What is the best method to calculate lattice constant using X-ray diffraction pattern
In x ray diffraction pattern readily we get lattice constant and alpha beta gamma and wavelength of light used if you want to calculate you can use platon software with this you can determine all geometric parameters
I used Nelson Reilly method and it give very satisfactory results. Search Nelson Reilly method on google and use it is just an equation and after plotting the graph between Nelson Reilly coefficient and 'a' value, the intercept will be your precise lattice parameter.
Following is the link of similar question, you can take some inputs from there,
https://www.researchgate.net/post/How_to_calculate_lattice_constant_from_XRD_pattern
Basic intro background:
Bragg’s Law n λ =2dsinθ
- English physicists Sir W.H. Bragg and his son Sir W.L. Bragg developed a relationship in 1913 to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (theta, θ).
- The variable d is the distance between atomic layers in a crystal, and the variable lambda λ is the wavelength of the incident X-ray beam; n is an integer.
- This observation is an example of X-ray wave interference (Roentgenstrahlinterferenzen), commonly known as X-ray diffraction (XRD), and was direct evidence for the periodic atomic structure of crystals postulated for several centuries.
- Fun fact, the Braggs father and son do well; one theNobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS and diamond.
- Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.
- Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, and now due to their findings; diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.
- To measure the average spacings between layers or rows of atoms-ray Diffraction (XRD).
- To Determine the orientation of a single crystal or grain.
- To find The crystal structure of an unknown material.
- To measure the size, shape and internal stress of small crystalline regions.
What is ex-ray defraction aka XDR?WhatWhat is
- The atomic planes of a crystal cause an incident beam of X-rays to interfere with one another as they leave the crystal. The phenomenon is called X-ray diffraction.
- The cause and Effect of sample thickness on the absorption of X-ray
3. Bragg’s Law and Diffraction:
- How waves reveal the atomic structure of crystals n λ = 2dsinθ *where n = integer
- Diffraction occurs only when Bragg’s Law is satisfied Condition for constructive
4. What is the best method?
- Diffr actomion of Diffracted X-rays by a Diffractometer As explained below
d-spacings & lattice parameters λ = 2dhk lsinθhkl
dhkl = 1.54Å/2sinθhkl
2. For a simple cubic
(a = b = c = a0)Ma0 = dhkl /(h2+k2+l2)1⁄2
e.g., for NaCl, 2θ220=46o, θ220=23o, d220 =1.9707Å, a0=5.5739Å
• XRD is a nondestructive technique
• To identify crystalline phases and orientation
• To determine structural properties: Lattice parameters (10-4Å), strain, grain size, expitaxy, phase composition, preferred orientation (Laue) order-disorder transformation, thermal expansion
• To measure thickness of thin films and multi-layers*
• To determine atomic arrangement
• Detection limits: ~3% in a two phase mixture; can be ~0.1% with synchrotron radiation and Spatial resolution: normally none. @http://web.pdx.edu/~pmoeck/phy381/Topic5a-XRD.pdf
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- Methodology
- Crystallography
- X-ray Diffraction