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

getVoigtParam(scale_G, scale_L)

## Arguments

scale_G Vector of standard deviations $$\sigma_j$$ of the Gaussian components. Vector of scale parameters $$\phi_j$$ of the Lorentzian components.

## Value

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

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

## 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