function symm = gtCrystGetSymmetryOperators(crystal_system, spacegroup)
% GTCRYSTGETSYMMETRYOPERATORS Gives the list of symmetry operators.
% symm = gtCrystGetSymmetryOperators(crystal_system[, spacegroup])
% ----------------------------------------------------------------
% With no input, everything is read from the parameters.mat file
%
% OPTIONAL INPUT:
% crystal_system = <string> Name of the crystal system
% ('cubic', 'hexagonal', 'trigonal')
% spacegroup = <int> Space group number
%
% This function returns the crystal symmetry operators for different crystal systems:
% - cubic
% - hexagonal (sg = 194, 663)
% - trigonal (sg = 167)
% The symmetry operators as tabulated from table 3.2 in Hansen et al, Randle & Engler, 2000
%
%
% Version 001 05-10-2012 by YGuilhem yoann.guilhem@esrf.fr
if ~exist('crystal_system', 'var') || isempty(crystal_system)
if exist('parameters.mat','file')
parameters = load('parameters.mat');
crystal_system = parameters.parameters.cryst.crystal_system;
else
gtError('gtCrystGetSymmetryOperators:wrong_input', ...
'crystal_system was not given and there is no parameters file in the current directory!');
end
elseif ~exist('spacegroup', 'var') || isempty(spacegroup)
if exist('parameters.mat','file')
disp('Guessing spacegroup from parameters file...');
parameters = load('parameters.mat');
spacegroup = parameters.parameters.cryst.spacegroup;
end
end
switch crystal_system
case 'cubic'
if exist('spacegroup', 'var') && ~isempty(spacegroup)
if ~between(spacegroup, 195, 230)
gtError('gtCrystGetSymmetryOperators:wrong_input', [ ...
'Given spacegroup (' num2str(spacegroup) ')' ...
'does not match with the crystal system (' crystal_system ')!']);
end
end
symm(1).g = [ 1 0 0 ;...
0 1 0 ;...
0 0 1 ];
symm(2).g = [-1 0 0 ;...
0 1 0 ;...
0 0 -1 ];
symm(3).g = [-1 0 0 ;...
0 -1 0 ;...
0 0 1 ];
symm(4).g = [ 1 0 0 ;...
0 -1 0 ;...
0 0 -1 ];
symm(5).g = [ 0 1 0 ;...
0 0 1 ;...
1 0 0 ];
symm(6).g = [ 0 -1 0 ;...
0 0 1 ;...
-1 0 0 ];
symm(7).g = [ 0 -1 0 ;...
0 0 -1 ;...
1 0 0 ];
symm(8).g = [ 0 1 0 ;...
0 0 -1 ;...
-1 0 0 ];
symm(9).g = [ 0 0 1 ;...
1 0 0 ;...
0 1 0 ];
symm(10).g = [ 0 0 -1 ;...
1 0 0 ;...
0 -1 0 ];
symm(11).g = [ 0 0 -1 ;...
-1 0 0 ;...
0 1 0 ];
symm(12).g = [ 0 0 1 ;...
-1 0 0 ;...
0 -1 0 ];
symm(13).g = [ 0 0 -1 ;...
0 -1 0 ;...
-1 0 0 ];
symm(14).g = [ 0 0 1 ;...
0 -1 0 ;...
1 0 0 ];
symm(15).g = [ 0 0 1 ;...
0 1 0 ;...
-1 0 0 ];
symm(16).g = [ 0 0 -1 ;...
0 1 0 ;...
1 0 0 ];
symm(17).g = [-1 0 0 ;...
0 0 -1 ;...
0 -1 0 ];
symm(18).g = [ 1 0 0 ;...
0 0 -1 ;...
0 1 0 ];
symm(19).g = [ 1 0 0 ;...
0 0 1 ;...
0 -1 0 ];
symm(20).g = [-1 0 0 ;...
0 0 1 ;...
0 1 0 ];
symm(21).g = [ 0 -1 0 ;...
-1 0 0 ;...
0 0 -1 ];
symm(22).g = [ 0 1 0 ;...
-1 0 0 ;...
0 0 1 ];
symm(23).g = [ 0 1 0 ;...
1 0 0 ;...
0 0 -1 ];
symm(24).g = [ 0 -1 0 ;...
1 0 0 ;...
0 0 1 ];
case 'hexagonal'
if exist('spacegroup', 'var') && ~isempty(spacegroup)
if ~between(spacegroup, 168, 194) && spacegroup ~= 663
gtError('gtCrystGetSymmetryOperators:wrong_input', [ ...
'Given spacegroup (' num2str(spacegroup) ')' ...
'does not match with the crystal system (' crystal_system ')!']);
end
else
spacegroup = 194;
end
switch spacegroup
%case {663, 194, 225} % Heritage from Sabine function..
% Why space group 225 was in hexagonal crystals?
% What is 663 space group?
case {194, 663}
symm(1).g = [ 1 0 0 0 ;...
0 1 0 0 ;...
