TeixeiraWater – jump-diffusion model for water¶
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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.
- 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
\(D\)
- integrated intensity
- Attributes:
- Momentum transfer
q
- Momentum transfer
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fwhm_expr
¶ Constraint expression for FWHM
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guess
(y, x=None, **kwargs)[source]¶ Guess starting values for the parameters of a model.
Parameters: Returns: parameters with guessed values
Return type:
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height_expr
¶ Constraint expression for maximum peak height.