How did TOPAS define the Scale factor during Rietveld refinement?
Is it define by the area or some other form?
It is a full pattern refinement, i.e., excluding the background it scales everything which is caused by the specific phase inclusive preferred orientation, used profile functions, and structure parameters if required. This means you have a big sum which describes for 2theta the respective intensity, and it scales this proportionally. Least-square deviations are minimized by factors inside the sum but also by the scaling factor. Additional parameters are zero shift, defocusing etc. but these are global parameters.
The basic principle of the Rietveld method consists in the description of the set of experimental points of a diagram by the use of analytical functions.
The parameters of these functions, including those corresponding to the crystal structure, sample, instrument and background, are simultaneously refined at each iteration using the least squares method.
Programs that apply the Rietveld method, including TOPAS, make use of the following expressions:
yic = b(2ϴi)+Σ k [S Fk2 LP(2ϴk) Ak Hk Mk Ok]
S is the scaling factor and combines different experimental parameters (sample size, incident beam intensity, influence of slit widths).
LP is the term that accounts for the Lorentzian and Polarization factors.
F is he Structure Factor
A gives an account of the absorption phenomena produced by the sample.
H accounts for the phenomenon of extinction.
M is the Multiplicity of the peak and indicates the number of planes that contribute to it by having the same spacing.
O gives the preferential orientation factor.
S = Σ i [wi [yi(obs)-yi(exp)]2] → min
y are the intensities.
w is weight given to Intensities.
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