From literature survey, I am about to know the equation to find lattice parameters for hexaferrite. i.e.
1/d^2 = (4/3)*[(h^2 + hk + k^2) / a^2)] + (l^2 / c^2)
But, How to solve this equation to find values of "a" and "c".
The first "trick" is to use planes of the type h00 to obtain an approximative the "a" parameter, or 00l for the "c" parameter. However, the use of DICVOL free software (http://www.ccp14.ac.uk/solution/indexing/) for indexation is more easy and the values more reliable.
Best regards,
Pedro
This is hexagonal where a = b. First find d for example hkl=110 at 2 theta peak of 60 degree. From formula of wavelength lamda = 2 d sin theta, Say lamda of your X-ray = 1.54... Angstrom. Then 1.54 A= 2 d sin30. We get d = 1.54 A. Fill this d value to your formula of d = [4/3a^2(h^2+hk+k^2)+l^2/c^2]^-1/2. Because l = 0, so you can find the value of a. You can do the same calculation for obtaining other cell parameter. Sometime is better for us to calculate step by step than using sophisticated software especially if you are the beginner. Do this calculation in Excel. Hope can help.
Thank you, P. Grima Gallardo and Posman Manurung.
I am using other software also to indexing XRD graph. But I want the calculated values. I'll do calculation as sugested by Posman Manurung.
The determination of lattice parameters is not that easy as it looks like from this equation. Therefore, for many years as many as possible reflections are used in order to reduce errors. Sources of errors are doublex overlapping, zero shift of the detector, sample misalignement etc. All these parameters affecting the peak position. Therefore, refinement programs are used where the difference of all peaks with calculated reflection positions and their overlapping are considered. Thus or a general understanding it might be a good idea to solve it once but the resulting data are highly erroneous. If possible, don't do it and use free software. It also prevents a misinterpretation of single peaks since the data MUST fit to all other. It is simple to use PowderCell since it enables to "play" with all these parameters. You can calculate a diffraction pattern, save it as experimental, and then you can load the same phase again and the "experimental" pattern. By changing the zero shift or some sample alignment or lattice parameters you can see, how these values affect the peak positions.
Dear Gert Nolze
Thank you for your suggestion.
I am using PowderCell software but having doubt whether that software gives proper value or not. So I want to compare the calculated and observed values of parameters.
Oh, if you properly use the software it will definitely gives better values than the upper mentioned equation applied on a single reflection. How accurate the results finally will be depends on the tuning you are doing. Post the data and I guess some people will check them. Please also add the structure file.
Dear Yushi Yang
Thank you so much for the explanation. I'll follow the method and try to solve the equation for my data
Neha, the problem is not the equation which is in all software packages the same. The problem is, that this equation assumes a Bragg angle which you do not have. You have a peak and the maximum usually does not describe the Bragg angle. Which angle (or d-value) you want use as input data? Refinement software considers the intensity distribution of a mathematical function like Pseudo-Voigt or Pearson 7 in order to describe the experimental curvature. These software packages also take into account a possible misalignment of the detector or the sample (defocusing). All these different effects influencing the final result and are not yet considered in the equations given by Y. Yang. They are also only EXAMPLES.
Hello !
Neha Solanki
First make refinement of powered XRD pattern. Rietveld refinement methods utilize the entire diffraction of a crystal structure.
I have attached two pdf file for calculation of data in your question. One is for XRD peak position and other is for to know more about XRD Indexing. Feel free to ask more, if required.
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