# Bulk energy per atom

Hello Dear lammps users

I want to define bulk free energy per atom for the icosahedral copper cluster.

the code i used is as follow:

clear

units metal

dimension 3

boundary p p p

atom_style atomic

atom_modify map array

create atom

lattice fcc 3.61

mass 1 63.546

#define interatomic potential

pair_style eam

pair_coeff * * cu_u3.eam

neighbor 2 bin

neigh_modify delay 10 check yes

#compute

compute eng all pe/atom

compute eatoms all reduce sum c_eng

# run minimization

reset_timestep 0

fix 1 all box/relax iso 0.0 vmax 0.1

thermo 10

thermo_style custom step pe lx ly lz press pxx pyy pzz c_eatoms

min_style cg

minimize 0 0 500000 1000000

dump 1 all xyz 100 bulk.xyz

variable natoms equal “count(all)”

variable teng equal “c_eatoms”

variable length equal “lx”

variable ecoh equal “v_teng/v_natoms”

print “Total energy (eV) = \${teng};”

print “Number of atoms = \${natoms};”

print “Lattice constant (Angstoms) = \${length};”

print “Cohesive energy (eV) = \${ecoh};”

the problem is for different number of atoms in cluster,this code gives me different bulk energy per atom.

but i think it should be the same for different size of cluster.

what is the problem?

data.00309_ico (9.78 KB)

Hello Dear lammps users

I want to define bulk free energy per atom for the icosahedral copper
cluster.

[...]

the problem is for different number of atoms in cluster,this code gives me
different bulk energy per atom.

but i think it should be the same for different size of cluster.

what is the problem?

the problem is in your thinking. you are not computing the "bulk
energy"; you are computing the "total energy", i.e. you sum over atoms
at the surface as well as atoms below the surface and atoms deep
inside the cluster. only those buried deep inside will be "bulk-like",
and only if the cluster is large enough so that its environment deep
inside is, in fact, bulk-like. atoms close to the surface have
different interaction strength.

axel.

Dear Axel

I am calculating surface energy of this cluster with this formula:

where Ep-cluster is the potential energy of the cluster, Ep-bulk is

the potential energy of a bulk system containing the same

number of atoms, and A -cluster is the total cluster surface area.

you mean i calculated E-bulk in a wrong way?
so what should i do?

Hello Dear lammps users

I want to define bulk free energy per atom for the icosahedral copper
cluster.

[…]

the problem is for different number of atoms in cluster,this code gives me
different bulk energy per atom.

but i think it should be the same for different size of cluster.

what is the problem?

the problem is in your thinking. you are not computing the “bulk
energy”; you are computing the “total energy”, i.e. you sum over atoms
at the surface as well as atoms below the surface and atoms deep
inside the cluster. only those buried deep inside will be “bulk-like”,
and only if the cluster is large enough so that its environment deep
inside is, in fact, bulk-like. atoms close to the surface have
different interaction strength.

axel.

Dear Axel

I am calculating surface energy of this cluster with this formula:

[image: Inline image]

where Ep-cluster is the potential energy of the cluster, Ep-bulk is
the potential energy of a bulk system containing the same
number of atoms, and A -cluster is the total cluster surface area.

you mean i calculated E-bulk in a wrong way?

yes.

so what should i do?

do it correctly, i.e. do exactly as the formula you are quoting says.

axel.

while it is easy to compute the (potential) energy per atom of a bulk system and thus get your E_P,bulk and also to compute the (potential) energy of your cluster, there is the open question, how you compute the surface area? the formula you quote is easy to apply for slab geometries, but to triangulate the surface of a cluster, you need to make assumptions on the “size” of an atom, which is ill-defined.

i am also wondering how this all relates to the script you were quoting.

axel.

Dear axel

I used the q-hull software to calculate surface area for different size of cluster with different number of atoms to define size dependent surface energy.

http://www.qhull.org/

this surface area can be used directly in the formula.

After defining surface energy i can have a curve for surface energy vs number of atoms and see the results.

Best regards

Malihe Razavi

while it is easy to compute the (potential) energy per atom of a bulk system and thus get your E_P,bulk and also to compute the (potential) energy of your cluster, there is the open question, how you compute the surface area? the formula you quote is easy to apply for slab geometries, but to triangulate the surface of a cluster, you need to make assumptions on the “size” of an atom, which is ill-defined.

i am also wondering how this all relates to the script you were quoting.

axel.

Dear axel

I used the q-hull software to calculate surface area for different size of
cluster with different number of atoms to define size dependent surface
energy.

this surface area can be used directly in the formula.

but ​that doesn't make the cluster surface a well defined entity. you just
are using whatever heuristics are employed in this software.​ if i remember
correctly, the qhull code simply takes the positions of atoms without
considering their radii, which means that you will underestimate the
surface and systematically more so, the smaller the clusters are. and like
i mentioned before, this radius is not well defined.

axel.

Dear axel

Your advice was quite to the point ,that the code i wrote in my previous email doesn’t calculate bulk energy

because of the energy of atom on the surface.but i used periodic boundary condition.

when we use this boundary condition it gives us bulk property without considering the atoms on the surface.

I will be grateful if you help for this problem.

Thank you very much indeed

Malihe Razavi

Dear axel

I used the q-hull software to calculate surface area for different size of cluster with different number of atoms to define size dependent surface energy.

http://www.qhull.org/

this surface area can be used directly in the formula.

but ​that doesn’t make the cluster surface a well defined entity. you just are using whatever heuristics are employed in this software.​ if i remember correctly, the qhull code simply takes the positions of atoms without considering their radii, which means that you will underestimate the surface and systematically more so, the smaller the clusters are. and like i mentioned before, this radius is not well defined.

axel.

Dear axel

Your advice was quite to the point ,that the code i wrote in my previous
email doesn't calculate bulk energy
because of the energy of atom on the surface.but i used periodic boundary
condition.

​what has one to do with the other?​

when we use this boundary condition it gives us bulk property without
considering the atoms on the surface.

I will be grateful if you help for this problem.

​​i don't understand what you are asking for here. post a specific
(working) input deck and ask a specific question, and somebody might be