Spectral Slit Width Research Articles

Statistical analysis of the impact of spectral correlation on observed formation constants from UV-visible spectroscopic measurements.

Information retrieved from UV-visible spectroscopic data by application of a self-modelling factor analysis algorithm showed apparently systematically shifted thermodynamic properties for the same chemical system as a function of spectral slit widths. This empirical observation triggered a systematic investigation into the likely effects of residual and spectral correlation on the numerical results from quantitative spectroscopic investigations. If slit width was a nuisance factor it would reduce the comparability of information evaluated from spectroscopic data. The influence of spectral slit width was investigated by simulation, i.e. by generating and evaluating synthetic spectra with known properties. The simulations showed that increasing spectral correlation may introduce bias into factor analysis evaluations. By evaluation of the complete measurement uncertainty budget using threshold bootstrap target factor (TB CAT) analysis, the apparent shifts are insignificant relative to the total width of the quantity's measurement uncertainty. Increasing the slit widths causes some systematic effects, for example broadening of the registered spectral bands and reduction of spectral noise, because of higher light intensity passing to the detector. Hence, the observed systematic shifts in mean values might be caused by some latent correlation. As a general conclusion, slit width does not affect bias. However, the simulations show that spectral correlation and residual correlation may cause bias. Residual correlation can be taken into account by computer-intensive statistical methods, for example moving block or threshold bootstrap analysis. Spectral correlation is a property of the chemical system under study and cannot be manipulated. As a major result, evidence is given showing that stronger spectral correlation ( r<-0.7) causes non-negligible bias in the evaluated thermodynamic information from such a system.

Interferometric measurement of the modulation transfer function of a spectrometer by using spectral modulations

We present our results on measurement of the modulation transfer function (MTF) of a given spectrometer by using the sinusoidally modulated spectrum from a Michelson interferometer with white light. We studied the MTF by varying the periodicity of the spectral fringes produced by the interferometer. Experimental data are fitted to a theoretical model to derive the spectral slit width from the measured MTF of the spectrometer.

Condensation of a soft mode in the Raman spectrum of the second tetragonal phase of CsScF4

40 cording to the data obtained in that study, the structure of its high-temperature G0 phase ~space group D4h 1 , Z51) consists of a series of perovskite-like square layers of ScF6 octahedrons separated by Cs ions ~Fig. 1!. Lowering the temperature causes a transition to the G1 phase ~space group D4h 5 , Z52) at T15490 K and then to the G2 phase (D2h 13 , Z54) at T25317 K ~the temperatures cited are based on the data obtained in the present work and differ somewhat from the data in Ref. 1; the existence of such a spread of values was noted in Ref. 1!. Such a sequence is not typical of cesium-containing perovskites, but is similar to that previously observed in RbAlF4, 2,3 in which reorganization of the structure occurs as a result of displacive phase transitions associated with turning of the AlF6 octahedra. This similarity, as well as the closeness of several macroscopic characteristics of the phase transitions in these crystals, provided Aleksandrov et al.. with some basis to postulate that the phase transitions in CsScF6 are of the same type. In that case the phase transitions should be accompanied by the condensation of soft phonon modes, which can be observed in the Raman spectra. The present work was devoted to testing this hypothesis. Investigations were carried out in the vicinity of the lowtemperature D4h 1 2D4h 5 phase transition at T15490, below which condensation of the Raman-active totally symmetric soft mode should be observed according to the selection rules. Samples measuring 23334 mm, which were taken from the same crystallization batch as in Ref. 1 were cut so that they would be oriented along the crystallographic axes in the G1 phase. The crystals were optically transparent and did not contain microscopically visible defects or inclusions. The spectra were obtained on a DFS-24-based automated spectrometer and a Jobin and Yvon U-1000 Raman spectrometer. The spectral slit width was 2 cm, and the scan step was 1 cm. The precision of the stabilization of the sample temperature during the recording of a spectrum was better than 60.2 K. In accordance with the selection rules and the structural data, the spectra of the high-temperature G0 phase displayed two intense lines, at 160 cm (Eg) and 495 cm 21 (A1g), which correspond to vibrations of the axial fluorine atoms in the xy plane and along the z axis, respectively. The frequency of the latter is close to the frequency of the longitu-

