gtCrystGetSigmas : calculates sigma values for cubic and hcp materials...

gtCrystGetSigmas : calculates sigma values for cubic and hcp materials (extracted from GtAssembleVol3D). For hcp materials, 'X' and 'Y' conventions are taken into account.

Signed-off-by: Laura Nervo <laura.nervo@esrf.fr>

zUtil_Cryst/gtCrystGetSigmas.m

+function sigmas = gtCrystGetSigmas(crystal_system, latticepar, convention)
+% GTCRYSTGETSIGMAS  Calculates CSL sigmas values for cubic and hexagonal crystal
+%     sigmas = gtCrystGetSigmas(crystal_system, latticepar, [convention])
+%     -------------------------------------------------------------------
+%     INPUT:
+%       crystal_system = 
+%       latticepar     = 
+%       convention     = <string>   hcp axes convention {'X'}|'Y'
+
+if ~exist('latticepar','var') || isempty(latticepar)
+    parameters = [];
+    load('parameters.mat');
+    latticepar = parameters.cryst.latticepar;
+    clear parameters
+end
+if ~exist('convention','var') || isempty(convention)
+    convention = 'X';
+end
+
+if strcmpi(crystal_system, 'cubic')
+
+    %sigma s: type, angle, axis cart, brandon criteria {, rodrigues}
+    sigmas = [ 3 60    1 1 1 0 0.333 0.333 0.333; ...
+               5 36.86 1 0 0 0 0.333 0     0; ...
+               7 38.21 1 1 1 0 0.199 0.199 0.199; ...
+               9 38.94 1 1 0 0 0.25  0.25  0; ...
+              11 50.47 1 1 0 0 0.333 0.333 0; ...
+              13 22.62 1 0 0 0 0.2   0     0; ...
+              13 27.79 1 1 1 0 0.143 0.143 0.143];
+    %add brandon criteria
+    sigmas(:, 6) = 15 * sigmas(:, 1) .^ (-0.5);
+    sigmaNorms = sqrt(sum(sigmas(:, 3:5) .* sigmas(:, 3:5), 2));
+    %normalise axis
+    sigmas(:, 3:5) = sigmas(:, 3:5) ./ sigmaNorms(:, [1 1 1]);
+
+elseif strcmpi(crystal_system, 'hexagonal')
+    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+    % added on 2013-10-09 by LNervo
+    % R. Bonnet, E. Cousineau, D.H. Warrington (1981) "Determination of
+    %     near-coincident cells for hexagonal crystals. Related  DSC
+    %     lattices" Acta Crystallographica, A37, 184-189
+    % Bozzolo et al. (2010) "Misorientations induced by deformation
+    %     tiwnning in titanium" J. Appl. Cryst. 43, 596-602
+    % CSL values for HCP; cartesian axis in Y-convention originally
+
+    % sigma for hcp s: type, angle, axis hex, brandon criteria, axis cart
+    sigmas = [  7 21.8   0  0  0  1   0  0 0 1; ... %7a
+                7 64.6   1  0 -1  0   0  1 0 0; ... %7b
+               11 35.1   1  0 -1  0   0  1 0 0; ... %11a
+               11 84.8   2 -1 -1  0   0  0 1 0; ... %11b
+               13 27.8   0  0  0  1   0  0 0 1; ... %13a
+               13 57.4   2 -1 -1  0   0  0 1 0; ... %13b
+               13 76.7   1  0 -1  0   0  1 0 0; ... %13c
+               17 40.1   2 -1 -1  0   0  0 1 0; ... %17a NO Ti
+               17 79.8   3 -1 -2  0   0  0 0 0; ... %17b NONE
+               19 13.2   0  0  0  1   0  0 0 1; ... %19a
+               19 65.1  10 -5 -5  3   0  0 0 0; ... %19b
+               19 87.0   1  0 -1  0   0  1 0 0; ... %19c
+               23 55.6   1  0 -1  0   0  1 0 0; ... %23a NONE
+               23 72.3   2 -1 -1  0   0  0 1 0; ... %23b NO Ti
+               23 86.3  10  0 -10 3   0  0 0 0; ... %23c NONE
+               ];
+
+
+    if strcmpi(convention, 'X')
+        sigmas(:, 8:10) = gtHex2Cart(sigmas(:, 3:6), latticepar, convention);
+    end
+
+    %add brandon criteria: is it also for hcp? (laura)
+    sigmas(:, 7) = 15 * sigmas(:, 1) .^ (-0.5);
+    sigmaNorms = sqrt(sum(sigmas(:, 8:10) .* sigmas(:, 8:10), 2));
+    %normalise axis
+    sigmas(:, 8:10) = sigmas(:, 8:10) ./ sigmaNorms(:, [1 1 1]);
+end
+
+end % end of function

