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Starting from the rhombohedral bulk calcite unit cell, we shall build its surface specified via Miller indices (104) corresponding to the hexagonal cell.  In this specific example we generate a 3x2 surface cell with 3 bulk layers.

1. Start tetr  and read the POSCAR file of the calcite bulk prepared in the previous tutorial.

2. Go to the MAIN MENU with the M command and then type Sr that will open a new menu.

3. You have two options for creating the surface. The one we are going to show you is Method 1 where you need to specify the Miller indices. In Method 2 you specify the normal vector to the plane instead (if known).

4a. At this point we need to generate the hexagonal cell (which is the same as the crystallographic cell of this system) since the Miller indices are known for this setting. This is done using the Su command. The vectors          of the rhombohedral sell are given as a linear combination of the initial vectors

5a. What is to be done next is to choose a new set of primitive lattice vectors which would give the first two vectors lying within the required plane, but would keep the same unit cell volume (so this is still a primitive bulk cell).  Mi command lets you to introduce the Miller indices. Thus type 1 0 4

5b. The required normal to the plane is obtained.

with the matrix U being:

It is easy to see that with this matrix the new vectors do indeed correspond to the hexagonal lattice: the 3rd vector is along the Z axis, and the 1st and the 2nd lie in the X-Y plane making an angle of 120 degrees with each other.

4b. Using Su, then 0 1 -1,  -1  0 -1  followed by 1 1 1 to specify the whole matrix, we get the required new vectors. Note that the new vectors correspond to the 3-fold extension of the cell (the determinant of the matrix U). This is not important as this step is only needed to find the direction corresponding to the Miller indices. The whole construction will be done using the primitive cell we started from.