Plotting a 2D crystal lattice from two primitive lattice vectors

I am trying generate a plot of a crystal lattice based on two prmitive lattice vectors:

v1= -0.5i + -sqrt(3)/2j

v2= 1i

where i and j are orhtogonal unit vecotors to represent the x and y directions.

I am not sure where to begin.

[darova]

That is what you want?

[Jennifer Garrison]

It only needs to be 2D but yes. I basically need to define my own coordinate system that is not the standard cartesian one with those vectors and display the lattice points like you did.

Answer 1

[John D'Errico]

First, you need to understand that MATLAB does not understand what you intend by this notation:

v1= -0.5i + -sqrt(3)/2j

Both i and j are sqrt(-1) in MATLAB. They are not distinct. Instead, just write them as vectors:

v1= [-0.5, -sqrt(3)/2];
v2= [1 , 0];

[x,y] = meshgrid(0:10,0:5);
xy = [x(:),y(:)];
T = [v1;v2];

xyt = xy*T;
xt = reshape(xyt(:,1),size(x));
yt = reshape(xyt(:,2),size(y));

plot(xt,yt,'ro-')
hold on
plot(xt',yt','r-')
axis equal
axis square

[Nayem Mohammed Reza Shah]

Hello,

I was trying to plot a 3D crystal lattice with vectors like following:

v1 = 0.5i + 0j + 0.5k;

v2 = 0i + 0.5j + 0.5k;

v3 = 0.5i + 0.5j + 0 k;

Can anyone please give some idea?

Thanks

[Bjorn Gustavsson]

Simply extend John's or my suggestion to 3-D. You can call meshgrid (or ndgrid) with 3 inputs and 3 outputs:

[i1,j2,k3] = meshgrid(0:3,0:4,0:2);

Then define your 3 lattice-vectors, and use plot3 to plot the grid.

[savitha muthanna]

@John D'Errico Would you know the primitive lattice vectors to generate a hex lattice with triangular(equilateral) cells?

Answer 2

[Bjorn Gustavsson]

If you do it stepwise it becomes "not too tricky":

e1 = [-0.5; -sqrt(3)/2]; % Your unit
e2 = [1; 0];              % vectors
[I1,I2] = meshgrid(-10:10,-8:8); % A 2-D set of points
r_crystal = [e1,e2]*[I1(:)';I2(:)']; % calculate r_c = n*e1 + m*e2 for all points
plot(r_crystal(1,:),r_crystal(2,:),'.')

You can dood.e with how big crystal you want or what shape, but this should give you something.

HTH

[Jennifer Garrison]

Thank you so much that's exactly what I needed!

Answer 3

[Yarlapati Akshay]

r_1st=2

N_1st=