Could you explain the difference between the Voigt and VoigtA fitting functions?

[Byungrok Moon (문 병록)]

I need to fit neutron diffraction data using a Voigt function. However, the manual says that the Voigt function is fast but inaccurate, while there's no such explanation for the VoigtA fitting function. The equations for the Voigt and VoigtA functions are also different, and since the manual doesn't provide a proper explanation, I don't know which one I should use.

Could you tell me which fitting function is more accurate and optimal for my data?

[Marcin Wojdyr]

Both Voigt and VoigtA are the same function and they use the same
approximation from the literature. They are only parametrized
differently, one in terms of the height, the other in terms of the
area.

Marcin

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[Manoel Lourenço Alves Neto]

Na análise de dados de difração de nêutrons (ou raios-X), a função Voigt é extremamente usada como função de ajuste (fitting function) para os picos de difração.

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Significado da função Voigt

• A Voigt é a convolução de uma função Lorentziana (ou de Cauchy) com uma Gaussiana.

• Em termos físicos, ela combina os dois principais mecanismos de alargamento de picos em difração:

1. Contribuição Gaussiana (instrumental):

   • Associada principalmente à resolução instrumental do difratômetro (tamanho finito da fonte, espalhamento geométrico, largura do feixe).

   • Resulta em um alargamento simétrico em forma de sino.

2. Contribuição Lorentziana (intrínseca):

   • Vem de efeitos relacionados à amostra, como tamanho finito de cristalito (crystallite size) ou microdeformações (microstrain).

   • Apresenta caudas mais longas em relação à Gaussiana.

Assim, a Voigt é uma função que permite modelar realisticamente o perfil de um pico de difração, capturando ao mesmo tempo os efeitos instrumentais e os efeitos microestruturais.

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Por que usar a Voigt em difração de nêutrons?

• Os picos experimentais de difração dificilmente são puramente gaussianos ou lorentzianos.

• A Voigt fornece uma aproximação fisicamente significativa e matematicamente flexível.

• Isso permite:

  • Ajustar a posição dos picos → obter parâmetros de rede.

  • Ajustar a largura e forma dos picos → separar efeitos de instrumento e amostra.

  • Quantificar tamanho médio de cristalito e microdeformação da rede via análise de largura de pico (método de Williamson–Hall, Rietveld, etc.).

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Em resumo

A função Voigt, ao fitar dados de difração de nêutrons, significa usar um modelo matemático que combina alargamento gaussiano (instrumental) e alargamento lorentziano (intrínseco da amostra).
Ela é crucial porque descreve de forma realista o formato dos picos difratados, permitindo separar contribuições físicas diferentes e obter parâmetros estruturais confiáveis.

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[Manoel Lourenço Alves Neto]

• Voigt in Fittyk is the true Gaussian⊗Lorentzian convolution, computed with the Wells (1999) fast approximation. The manual explicitly warns: “very fast, but not very exact.” It also estimates FWHM via the modified-Whiting formula. Fityk

• VoigtA is the area-parametrized Voigt (same convolution kernel, but the peak is parameterized by area instead of height), with a different normalization. The manual lists the analytic form but doesn’t attach the ‘inaccurate’ warning to this entry. Fityk

Which should you use?

For neutron (or X-ray) powder diffraction, where tails and overlap matter, the safer choice in Fittyk is VoigtA because:

1. It uses the same physical kernel (Voigt), but parameterized by area, which tends to behave better in multi-peak fits (less correlation between height and width, more stable areas). Fityk

2. The only place the manual highlights reduced accuracy is the Voigt entry that uses Wells’ approximation and an approximate FWHM formula. If you care about precise profile shape and integrated intensity, prefer the area form. Fityk

TL;DR: VoigtA is generally the more accurate/optimal choice in Fittyk for neutron diffraction peak profiles; reserve Voigt if you need speed and your results are demonstrably equivalent.

Practical checklist (Fittyk)

1. Fit both VoigtA and Voigt on the same window; compare χ²_red and residuals (look for structured tails).

2. Use AIC/BIC to compare models with equal peak counts; choose the lower criterion.

3. Constrain widths to be positive; avoid over-parameterization unless needed. (Fittyk allows split profiles if asymmetry is real.) Fityk

4. If peaks overlap, prefer area-based (VoigtA) to stabilize intensities.

Where in the manual

• Pseudo-Voigt (sum, not convolution) is also available—good for speed but less physical. Don’t use it when accuracy matters. Fityk

• Voigt entry explicitly: fast Wells approximation, “not very exact,” FWHM via modified-Whiting. Fityk

• VoigtA entry shows the area-normalized integral form (no “inaccurate” note). Fityk

If you want, tell me your peak layout (2θ/TOF range, overlap, S/N). I can suggest starting bounds and a short Fittyk script to batch-fit VoigtA across patterns and export areas/FWHM.