0 0 1 0 ;...
0 0 0 1 ] ;
symm(2).g = [ 0 0 1 0 ;...
1 0 0 0 ;...
0 1 0 0 ;...
0 0 0 1 ];
symm(3).g = [ 0 1 0 0 ;...
0 0 1 0 ;...
1 0 0 0 ;...
0 0 0 1 ];
symm(4).g = [ 1 0 0 0 ;...
0 1 0 0 ;...
0 0 1 0 ;...
0 0 0 -1 ];
symm(5).g = [ 0 0 1 0 ;...
1 0 0 0 ;...
0 1 0 0 ;...
0 0 0 -1 ];
symm(6).g = [ 0 1 0 0 ;...
0 0 1 0 ;...
1 0 0 0 ;...
0 0 0 -1 ];
symm(7).g = [-1 0 0 0 ;...
0 -1 0 0 ;...
0 0 -1 0 ;...
0 0 0 1 ];
symm(8).g = [ 0 0 -1 0 ;...
-1 0 0 0 ;...
0 -1 0 0 ;...
0 0 0 1 ];
symm(9).g = [ 0 -1 0 0 ;...
0 0 -1 0 ;...
-1 0 0 0 ;...
0 0 0 1 ];
symm(10).g = [-1 0 0 0 ;...
0 -1 0 0 ;...
0 0 -1 0 ;...
0 0 0 -1 ];
symm(11).g = [ 0 0 -1 0 ;...
-1 0 0 0 ;...
0 -1 0 0 ;...
0 0 0 -1 ];
symm(12).g = [ 0 -1 0 0 ;...
0 0 -1 0 ;...
-1 0 0 0 ;...
0 0 0 -1 ];
% 3 components version, should not match with g order, i.e g(i) ~= g3(i)
% From "Introduction to Texture Analysis", by Randle & Engler, 2000
% Rotation operator of 180 around x to emulate mirror symmetry without turning to left-handed CS
mirror = [ 1 0 0 ;...
0 -1 0 ;...
0 0 -1 ];
for ii=1:6
a = (ii-1)*60;
ca = cosd(a);
sa = sind(a);
symm(ii).g3 = [ ca sa 0 ;...
-sa ca 0 ;...
0 0 1 ];
symm(ii+6).g3 = mirror * symm(ii).g3;
end
otherwise
gtError(['Unsupported spacegroup: ', num2str(spacegroup)]);
end
case 'trigonal'
if exist('spacegroup', 'var') && ~isempty(spacegroup)
if ~between(spacegroup, 143, 167)
gtError('gtCrystGetSymmetryOperators:wrong_input', [ ...
'Given spacegroup (' num2str(spacegroup) ')' ...
'does not match with the crystal system (' crystal_system ')!']);
end
else
spacegroup = 167;
end
switch spacegroup
case {167}
% 6 operators, also return in 3 index format
% however, this doesn't seem right when looking at the alumina
% datasets... more work to do.
% Reference
symm(1).g = [ 1 0 0 0 ;...
0 1 0 0 ;...
0 0 1 0 ;...
0 0 0 1 ];
% Rotate 120 around z
symm(2).g = [ 0 1 0 0 ;...
0 0 1 0 ;...
1 0 0 0 ;...
0 0 0 1 ] ;
% Rotate 240 around z
symm(3).g = [ 0 0 1 0 ;...
1 0 0 0 ;...
0 1 0 0 ;...
0 0 0 1 ];
% Rotate 180 around x
symm(4).g = [ 1 0 0 0 ;...
0 0 1 0 ;...
0 1 0 0 ;...
0 0 0 -1 ];
% Rotate 180 around y
symm(5).g = [ 0 0 1 0 ;...
0 1 0 0 ;...
1 0 0 0 ;...
0 0 0 -1 ];
% Rotate 180 around dummy
symm(6).g = [ 0 1 0 0 ;...
1 0 0 0 ;...
0 0 1 0 ;...
0 0 0 -1 ];
% 3 axis
% Reference
c = cosd(120);
s = sind(120);
symm(1).g3 = [ 1 0 0 ;...
0 1 0 ;...
0 0 1 ];
% hkil -> ihkl : Rotate 120 around z
symm(2).g3 = [ c s 0 ;...
-s c 0 ;...
0 0 1 ];
% hkil -> kihl : Rotate 240 around z
symm(3).g3 = [ c -s 0 ;...
s c 0 ;...
0 0 1 ];
% Rotate 180 around hex axis 1 (// y in cart)
symm(4).g3 = [-1 0 0 ;...
0 1 0 ;...
0 0 -1 ];
% Rotate 180 around hex axis 2
symm(5).g3 = symm(2).g3 * symm(4).g3 * symm(3).g3;
% Rotate 180 around hex axis 3
symm(6).g3 = symm(3).g3 * symm(4).g3 * symm(2).g3;
otherwise
gtError(['Unsupported spacegroup: ', num2str(spacegroup)]);
end
end % end switch crystal_system
end % end of function