Calculates the mixing parameter \(\eta_j\) from the scales of the Gaussian/Lorentzian components.
getVoigtParam(scale_G, scale_L)
| scale_G | Vector of standard deviations \(\sigma_j\) of the Gaussian components. |
|---|---|
| scale_L | Vector of scale parameters \(\phi_j\) of the Lorentzian components. |
The Voigt mixing weights for each peak, between 0 (Gaussian) and 1 (Lorentzian).
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: $$\eta_j = 1.36\frac{\phi_j}{f_{G,L}} - 0.47(\frac{\phi_j}{f_{G,L}})^2 + 0.11(\frac{\phi_j}{f_{G,L}})^3$$
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