Background function

The function y r) is called the cavity function or background function. If u r) is discontinuous, g r) is discontinuous for the same values of r. Flowever, y r) is continuous. Eq. (12) is more correctly written as... 

Toraya s Method. The WPPD as implemented by Toraya et al.11 decomposes the peak profiles and background functions to obtain the best fit to the experimental powder pattern of the individual pure phase data by least-squares refinement. The integrated intensities of the pure phases are then stored with the other refined parameters, such as the profile parameters and the unit-cell parameters of the phases to be quantified. During quantification step, the integrated intensity of the phase being quantified is scaled, as defined in Eq. (12.4), such that the total of the scale factors for the component phases sum to unity. The scale factors of the individual components are then refined by least-squares methods until a best fit is observed with respect to the pattern of unknown composition. 

Pj is a preferred orientation correction, which is not included in the previous intensity of a diffraction peak function A is an absorption factor y° is the pattern background function... 

This function is called the cavity function or background function. At low densities... 

The determination of plasma parameters using He-like spectra is based on a self-consistent modeling of the theoretical spectra. The following variables take part in the variation procedure based on least-squares fitting electron and ion temperatures, toroidal plasma velocity, concentrations of H-, He-and Li-like ions. In addition, a background function was used to subtract the plasma background from the experimental spectra. The background consists of continuum radiation from the plasma and detector noise. 

Subtract a background function post-edge to obtain % E. ... 

Finally, the resultant powder diffraction pattern is a sum of the individual peak shape functions and a background function as illustrated in Figure 2.38d, where the background function was assumed constant for clarity. 

Diffuse background function to account for a peculiar scattering from amorphous phases (e.g. see Figure 4.2, specimen C) or from a noncrystalline sample holder ... 

In Eqs. 4.1 to 4.6, A/ typically varies from 6 to 12 when the entire powder diffraction pattern is of concern. In some instances, when profile fitting is applied to short fragments of the powder diffraction pattern, the most suitable background function is that given by Eq. 4.1 with iV = 1 or 2, i.e. a linear or parabolic background. 

A specific of the Le Bail s approach nearly always requires that early refinement includes the simplest suitable background function with all other relevant parameters kept fixed at their default or approximately known values. This ensures the proper determination of the individual integrated intensities, which are initially set to identical values, and the overall success of the full pattern decomposition. 

The background function will typically be a quadratic, that is. 

Figure 15.5 Comparison of the peak at about channel 1011 in the GllOO spectrum with a pure Gaussian (continuous line) plus step background function (short dashed line)...

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