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# Ni 100 surface relaxation

## Contents

Relaxation of the first two layers of a Ni (100) surface.

## Input

### 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$\AA$  .
• 1 atom per layer: p(1x1) cell.
• 5 nickel layers.
• First two layers (of one side) relaxed.
• $3\times 3.53=10.59\AA$  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

• Equally spaced mesh.
• Odd mesh, centered on $\Gamma$  .
• 15 k points in irreducible Brillouin zone (IBZ).
• Only one k point in z-direction for surface.

## Calculation

• 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 $E^{{{\mathrm {rel}}}}=-15$  meV. Use p4vasp to check the convergence:
• The surface energy of 0.86 eV for the unrelaxed surface is calculated in the following:

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

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

$\sigma =\sigma ^{{{\mathrm {unrel}}}}+E^{{{\mathrm {rel}}}}=0.84$  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:
• $\Delta d_{{12}}$  = ((0.3979-0.3018)-0.1)/0.1*100=-3.9%.
• $\Delta d_{{12}}$  = ((0.3018-0.2000)-0.1)/0.1*100=+1.8%.
• Use p4vasp to visualize the relaxation: