Negative slope in Williamson-Hall model

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Thread starter Cloruro de potasio
Start date Dec 24, 2022
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Model Negative Slope Structural analysis Xrd

In summary, the speaker is discussing their analysis of a powder diffraction experiment and has found a negative slope value, indicating a negative strain coefficient for the material. They are unsure how to interpret this result, as it seems to contradict the expected effect of inhomogeneous voltages. They are looking for information on whether this type of result is possible and how to understand it intuitively.

Dec 24, 2022

Cloruro de potasio

Good afternoon,

I am analyzing a diffraction diagram (XRD) corresponding to a powder diffraction experiment , and I have obtained a negative slope value when plotting ##\left(\beta_{exp}-\beta_{inst}\right)\cos\theta## vs ##\sin\theta##.

This implies that the strain coefficient is negative for the material. However, I don't quite understand how to interpret the result. In principle, inhomogeneous voltages should contribute to a broadening of the diffraction peak, but in this case it is as if the opposite were happening, that is, the diffraction peak is narrowing due to the effect of the applied strain.

I would be very grateful if you could inform me about whether it is possible to obtain a result of this type, and if so, about how to understand this phenomenon intuitively.

Thank you very much in advance and regards,

1. What is a negative slope in the Williamson-Hall model?

A negative slope in the Williamson-Hall model refers to the decreasing trend of the peak width of a diffraction pattern as the diffraction angle increases. This indicates that the crystallite size is decreasing with increasing diffraction angle, which is a characteristic of small and imperfectly crystalline materials.

2. How is the negative slope related to crystallite size?

The negative slope in the Williamson-Hall model is directly related to the crystallite size. As the crystallite size decreases, the diffraction peaks become broader and the slope of the peak width versus diffraction angle becomes more negative.

3. Why is the negative slope important in materials characterization?

The negative slope in the Williamson-Hall model is important because it provides information about the size and quality of crystalline materials. It can be used to determine the average crystallite size and the amount of strain present in the material.

4. What factors can affect the negative slope in the Williamson-Hall model?

The negative slope in the Williamson-Hall model can be affected by several factors, including the size and shape of the crystallites, the type and amount of defects present, and the crystalline structure of the material. Changes in these factors can cause the slope to become more or less negative.

5. How is the negative slope calculated in the Williamson-Hall model?

The negative slope in the Williamson-Hall model is calculated by plotting the peak width (in radians) versus the diffraction angle (in degrees) and determining the slope of the resulting line. This slope can then be used to calculate the average crystallite size and strain in the material.

Oct 12, 2018

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