The cylindricity index uses eigenvector analysis, wherein an orientation tensor (Scheidegger, 1965) is calculated by matrix summation of three-unit column eigenvectors that represent the orientation of each crystal (Vollmer, 1990). Which functions are used to calculate the cylindricity (B) in MTEX?
In MTEX, the cylindricity index (B) can be calculated using the calcCylindricity function, which is based on the eigenvalue and eigenvector analysis of the fabric tensor. The fabric tensor describes the preferred orientation of the crystals, and its eigenvalues and eigenvectors can be used to calculate the cylindricity index. The calcCylindricity function calculates the eigenvalues and eigenvectors of the fabric tensor using the eig function and then computes the cylindricity index based on the resulting eigenvectors.
Here's an example code using the calcCylindricity function in MTEX:
iniCopy code% Load data data = load('myData.txt'); % Create an MTEX orientation data set ori = orientation('matrix', data); % Calculate the fabric tensor ft = calcFabricTensor(ori); % Calculate the cylindricity index B = calcCylindricity(ft);
The resulting value of B is the cylindricity index for the given data set.
Thank you, and I have written the relevant script files.
o = calcMisorientation(ebsd('Quartz-new'), 'orientations')
v = o*Miller(0, 0, 1, CS{1, 2}, 'Quartz-new', 'hkil')
[x,y,z] = double(v)
OT = 1./numel(x)*[x,y,z]'*[x,y,z]
[Vec, Diagonal] = eig(OT)
value = diag (Diagonal)
[value,index] = sort (value, 'descend')
vec1(1:3) = Vec (: ,index(1));
vec2(1:3) = Vec (: ,index(2));
vec3(1:3) = Vec (: ,index(3));
NORM = value(1) + value(2) + value(3);
% Point maximum
P100 = (value(1)-value(2))/NORM
% Girdle
G100 = (2.0*(value(2)-value(3)))/NORM
B = P100 + G100
R = 1 - P100 - G100
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