From XRD data the nano particle structure is hexagonal. How can I calculate a,c and volume if my two theta value is slightly deviated from standard value?
Hi Jasper. To clarify your question, are you asking how to determine your lattice parameters (a and c) and also the volume of your unit cell or are you asking how to estimate the size of of your nanoparticles from the diffraction pattern?
Either way, Rietveld refinement of the data will help you answer the question. If your peaks are shifted, it could be because the lattice parameters are different or it could just be zero-point offset. Alternatively, if you are asking about the size of your nanoparticles, a reduction in the crystallite size will lead to Scherrer broadening of the peaks but won't nesessarily shity the peak position.
By doing a refinement, you treat your diffraction data quantitatively instead of qualitatively and can answer these questions. For example, nanoscopic crystallites will lead to peak broadening but so will strain in the system. If you prepared this powder via ball milling, it is likely that residual strain is present. However, these two effects have different dependence with 2theta and can be separated by doing a structural refinement. The lattice parameters and unit cell volume are given to you directly as a part of the refinement.
GSAS with EXPGUI is a free program which you can use to refine your data. I has a bit of a steep learning curve but it is open source and well documented. I recommend starting with this helpful page from the diffraction group at the APS: http://www.aps.anl.gov/Xray_Science_Division/Powder_Diffraction_Crystallography/
http://www.aps.anl.gov/Xray_Science_Division/Powder_Diffraction_Crystallography/
I have to agree: yor question is quite unclear since you are obviously mixing two terms, the volume of nano particles and the volume of the unit cell. Both are not connected. The volume of the unit cell is not related to the volume of the nanoparticles. You could also have nano particles which are amorphous. On the orther hand you could know your nano-particle size but don't know anything about your lattice parameter.
You could perhaps use the XRD data to estimate the size of your diffracting crystals but then you still do not know whether your nano-particles consisting of one or more crystals. For the size determination I would recommend Laser techniques. About the unit cell volume Travis already mentioned typical ways.
Thanks a lot.I want to determine the unitcell parameters and volume of the unitcell.My peaks are slightly shifted from standard values.How can I calculate strain? I have prepared three different samples and their values are given below. Would you please help me to calculate a,c and cell volume.
h k l standard values obtained values (2theta)
100 23.882 24.447 24.447 24.447
002 25.391 25.581 25.581 25.907
101 27.097 29.922 27.350 27.831
110 41.999 - 42.003 42.003
103 45.810 46.040 46.195 46.040
1 1 2 49.718 50.232 50.541 50.232
I think it is not too much to ask for a calculation of d-values using Braggs law. From my point of view you have NO STRESS but only different lattice parameters, Stress means that you have something like a gradient in your lattice parameters within one grain (approximated by many grains using sin²psi technique. But your particles are totally free and relaxed. They cannot have stress... Only if they would be e.g. in a glass matrix under certain conditions you could discuss something like a hydrostatic stress. But as far as I kept in mind you are dealing with powder.
Thank you.My samples are in powder form.Can you please tell me the formula for volume of the hexagonal?
Please follow the detailed method as described in this Research paper:
http://www.banglajol.info/index.php/JSR/article/view/11578
All the demanded parameters have been calculated here and their methods and formulas are given in above paper.
If you feel any problem, you may contact me.
The volume of the unit cell for powder material having hexagonal crystal structure, can be calculated by:
V = √3 × a2 × (c/2) = 0.866 a2 c
For more details, please study following Research Paper:
http://www.banglajol.info/index.php/JSR/article/view/11578
The parameter lattice extracted from XRD is associated with the error. Because, the location of peaks is affected by tension or by nano-sized particle.
TEM and its diffraction patterns is the best method for determine of parameter lattice e.g. a, and c in hcp materials.
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