TeixeiraWater – jump-diffusion model for water

class qef.models.teixeira.TeixeiraWaterModel(independent_vars=['x'], q=0.0, prefix='', missing=None, name=None, **kwargs)[source]

Bases: lmfit.model.Model

This fitting function models the dynamic structure factor for a particle undergoing jump diffusion.

  1. Teixeira, M.-C. Bellissent-Funel, S. H. Chen, and A. J. Dianoux. Phys. Rev. A, 31:1913-1917
\[S(Q,E) = \frac{A}{\pi} \cdot \frac{\Gamma}{\Gamma^2+(E-E_0)^2}\]
\[\Gamma = \frac{\hbar\cdot D\cdot Q^2}{1+D\cdot Q^2\cdot \tau}\]

\(\Gamma\) is the HWHM of the lorentzian curve.

At 298K and 1atm, water has \(D=2.30 10^{-5} cm^2/s\) and \(\tau=1.25 ps\).

A jump length \(l\) can be associated: \(l^2=2N\cdot D\cdot \tau\), where \(N\) is the dimensionality of the diffusion problem (\(N=3\) for diffusion in a volume).

Fitting parameters:
  • integrated intensity amplitude \(A\)
  • position of the peak center \(E_0\)
  • residence time center \(\tau\)
  • diffusion coefficient dcf \(D\)
Attributes:
  • Momentum transfer q
fwhm_expr

Constraint expression for FWHM

guess(y, x=None, **kwargs)[source]

Guess starting values for the parameters of a model.

Parameters:
  • y (ndarray) – Intensities
  • x (ndarray) – energy values
  • kwargs (dict) – additional optional arguments, passed to model function.
Returns:

parameters with guessed values
Return type:

Parameters
height_expr

Constraint expression for maximum peak height.

qef.models.teixeira.teixeira_water(x, amplitude=1.0, center=1.0, tau=1.0, dcf=1.0, q=1.0)[source]