Hi Kamsing,

I would say that the first method will always be closer to the truth as it somehow takes into account the realistic distribution of grain sizes into your microstructure. The assumption used in the second method seems to me very dependent of the microstructure you are studying. If you take, for example, microstructures with gradient-sized grains, the second method would not be appropriate at all as you only take into account the number of total grains in the map.. Maybe in cases where the scanned area is sufficiently large and/or if your microstructure mainly show equiaxed grains, the difference between the two calculated values would be significantly lower. However, exporting the distribution of grains sizes seems more relevant to me than calculating an average grain size based only on the number of scanned grains. (PS: on top of that, no matter the method, please keep in mind that this size is derived from 2D data and will always be an estimation of the real 3D value).

Best regards,

Julien.

Hi Kamsing Chung

I have tried these two methods to measure the average grain size. But I realized that both of them didn't determine the correct value according to the map. I agreed with Julien that these methods can be useful to show the distribution of grain sizes.

If you intend to measure the average, I suggest you measure all the grain sizes by the first method via ATEX. Then, count all the grains on your map. Considering that you should consider each grain on the edge of the map as half of the grain and the grain on the corners of the map as a quarter of a grain. Finally, divide the total area of grains by the total number of them to measure the average grain size.

This method was very practical for my study.

Kind regards,

Hi Kamsing Chung

The first method i.e. the area weighted approach makes more sense and is most widely used in the community as well as usually implemented in commercial EBSD software's. On the other hand, the second approach should be used with caution as pointed out by Julien Genée . Also, as Julien Genée mentioned, it is always better to show the data in the form grain size distribution. Also, please be aware that the definition of grain diameter varies from software being used, for example: in most commercial software's the grain diameter is calculated considering a circular grain whereas in open source codes such as MTEX, it is the longest distance between the two vertices of the grain boundary. This can have a significant influence on your final average grain size.

Hi,

I can recommend the first method, followed by it.

Thank you.

As already mentioned, the first method is better. In addition, there are two ways to define the "average" diameter:

The second method is preferable, because it reflects the fact that large grains are more "visible" in a microstructure. Think about a microstructure consisting in one huge grain (say 500 µm eq. diameter), surrounded by 999 small grains (say 1 µm). The two aforementioned methods will lead to mean diameter equal to 1.5 µm and 498 µm, respectively.

As far as I know, the ASTM mean size is computed based on the second method.

Hi Kamsing,

the optimal method depends largely on your goals. Both methods are also covered in the ASTM guides (if I remember correctly). If you want to compare your data with previous studies you should use the same protocol as those works. If not, you are free to use other protocols. Having said that, you should take into account the following considerations when determining average grain sizes:

- Always plot the grain size distribution. Averaged grain sizes only make sense if the distribution is unimodal. If it is bimodal (or multimodal), you should segment your grain size populations first.

- If you use a grain-by-grain approach you should remove all grains cut by the edge of the EBSD map. Normally you should also remove all the grains formed by a few pixels (i.e. EBSD measurements) to prevent the introduction of artefacts produced during grain reconstruction. Most authors remove all grains formed by 6 pixels or less, although cut-off values between 4 and 10 are also common. (Btw, in MTEX you can easily estimate the areas of the grains and thus the equivalent circular diameters).

Regarding the measure of central tendency (i.e. average) to use:

- For comparisons, always use the same average as the data you are comparing with.

- For lognormal populations, the geometric mean provides the best balance between efficiency and robustness. The median is also a good alternative. If you are interested in the topic you might want to take a look at this paper:

Article Which average, how many grains, and how to estimate robust c...

Hope this helps.

Best,

Marco

You forgot to specify two things.

Firstly, the type of alloy considered and secondly the criteria for distinguishing between different grains.

Regarding the type of alloy, it is important to know if you are talking about transformed phases such as martensite, from which the main feature is given by laths or plates that correspond to sub-structures when compared to the parent grain. EBSD can give you the size of these sub-structures, but you need to use specifi algorithm the determine the parent grain size under a reconstruction approach.

Take a look on this paper from Cyril Cayron Article Reconstruction of Parent Grains from EBSD Data

For the second criterion, it is linked to the misorientation which is taken into account. Therefore Low angle grain boundaries (LAGBs) are distinguished from High angle grain boundaries (HAGBs) when setting the threshold misorientation value at 15°, which is a standard. See this paper for better understanding Article Transition between low and high angle grain boundaries

Generally speaking, it is considered that dislocations will easily cross LAGBs while they will pile up leading to subsequent hardening when reaching HAGBs. It is every time a question of scale at which the study is carried out, even through EBSD.

Article Recent Advances in EBSD Characterization of Metals