When a polycrystalline material is deformed elastically such that the strain is uniform over relatively large distances the lattice plane spacings in the crystal change from their srtrss free values to new values corressponding with the stress and appropriate elastic constants,These are usually reffered as macrostrains.Where plastic deformation occurs the local distorsion of lattice planes gives rise to nonuniform variations in the interplanar spacings called as microstains.Microstrains occur in metal like bending , rolling and affect many properties of metal such as corrosion, fatigue strength , hardness and cracking.

So microstrain  studies are done using XRD to check these parameters.

Dear Yushi,

From the same Williamson-Hall method the negative slope  indicate the broadening from small internal strain therefore result suggest for the compressive strain in the crystal lattice of the examine film. Usually some of the polymer composites shows this kind of property. 

Hi there everyone, currently I am working with a system that presents a substitution of ion in the A site of a perovskite. I'm replacing some given ions with small ones (as my XRD analysis tells), so I was wondering if the strain should it be positive or negative? I am currently using MAUD software, and my microstrain analysis gives positive values.

The microstrain is the root mean square of the variations in the lattice parameters across the sample. By definition, it cannot be negative.

Another thing is the overall decrease of the lattice parameters when the bigger ion is partially substituted by the smaller one. This decrease can be regarded as macrostrain of the initial material. Many scientists use the term 'chemical pressure' to describe such cases.

Hi Alexander,

Will my experimental samples produces unusual results when calculated from  Williamson-Hall method or there is wrong conclusions?

Just see the graphs.

With regards.

Dear Rinkesh,

I can propose at least two explanations of your plots:

1. The broadening is anisotropic and you have to calculate the size-strain parameters for the different directions separately.

2. PVA has two close peaks around 2θ=19.6 ({101} and {-101}) with almost the same intensity. If the broadening is large, they will overlap, and become observed as a single peak with larger FWHM.

I know that it is difficult for polymers, but try to get more points. I suspect that most of them will give βcosθ

Thanks a lot Alexander B. Missyul'

Mr Yushi Yang, kindly tell how to calculate ∆θ?

Please, how did you get ∆θ ?