zUtil_Cryst/gtCrystTwinTest.m

+function [info, sigma] = gtCrystTwinTest(R1, R2, phaseID, varargin)
+% GTCRYSTTWINTEST  Tests if the two orientations are from two twins
+%     [info, sigma] = gtCrystTwinTest(R1, R2, [phaseID], varargin)
+%     ------------------------------------------------------------
+%     INPUT:
+%       R1 and R2   = Rodriguez vectors of the two different orientations
+%       phaseID     = current phase
+%
+%     OPTIONAL INPUT (parse by pairs):
+%       symm        = symmetry operators from gtCrystGetSymmetryOperators {[]}
+%       sigmas      = sigma values from gtCrystGetSigmas {[]}
+%       merge_angle = a threshold to decide if the angle is small {5}
+%       convention  = hcp crystal axes convention {'X'}
+%
+%     Version 001 13-11-2013 by LNervo
+
+if ~exist('phaseID','var') || isempty(phaseID)
+    phaseID = 1;
+end
+
+app.symm   = [];
+app.sigmas = [];
+app.merge_angle = 5;
+app.convention = 'X';
+app = parse_pv_pairs(app, varargin);
+
+parameters = [];
+load('parameters.mat');
+crystal_system = parameters.cryst(phaseID).crystal_system;
+latticepar = parameters.cryst(phaseID).latticepar;
+spacegroup = parameters.cryst(phaseID).spacegroup;
+if isempty(app.symm)
+    app.symm = gtCrystGetSymmetryOperators(crystal_system, spacegroup);
+end
+if isempty(app.sigmas)
+    app.sigmas = gtCrystGetSigmas(crystal_system, latticepar, app.convention);
+end
+
+sigmas = app.sigmas;
+
+sigma   = []; % default sigma
+if strcmp(crystal_system, 'cubic')
+
+    [mis_angle, mis_axis, mis_info] = gtDisorientation(R1.', R2.', app.symm, 'sort','descend');
+    if mis_angle > 90 
+         mis_angle = 180 - mis_angle;
+    end 
+   
+    sigmaOr = [];
+    if ~isempty(mis_axis)
+        % determine sigma type
+        test_angle = abs(mis_angle - sigmas(:, 2)) < sigmas(:, 6);
+        test_axis  = abs(acosd(dot(repmat(mis_axis,size(sigmas,1),1), sigmas(:, 3:5), 2))) < sigmas(:, 6);
+        sigmaOr = sigmas(find(test_angle | test_axis), :);
+        sigma = sigmas(find(test_angle & test_axis), 1);
+    end
+
+elseif strcmp(crystal_system, 'hexagonal')
+
+    % In the case of hexagonal crystals
+    [mis_angle, mis_axis, mis_info] = gtDisorientation(R1.', R2.', app.symm, ...
+        'latticepar', latticepar, 'convention', app.convention);
+    if mis_angle > 90 
+         mis_angle = 180 - mis_angle;
+    end
+
+    sigmaOr = [];
+    if ~isempty(mis_axis)
+        % determine sigma type
+        test_angle = abs(mis_angle - sigmas(:, 2)) < sigmas(:, 7);
+        test_axis  = abs(acosd(dot(repmat(mis_axis,size(sigmas,1),1), sigmas(:, 8:10), 2))) < sigmas(:, 7);
+        sigmaOr = sigmas(find(test_angle | test_axis), :);
+        sigma   = sigmas(find(test_angle & test_axis), :);
+    end
+else
+    disp('Crystal system is not currently supported... Quitting')
+    return
+end
+
+% add low angle (merge grains) criteria
+if (mis_angle < app.merge_angle)
+    sigma = -1;
+end
+
+info.R1           = R1;
+info.R2           = R2;
+info.mis_angle    = mis_angle;
+info.mis_axis     = mis_axis;
+info.sigmaOr      = sigmaOr;
+info.sigmaAnd     = sigma;
+info.sigmas       = app.sigmas;
+info.merge_angle  = app.merge_angle;
+info.convention   = app.convention;
+info = gtAddMatFile(info, mis_info, true, true);
+
+end % end function twinTest