I work on Ti-6Al-4V alloy with bimodal microstructure.
Parameters of my scan:
Area- 400x400 microns
Step size- 0.2 micron
I clean up the scan using confidence interval ≥ 0.1 condition. I have attached the IPF and grain size distribution for reference. In all my scans I find the average of the grain size (grain diameter) is smaller than the standard deviation. For example, the average grain size for IPF attached is 1.98 and standard deviation is 2.25. Is there any mistake in my analysis.
Yes, thats certainly possible.
The distribution is multimodal log-normal (note the logarithmic scale of the x-axis in the distribution plot).
You can check the formulas for mean and variance of the lognormal in https://en.wikipedia.org/wiki/Log-normal_distribution.
For the proof-of-principle, take µ = 1 and σ = 1, you get
mean = 1+1/2 = 1.5
sd = sqrt(variance) = sqrt(|exp(1)-1|exp(2+1)) = 5.87
So sd > mean. One may solve the inequality equation to find all relations between µ and σ for which sd > mean. But I'll leave that to the experts :)
Yes, the average can be smaller than the standard deviation. Here is a thread discussing the same on research gate that you might find useful- https://www.researchgate.net/post/Can-Standard-Deviation-SD-be-greater-than-MEAN
All the best with your research!
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