I have XRD pattern and already I have calculated particle size but now I want calculate strain and stress. How should I calculate it?
First go for TEM analysis so that you will know the geometry of the compound. From the geometry you can observe the strain/stress in the molecule. If the particle size is very small in nanometers scale and irregular geometry then it would have more stress and strain in the surface. If the particle size is large and spherical then it would have less strain and stress, according to Ostwald ripening and wuff construction theory.
Direct calculation of the stress from the classical XRD pattern (Bragg-Brentano geometry) are subject to a large inaccuracy. The peak maximum offset as compared to the reference peak position is proportional to the strain. Knowing the value of Young's modulus can be calculated stress according to Hook's law. But this method is very inaccurate.
The measurement of the stress in diffractometry method is based on non-symmetric geometry (e.g. Omega-sin2psi geometry). The only instrumental necessary changes are the addition of a specimen holder which will allow independent rotation of the specimen about the diffractometer axis, and a change in the position of the receiving slit.
In XRD powder pattern you can only roughly determine cvrystal size and strain (as effect of the peak width which is interpreted as increase of lattice defects) using Scherrers equation. This describes more an "isostatic" lattice strain.
In contrast, the strain determination with XRD at bulk materials determines another effect which is related to the sample geometry (surface). There differently oriented crystals are investigated (byi tilt of the sample around psi, an axis within the beam plane) and their variation of the peak position is used to derive the existing lattice strain. Ideally (or better for very simple cases) a linear dependency of peak shift (of a single peak) and sin²psi is used to derive the lattice strain.
@ Krzysztof: Could you shortly explain why the symmetric sin²psi technique (in Bragg-Brentano geometry) is worse than the Omega-sin²psi geometry (or do we talk about different things since I know this technic as Omega-2Theta technique, i.e. the tilt does not happen around psi but around Omega)? There you have the problem of different absorption length and also a focusing problem. When I remember correctly Omega-sin²psi has been used because of limitations in Bragg-angle or for strong surface gradients. Or am I wrong?
Finally a short remark: you can only measure lattice STRAIN with XRD. STRESS you might calculate if Young's modulus is available and correct (as you mentioned of course).
I recommend you to do 2D XRD
which is more precise for strain evaluation.
I am also suggest to follow the Williamson Hall method and size strain plot.
Best wishes
I am also calculated the strain value from william's- Hall plot. but reviewer ask a question how to calculate the strain value using william's -Hall equation.
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