Retrieving errors (uncertainties) for sigma2 = eins(temperature, thetae) in Artemis
I am modeling the Debye-Waller factor by using the Einstein model in Artemis, where the Einstein temperature (thetae) is a guess parameter and sigma2 is a defined parameter as eins(temperature, thetae). Although, after running the fit, the error for the estimation of thetae is given by the fit report, the error for the corresponding defined sigma2 is missing. I am working on some models to reduce the errors in the estimation of the Debye-Waller factor, so it's an important value for my research. I tried to propagate the errors by using the equation in the ref paper (E. Sevillano, H. Meuth, and J. J. Rehr. Extended x-ray absorption fine structure Debye-Waller factors. I. Monatomic crystals. Phys. Rev. B, 20:4908–4911, Dec 1979. doi:10.1103/PhysRevB.20.4908.) However, I cannot obtain the same value of sigma2 when I substitute thetae into the equation from the paper compared to the value reported in the fit. Can anyone help clarify the equation (or script) used in Artemis? Thank you! Wilson Henao
Hi Wilson,
I am modeling the Debye-Waller factor by using the Einstein model in Artemis, where the Einstein temperature (thetae) is a guess parameter and sigma2 is a defined parameter as eins(temperature, thetae).
Although, after running the fit, the error for the estimation of thetae is given by the fit report, the error for the corresponding defined sigma2 is missing.
Yes, Ifeffit did not do a great job of propagating errors from "variables" to Path Parameters. It turns out that Larch does report errors for sigma2 for each path when using the Einstein or correlated Debye model. It reports uncertainties in all Path Parameters using automated uncertainty propagation. This is one of the many benefits of using the scientific Python libraries. The equation for the Einstein model for sigma2 is pretty straightforward: sigma2 = EINS_FACTOR/(theta * rmass * tanh(theta/(2*t))) where EINS_FACTOR ~= 24.25 = hbar**2/(2*k_Boltz*AMU), rmass is the reduced mass (in AMU), t is the temperature, and theta is the Einstein temperature. You could differentiate "1/(theta*tanh(theta*x))" with respect to theta (either analytically or numerically) to convert an uncertainty in theta to an uncertainty in sigma2. --Matt
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albeiro.henaow＠gmail.com -
Matt Newville