# How the x-ray diffractometer caculate the lattice constant or miller indices?

yy.toh
Bragg's law n.lambda=2d sin theta. d=1/{h^2/a^2+k^2/b^2+l^2/c^2} for orthorombic structure.

thus d=n.lambda/2 sin theta=1/{h^2/a^2+k^2/b^2+l^2/c^2}
lambda and theta are given.

Look, there are two types/sets of unknowns in the d formula, they are miller indices h, k, l and lattice constant a, b, c. Normally the x-ray diffractometer analysis would give the significant theta according to the count, and also the h, k l and a, b, c. Now I wonder what method the machine has used to figure out the h, k, l and a, b, c?there are two sets of unknown remember?how it is solved by using only one equation?

Looking forward for experts answers...
thanks

## Answers and Replies

abhi2005singh
Now I wonder what method the machine has used to figure out the h, k, l and a, b, c?
Diffractometer only gives you the counts and the corresponding 2$$\theta$$. It does not give you the hkl or abc.

yy.toh
Diffractometer only gives you the counts and the corresponding 2$$\theta$$. It does not give you the hkl or abc.

is that so. Do you know how to determine h, k, l and a, b, c from the XRD data for orthorombic sturcture?

abhi2005singh
The general approach for extraction of structure information from the XRD data is that you know what elements you have in your material. Then match the observed spectra with that of the various compounds of that element. This gives you the information about the phase formation along with the abc and hkl values.

If you already have some information about the structure (by following above procedure or a priori), then you can use the equations (as given by you) to predict the 2$$\theta$$ values for given hkl values. This way you can identify as to which peak corresponds which reflection plane. More accurate values are obtained by modifying the abc and $$\alpha \beta \gamma$$ values in such a way that you get the peak positions matching with the experimental spectra.

More things can also be done, but I guess this suffices for your needs.

All of this procedure can be quite tedious. There are softwares available to do the job.

yy.toh
The general approach for extraction of structure information from the XRD data is that you know what elements you have in your material. Then match the observed spectra with that of the various compounds of that element. This gives you the information about the phase formation along with the abc and hkl values.

If you already have some information about the structure (by following above procedure or a priori), then you can use the equations (as given by you) to predict the 2$$\theta$$ values for given hkl values. This way you can identify as to which peak corresponds which reflection plane. More accurate values are obtained by modifying the abc and $$\alpha \beta \gamma$$ values in such a way that you get the peak positions matching with the experimental spectra.

More things can also be done, but I guess this suffices for your needs.

All of this procedure can be quite tedious. There are softwares available to do the job.

please explain more on the $$\alpha\beta\gamma$$ modification please

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abhi2005singh
Most of the times introduction of impurity atoms or due to the other electronic interaction, the structure of the material can deviate from the ideal structure we read in the books. This generally leads to stretching/bending of bonds and bond angles. Such changes may lead to the changes in the angles. This information is available in the XRD spectra of those materials. You need to make changes accordingly in the input values of abc and $$\alpha\beta\gamma$$ and try to reproduce the experimental spectra.