Spectra summing

Note that the maximum use temperature of GS-44 per the manufacturer is 1100 C. However, as this experiment was to take place in vacuum, there would be a greater viscosity of the grain boundary phase compared to a test in air, due to a lack of available oxygen [7]. Thus, a higher temperature was chosen to facilitate the onset of creep. Diffraction spectra were obtained every 20 minutes during creep. This acquisition time was the minimum necessary for high-quality patterns, thus each spectra sums the behavior over the 20 minute time span. 

Figure 2.28 Ion trap scan function. The sequence of events used to generate a mass spectrum in a typical Paul trap is shown. This sequence is typically repeated many times with the individual spectra summed or averaged to produce the final spectrum. The generic parts of the scan function shown include (1) ion injection and trapping, (2) ion relaxation/cooling, (3) auxiliary excitation for selective ejection/storage of desired ions and (4) mass-selective instability scan. The timing of the resonant excitation function is also indicated two sine waves shown indicate a first pulse for selective excitation and a second pulse for enhancing the mass selective instability scan...

Thomas GF, Meath WJ (1977) Dipole spectrum, sums and properties of ground-state methane and their relation to the molar refractivity and dispersion energy constant. Mol Phys 34 113—125... 

Therefore, XAS—especially with respect to EXAFS—has many advantages as a probe of transition metal centers in biological materials. Beyond the absence of a requirement for crystalline materials, the major attractions are the specificity, and sensitivity of the technique and the provision of interatomic distances with an accuracy of 0.02 A within (say) 4 A of the primary absorber. However, it should be noted that (1) no angular information is usually obtained (2) rarely does the structural information extend beyond 4 A, (3) the spectrum sums data for all atoms of a particular element and, if the element of interest is present in more than one chemical form, an average environment is obtained (4) the possibility of radiation damage must be anticipated and the integrity of samples should be monitored after, and if possible... 

Fig. 51. Merlinoite. (a) MAS NMR spectrum of a sample with Si/Al = 1.8 at 158.90 MHz, at a spinning rate of 10.0 kHz using a ti/3 rad pulse length of 2.7 ps, and a recycle delay of 60 s. 1094 scans were accumulated. The individual components of a fit spectrum (a) are shown in (c) and the calculated spectrum, sum of individual components, is given in (b)...

In the case of mixtures, especially those of petroleum, a variety of compounds can give ions having the same mass the mass spectrum is then the sum of the spectra of each component ... 

This expression assumes a system with a discrete level structure for systems with both a discrete and a continuous portion to their spectrum the expression consists of a sum over the discrete states and an integral over the continuous states.) Flere, ifi (v) is a solution of the time-independent Sclirodinger equation,... 

Figure Bl.5.15 SFG spectrum for the water/air interface at 40 °C using the ssp polarization combination (s-, s- and p-polarized sum-frequency signal, visible input and infrared input beams, respectively). The peaks correspond to OH stretching modes. (After [ ].)...

Figure Bl.22.8. Sum-frequency generation (SFG) spectra in the C N stretching region from the air/aqueous acetonitrile interfaces of two solutions with different concentrations. The solid curve is the IR transmission spectrum of neat bulk CH CN, provided here for reference. The polar acetonitrile molecules adopt a specific orientation in the air/water interface with a tilt angle that changes with changing concentration, from 40° from the surface nonnal in dilute solutions (molar fractions less than 0.07) to 70° at higher concentrations. This change is manifested here by the shift in the C N stretching frequency seen by SFG [ ]. SFG is one of the very few teclnhques capable of probing liquid/gas, liquid/liquid, and even liquid/solid interfaces.

