Dear Ram Prashanth,

Precise lattice parameter measurements from XRD can be done using Nelson-Riley function {(cos2θ/sinθ) + (cos2θ/θ) } or Bradley-Jay (cos2θ) function.

XRD pattern gives 2θ vs Intensity. Diffracted peaks (say 5 high intense peaks) correspond to 2θ positions have to be noted.

A table has to be made to get (cos2θ/sinθ) + (cos2θ/θ) along with lattice parameter obtained for different θ values using the eqn

λhkl = 2 dhkl sinθ where dhkl is the interplanar spacing, which is related to lattice parameter, a

d = a/ (h2+k2+l2)1/2. (hkl) is the miller index of diffracted plane.

The intercept of linear plot of Nelson-Riley function {(cos2θ/sinθ) + (cos2θ/θ) } vs lattice parameter, a, for different diffracted planes gives the accurate lattice parameter value.

Ref: (1) X-Ray diffraction: A practical approach, C. Suryanarayana and M. Grant Norton

(2) Elements of X-ray diffraction, B. D. Cullity

Dear Ram Prasanth Ramesh,

please make sure to search well for anything before just ask it. your are in the start of ur research life. However, in regards of answering ur question there are two very rich conversation about this issue.

https://www.researchgate.net/post/How_to_calculate_lattice_constant_from_XRD_pattern

https://www.researchgate.net/post/How_can_we_find_Lattice_parameter_from_XRD_plot

Dear Ram Prashanth,

Precise lattice parameter measurements from XRD can be done using Nelson-Riley function {(cos2θ/sinθ) + (cos2θ/θ) } or Bradley-Jay (cos2θ) function.

XRD pattern gives 2θ vs Intensity. Diffracted peaks (say 5 high intense peaks) correspond to 2θ positions have to be noted.

A table has to be made to get (cos2θ/sinθ) + (cos2θ/θ) along with lattice parameter obtained for different θ values using the eqn

λhkl = 2 dhkl sinθ where dhkl is the interplanar spacing, which is related to lattice parameter, a

d = a/ (h2+k2+l2)1/2. (hkl) is the miller index of diffracted plane.

The intercept of linear plot of Nelson-Riley function {(cos2θ/sinθ) + (cos2θ/θ) } vs lattice parameter, a, for different diffracted planes gives the accurate lattice parameter value.

Ref: (1) X-Ray diffraction: A practical approach, C. Suryanarayana and M. Grant Norton

(2) Elements of X-ray diffraction, B. D. Cullity

Dear colleague,

The answer to your question you will find in any accessible textbook on the methods of structural analysis.

HI

you can get all the parameters by X'pert Highg score plus only if you have the idea about the material (by a cif file). otherwise you can install match software and then isntall some free database. then you can match your xrd and the file that matches the best with your xrd data you export it to a .cif file and get the lattice parameters from xpert.

Best

Shoaib

Dear Ram Prashanth,

Mr. Anash has explained very well about calculating lattice parameter from XRD data.

The other method is to calculate from combining d-spacing and Bragg's law formula. As there are seven crystal system,: Cubic, Tetragonal, Trigonal, Hexagonal, Triclinic, Monoclinic and orthorhombic. And each has unique formula of d-spacing. By solving equations for more than two intense peak, you will get the lattice constant a, b, and c.

I am attaching the reference.

Thanks and regards.

https://www.khwarizmi.org/system/files/activities/146/csd1.pdf