How to rotate the unit cell in crystal?

Hi,

I have a structure (attached in the question, it is in xyz file), i wnanto to rote it the crystal. Here is my code for rotae

% around the z axis [0 0 1]
x = x1*cosd(ang) - y1*sind(ang);
y = x1*sind(ang) + y1*cosd(ang);
z = z1 ;

What want to make the rotate in 1 1 0 or 0 1 1 or 1 1 1, I know already how to 1 0 0 or 0 1 0

Answer 1

[Alex Hanes]

You can use quaternions to rotate about an arbitrary axis in 3-dimensions. The quatrotate is capable of performing a rotation of all of your atoms in the unit cell by a quaternion (you will have to specify the quaternion using the x, y, z coordinate of the vector to perform the rotation about and the angle to rotate by). If you want to rotate about an axis K = (kx, ky, kz) by angle theta, then your quaternion for "quatrotate" is:

clear; clc; 

% Rotate about the (1,4,3) axis by theta = 60 deg:
theta = pi/3;       % (rad), angle to rotate by
K = [1, 4, 3];      % [kx,ky,kz], axis to rotate about
k = K./vecnorm(K);  % unit vector
r = [1, 1, 1];      % vector to rotate

% Define Quaternion:
    q = [cos(theta/2), sin(theta/2).*k]; 
    vOut = quatRotate(q,r); % call quatRotate()

% Example from quatrotate() page:
    q = [1 0 1 0];
    r = [1 1 1];
vOut = quatRotate(q,r); 

% Use Home-Written quatRotate following quatrotate documentation:
% (https://www.mathworks.com/help/aerotbx/ug/quatrotate.html)

function vOut = quatRotate(q,vIn)

q = q./vecnorm(q); % ensure quaternion is unit vector
q0 = q(1); q1 = q(2); q2 = q(3); q3 = q(4); % sort quaternion components

Q = [ (1 - 2*q2^2  - 2*q3^2),  (    2*q1*q2 + 2*q0*q3), (    2*q1*q3 - 2*q0*q2); ...
     (     2*q1*q2 - 2*q0*q3), (1 - 2*q1^2  - 2*q3^2),  (    2*q2*q3 + 2*q0*q1); ... 
     (     2*q1*q3 - 2*q0*q2), (    2*q2*q3 - 2*q0*q1), (1 - 2*q1^2 - 2*q2^2) ]; 

vOut = Q*vIn'; 

end

You could also use Euler angles, but the quaternion method is compact and numerically more stable.

EDIT: I wrote a simple script that uses "quatRotate" if you don't have the Aerospace Toolbox. You can modify this to take array inputs for "vIn" as necessary.

[Sara]

Thank you for your comment,

I want able to connect my coordnates x y z in my input fille.

I did change the folwoing

r = [1, 1, 1]; 
to
r = [x, y, z]; % as my coordinates

Alos chnage to the degree instead of rad,in sin and cos.