Ni 100 surface relaxation

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Task

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 $\mathrm{\Gamma }$.
• 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 $E^{\mathrm{r}\mathrm{e}\mathrm{l}}=-15$ meV. Use p4vasp to check the convergence:

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

${\sigma }^{\mathrm{u}\mathrm{n}\mathrm{r}\mathrm{e}\mathrm{l}}=\frac{1}{2}(E_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}-N_{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}}\cdot E_{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}})=\frac{1}{2}(-25.556-5\cdot (-5.457))=0.86$ eV.

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

$\sigma ={\sigma }^{\mathrm{u}\mathrm{n}\mathrm{r}\mathrm{e}\mathrm{l}}+E^{\mathrm{r}\mathrm{e}\mathrm{l}}=0.84$ 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:
  • $\mathrm{\Delta }{d}_{12}$ = ((0.3979-0.3018)-0.1)/0.1*100=-3.9%.
  • $\mathrm{\Delta }{d}_{12}$ = ((0.3018-0.2000)-0.1)/0.1*100=+1.8%.

• Use p4vasp to visualize the relaxation:

Download

Ni100clean_rel.tgz

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