getVoigtParam {serrsBayes}

Compute the pseudo-Voigt mixing ratio for each peak.

Description

Calculates the mixing parameter \eta_j from the scales of the Gaussian/Lorentzian components.

Usage

getVoigtParam(scale_G, scale_L)

Arguments

scale_G

Vector of standard deviations \sigma_j of the Gaussian components.

scale_L

Vector of scale parameters \phi_j of the Lorentzian components.

Details

First, calculate a polynomial average of the scale parameters according to the approximation of Thompson et al. (1987):

f_{G,L} = (\sigma_j^5 + 2.69\sigma_j^4\phi_j + 2.42\sigma_j^3\phi_j^2 + 4.47\sigma_j^2\phi_j^3 + 0.07\sigma_j\phi_j^4 + \phi_j^5)^{1/5}

Then the Voigt mixing parameter \eta_j is defined as:

\eta_j = 1.36\frac{\phi_j}{f_{G,L}} - 0.47(\frac{\phi_j}{f_{G,L}})^2 + 0.11(\frac{\phi_j}{f_{G,L}})^3

Value

The Voigt mixing weights for each peak, between 0 (Gaussian) and 1 (Lorentzian).

References

Thompson, Cox & Hastings (1987) "Rietveld refinement of Debye–Scherrer synchrotron X-ray data from Al_2 O_3," J. Appl. Crystallogr. 20(2): 79–83, doi: 10.1107/S0021889887087090