Voigt line analysis

Fig. 8 a Changes in mass open circles), obtained through a Voigt-based analysis of combined / and D measurements at multiple harmonics, and SPR mass open squares), obtained through an analysis of changes in interfacial refractive index. The difference between the QCM mass and the SPR mass corresponds to the amoimt of coupled water sensed by QCM solid line), b Separation of the contribution to the total mass uptake from adsorbed non-ruptured vesicles open circles) and planar bilayer patches open squares) versus time was made possible, as detailed in [35]... 

Another typical problem met in this kind of analysis is known as the hook effect . It is due to an overestimation of the background line to the detriment of the peak tails. As a consequence, the low order Fourier coefficients of the profile are underestimated. In the fitting procedure by pseudo-Voigt functions, this problem occurs if the Gauss content is so high that the second derivative of the Fourier coefficients is negative this is obviously physically impossible because it represents a probability density. 

In these and in many other reports, the size analysis is based on a full profile fit determined by using predefined line profiles (Voigt, pseudo-Voigt) and an intensity fitting according to the Rietveldt method (McCusker et al., 1999). This procedure, which requires substantial effort in data analysis, is reliable, provided that no changes in sample geometry... 

Similar to a Voigt profile, this line shape expression is a convolution of Equation (11) and a Gaussian distribution to account for inhomogeneous broadening [12,31]. This profile is the best profile currently employed for the analysis of spectra exhibiting significant overlap of modes of different phases. 

Consequently, if the peak shifts for one or more peaks are measured as a function of T in the range (0, ujl) at y and y + re for three fixed values of y e.g., 0, 71/4 and nj2) the stress tensor elements 5, can be determined from the intercept and the slopes of these lines. It is presumed that the single-crystal elastic constants are known and the diffraction elastic constants in Equations (109) and (110) can be calculated following one of the models presented before. This is the conventional sin T method. Alternatively Equation (107) can be used in a least-square analysis or implemented in the Rietveld codes. If diffraction patterns measured in several points (T, y) are available the stress tensor elements 5,- can be refined together with the structural and other parameters. The implementation in GSAS is the Voigt formula Equation (90) and not Equation (107). In this case refinable parameters are the strain tensor elements e,. 

Calculation of mean crystallite size, lattice strain and frequency distributions of crystallite sizes from the same XRD line-profiles used for crystallinity determinations. In addition to the application of the Scherrer equation, two single-line methods were used the variance method of Wilson (1963) (Akai and To th 1983 Nieto and Smchez-Navas 1994), and the Voigt method of Langford (1978) in combination with single-line Fourier analysis (Akai et al. 1996, 1997, 2000 Warr 1996 Jiang et al. 1997 Li et al. 

A baseline was formed by fitting a third-order polynomial to the data in the averaged scans adjacent to the absorption lines of interest. Linear multiline Voigt fits were used to model the absorption line shapes and derive the resulting line areas. Concentrations of CO and H2O were calculated using an analysis similar to that described in Section 14.2.2. 

The Thompson-Cox-Hastings function is often used to refine profiles with broad diffraction peaks because it is the more appropriate model for line-broadening analysis where the Lorentzian and Gaussian contributions for crystallite size and for microstrains are weighted. So in this case, the peak shape is simulated by the pseudo-Voigt function, which is a Unear combination of a Gaussian and a Lorentzian function (Table 8.5). 

Detailed analysis has proved that at pressures between 0-20 Torr and temperatures between 85-300 K the profiles of these lines are accurately represented by Voigt functions. The Lorentzian widths, are found to be a linear function... 

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