Suggesting that volume distribution of the precipitates is the same as in the TEM image you may just calculate the ratio between surface area occupied by precipitates and the total area.

Dr. Sergei Tarasov,

Thanks for the reply. Actually, obtaining the third dimension is the challenge.

For understanding the third dimension, you can use probability distribution function based on woodhead or Schwartz-Saltykov method. In the process you need to have thickness values of your region of interest. Check this good review article by Underwood 1972 in Microscopie Quantitative, Chapitre 6 pp 147-196. Or for the application of method, look for Jensen's paper: Article Estimation of the size distribution of spherical, disc-like ...

Thanks Dr, Vishnu.

I am unable to get the review article by Underwood. If you have it, then please send it as a message or e-mail: [email protected]

Actually Sergei is correct. You do not need to know the thickness to get the volume distribution. See: F Chayes “The relation between area and volume in micrometric analysis” Mineralogical Magazine 30,147-149, (1953)

I attach this.

See also:

November 19th, 2015 The mathematics of image analysis

https://www.brainshark.com/malvern/vu?pi=312905118&b=1&tx=120486&c1=22

Thanks Dr. Alan, for your suggestion. But, I am not sure whether it is applicable for all different shaped particles. For eg: A circular disc particle when projected from top looks like a needle or a plate. In the thickness direction we could be able to see the original shape as disc.

So, If it is not considered, we may end up with erroneous values.

If I am wrong, please guide me..

Anas

any answer for this question so far?

I have the same issue while using ImageJ

Anas N S

If your (circular) disc material is oriented with all the edges in one direction or the discs in one direction then the projected area calculations will be identical to the volume. If not (e.g. random orientation) then you have indicated one fallibility in sample preparation for electron microscopy (especially TEM, if microtoming is involved). Consider slicing a cube. See attached from Claude Bragdon A Primer of Higher Space Manas Press (1913)

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

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