How to do a Surface Relaxation of Ni (100)

We take the example  of the surface of Nickel (100)

 

POSCAR

fcc (100) surface
 3.53
   .50000   .50000   .00000
  -.50000   .50000   .00000
   .00000   .00000  5.00000
  5
Selective Dynamics
Kartesisch
   .00000   .00000   .00000 F F F
   .00000   .50000   .50000 F F F
   .00000   .00000  1.00000 F F F
   .00000   .50000  1.50000 T T T
   .00000   .00000  2.00000 T T T
 

• Ni lattice constant of 3.53${\displaystyle \mathrm {\AA} }$.
• 1 atom per layer: p(1x1) cell.
• 5 nickel layers.
• First two layers (of one side) relaxed.
• ${\displaystyle 3\times 3.53=10.59\mathrm {\AA} }$ vacuum.

 

INCAR

   ISTART = 0; ICHARG = 2

 general:
   SYSTEM = clean Ni(100) surface
   ENCUT  = 270 
   ISMEAR =    2  ; SIGMA = 0.2
   ALGO= Fast
   EDIFF = 1E-6

 spin:
   ISPIN=2
   MAGMOM = 5*1

 dynamic:
   NSW   = 100
   POTIM = 0.8
   IBRION = 1

• Initial charge-density in startjob from overlapping atoms.
• Default energy cut-off of 270 eV.
• MP-smearing (metal).
• Spin-polarized calculation with initial moment of 1.
• Ionic relaxation used.

 

KPOINTS

K-Points
0
Monkhorst-Pack
9 9 1
0 0 0

 POTCAR

Download the pseudopotential file from this link Ni100clean_rel.tgz

Calculation

/Ni-sur_rel> vasp_std

 

• The sample output for the forces in the OUTCAR file should look like this (first and last step):

First step:

POSITION                                       TOTAL-FORCE  (eV/Angst)
-----------------------------------------------------------------------------------
     0.00000      0.00000      0.00000         0.000000      0.000000      0.391352
     0.00000      1.76500      1.76500         0.000000      0.000000     -0.397024
     0.00000      0.00000      3.53000         0.000000      0.000000      0.005117
     0.00000      1.76500      5.29500         0.000000      0.000000      0.391161
     0.00000      0.00000      7.06000         0.000000      0.000000     -0.390607
-----------------------------------------------------------------------------------
   total drift:                                0.000000      0.000000      0.016391

Last step:

POSITION                                       TOTAL-FORCE  (eV/Angst)
-----------------------------------------------------------------------------------
     0.00000      0.00000      0.00000         0.000000      0.000000      0.399012
     0.00000      1.76500      1.76500         0.000000      0.000000     -0.377003
     0.00000      0.00000      3.53000         0.000000      0.000000      0.105799
     0.00000      1.76500      5.32685         0.000000      0.000000     -0.062054
     0.00000      0.00000      7.02377         0.000000      0.000000     -0.065753
-----------------------------------------------------------------------------------
   total drift:                                0.000000      0.000000     -0.042925

• Energy changes during relaxation from -25.556 to -25.571 eV which gives a relaxation energy of ${\displaystyle E^{\mathrm {rel} }=-15}$ meV. Use p4vasp to check the convergence:

• The surface energy of 0.86 eV for the unrelaxed surface is calculated in the following:

${\displaystyle \sigma ^{\mathrm {unrel} }={\frac {1}{2}}(E_{\mathrm {surf} }-N_{\mathrm {atoms} }\cdot E_{\mathrm {bulk} })={\frac {1}{2}}(-25.556-5\cdot (-5.457))=0.86}$ eV.

• The surface energy of 0.84 eV for the relaxed surface is then calculated as:

${\displaystyle \sigma =\sigma ^{\mathrm {unrel} }+E^{\mathrm {rel} }=0.84}$ eV.

• The final geometry (from the CONTCAR or OUTCAR file) should look as follows:

fcc (100) surface
   3.53000000000000
     0.5000000000000000      0.5000000000000000      0.000000000000000
    -0.5000000000000000      0.5000000000000000      0.000000000000000
     0.0000000000000000      0.0000000000000000      5.000000000000000
   Ni
     5
Selective Dynamics
Direct
0.0000000000000000   0.0000000000000000   0.0000000000000000 F F F
0.0000000000000000   0.5000000000000000   0.1000000000000014 F F F
0.0000000000000000   0.0000000000000000   0.2000000000000028 F F F
0.5000000000000000   0.5000000000000000   0.3018043743226639 T T T
0.0000000000000000   0.0000000000000000   0.3979474020596729 T T T 

• Inward relaxation of surface layers:
  • ${\displaystyle \Delta d_{12}}$ = ((0.3979-0.3018)-0.1)/0.1*100=-3.9%.
  • ${\displaystyle \Delta d_{12}}$ = ((0.3018-0.2000)-0.1)/0.1*100=+1.8%.

• Use p4vasp to visualize the relaxation: