SPO strength

[DriptD]

Hello,

I have a set of two SPO rose plots produced using the area-weighted method suggested in the MTEX documentation. I am trying to quantify the strength of individual SPO plots using the formula of Barraud (2006, JVGR) (screenshot below). I'm using MTEX 5.6.0 in Matlab 2020b.

However, I'm not sure if I get the correct result when the no. of grains is <50. Below is the part of the code:

---

grain_LA = grains('phase_name').longAxis;
grain_length = grains('phase_name').diameter;

t_sum = [0 0; 0 0]; % empty square matrix to store the sum of 'n' square matrices

x2 = (grain_LA.x).^2; % square of the x-component of the long axis unit vector

xy = (grain_LA.x).*(grain_LA.y); % product of the x- and y- components of the long axis unit vector

y2 = (grain_LA.y).^2; % square of the y-component of the long axis unit vector

for n = 1:length(grain_LA)
t{1,n} = [x2(n,:),xy(n,:);xy(n,:),y2(n,:)].*grain_length(n,:);
t_sum = t_sum + t{1,n};
end
D = t_sum./n;
e = eig(D)';
AF = (max(e)-min(e))/(max(e))*100;

---

Here is what I got:

Following are the questions I have:
1. I think the plot to the right should have a lower AF because the grain set seems to have a less preferred alignment than that of the other. But it isn't so. Could anyone please point out if there's something wrong with the code?

2. Is it that the SPOs are 'area-weighted', and while computing the AF, I'm not taking that into account? Could anyone please suggest how to do that?

3. Is there any other method that could be used to quantify the SPO strength instead of this one?

Thank you !!

Best,
Dripta

[kilir]

Hi Dripta,
you should probably treat your grain long axes as axes not directions - unless you have a way to distinguish between the "head" and the "tail" of a grain.

You should be able to weight your data by scaling the length of your grain long axes. Mtex also has eig() for vector3d.

Cheers,
Rüdiger

[DriptD]

Oh, I'm so sorry.

If the same weights are used for both the histogram and eigenvalue calculation, then the mean directions are 0.1 and 38.8 for the first and second plots, respectively.

The e1 values are 0.65 and 0.54 in that case.

Best,
Dripta

[kilir]

I still don't really see the 38 degree, so something seems to be not right. If you like, you could share the variables grain_LA and grain_area. (Just save them as mat and zip them up)
Cheers,
Rüdiger

[DriptD]

Hello,

Here it is.
Grain_LA_Area.zip

Best,
Dripta

[kilir]

I think you have a sampling problem with the data. Smoothing grains may help, but in general, you should discard grains below a certain size (i.e. < 50 pixels, but depends on the type of analysis) for shape analysis.

First figure: your data as is

Second figure: only those direction corresponding to areas > 12 (wild guess, no idea what this is in pixels in your case)

And here, the reasonable data as density:

Cheers,
Rüdiger

[DriptD]

Hello,

Thanks a lot. I was thinking of discarding finer grains and during processing the raw data I had only considered grains with at least 3 pixels. But I guess, maybe for the shape analysis, I'll have to raise that cutoff.

Thanks again.

Best,
Dripta