Deconvolution of lorentzian Raman Linewidth: Techniques of polynomial fitting and extrapolation

AbstractA simple, convenient and precise technique for deconvolving the Lorentzian (true) Raman linewidth, ΓL, from the observed Raman linewidth, (Δ1/2)R [the FWHM (full width at half‐maximum) of the Raman line in question], through polynomial fitting, was developed. The precision of this technique is a consequence of the fact that the values of ΓL/(Δ1/2)R (= Y), obtained by exact numerical evaluation of the Voigt profiles for the Raman bands, were flitted to third‐ and fourth‐degree polynomials in S/(Δ1/2)R (= X), S being the spectral slit width measured as the linewidth (FWHM) of a narrow spectral line recorded at the same slit settings as the Raman line. The procedure of obtaining ΓL, from the knowledge of S,(Δν1/2)R and X, which yields better results, is discussed. Another technique of deconvolution is described and discussed, involving the measurement of Raman linewidths of a particular Raman line for about five or six different slit widths. The measured linewidths (Δ1/2)R, when extrapolated to S → 0, give the value of ΓL directly. A careful comparison with the other deconvolution techniques reveals that the method of polynomial fitting is relatively more precise than other semi‐analytical deconvolution techniques, and the extrapolation technique also gives reasonably good results. The applicability of both methods was tested by taking some selected Raman lines.

Effect of pressure on the Raman depolarization ratio and the vibrational relaxation of thev1mode of liquid carbon tetrachloride at 22°C and 0–1·1 kbar

The depolarization ratio of the v 1 Raman bands and the vibrational relaxation time of liquid carbon tetrachloride at 1 bar to 1·1 kbar were obtained by resolving the overlapping v 1 fundamental bands of five isotopic species and three broad combination bands by least-squares fitting. The eight component bands were represented by Voigt functions, the Gaussian widths of which were determined from the spectral slit widths. The resulting depolarization ratio of the v 1 fundamental bands at 1 bar is 0·0040, which is about 40% smaller than the depolarization ratio obtained from the whole region of the v 1 band. It decreases to 0·0033 at 1·15 kbar, which follows approximately the theoretical curve of the fluctuating-local-field model. The vibrational relaxation time obtained from the band width of the v 1 fundamental band of C35Cl4 decreases linearly from 6·0 ps at 1 bar to 4·7 ps at 1·15 kbar. The change is well reproduced by Schweizer and Chandler's kinetic model.

On the design and performance of the Czerny-Turner monochromator in ICP-AES

The optical arrangement of the Czerny-Turner (CT) monochromator and the theoretical dependence of dispersion and spectral slit width on wavelength, order and groove density are discussed in detail. Because a given spectral line appears at the grating under higher angles for higher order or higher groove density, the improvement in spectral slit width is always greater than the ratio of the orders or the ratio of the groove densities. Attention is drawn to the magnification of the image of the entrance slit by the CT optics and its influence on spectral slit width and the proper choice of the exit slit width. The improvement of spectral slit width by an apodization mask is theoretically discussed and experimentally verified. An extended convolution formula which includes the magnification factor is proposed and compared with known models. Coma as a source of residual lack of fit and the conditions for coma-free imaging in the CT system are discussed. The theoretically predicted performance of Czerny-Turner monochromators is compared with results obtained with two commercially available 1-m instruments with gratings of 2400 and 3600 linesmm.

Present and future roles of high performance charge transfer device detectors in spectrochemical analysis

The inductively coupled plasma is widely used as a radiation source in analytical emission spectrometry. Because of the richness of the spectra and the line broadening, the role of the resolving power of the dispersive system is very important. Monochromators allow a flexibility in line selection and can be optimized to obtain the best experimental resolution. Considering the range of the physical line widths of analytes observed in the plasma, specifications can be given for the instrumental broadening of the monochromator. Parameters influencing the instrumental broadening will be described with an emphasis on the resultant spectral slit width. Consequences on the optimization of the signal to background ratio will be discussed.