Figure B2.4.3. Proton NMR spectrum of the aldehyde proton in N-labelled fonnainide. This proton has couplings of 1.76 Hz and 13.55 Hz to the two amino protons, and a couplmg of 15.0 Hz to the nucleus. The outer lines in die spectrum remain sharp, since they represent the sum of the couplings, which is unaffected by the exchange. The iimer lines of the multiplet broaden and coalesce, as in figure B2.4.1. The other peaks in the 303 K spectrum are due to the NH2 protons, whose chemical shifts are even more temperature dependent than that of the aldehyde proton.

The observable NMR signal is the imaginary part of the sum of the two steady-state magnetizations, and Mg. The steady state implies that the time derivatives are zero and a little fiirther calculation (and neglect of T2 tenns) gives the NMR spectrum of an exchanging system as equation (B2.4.6)). 

Recall that L contains the frequency or (equation (B2.4.8)). To trace out a spectrum, equation (B2.4.11)) is solved for each frequency. In order to obtain the observed signal v, the sum of the two individual magnetizations can be written as the dot product of two vectors, equation (B2.4.12)). 

Vo + V2 and = Vo — 2 (actually, effective operators acting onto functions of p and < )), conesponding to the zeroth-order vibronic functions of the form cos(0 —4>) and sin(0 —(()), respectively. PL-H computed the vibronic spectrum of NH2 by carrying out some additional transformations (they found it to be convenient to take the unperturbed situation to be one in which the bending potential coincided with that of the upper electi onic state, which was supposed to be linear) and simplifications (the potential curve for the lower adiabatic electi onic state was assumed to be of quartic order in p, the vibronic wave functions for the upper electronic state were assumed to be represented by sums and differences of pairs of the basis functions with the same quantum number u and / = A) to keep the problem tiactable by means of simple perturbation... 

Total ion current (TIC), (a) After mass analysis the sum of all the separate ion currents carried by the different ions contributing to the spectrum, (b) Before mass analysis the sum of all the separate ion currents for ions of the same sign. 

For simplicity, n should be as low as is consistent with small error. The retention of but two terms is feasible when one considers that if Otci is so fitted that the first absorption and the second following surface reflec tion are correct, then further attenuation of the beam by successive surface reflections makes the errors in those absorptions decrease in importance. Let the gas be modeled as the sum of one gray gas plus a clear gas, with the gray gas occupying the energy frac tion a of the blackbody spectrum and the clear gas the frac tion (1 — ). Then... 

Figure 16-1. Decomposition of a time signai into a sum of osciiiatory functions from which a spectrum can be obtained.

The number of Auger electrons from a particular element emitted from a volume of material under electron bombardment is proportional to the number of atoms of that element in the volume. However it is seldom possible to make a basic, first principles calculation of the concentration of a particular species from an Auger spectrum. Instead, sensitivity factors are used to account for the unknown parameters in the measurement and applied to the signals of all of the species present which are then summed and each divided by the total to calculate the relative atomic percentages present. 

Fig. 3.52. Normalized back-scattering yields of ions from Pb near the melting point, with the incident beam and scattered beam directed along <101 > crystal axes (double alignment) curve a, 295 K curve b, 506 K curve c, 561 K curve d, 600.5 K curve e, 600.8 K. Spectrum d is fitted by a sum of contributions M, from a liquid surface layer, and I, from a partially ordered transition layer [3.133].

When an element is present on the surface of a sample in several different oxidation states, the peak characteristic of that element will usually consist of a number of components spaced close together. In such cases, it is desirable to separate the peak into its components so that the various oxidation states can be identified. Curve-fitting techniques can be used to synthesize a spectrum and to determine the number of components under a peak, their positions, and their relative intensities. Each component can be characterized by a number of parameters, including position, shape (Gaussian, Lorentzian, or a combination), height, and width. The various components can be summed up and the synthesized spectrum compared to the experimental spectrum to determine the quality of the fit. Obviously, the synthesized spectrum should closely reproduce the experimental spectrum. Mathematically, the quality of the fit will improve as the number of components in a peak is increased. Therefore, it is important to include in a curve fit only those components whose existence can be supported by additional information. 

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