How dose TOPAS calculate error for phase percentages?

iangie

Dear TOPAS user,

We know when "do_errors" is defined, error for each refined parameter will be report in output file.
May I ask where can I find the equations TOPAS used to calculate these Rietveld errors?

I want to find out the error calculation equation in TOPAS becaue I want to know what parameter errors are considered when TOPAS report error for phase weight percent in MVW( , , wt%_error).

According to the basic Rietveld quant equation: wt%=(scale*ZMV)/Σ(scale*ZMV), error of phase weight percent will definetely include error propagation of refined scale factors. Any other error source considered?

Thank you very much.

Tony Wang
------------
Curtin University

oscar

I would like to second this request, and expand it to estimates of strain and crystallite size.

All I can find on the 'do_errors' command on the wiki is:

Errors for refined parameters (ESD's) and a correlation matrix are calculated at the end of refinement. The correlation matrix if defined using C_matrix_normalized is updated, if not defined then C_matrix_normalized is automatically defined and appeneded to the OUT file.

I can't find any information (in the Topas manuals or online) on how these error estimates are calculated.

Any help much appreciated.

Oscar.

alancoelho

Errors for independent parameters are calculated from:

Error in parameter pi = Sqrt[Cov(i,i)] * r_wp / r_exp

Dependent parameters, Dep for example, errors are calculated using:

Error(Dep) = Sqrt[ Sum[ (Error(Ind(i)) dInd)(i)/dDep)^2, i] ]

where Ind(i) are the independent parameters that Dep is a function of.

wt% has the following dependents:
scale
cell mass
cell volume
If Brindley is used then {
mixture_MAC
mixture_density_g_on_cm3
phase_MAC
brindley parameter
}

Each of these may also have dependents and if the dependents are refined then the errors for those dependents are included. For example, phase_MAC has occupancies as dependents and any occupancies that are refined are included in the error refinement.

The program keeps a Dependent tree and an Independent tree. It also performs Intersection on these trees to minimize the amount of calculation necessary when calculation derivatives.

iangie

Dear Alan, thank you very much for your reply.
This align with the classiacal uncertainity propagation equation, allowing some typing error:
Error(Dep) = Sqrt[ Sum[ (Error(Ind(i)) dDep/dInd(i))^2, i] ]

May I ask, for the error of independent parameters, what dose Cov(i,i) mean?
Thank you. :)

alancoelho

Cov(i,i) is the diagonal elements of the inverse of A matrix. The A matrix is the A matrix of the "normal" equations that occurs in least squares; ie.

A x = b