Shahid - are you asking how to measure local strains, macrostrain, microstrain?

If you are interested in strains resulting from residual stress, this subject is readily covered in various books - my personal recommendation is Noyan and Cohen - out of print but available second hand:

http://www.abebooks.com/products/isbn/9781461395713/9171275924

Manas - I would only use your method with a lot of caution, since it assumes that the "JCPDS" (long since become the ICDD) powder diffraction file lattice parameter is the correct stress-free value for your sample, and also that your measured d-spacings are accurate and free of peak shifts due to systematic errors. In many cases that won't be true.

lattice strain along one plain you can calculated from the change in the d- value(JCPDS d-value - experimental d- value, d= lattice spacing) divide to the experimental d-value along the plane.

Plz find the attachment .....

Shahid - are you asking how to measure local strains, macrostrain, microstrain?

If you are interested in strains resulting from residual stress, this subject is readily covered in various books - my personal recommendation is Noyan and Cohen - out of print but available second hand:

http://www.abebooks.com/products/isbn/9781461395713/9171275924

Manas - I would only use your method with a lot of caution, since it assumes that the "JCPDS" (long since become the ICDD) powder diffraction file lattice parameter is the correct stress-free value for your sample, and also that your measured d-spacings are accurate and free of peak shifts due to systematic errors. In many cases that won't be true.

You can see the recipe in "Powder diffraction" in Wikipedia. Section "Size and strain broadening"

You can see the following paper:

Measuring Strain Using X-Ray Diffraction. JAMES BELASCO (Villanova University, Villanova, PA, 19085) APURVA MEHTA (Stanford Linear Accelerator Center, Menlo Park, CA, 94025)

www2.slac.stanford.edu/suli/2007/papers_2007/Belasco.doc

I agree with Edward.. talking about "strain" is meaningless unless you specify which kind of strain you want to measure. And in most cases (e.g. when you talk about microstrain), what you want is not a strain but a value related to the variance of a strain distribution.

It is possible to measure this type of strain as well an there are several methods in the literaure. The choice of the method depends on whether you need a number to classify or compare your specimens (fast traditional techniques such as e.g. the Williamson-Hall plot) or a value related to the physics (i.e. knowing the source of this microstrain, such as e.g. the WPPM method).

@Manas: you better have a look at a good book on residual stress analysis, as the risks associated to the use of naive ways of measuring residual strain are larger than the advantages. Take pure gamma iron and take an austenitic steel: you find different cell parameters even without residual stress.. without considering that the cell parameter of gamma iron should be a high temperature one (where austenite is stable) and you usually measure your pattern at room temperature

by the way, I would noever propose wikipedia as a "scientific reference", especially considering the number of good books on the subject. For sure the part on the microstructure is very limited and obsolete (we are not longer in the '50s)

By lattice strain, it iusually means the inhomogeneous local strain in the material which gives rise to x-ray peak broadening. It is only one factor causing peak broadening. The other factors are small crystallite size and presence of lattice defects.

@Manas Rath, what you suggested is nothing but strain due to homogeneous residual stress in the material. It is not lattice strain.

The well known method to calculate lattice strain is to fit the xrd data with rietveld method and calculate lattice parameters. The ratio difference between lattice constants obtained from fitting and original value to original value gives the strain in material. i.e. strain = (a0 - a)/a where a0 gives lattice constant obtained from fitting and a - is original lattice constant.

I can tell this is an interesting question just based on the participant list so far.

Measuring or quantifying "crystallographic lattice strains" will remain a topic of tremendous interest for quite a while now. Using XRD data is perhaps the best known method for achieving this goal. However, as others have eloquently stated several parameters and facts need to be identified in order to be unequivocal with the interpretations.

1. Is the sample poly-crystalline or mono-crystalline?

2. What is the typical diffracting domain size? (Grain size, particle size...etc.)

3. Are you using the simple powder diffraction method?

4. Or, the more sophisticated XRD Rocking Curve method?

5. Do you have "known standards" to compare with?

6. Are you acquiring the conventional "equatorial scan" with a 0D detector?

7. Or, are you acquiring the entire 2D XRD pattern? Film, 1D or 2D detector?

The parameters to monitor would be:

1. Bragg Peak Position (Shift)

2. Bragg Peak FWHM (Broadening).

3. Bragg Peak Shape.

In general, the crystallographic strain fields are highly anisotropic in nature. Therefore, several (hkl)'s need to be studied in order to quantify the 3D "strain state".

"what you suggested is nothing but strain due to homogeneous residual stress in the material. It is not lattice strain"

Would homogeneous residual stress deform the crystal lattice uniformly and shift the Bragg Peak?

http://www.flickr.com/photos/85210325@N04/9419071407/

http://www.flickr.com/photos/85210325@N04/9419071407/

Ravi, yes, it will shift the Bragg peak. Please refer our paper I sent you earlier.

Sagar, can u send this paper as an attachment. I unable to download from the link send by you.

In strained lattices of thin-film materials, there are two lattice parameters of interest - an in-plane and an out-of-plane lattice parameter, measured separately. Even for cubic lattice, there will be measurable difference, and that can be related to lattice strain.

@ Shahid:

It appears that your question is somewhat misconstruing, as it can refer to different kinds of strain within the lattice. If you are talking about the measurement of lattice micro strain from X-ray analyses, then my explanation would be to try a Warren-Averbach analysis or even Rietveld analysis. Before attempting either of these analyses, you have to determine the instrumental broadening of the diffractometer and other peak shape parameters. Then a proper deconvolution of the specimen broadening is required and finally separating out the size and strain (micro) contributions will give you the desired result. These are fairly old techniques but very reliable and albeit indirect in nature!! There are ample literature as well as free and commercial programs for the said analyses.

All the best!!

Please find an article in the attachment. Hope it will help you.

The link given below may be important for you.

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

I found this discussion by accident.  But we are always looking for new things to do.  So if anyone is still paying attention to this, I wouldn't mind hearing from you.

Dr. Harder would you like to make any comment in this regard.

Dr. Harder would you like to make any comment in this regard.