Determination of carbon, silicon and boron content in semi‐insulating GaAs by infrared absorption spectroscopy

AbstractMeasurements of the local vibrational mode (LVM) absorption of 12CAs at 582 cm−1, 28SiGa at 384 cm−1 and (10)11BGa at (540 cm−1) 517 cm−1 can be used to determine the concentration of these residual impurities in semi‐insulating (SI) GaAs. Although the energy‐limited resolution of a grating spectrometer does not allow measuring the line shape of the narrow LVM bands in GaAs the intensity of it determined with definite spectral slit width (SSW) is a reliable measure for the respective impurity content. Calibration factors given in the literature and peculiarities in the measurements and evaluations for the different impurities are discussed.

Spectral slit width correction for infrared absorption bands of matrix isolated molecules based on line shape analysis

A method for correction of band contour distortion by finite spectral slit width based on line shape analysis is presented. For bands with Lorentzian line shape model calculations of apparent transmission resulting from convolution with a triangular slit function will be used to derive effective line parameters—integrated absorption, peak optical density and line width—by least squares approximation of the apparent optical density by effective Lorentzian band shapes. Figures and tables relating effective line parameters to true line parameters in dimensionless form will be presented. Systematic errors inherent in this type of approximation will be discussed. Furthermore the effective line width will be shown to depend dominantly and in a simple manner on slit width and only very slightly on true integrated absorption. The latter fact will prove essential for practical application to determination of approximate true line parameters and to deconvolution. The method will be demonstrated for complex band contours observed in vibrational spectra of matrix isolated molecules which consist of superpositions of bands of widely varying line width and integrated absorption. By subjecting such contours to line shape analysis with effective Lorentzian shapes and by deriving—with the aid of the tables presented—true approximate line parameters, the latter are found to be little affected by even relatively high noise levels. Systematic errors will be discussed.

Estimation of spectral slit width and blind deconvolution of spectroscopic data by homomorphic filtering

A numerical method is developed to estimate the spectral slit width of a spectrophotometer which degrades the spectral resolution of the measured data. The slit width is estimated from the measured spectrum in certain conditions. This method is based on homomorphic filtering and utilizes the cepstrum of the average log Fourier spectrum of the section spectra. Computer simulations and experimental examples for infrared absorption spectra of ammonia gas demonstrate the potential of the method for practical applications to the preprocessing of deconvolution. A blind deconvolution method is also examined through the experimental result with an ammonia gas spectrum.

The possibility of standardless furnace atomic absorption spectroscopy

The original papers of Walsh and L'vov anticipated that atomic absorption spectroscopy would be capable of absolute, or standardless analyses. This paper shows that the modern graphite furnace technique provides standardless analyses in varied and complex matrices within about 10–20% accuracy. Some of the conditions that control the remaining variability are the atomization temperature and spectroscopic variables such as spectral slit width and lamp current. Nevertheless, characteristic mass data collected from nominally similar conditions in different laboratories for many elements show a spread of about ±15%, in spite of all the variables. A group of materials was analysed for several elements using only characteristic mass data for calibration and the results were compared with previous analyses of these materials. The results supported the 10–20% accuracy of this approach

