Frequency of Triple alpha variant clustering for Titanium

[Rhalder322]

As we know that the transformation strains are minimized by self-accommodation mechanisms via triple alpha variants clustering in Ti64. Generally, Cluster I represents A/B/C, D/E/F, G/H/I, J/K/L; while Category II encompasses those that consist of variants A/E/I, B/D/L, C/G/K and F/H/J.

Is there any feature available within MTEX to estimate the number or area frequency of triple alpha variant boundaries?

[frankNiessen]

Hi @Rhalder322 ,

the answer is yes and no. There is no built-in turn-key solution, but it is rather straight forward to program what you are looking for with few lines of code. Assuming you have run Example 8 to the end you should have a reconstructed prior beta microstructure and a variant ID assigned to each transformed alpha grain. I don't know exactly which convention you use to define variants A/B/C etc, but the convention used in ORTools for variants 1-12 is plotted into the command window during execution of example 8. This code snippet will get you the variant Ids at each triple junction that is made up of transformed alpha grains:

% Get the triple points of all transformed alpha grains:
triplePoints = job.transformedGrains.triplePoints;
% Check that all grains at triple junction are transformed grains
ind = all(ismember(triplePoints.grainId, job.transformedGrains.id), 2)
triplePointGrains = job.transformedGrains(job.transformedGrains.id2ind(triplePoints(ind).grainId))
% Get the variant Ids
triplePointVariantIds = triplePointGrains.variantId
% Potentially sort them
sort(triplePointVariantIds,2)

Best wishes
Frank

[Rhalder322]

Hello Prof. Niessen,

The histogram plot of hist(triplePointVariantIds) provides me with the following plot:

**_

How do I figure out which triple alpha variants groups are which from this plot?

Moreover, I would like to define variant clusters and plot the number & area frequencies of them. How do I do that?

_**

% Define the groups of triple variant clusters
vGroupIds = {
[1 2 3],...
[4 5 6],...
[7 8 9],...
[10 11 12],...
[1 11 9],...
[2 12 6],...
[3 8 5],...
[10 7 4]
};

Secondly, how do we relate variants used in these two conventions mentioned in the image below?

Thank you for helping me with this.

Regards,
Rajib Halder

[frankNiessen]

Hi,

so all challenges you have from here on mostly not MTEX/ORTools challenges but MATLAB challenges.

Your first questions is essentially: How often is each row of vGroupIds represented in the array triplePointVariantIds, this is an easy task for ChatGPT these days. To compute this it is essential to sort the values of each row first. Then you also want to take into account how large each cluster is to not only count the number of occurences, but the area of each cluster.

The entire code looks like this.

% Get the triple points of all transformed alpha grains:
triplePoints = job.transformedGrains.triplePoints;
% Check that all grains at triple junction are transformed grains
ind = all(ismember(triplePoints.grainId, job.transformedGrains.id), 2);
triplePointGrains = job.transformedGrains(job.transformedGrains.id2ind(triplePoints(ind).grainId));

% Get the variant Ids
triplePointVariantIds = sort(triplePointGrains.variantId,2);
% Get the number of EBSD pixels per triple point grain cluster
clusterSz = sum(triplePointGrains.grainSize,2);
% Define the variantId groups
vGroupIds = sort([1 2 3;...
4 5 6;...
7 8 9;...
10 11 12;...
1 11 9;...
2 12 6;...
3 8 5;...
10 7 4],2);

% Check how many rows in triplePointVariantIds match the different vGroups
% and consider the area of each occurence
for i = 1:size(vGroupIds, 1)
    globalClusterSz(i) = sum(ismember(triplePointVariantIds, vGroupIds(i, :), 'rows').*clusterSz);
end

The numbers you get in globalClusterSz give you the number of EBSD pixels in your map that belong to each cluster.

Regarding the second question, if you run the latest ORTools version, the command ORinfo(job.p2c); will return this information. Alternatively you can type job.p2c.variants(1) into the command window to get this information.

Best wishes
Frank