triclinic_atom.m

This function transforms an orthogonal atom struct to a triclinic with
the angles alfa, beta, gamma or tilt factors xy, xz, yz

Version
Contact
Examples

Version

2.11

Contact

Please report problems/bugs to michael.holmboe@umu.se

Examples

atom = triclinic_atom(atom,Box_dim,[alfa beta gamma],'angle')
atom = triclinic_atom(atom,Box_dim,[xy xz yz],'tilt')

function atom = triclinic_atom(atom,Box_dim,angleparam,angletype)

if strncmpi(angletype,'angle',5)

%     disp('Using angles')
    lx=Box_dim(1);
    ly=Box_dim(2);
    lz=Box_dim(3);
    alfa=angleparam(1);
    beta=angleparam(2);
    gamma=angleparam(3);
    a = lx;
    b = ly/((1-cos(pi()/180*gamma)^2)^0.5);
    xy = b * cos(deg2rad(gamma));

    c=lz; % approx.
    c_temp=c+10;i=0;
    while i<100 % There should be a better way of doing this...
        xz = c*cos(deg2rad(beta));
        yz = (b*c*cos(deg2rad(alfa))-xy*xz)/ly;
        c = (lz^2 + xz^2 + yz^2)^.5;
        i=i+1;c_temp=c;
    end

else
%     disp('Using tilt values')
    lx=Box_dim(1);
    ly=Box_dim(2);
    lz=Box_dim(3);
    %     if size(Box_dim,2)==9
    %         xy=Box_dim(6);
    %         xz=Box_dim(8);
    %         yz=Box_dim(9);
    %     end
    xy=angleparam(1);
    xz=angleparam(2);
    yz=angleparam(3);
    a=lx;
    b=(ly^2+xy^2)^.5;
    c=(lz^2+xz^2+yz^2)^.5;
    alfa=rad2deg(acos((ly*yz+xy*xz)/(b*c)));
    beta=rad2deg(acos(xz/c));
    gamma=rad2deg(acos(xy/b));
    %     lx = a;
    %     ly = (b^2-xy^2)^.5;
    %     lz = (c^2 - xz^2 - yz^2)^0.5;
    %     alfa=rad2deg(acos((ly*yz+xy*xz)/(b*c)))
    %     beta=rad2deg(acos(xz/c));
    %     gamma=rad2deg(acos(xy/b));
end

% Straight from wikipedia
% From fractional coordinates
% FromFrac*ToFrac

% Straight from wikipedia
% From fractional coordinates
% v=a*b*c*(1 - cos(deg2rad(alfa))^2 - cos(deg2rad(beta))^2 - cos(deg2rad(gamma))^2 + 2*cos(deg2rad(alfa))*cos(deg2rad(beta))*cos(deg2rad(gamma)))^.5;
v=(1 - cos(deg2rad(alfa))^2 - cos(deg2rad(beta))^2 - cos(deg2rad(gamma))^2 + 2*cos(deg2rad(alfa))*cos(deg2rad(beta))*cos(deg2rad(gamma)))^.5;

FromFrac=[a b*cos(deg2rad(gamma)) c*cos(deg2rad(beta));...
    0 b*sin(deg2rad(gamma))  c*(cos(deg2rad(alfa))-cos(deg2rad(beta))*cos(deg2rad(gamma)))/sin(deg2rad(gamma));...
    0 0 c*v/sin(deg2rad(gamma))];

% To fractional coordinates
ToFrac=[1/a -cos(deg2rad(gamma))/(a*sin(deg2rad(gamma))) (cos(deg2rad(alfa))*cos(deg2rad(gamma))-cos(deg2rad(beta)))/(a*v*sin(deg2rad(gamma)));...
    0 1/(b*sin(deg2rad(gamma)))  (cos(deg2rad(beta))*cos(deg2rad(gamma))-cos(deg2rad(alfa)))/(b*v*sin(deg2rad(gamma)));...
    0 0 sin(deg2rad(gamma))/(c*v)];

% FromFrac*ToFrac

if size(atom,2)>0

    XYZ_labels=[atom.type]';
    XYZ_data=[[atom.x]' [atom.y]' [atom.z]'];
    XYZ_data_frac=XYZ_data;XYZ_data_tric=XYZ_data;
    for i=1:size(atom,2)
        XYZ_data_frac(i,:)=[XYZ_data(i,1)/lx XYZ_data(i,2)/ly XYZ_data(i,3)/lz]';
        XYZ_data_tric(i,:)=FromFrac*[XYZ_data_frac(i,1) XYZ_data_frac(i,2) XYZ_data_frac(i,3)]';
        atom(i).x=XYZ_data_tric(i,1);
        atom(i).y=XYZ_data_tric(i,2);
        atom(i).z=XYZ_data_tric(i,3);
    end

end

Box_dim=[lx ly lz 0 0 xy 0 xz yz];

Box_dim(Box_dim<0.00001&Box_dim>-0.00001)=0;
if sum(Box_dim(4:end))== 0
    Box_dim=Box_dim(1:3);
end

assignin('caller','triclinic_Box_dim',Box_dim);

triclinic_atom.m

Contents

Version

Contact

Examples