Thompson-cox-hastings Pseudo-voigt Function: Better
| Feature | Simple Pseudo-Voigt | TCH Pseudo-Voigt | | :--- | :--- | :--- | | $\eta$ refinement | Free parameter, unphysical correlations | Calculated analytically from $H_L/H_G$ | | Physical basis | Empirical | Approximates true Voigt convolution | | Behavior at extremes | Manual constraints needed | Handles pure G/L automatically | | Correlation with FWHM | Severe | Minimal | | Caglioti compatibility | Indirect | Direct |
) of the TCH pseudo-Voigt profile is calculated using a semi-empirical formula involving the individual Gaussian ( cap gamma sub cap G ) and Lorentzian ( cap gamma sub cap L ) components: ResearchGate The plot illustrates how the TCH pseudo-Voigt
) components can be easily separated. This allows researchers to directly relate fitting parameters to physical properties like crystallite size micro-strain The Mixing Parameter ( thompson-cox-hastings pseudo-voigt function
Consider a CeO₂ sample with 10 nm crystallites and 0.1% microstrain.
As the demand for accurate peak modeling continues to grow, the Thompson-Cox-Hastings pseudo-Voigt function is likely to remain a valuable tool in the field of spectroscopy and diffraction analysis. | Feature | Simple Pseudo-Voigt | TCH Pseudo-Voigt
The success of TCH inspired several improvements:
# Normalized Gaussian & Lorentzian with FWHM = G_V sigma = G_V / (2*sqrt(2*log(2))) # Gaussian sigma gamma = G_V / 2 # Lorentzian half-width at half-max t = (x - x0) The success of TCH inspired several improvements: #
The TCH function eliminated the infamous "$\eta-H$ correlation" that plagued early Rietveld refinements, allowing stable convergence even for complex multiphase samples.
(Note: This cubic polynomial is a fit to the true Voigt mixing; some implementations use an alternative form from Thompson, Cox, Hastings, J. Appl. Cryst. (1987) .)