The Thompson-Cox-Hastings pseudo-Voigt function is a mathematical model used to describe the shape of peaks in spectroscopic and diffraction data. It is a combination of two Lorentzian and one Gaussian functions, which provides a flexible and accurate way to model a wide range of peak profiles. The function is named after its developers, who introduced it in the 1980s as an improvement over traditional Voigt functions.
The TCH function eliminated the infamous "$\eta-H$ correlation" that plagued early Rietveld refinements, allowing stable convergence even for complex multiphase samples.
One of the greatest strengths of the TCH pseudo-Voigt is that its components map directly to physical models. thompson-cox-hastings pseudo-voigt function
If you are looking for improved accuracy or specific implementations, these papers are also highly relevant:
The challenge is that $\eta$ is not constant; it varies with the ratio of Lorentzian to Gaussian widths. This is where Thompson, Cox, and Hastings provided their seminal contribution. This is where Thompson, Cox, and Hastings provided
The TCH function is the default in FullProf (profile number 7). It's defined with parameters:
The true Voigt is computationally expensive. Thus, the ($pV$) approximates it as a linear combination of a Gaussian and a Lorentzian, with the same full width at half maximum (FWHM, denoted $H$): $$pV(x) = \eta \cdot L(x) + (1-\eta) \cdot G(x)$$ Here, $\eta$ is the mixing parameter , ranging from 0 (pure Gaussian) to 1 (pure Lorentzian). $\eta$ is the mixing parameter
Allowed researchers to separate Gaussian (instrumental/strain) and Lorentzian (size) contributions directly during refinement.
Do not simultaneously refine Lorentzian size broadening and Gaussian microstrain without constraints. Use Williamson-Hall plots or separate 1/d² vs. d* plots to check consistency. The TCH function will happily refine nonsense if you overparameterize.