epdfsuite.pdf_extraction

Functions

`compute_avg_scattering_factor`(formula, ...)	Compute the composition-averaged atomic scattering factor f_avg(q).
`compute_ePDF`(q, Iexp, composition[, Iref, ...])	Compute the electron Pair Distribution Function G(r) from a SAED intensity profile.
`compute_f2avg`(formula, x_max, x_step[, ...])	Compute the composition-averaged squared scattering factor <f²>(q).
`fit_polynomial_background`(q, Fm[, rpoly, ...])	Fit and return a polynomial background to the reduced structure function F(Q).
`parse_formula`(formula)	Parse a chemical formula string into element symbols and molar fractions.

epdfsuite.pdf_extraction.parse_formula(formula)[source]

Parse a chemical formula string into element symbols and molar fractions.

Parameters:

formula (str) – Chemical formula, e.g. 'SiO2', 'Al2O3', 'Fe0.5Ni0.5'.

Returns:

elements (list of str) – Element symbols in the order they appear in the formula.
ratios (list of float) – Molar fractions of each element (sum to 1).

epdfsuite.pdf_extraction.compute_avg_scattering_factor(formula, x_max, x_step, qvalues=True, xray=False)[source]

Compute the composition-averaged atomic scattering factor f_avg(q).

The average is the weighted sum over all elements: f_avg(q) = sum_i x_i * f_i(q) where x_i are the molar fractions parsed from formula.

Parameters:

formula (str) – Chemical formula of the sample (e.g. 'SiO2').
x_max (float) – Upper limit of the scattering variable axis. Interpreted as q (Å⁻¹) if qvalues=True, otherwise as s = q/(2π).
x_step (float) – Sampling step of the scattering variable axis, same units as x_max.
qvalues (bool, optional) – If True (default), x_max and x_step are in q units (Å⁻¹). If False, they are in s = q/(2π) units.
xray (bool, optional) – If True, use X-ray scattering factors instead of electron scattering factors. Default is False (electron factors).

Returns:

q (ndarray) – Momentum transfer axis in Å⁻¹.
favg (ndarray) – Composition-averaged scattering factor f_avg(q).

epdfsuite.pdf_extraction.compute_f2avg(formula, x_max, x_step, qvalues=True, xray=False)[source]

Compute the composition-averaged squared scattering factor <f²>(q).

The average is the weighted sum of squared individual factors: <f²>(q) = sum_i x_i * f_i²(q) where x_i are the molar fractions parsed from formula. This quantity is used for the normalisation of the reduced structure function F(Q) in the PDFgetX3 formalism.

Parameters:

formula (str) – Chemical formula of the sample (e.g. 'SiO2').
x_max (float) – Upper limit of the scattering variable axis. Interpreted as q (Å⁻¹) if qvalues=True, otherwise as s = q/(2π).
x_step (float) – Sampling step of the scattering variable axis, same units as x_max.
qvalues (bool, optional) – If True (default), x_max and x_step are in q units (Å⁻¹). If False, they are in s = q/(2π) units.
xray (bool, optional) – If True, use X-ray scattering factors. Default is False (electron scattering factors).

Returns:

q (ndarray) – Momentum transfer axis in Å⁻¹.
f2avg (ndarray) – Composition-averaged squared scattering factor <f²>(q).

epdfsuite.pdf_extraction.fit_polynomial_background(q, Fm, rpoly=0.9, qmin=0.3, qmax=None)[source]

Fit and return a polynomial background to the reduced structure function F(Q).

Follows the PDFgetX3 convention: the polynomial degree is determined by deg = round(rpoly * qmax / π), and the fit is performed on F(Q)/Q to enforce the correct low-Q behaviour.

Parameters:

q (ndarray) – Momentum transfer axis in Å⁻¹.
Fm (ndarray) – Reduced structure function F(Q) = Q * (I_norm / I_inf - 1).
rpoly (float, optional) – Polynomial degree control parameter (PDFgetX3 convention). Default is 0.9.
qmin (float, optional) – Lower bound of the fitting range in Å⁻¹. Default is 0.3.
qmax (float, optional) – Upper bound of the fitting range in Å⁻¹. Defaults to q.max().

Returns:

background (ndarray) – Polynomial background evaluated on the full q grid, same shape as Fm.

epdfsuite.pdf_extraction.compute_ePDF(q, Iexp, composition, Iref=None, bgscale=1.0, qmin=0.3, qmax=None, qmaxinst=None, rmin=0.0, rmax=50.0, rstep=0.01, rpoly=1.4, Lorch=True, plot=False)[source]

Compute the electron Pair Distribution Function G(r) from a SAED intensity profile.

Follows the PDFgetX3 formalism adapted for electron scattering:

Optional background subtraction: I = Iexp - bgscale * Iref
Normalisation by the composition-averaged squared scattering factor <f²>(Q)
Construction of the reduced structure function: F(Q) = Q * (I_norm / I_inf - 1)
Polynomial background removal (PDFgetX3 convention, controlled by rpoly)
Optional Lorch modification function to suppress Fourier ripples
Sine Fourier transform to obtain G(r)

Parameters:

q (ndarray) – Momentum transfer axis in Å⁻¹.
Iexp (ndarray) – Experimental azimuthally averaged intensity profile.
composition (str) – Chemical formula of the sample (e.g. 'SiO2', 'Al2O3').
Iref (ndarray, optional) – Reference (background) intensity profile. If its length differs from Iexp, it is interpolated onto the q grid. Default is None.
bgscale (float, optional) – Scaling factor applied to the reference before subtraction. Default is 1.0.
qmin (float, optional) – Minimum Q used for the Fourier transform (Å⁻¹). Default is 0.3.
qmax (float, optional) – Maximum Q used for the Fourier transform (Å⁻¹). Defaults to q.max().
qmaxinst (float, optional) – Maximum Q used for the polynomial background fit. Defaults to qmax. Useful when the data are noisy near qmax.
rmin (float, optional) – Minimum real-space distance r (Å). Default is 0.0.
rmax (float, optional) – Maximum real-space distance r (Å). Default is 50.0.
rstep (float, optional) – Step size in real space (Å). Default is 0.01.
rpoly (float, optional) – Polynomial degree control for background removal (PDFgetX3 convention). Default is 1.4.
Lorch (bool, optional) – If True (default), apply the Lorch modification function sinc(Q/Qmax) before the Fourier transform to reduce termination ripples.
plot (bool, optional) – If True, display diagnostic plots of the raw intensities, F(Q), and G(r). Default is False.

Returns:

r (ndarray) – Real-space distance axis in Å.
G (ndarray) – Reduced pair distribution function G(r) in Å⁻².

Notes

The normalisation factor I_inf is estimated as the mean intensity in the top 10 % of the Q range (q > 0.9 * qmax).