Thompson-cox-hastings Pseudo-voigt Function Jun 2026

) map directly to physical phenomena like instrument geometry and crystal defects.

where w is the full width at half-maximum (FWHM) and x0 is the peak position. thompson-cox-hastings pseudo-voigt function

The TCH pseudo-Voigt is the industry standard for several reasons: ) map directly to physical phenomena like instrument

For a given Bragg reflection at $2\theta$, the observed profile $y(2\theta_i)$ is: $$y(2\theta_i) = I_0 \left[ \eta \frac2\pi H \frac11 + \left( \frac2(2\theta_i - 2\theta_0)H \right)^2 + (1-\eta) \sqrt\frac4\ln 2\pi H^2 \exp\left( -4\ln 2 \frac(2\theta_i - 2\theta_0)^2H^2 \right) \right]$$ Where: Then: $$\eta = 1

Let $m = \fracH_LH_G$, where $H_L$ and $H_G$ are the Lorentzian and Gaussian FWHM components. Then: $$\eta = 1.36603 \left( \fracH_LH_V \right) - 0.47719 \left( \fracH_LH_V \right)^2 + 0.11116 \left( \fracH_LH_V \right)^3$$

When using software like , FullProf , or TOPAS , the TCH pseudo-Voigt is often the default choice. Researchers use it to: Determine Crystallite Size: By isolating the Lorentzian Analyze Microstrain: By focusing on the dependence. Instrument Calibration: Using a standard (like LaB6cap L a cap B sub 6 before analyzing unknown samples. If you'd like, I can help you: Find the mathematical constants for the approximation. Explain how to extract grain size from TCH parameters. Compare TCH to the Pearson VII function.

) shapes based on their respective full widths at half maximum (FWHM). Angular Dependence