Determination of molar IR absorptivities and their errors

Abstract Molar absorptivities of band maxima of acetonitrile, n-heptane, benzene, and toluene were determined from difference spectra. The statistical and most important systematic errors are given. Recently, we studied statistical and systematic errors occuring in the determination of IR absorptivities e of liquids (ref. 1). Considerable systematic errors are caused by reflection losses at the outer and inner surfaces of the cell windows. It was shown that these are compensated for if the ratio of two transmittance spectra (T1, T2) due to different sample thicknesses (d1, d2) is used: In such a case Bouguer—Lambert-Beer's laws leads to where c denotes the concentration. The reliability of the absorptivities derived in this way, is mainly affected by the statistical error comprising the standard deviations of the transmittance measurements as well as by the systematic errors from multiple beam interference within the cell (the fringes do not compensate for each other because of their different periods) and from the finite slit width. Experimental conditions can be chosen so that errors from beam convergence, polarization, temperature variations, and thermal emission are negligible. The influences on the transmittance measurement by drift, unwanted radiation, reliability of wavenumber reading, and non-linearity of the detector system are not considered. The molar absorptivities of band maxima of acetonitrile, n-heptane, benzene, and toluene have been determined using equation (1) and are listed in the Table. The values ofΔd employed were in the order of 10 μm to 40 μm, therefore, the strongest bands could not be evaluated. The statistical error was calculated from and the systematic error due to finite spectral slit width (s) from with the band half-width 2γ. The deviation of the cell from planoparallel shape has been taken into account quantitatively, this is different to the method used previously (ref. 1). If the cell is wedge shaped so that its thickness varies linearly from (d0 - δ) to (d0 + δ), the interference pattern of a cell filled with a compound of refractive index ns is described by where φ = 4 π ns ν d and r denotes the reflectance, T the true transmittance, and ν the wavenumber. Since ns( ν ) is not known precisely, only a range can be given for TA limited by the values for cos φ = ± 1. For the absorptivities derived from a difference spectrum this uncertainty is but only as far as the average refractive index n s is a sufficient approximation. fi is the smaller the further the cell deviates from planoparallel shape. On the other hand, this causes an additional error which, however, can be neglected up to δ/d0 ∼- 0.05. Equation (5) has been used to calculate the values fi given in the Table. The comparison of the here presented absorptivities with those obtained by a different method (ref. 2, no data for n-heptane) shows a good agreement in value and precision.

Vibrational relaxation in molecular crystals. High-resolution Raman band profiles of some naphthalene and naphthalene-d8 phonons at low temperature

Abstract The accurate determination of the shape of phonon Raman bands in crystals is of great importance for the determination of the phonon lifetimes and for the study of their relaxation mechanisms. Several molecular crystals show at low temperatures the occurrence of long-living phonons with Raman bandwidths which are much narrower than the spectral slitwidth of standard Raman instruments. Information on their relaxation processes is thus normally extracted only from time domain experiments using picosecond CARS techniques. In order to extend these measurements to the frequency domain high resolution is needed. For this purpose we have built a high-resolution Raman instrument coupling together a Raman spectrometer and an interferometer. The tandem instrument has a limiting resolution of 0.02 cm −1 , largely sufficient to measure the bandwidths of long-living phonons in molecular crystals. With this instrument we have measured the profile of the six Raman-active phonons of naphthalene- h 8 at 57.5, 69, 511, 514, 766 and 1385 cm −1 and of three corresponding phonons of naphthalene- d 8 at 54, 64 and 493 cm −1 at 5 K. The observed bandwidths are well fitted by lorentzian curves. Comparison with available recent picosecond CARS data is used to prove the competitivity of high-resolution Raman with time-delayed spectroscopy. Bandwidths measured with the two techniques show differences of a few thousands of cm −1 for most of the bands studied. Only in the case of the two lowest phonons of naphthalene- h 8 larger differences are observed. These are interpreted in terms of optical crystal quality. The observed band profiles are interpreted in terms of population decay mechanisms based on anharmonic calculations of three-phonon decay processes. Pure dephasing processes are shown to give vanishing contributions to the low-temperature widths.

Accurate determination of the low frequency dielectric dispersion in SrTiO3by hyper-Raman scattering

Abstract The hyper-Raman effect is utilized to study infrared-active, but Raman-forbidden modes by light scattering. We have accurately measured the lowest and highest frequency hyper-Raman line of SrTiO3 at room temperature with a spectral slit width of less than 4 cm−1. Applying the fluctuation-dissipation theorem we relate the hyper-Raman lineshapes to the dielectric function ϵ (Ω). Absolute values of ϵ (Ω) are deduced for the frequency range of the ferroelectric soft mode. We compare our results with far-infra-red data and discuss the soft mode self-energy calculated from our ϵ (Ω).

