Is there a formula for finding, a and c?
In my case, d spacing=2.6 A, 2theta=34.2 deg and the JCPDS reports a=3.2 and c=5.2.
Dear Cyril,
the dhkl spacing for hexagonal structure is calculated by:
dhkl = [(4/3a²)(h²+k²+hk) +(l²/c²)] -1/2
(see for example the book of H. P. Klug and L. E. Alexander; X-ray Diffraction Procedures, Table 1-3)
for d= 2,6A and h=0, k=0 and l=2 you will get c= 5,2 A (your result from above).
The parameter a is not involved for h=0 and k=0.
So you have to take an additional peak position with index h or k not equal to zero.
@Gerhard Martens, Dear Professor Gerhard, Thank you for the reply. I obtained c using the formula, but with a, I am stuck.
Yes, with lattice constant a your are stuck as far as you use only the 002 peak.
This peak position has got not enough information for you. As I stated above you need another one with index h or k different from zero.
Remark onto Rana's anwer: doing Rietveld refinement with only the 002 peak will also fail in determining lattice constant a for the hexagonal system.
Dear Gerhard Martens ,
you gave the clear explanation. if the parameters such as "a and c" are not given. in such case how can we calculate the "a and c" parameter values. i have a data that plane hkl values are (002) and their d-space value is 3.2 nm. using these data is it possible we can do the parameter calculation?
Can you explain me?
Dear Baskaran Palanivel ,
first of all, sorry, for the late answer.
please read carefully the my answer above.
When you have only got the 002 peak of hexgonal system you can only calculate c for given d002 spacing. The lattice constants a and b are skipped when applying the d-spacing formula for hexagonal system. In this case you have to use other peaks in which h and k are involved different from zero, such as 100 and 010.
For examples of the variety of hexagonal peaks please have a look at the examples gives in:
Article Chemical synthesis of zinc oxide nanorods for enhanced hydro...
Article Hydrothermal synthesis and chromic properties of hexagonal W...
Article Template-free synthesis of BiVO4 nanostructures: I. Nanotube...
In general you need three peaks in order to solve for the lattice constants a, b, c independent of the lattice type. One peak is not enough...
Cyril R. A. John Chelliah
In this video tutorial, I have explained in detail how and how to calculate lattice constants for cubic and orthorhombic structures from the XRD data using OriginLab software. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice as well as calculations files here. Thanks
https://youtu.be/Hr3S_f4lktw
how to calculate lattice constants for hexagonal structures from the XRD data
for hexagonal system the d spacing and lattice parameters go like this,
dhkl= lambda/(2*sin(thetahkl) ..., n = 1, also remember to half your diffraction angle as you get the 2theta from XRD.
dhkl = 1/(4 (h2+k2+hk)/3(a2) +l2/c2)1/2 , since a=b, use (002) to get 'c' and (hk0) to get 'a'.
hope this helps Cyril R. A. John Chelliah
you have to take another peak for example (2 0 0) to calculate a lattice parameter.
a= SQRT (4/3) * h*d
d= lamda/2 sin (th)= nm
h=2
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