## How to Calculate Surface Formation Energy for Aluminum

### Surface Formation Energy Calculation

The necessary tools to perform the surface formation energy is shown in this page.

For further information see here.

Figure 1. (111) surface of fcc Al system along Z direction. The transverse directions are: X: [-1 -1 2] the longer one; and the Y: [1 -1 0], shorter one.

In order to create a surface, one needs to extend the simulation box along that particular direction. Please be reminded that the (hkl) surface has the [hkl] direction. Hence, if you extend the simulation box along the [hkl] direction and then remove a few layers of atoms or extend the simulation box length to 10 angstroms along the [hkl] direction to make an (hkl) surface. In order to generate a (110) surface, one might need to develop an orthogonal simulation box along the directions of X: [110], Y: [-110], and Z: [002]; and then extend the simulation box three dimensionally. Since the extension along the direction of the concerned surface (110) direction is crucially important,the middle of the simulation cell of atoms should behave a bulk-like structure. Due to the periodic boundary condition along the transverse directions (Y and Z in this case)of the simulation box, atoms behave like a substrate.

#### KPOINTS

```MK11x11x2	#header file
0
Monkhorst	#Style of Kpoints
3  5  1	#Numbers
0  0  0
```

#### POSCAR file for (111) surface having 10 Angstrom vacuum containing 104 atoms

```Al_FCC
1.00000000
7.3485      0.00000000      0.00000000
0.00000000   4.24264        0.00000000
0.00000000   0.00000000     30.7846000
104
CARTESIAN
0            2.1213203                    0
1.8371173            3.1819805                    0
1.8371173            1.0606602                    0
0.61237244            3.1819805            1.7320508
0                    0                    0
0.61237244            1.0606602            1.7320508
3.6742346                    0                    0
3.6742346            2.1213203                    0
2.4494897            2.1213203            1.7320508
2.4494897                    0            1.7320508
5.5113519            3.1819805                    0
5.5113519            1.0606602                    0
4.286607            3.1819805            1.7320508
4.286607            1.0606602            1.7320508
7.3484692            2.1213203                    0
7.3484692                    0                    0
6.1237244                    0            1.7320508
6.1237244            2.1213203            1.7320508
3.0618622            3.1819805            3.4641016
1.2247449                    0            3.4641016
3.0618622            1.0606602            3.4641016
1.2247449            2.1213203            3.4641016
0            2.1213203              5.19615
1.8371173            3.1819805              5.19615
1.8371173            1.0606602              5.19615
0                    0              5.19615
3.6742346                    0              5.19615
3.6742346            2.1213203              5.19615
4.8989795            2.1213203            3.4641016
6.7360968            3.1819805            3.4641016
6.7360968            1.0606602            3.4641016
4.8989795                    0            3.4641016
5.5113519            3.1819805              5.19615
5.5113519            1.0606602              5.19615
7.3484692            2.1213203              5.19615
7.3484692                    0              5.19615
0.61237244            3.1819805            6.9282008
0.61237244            1.0606602            6.9282008
2.4494897            2.1213203            6.9282008
3.0618622            3.1819805            8.6602516
2.4494897                    0            6.9282008
1.2247449                    0            8.6602516
3.0618622            1.0606602            8.6602516
1.2247449            2.1213203            8.6602516
4.286607            3.1819805            6.9282008
4.286607            1.0606602            6.9282008
6.1237244                    0            6.9282008
6.1237244            2.1213203            6.9282008
4.8989795            2.1213203            8.6602516
6.7360968            3.1819805            8.6602516
6.7360968            1.0606602            8.6602516
4.8989795                    0            8.6602516
0            2.1213203              10.3923
1.8371173            3.1819805              10.3923
1.8371173            1.0606602              10.3923
0.61237244            3.1819805            12.124351
0                    0              10.3923
0.61237244            1.0606602            12.124351
3.6742346                    0              10.3923
3.6742346            2.1213203              10.3923
2.4494897            2.1213203            12.124351
2.4494897                    0            12.124351
5.5113519            3.1819805              10.3923
5.5113519            1.0606602              10.3923
4.286607            3.1819805            12.124351
4.286607            1.0606602            12.124351
7.3484692            2.1213203              10.3923
7.3484692                    0              10.3923
6.1237244                    0            12.124351
6.1237244            2.1213203            12.124351
3.0618622            3.1819805            13.856402
1.2247449                    0            13.856402
3.0618622            1.0606602            13.856402
1.2247449            2.1213203            13.856402
0            2.1213203             15.58845
1.8371173            3.1819805             15.58845
1.8371173            1.0606602             15.58845
0                    0             15.58845
3.6742346                    0             15.58845
3.6742346            2.1213203             15.58845
4.8989795            2.1213203            13.856402
6.7360968            3.1819805            13.856402
6.7360968            1.0606602            13.856402
4.8989795                    0            13.856402
5.5113519            3.1819805             15.58845
5.5113519            1.0606602             15.58845
7.3484692            2.1213203             15.58845
7.3484692                    0             15.58845
0.61237244            3.1819805            17.320501
0.61237244            1.0606602            17.320501
2.4494897            2.1213203            17.320501
3.0618622            3.1819805            19.052552
2.4494897                    0            17.320501
1.2247449                    0            19.052552
3.0618622            1.0606602            19.052552
1.2247449            2.1213203            19.052552
4.286607            3.1819805            17.320501
4.286607            1.0606602            17.320501
6.1237244                    0            17.320501
6.1237244            2.1213203            17.320501
4.8989795            2.1213203            19.052552
6.7360968            3.1819805            19.052552
6.7360968            1.0606602            19.052552
4.8989795                    0            19.052552
```