ABINIT Discussion Forums

I'm trying to perform a calculation of Si surface energy and I got the following questions:
1.How to I build a unit cell with a couple of layers of Si and vacuum (including dependence on crystallographic directions 100 or 111)? In tutorial 4 there is a solved problem for Al in 100 direction, but how do they find coordinates for atoms in a unit cell? And what if i want to add one more layer or change a direction for 111?
2. Another question is how to calculate surface energy or energy per atom or per unit cell out of a total energy given by an ABINIT output?
Say, there is following data, again from Tutorial 4: etotal -6.2622251351E+00 in Hartree
surface energy per unit cell 0.015885 Ha = 0.432eV
How do they devide it??

Well, it seems I have to reformulate a question:
The solved problem for Al (Tutorial 4) is as following. If we want to consider bulk Al we build unit cell with one atom in it:
xred 0.0 0.0 0.0
This is crystal clear.
But if we consider a surface (1 0 0) with two layers of atoms and vacuum above them we need to add two more atoms into the unit cell
xred 0.0 0.0 0.0
0.0 0.0 0.5
0.5 0.5 0.25

and this is not obvious for me how to choose these coordinates. CAN ANYONE HELP PLEASE???

Now, I want to repeat these calculations (surface) for Si.
Again if we consider bulk Si it sufficient to use 2 atoms per unit cell
xred 0.0 0.0 0.0
1/4 1/4 1/4
So far so good.
But, How the unit cell will look like if I want to consider a couple of layers of Silicon? (say 2 for instance in the most simple 100 direction)

I would really appreciate any contribution!

Dear deepdrew,

So the idea is that Abinit will replicate your primitive cell in the 3 directions. If you want to simulate a slab you can do for exemple:

3 layers of Si then 3 layers of vacuum then by replication it will again be three layer of Si etc..

To simulate a real slab you do not want the different layers of Si to interact so you want enough vacuum between them.

For example you could put something like
acell 6 6 60 Bohr (random number here but you get the idea.

You can see that the dimension in the z direction is 10x larger. It mean you can put 10 layers. If you want to work in reduce coordinate you will have to put
something like
xred 0 0 0
0 0 0.1
0 0 0.2

This mean that you will have 3 atoms space in the z direction by 0.1*60 = 6 Bohr. The fact that you put nothing for the 7 other layers means that it will be vacuum.

You off course have to put xred numbers in agreement with your rprim variables.

For you second question I guess it would look
xred 0 0 0
1/4 1/4 1/8

This will put a vacuum layer in between.

Cheers!

Samuel

Dear Samuel,
Thank you so much for your input and your answer!
It really helps to grab the idea more clearly!

I guess this becomes a bit more tricky if we change a direction on (111)? Just curious.

And ones again,
What is the formula that allows for devision of total energy from ABINIT output to obtain surface energy?

example from Tutorial 4: etotal -6.2622251351E+00 in Hartree
surface energy per unit cell 0.015885 Ha = 0.432eV

Thank you!

Andrii

The surface energy is simply the difference of energy between the bulk and the surface calculation.

For exemple:

If I get a total energy of -20 Ha for the primitive bulk cases (1 atom per unit cell for exemple) and a total energy
of -58 Ha for three layers of Si and 7 layers of vacuum it means that the surface energy will be 2 Ha (20 Ha times 3 = 60 Ha minus 58 Ha = 2Ha).

Usually the total energy of the system with the vacuum will be higher in energy (thus less stable) than the bulk system.

Cheers!

Samuel

Thank you very much for your help, Samuel.
Sorry that it took me too long to response.