Do not base any conclusions about stress on a single peak.

Do not base any conclusions about stress on multiple peaks with a single orientation (of the scattering vector).

There are a whole lot of reasons you can get a change in lattice parameter.

To determine if the change is due to stress, plot d vs (sin(ψ))^2, called a sin-squared-psi plot. To get the data, pick a peak with 2theta>130 deg. Tilt the sample off of the theta-2theta Bragg Brentano geometry, for which ψ=0 always. Measure the peak's d-spacing for ψ up to about 30 degrees; tilt both directions (ψ0); collect data for at least 11 tilts, for a reliable result. The slope of the sin-squared-psi plot is proportional to stress.

Read up on stress measurement by XRD.

Note, ψ is the angle between the scattering vector and the sample normal. The scattering vector is the bisector of the incoming and outgoing x-ray paths.

Do not base any conclusions about stress on a single peak.

Do not base any conclusions about stress on multiple peaks with a single orientation (of the scattering vector).

There are a whole lot of reasons you can get a change in lattice parameter.

To determine if the change is due to stress, plot d vs (sin(ψ))^2, called a sin-squared-psi plot. To get the data, pick a peak with 2theta>130 deg. Tilt the sample off of the theta-2theta Bragg Brentano geometry, for which ψ=0 always. Measure the peak's d-spacing for ψ up to about 30 degrees; tilt both directions (ψ0); collect data for at least 11 tilts, for a reliable result. The slope of the sin-squared-psi plot is proportional to stress.

Read up on stress measurement by XRD.

Note, ψ is the angle between the scattering vector and the sample normal. The scattering vector is the bisector of the incoming and outgoing x-ray paths.

Although I do not know the exact answer to your question, I think it is also important to note that reflection positions in PXRD patterns are also prone to shift due to the instrumental (geometry) issues. This phenomenon (usually) concerns high-angle reflections, and is related to the position of the source against the sample. The other issue is the instrument precision, e.g., 0.0001 A is a very tiny shift, most likely below the precision capabilities of at least most of the modern diffractometers.

Thanks for your answers...

What about strain calculation ?

can I take the d-value shift for that calculations.

but again the question is how much shift should be considered as actual shift ?

my step size of measurement is 2θ=0.02 degree.

so how much minimum shift in d-value is required for considering it actual shift (not a measurement limitation)

2dsinθ=nλ

gives

d1-d2=nλ/2(1/sinθ1-1/sinθ2)

using this equation for same 2θ variation at lower and higher 2θ values, d-value variation is different. for example at 2θ = 28.43 degree, for step size 0.02 degree, d-value variation is 0.002139 angstrom while for 2θ = 87.6 degree, for step size 0.02 degree, d-value variation is 0.000183 angstrom

So if I get the 0.002 angstrom shift in d-value at 2θ = 28.43, should I not consider it because it is within measurement limitations and same shift (0.002 angstrom) at 2θ = 87.6 is considerable as it is more than 10 times of the measurement limit ???

Is this statement is true ???

re "What about strain caclulations?" Everything I said about stress applies equally to strain. To a first approximation, they differ only by a factor (the modulus).

Ideally, if there is a residual stress in material it will shift more than 1 degree depend on type of stress. But before come to conclustion It is very important to calculate few things first such as: d value, how much expansion is there delta d/d0 and micro strain value. Some time shift in peak is also happen due to change in crystallographic phase of the material.

Hi Krishnanand Shukla ,

Thanks for the answer.

I have strain values as follow for different samples and peaks:

1. deltaD/d = 0.01/2.22 = 0.0045

2. deltaD/d=0.003/1.11=0.0027

3. deltaD/d=0.02/3.13= 0.0064

4. deltaD/d=0.0001/1.63 = 0.000061

Which can be considered as actual shift and which can not be ?

Is there any threshold value of deltaD/d above which it can be considered as shift and below that it should be ignored ?

Regards,

Sagar

Either your instrument and sample alignment and calibrations are correct, in which case you don't ignore any of these shifts, or they are not, in which case you should ignore all of them.

Hi Edward Andrew Payzant ,

Thanks for your answer. I understand that point.

Well I don,t know about the alignment part of the instrument but as the these shifts are from different samples prepared in different heating conditions, I want to be sure that peak shift is because of stress or any other reason before I interpret my data. We do not have ψ angle measurement facility in our instrument so I was trying to conclude on the basis of the shift only. However I can clearly see the banding in some of the substrate which indicates the shifting may be due to stress in the film but there are some samples which do not show banding with naked eye but still show some shift. So I need to have some idea about numbers to confirm the reason of this peaks.

If the shift is measured in conventional Bragg-Brentano geometry (e.g., with the sample at theta and detector at 2theta, so phi = 0), then these shifts have nothing to do with stress. There may be stress, but this is not how you measure it.

Hi Sagar,

I am agree to edward. alignment and calibration is a major parameter need to consider before measurement. I would suggest you to try glancing angle to measure the esaxct shift in peak. As most of time background affects the measurement. If I am aware about your material (thin film). you need to measure using GA setup. try 0.5 to 2 degree to see exact difference in measurement.

Also, no residual strain means no shift in peak. If there is any kind of microstrain present in the film. It will shift depend on the type.

for calculation of deltaD which formula you are using?

d-d0; d is for film and d0 value of substrate.

best