Graphite have low thermal expansion coefficients (~e-6 /deg C). Will these small coefficient have pronounced effect on peak shift as function of temperature?
Yes, it is technically possible to measure the thermal expansion coefficient of graphite with XRD data.
You first need to know that, for a given strain e, the corresponding peak shift DeltaTheta is given by:
DeltaTheta=sin-1(sin(Theta0)/(1+e))-Theta0
Thus, for the peak shift to be important, you need to choose a lattice plane with a high Bragg angle. For instance, for a plane whose Bragg angle (Theta0) is initially around 80° in a reference state (e.g. 20°C), a strain of 10-4 would generate a peak shift of 0,066°. Such a peak shift is usually easily evaluated with a standard diffractometer.
However, if you choose a lattice plane with a Bragg angle Theta0 of 40°, the peak shift associated with a strain e of 10-4 is only 0,01°.
The conclusion is that, for your estimation of the thermal expansion coefficient, you need an important temperature increase and a high Bragg angle.
Also, because of the hexgonal crystal system of graphite, the thermal expansion coefficient is anisotropic. It means that, you will obtain different values depending on the lattice plane you choose. For a hexagonal system, the thermal expansion tensor can be defined from two independent thermal expansion coefficients. You will therefore need to measure the peak shifts associated with a temperature increase for at least two independent lattice planes.
I hope this helps.
Dear Ravikumar Iyyamperumal,
If you can not make long samples of your material for the direct measurement of the linear expansion coefficients, it remains only to determine the change in the crystal lattice parameters at different temperatures and then extrapolate them to the macroscopic material.
Sincerely Professor Pavel Kudryavtsev
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