Verifying lattice constant-Nickel

Lattice constant for Nickel is 3.52 angstrom. But how do we know it is correct? There is a computational technique using which we can verify the lattice constant values. Let's see how.

Generally, every atom, molecule, crystal whatever it is, tend to have the lowest potential energy state, possible for that. That's nature. This potential energy of atoms depends directly on the lattice constant corresponding to its crystal structure. So the crystal will have lattice constant which corresponds to the lowest potential energy. Here I am going to calculate the potential energy of nickel for various lattice constants. 

Input script

units           metal
atom_style      atomic
boundary        p p p
variable a index 3.22 3.24 3.26 3.28 3.30 3.32 3.34 3.36 3.38 3.40 3.42 3.44 3.46 3.48 3.50 3.52 &
                           3.54 3.56 3.58 3.60 3.62 3.64 &
                           3.66 3.68 3.70 3.72 3.74 3.76 3.78 3.80 3.82
lattice fcc ${a}
region          myreg block     0 10 0 10 0 10
create_box      1 myreg
create_atoms 1 region myreg
# Minimize  using Embedded atom method potential for Ni
pair_style      eam
pair_coeff * * Ni_u3.eam
minimize 1e-25 1e-25 100000 100000
variable latice_constant equal ${a}
thermo_style custom v_latice_constant pe
thermo 1
run 1
next a
#Go to the next variable a
clear
#Deletes all atoms and restores to default values
#Does not affect input script variables
jump Ni.in #I saved the file in the name Ni.in

#Closes the current file and opens another file. In this case, the name of this file is given so that it recalculates for a  different value of a
#end
#-------------------------------------------------------------------------------------------------------------------------
Visit LAMMPS Manual for a detailed explanation of commands used.

Results

Lattice constant      Potential energy 3.22 -15673.542 3.24 -15982.398 3.26 -16262.146 3.28 -16514.139 3.3 -16739.678 3.32 -16940.016 3.34 -17116.354 3.36 -17269.849 3.38 -17401.612 3.4 -17512.717 3.42 -17604.167 3.44 -17676.97 3.46 -17732.065 3.48 -17770.359 3.5 -17792.725 3.52 -17800 3.54 -17792.987 3.56 -17772.458 3.58 -17739.151 3.6 -17693.776 3.62 -17637.013 3.64 -17569.514 3.66 -17491.905 3.68 -17404.784 3.7 -17308.726 3.72 -17204.28 3.74 -17091.973 3.76 -16972.309 3.78 -16845.771 3.8 -16712.82 3.82 -16573.899

(These values are stored in the log file generated)

Explanation

1. I have calculated potential energy for various lattice constant values around the value 3.52.

2. If you observe the value 3.52 angstrom corresponds the lowest potential energy value, so we take that value as lattice constant for Nickel. Thus we verified the lattice constant value of Nickel. 

3. This method can be used to verify the lattice constant for any given crystal. 

4. This simulation does not generate any dump file since I haven't given dump command. You can try generating dump file yourself and you can tell me what you have observed in the visualisation, in the comment section!  

If you have any doubts, mention them in the comment section. Do visit the blog for further updates!