hello
i am triying to obtain cristallite size of titanium dioxide by scherrer equation using FWHM of XRD analysis. how i can get the correcte answer of this parameter i have 75% of anatase and 25% of rutile .
can i get cristallite size of each phase and i calculate the average by multiplaying the cristallite size of each phase by X% of anatase and rutile?
Apply Scherrer equation separatley onto the rutil peaks and onto the anatase peaks respectively. So you get the average crystallite size of each phase. To my opinion there is no necessity to average both values; it makes no sense because you discard valuable information. But please feel free to apply a weighted sum according to the relative percentages, as you proposed above.
Your applied weighting is proportional to the relative masses of the two phases.
You may alternatively weigth the crystallite sizes proportional to the relative numbers (~ X%/size³) of crystallites in your sample:
So average size = [sa*a%/(sa)³ + sr*r%/(sr)³]/[(a%/(sa)³ + r%/(sr)³]
with a% and r% as the relative mass percentages of anatase and rutil,
and sa and sr the crystallite sizes of the two phases.
But I do not know which of the average procedures will be the 'best' in your application.
You may insist that there are two different densities rhoa and rhor with respect to the two phases, which would enter the calculation of the relative crystallite numbers.
When including the different densities of the phases the above average size is rewritten as:
aver. size = {sa*a%/[rhoa*(sa)³] + sr*r%/[rhor*(sr)³]}/{(a%/[rhoa*(sa)³] + r%/[rhor*(sr)³]}.
But we should no stress the derived crystallite size numbers too much. They are only very rough estimates of the mean crystallite sizes (Please think on the uncertainty of the K number involved in the Scherrer equation, even if you know the type of crystallite shape).
Dear Gerhard
How I can obtain the percentage of each phase I am using match software and he give a 75% , 25% of anatase and rutile respectively . can i consider those values masse percentage of each phase?
In these case of the presence of both phase how I can comment about Miller indices??
For equations that you give me above can you attach a suggestion or reference ??
Thank you very much
Have a nice day
Dear Allouche Sidali,
It is very useful to read the follwoing discussion before proceeding.
https://www.researchgate.net/post/What_is_the_difference_between_crystallite_size_grain_size_and_particle_size
Dear Allouche,
with respect to the % value, I think it is mass %.
With respect to Miller indices ,
please
a) google for XRD pattern of both phases,
(one of the results is : https://www.researchgate.net/post/How_do_I_calculate_age_of_each_phases_of_TiO2)
or
b) calculate peak positions by yourself via the well known lattice type(s), lattice parameters and Bragg equation (it will be a good exercise); formulas for d-spacings are attached.
With respect to the above given averaging formula there is no reference known to me. You can derive these equations by yourself.
Kindly refer the attached link for the same.
https://www.sciencedirect.com/science/article/pii/S0921883117304260
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