) Topography.- i) Standing wave excited Fluorescence.- j) Fluorescence Excitation.- k) Compton Scattering.- 1) Resonant Raman Scattering.- m) Photoelectron Spectroscopy (XPS).- 3.7 Acknowledgements.- References.- 4. Theoretical Aspects of Inner-Level Spectroscopy.- 4. 1. Basic Concepts and Relations in Radiative Processes.- 4.1.1 Polarizability and Dielectric Function.- a) Self-consistent field Method.- b) Direct Method for Longitudinal Part.- 4.1.2 Absorption Coefficient and Oscillator Strength.- 4.1.3 Dispersion Relations and Sum Rules.- 4.2 Distribution of Oscillator Strength.- 4.2.1 Absorption Spectra in Atoms.- 4.2.2 A Unified Picture for Spectra in Atoms, Molecules and Solids.- a) Cancellation of Oscillator Strength, Giant and Subgiant Bands.- b) Pseudo Potential and Energy Band Effect.- c) Effect of Coulomb Attraction.- 4.2.3 Extended X-Ray Absorption Fine Structure (EXAFS).- 4.3 Electron-Hole Interactions.- 4.3.1 General Treatment of Excitons.- 4.3.2 Wannier and Frenkel Excitons.- a) Wannier Exciton.- b) Frenkel Exciton.- 4.3.3 Optical Absorption Spectra.- a) First Class Transition.- b) Second Class Transition.- 4.3.4 Effects of Spin and Orbital Degeneracies.- 4.4 Configuration Interactions.- 4.4.1 Aulger Process.- 4.4.2 Fano Effect.- 4.5 Simultaneous Excitations and Relaxations.- 4.5.1 Localized Excitation and Relaxation in Deformable Lattice.- 4.5.2 Host Excitation in Deformable Medium.- a) Slow Modulation Limit.- b) Rapid Modulation Limit.- 4.5.3 Sideband Structures.- 4.5.4 Relaxation in Exciton-Phonon Systems.- 4.6 Many Body Effects in Metals.- 4.6.1 Friedel Sum Rule and Anderson Orthogonality Theorem.- 4.6.2 Infrared Divergence.- 4.6.3 Fermi Edge Singularity.- 4.7 Final State Interactions Associated with Incomplete Shells.- 4.7.1 Multipiet Splitting.- 4.7.2 Local Versus Band Pictures.- 4.7.3 Correlation Effects in Narrow d-Band.- 4.8 Inelastic X-Ray Scattering.- 4.8.1 Compton and Raman Scattering.- 4.8.2 Resonant Raman Scattering.- 4.9. Topics of Recent and Future Interest.- References.- 5. Atomic Spectroscopy.- 5.1. Atomic Photoabsorption Spectroscopy in the Extreme Ultraviolet.- 5.2 The Basic Experiments in Photoabsorption Spectroscopy.- 5.2.1 Photoabsorption Spectroscopy.- 5.2.2 Photoelectron Spectroscopy.- 5.2.3 Mass Spectrometry.- 5.2.4 Fluorescence.- 5.3 Limitations of Photon Absorption Experiments.- 5.4 The General Theoretical Framework.- 5.5 Experimental Results.- 5.5.1 Photoabsorption Spectroscopy.- a) Discrete Resonances.- b) Gross Features.- 5.5.2 Photoelectron Spectroscopy.- a) Partial Photoionisation Cross Sections.- b) Angular Distributions of Photoelectrons.- 5.5.3 Mass Spectrometry.- 5.6 Future Work.- References.- 6. Molecular Spectroscopy.- 6.1 Concepts.- 6.2 Absorption Spectroscopy.- 6.2.1 Valence Spectra of Simple Di- and Tri-Atomic Molecules.- 6.2.2 Valence and Rydberg Excitations in N2.- 6.2.3 Rydberg Series in the Valence Absorption Spectrum of H2O and D2O.- 6.2.4 Core-Spectra of Simple Di-Atomic and Tri-Atomic Molecules.- a) N2.- b) NO.- 6.2.5 d-Spectra of Se2, Te2 and I2.- a) Se2.- b) Te2.- c) I2.- 6.2.6 Alkali Halides.- a) Li ls-absorption in LiF.- b) Cs-halides.- 6.2.7 Xenon Fluorides.- 6.2.8 Inner-well Resonances.- 6.2.9 EXAFS.- 6.2.10 Valence Shell Spectra of Organic Compounds.- a) Saturated Hydrocarbons: Alkanes, Neopentane.- b) Molecules with bonding o- and -?-orbitals.- 6.2.11 Core Spectra of Organic Compounds.- 6.3 Photoelectron Spectroscopy.- 6.3.1 Intensities of Photoelectron Spectra and Partial Photoionization Cross Sections.- 6.3.2 Photoionization Resonance Spectroscopy and Coincidence Measurements.- 6.4 Fluorescence.- 6.4.1 Fluorescence- and Excitation-Spectra.- 6.4.2 Time resolved Fluorescence Spectroscopy.- 6.5 Mass-Spectrometry.- 6.6. Acknowledgments.- 6.7. Appendix.- References.- 7. Solid-State Spectroscopy.- 7.1 Quantitative Description of Optical Properties.- 7.1.1 Macroscopic Optical Properties.- 7.1.2 Microscopic Description.- 7.1.3 Modulation Spectroscopy.- 7.1.4 Summary.- 7.2 Metals and Alloys.- 7.2.1 Vacuum Ultraviolet.- a) Simple Metals.- b) Noble Metals.- c) Transition Metals.- d) Rare Earths.- 7.2.2 Soft X-Ray.- a) Simple Metals.- b) Transition Metals.- c) Rare Earths.- 7.2.3 Summary.- 7.3 Semi conductors.- 7.3.1 Vacuum Ultraviolet.- a) II-VI Compounds.- b) Pb-Chalcogenides.- c) Other Semiconductors.- 7.3.2 Soft X-ray.- 7.3.3 Summary.- 7.4 Insulators.- 7.4.1 Rare Gas Solids.- 7.4.2 Alkali Hal ides.- 7.4.3 Other Metal Hal ides.- 7.4.4 Other Inorganic Insulators.- 7.4.5 Organic Insulators.- 7.4.6 Summary.- References.- Additional References with Titles.

Detection of SO2 in the UV spectrum of Venus

Abstract: The broad absorption feature below 3300 A in the Venus UV spectrum is identified as primarily due to SO2 absorption based on new higher resolution spectra of the 3000-3400 A region showing broad (10 A), unresolved absorptions in the regions at all SO2 band origins between 3000 and 3300 A. SO2 mixing ratios vary from 5 x 10 to the -7th down to an upper limit of 2 x 10 to the -8th at a phase angle of 138 deg. Previous observational determinations of the SO2 mixing ratio were biased toward large phase angles, and consequently did not detect any SO2 absorption at the 10 to the -8th level. The upper limit derived from the CS2 band head at 3206 A is not greater than 5 x 10 to the -8th. The observed range of SO2 mixing ratios is consistent with model predictions based on the sulfur photochemistry at the cloud tops. Ground-based observations of SO2 mixing ratio will provide constraints on models and check on the Venera and Pioneer Venus measurements of the mixing ratios of SO2 and other sulfur-bearing gases with altitude.