Experimental Determination of True Raman Linewidths from Measurements of Linewidths Observed at Different Slit Openings

A method is proposed to determine a true Raman linewidth from linewidths observed at different slit openings, without knowing accurate spectral slit widths. It is applied to various Raman lines of liquid molecules to assess the utility of the method.

High resolution rotation–vibration Raman spectra of acetylene. II. The spectra of C2D2 and C2HD

The Raman spectra of gaseous C2D2 and C2HD were excited in a multiple-reflection Raman cell by a single-moded Ar+ laser and recorded photographically; the gas pressures were in the range, 130–200 Torr, and the spectral slit width was ~ 0.1 cm−1. The ν1, ν2, and ν41 bands of C2D2 and the ν1 and ν2 bands of C2HD were recorded. These were analyzed to give the band origin, ν0, and the upper state constants, B1 and D1; accurate infrared values of the ground state constants, B0 and D0, were assumed in the analyses. Values of the rotation–vibration interaction constants, αi, assembled from Raman and infrared studies of C2H2, C2D2, and C2HD, were used to calculate the equilibrium internuclear distances for the acetylene molecule: re(C—H) = 1.06250 ± 0.00010 and re(C≡C) = 1.20241 ± 0.00009 Å.

The v1/5 - v1/4 far-infrared bands of (D1)acetylene and (D2)acetylene

Rotational lines in the v1/5 v1/4 band of DC=CH and DC=CD have been located and measured at a spectral slit width of 0.3-0.4 cm-1. Spectroscopic constants obtained from analysis of the lines are consistent with more accurate constants obtained from mid- and near-infrared, and microwave work.

High resolution rotation–vibration Raman spectra of benzene. III. The spectrum of C6D6

The Raman spectrum of benzene-d6 vapour was excited in a multiple reflection cell by an Ar+ laser and was photographed with a spectral slit width of ~0.15 cm−1. Extensive structure (164 maxima) was observed for the ν2 (C—C stretching) fundamental but only the S branch (39 maxima) of the ν1 (C—D stretching) band was well-resolved. These totally symmetric bands were analysed and molecular constants determined from a least-squares fit. Three doubly degenerate bands were observed; ν15 and ν16 were unresolved, and in ν17 only 19 lines could be measured. Consequently, no detailed analyses were possible but the values of some molecular constants were estimated.

High resolution rotation–vibration Raman spectra of benzene. II. The doubly degenerate bands of C6H6

The Raman spectrum of benzene vapour was excited in a multiple reflection Raman cell by an Ar+ laser and was photographed with a spectral slit width of ~ 0.15 cm−1. The results for the five doubly degenerate Raman-active fundamentals are given in this communication. More than 150 maxima were resolved in the ν17 band and the spectrum was analyzed with a computer program to give ν17 = 1177.776(10) cm−1, B1 – B0 = 1.00(4) × 10−4, C1 – C0 = −0.50(2) × 10−4 cm−1, and ζ17 = 0.010(1). About 60 maxima were recorded in the ν18 band; molecular constants were determined but with less precision than for ν17. The ν15 band (partially overlapped by ν1) and the (ν16, ν2 + ν18) Fermi diad showed resolved structure but no detailed analyses were possible. The ν11 band showed no resolved structure.

High resolution rotation–vibration Raman spectra of benzene. I. The totally symmetric bands of C6H6

The Raman spectrum of benzene vapour was excited in a multiple reflection Raman cell by an Ar+ laser and was photographed with a spectral slit width of ~0.17 cm−1. All seven Raman-active fundamentals were observed. Analyses of the totally symmetric ν1 and ν2 bands are given in this article. About 150 maxima were observed for ν2 (C—C stretching) and ~100 for ν1 (C—H stretching); the latter was to some extent obscured by the ν15 band. These partially resolved rotational structures were analyzed by setting up suitable schemes of approximate assignments for the maxima and calculating the band constants by a linear least-squares minimization.