Rajasekarakumar Vadapoo

S.NO: 401-03-9023

Electronic Structure Theory: HW# 4

Calculate the electronic structure of bulk-Nickel using VASP

AIM:

1. To find the equilibrium crystal structure of bulk-Nickel (Ni) by optimizing the lattice

constant

2. To find the ground state magnetization per atom of Ni in bulk.

3. To find the spin polarized density of states (DOS) of bulk Ni.

4. To find the spin polarized band structure (BS) of bulk Ni between few high-symmetry

points.

INTRODUCTION:

In this calculation we have used VASP code to calculate the electronic structure of Bulk

Nickel. Nickel exibit the face centered cubic structure with the space group Fm-3m (Number: 225). The spin polarized electronic structure calculations have been carried out. The calculation parameters and the results would be discussed.

CALCULATIONS:

Here we would find the INPUT files used for the calculations and the appropriate reasons for

that.

� GROUND STATE CALCULATION

KPOINT:

We have used the KPOINT of automatic mesh with Gamma centered grid consists of 4x4x4 kpts with the shift 0x0x0.

POSCAR:

We have used the following POSCAR as a initial position for the ground state calculations, which correspond to the Ni with initial lattice parameter 3.52 Å and the atoms positioned as shown below:

-------------

University of Puerto Rico, PR-00931, USA.

Course by: Prof. Julian Velev

Ni

3.52

0 0.5 0.5

0.5 0 0.5

0.5 0.5 0

1

direct

0 0 0

~

POTCAR:

We have used POTCAR of PAW with PBE for this calculations.

INCAR:

We have used the following INCAR for the ground state calculations. Since, nickel is an metal we can use the tag of ISMEAR with 1 and 2 and with appropriate sigma value which would give the entropy term less than 1 meV per atom. To find the appropriate sigma value and the ISMEAR value we have taken series of calculations and the results have been tabulated in Table 1. During this calculations we have used ISIF=7 since its an FCC structure we have changed only volume thus lattice parameter to find the ground state. The symmetry is switched off using ISYM = 0. The INCAR file of the calculation with ISMEAR=1 and default SIGMA ( which is 0.2) is shown below:

----

System = Ni

ISMEAR =1

ISYM = 0

LPLANE=.FALSE.

NPAR=4 number of nodes to use

LSCALU=.FALSE. do you have SCALAPACK

NSIM=1 nodes grouping for efficiency

NSW = 400 number of steps for IOM

IBRION = 2 ionic relax: 0-MD 1-quasi-New 2-CG

ISIF = 7 stress and relaxation

IWAVPR = 11 prediction: 0-non 1-charg 2-wave 3-comb

ISPIN= 2

~

Appropriate ISMEAR tag SIGMA tag values have been used for the calculations.

Table.1. Calculations carried out with different INPUT tags to find out the appropriate sigma value for the ground state calculation.

� Density of States (DOS)

For the density of state calculations we have used the CONTCAR of the ground state calculations as a POSCAR. We have taken here the ISMEAR =1 with SIGMA= 0.05 which gave the entropy of 1 meV per atom as shown in Table.1. We have modified the value of NSW tag as 0, IBRION as -1 for the DOS calculations. The calculated DOS details found in DOSCAR file.

� Band Structure (BS) Calculations

For the bandstructure calculations we have used the high symmetry lines Gamma, X, L and W. as the corresponding data taken for the space group: Fm-3m (Number: 225). The table 2. Shows the symmetry pt and the corresponding ITA positions. Fig.1. shows the brillouin zone with the high symmetry lines for Nickel (corresponding space group). Courtesy to: http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-kv-list?gnum=225&fig=fm3qmf . Since the positions of other symmetry points are not readily available they haven’t taken for BS calculations. The calculated eigen value details found to be in the file EIGENVAL.

parameters ISMEAR= 1 ISMEAR= 2

SIGMA = 0.2

SIGMA = 0.1

SIGMA = 0.05

SIGMA = 0.2

SIGMA = 0.1

SIGMA = 0.05

Energy (eV) -5.642702 -5.640543 -5.640633 -5.641329 -5.640318 -5.640872

Pressure without entropy(kB)

3.67 11.81 13.43 -9.14 9.12 11.26

Entropy (eV/atom)

- 0.0054624 -0.00133019 0.00013927 -0.0072128 -0.0028997 0.00084013

Fig.1. Brillouin zone with the corresponding high symmetry lines for Nickel.

Table. 2. High symmetry points with corresponding ITA positions for Nickel.

KPOINT:

----------

k-points along high symmetry lines

10 ! 10 intersections

Line-mode

rec

0 0 0 ! gamma

0 0.5 0 ! X

0 0.5 0 ! X

0.25 0.25 0.25 ! L

0.25 0.25 0.25 ! L

0.25 0.5 0 ! W

~

RESULTS & DISCUSSION:

� Ground state lattice parameter

Here is the ground state lattice parameter details found in CONTCAR file with our calculations details as given in our calculations section.

---------

Ni

3.520000000000000

0.0000000000000000 0.4940882755357110 0.4940882755357110

0.4940882755357110 0.0000000000000000 0.4940882755357110

0.4940882755357110 0.4940882755357110 0.0000000000000000

1

Direct

0.0000000000000000 0.0000000000000000 0.0000000000000000

0.00000000E+00 0.00000000E+00 0.00000000E+00

~

The optimized ground state lattice parameter from these details is

a= 2 x 0.4940882755357110 x 3.52 = 3.478 Å.

� Ground state magnetization per atom

The detail of ground state magnetization per atom got from the OSZICAR file of the calculation. We used the calculation parameters as we discussed in the calculation section. The calculation shows that the nickel have the value of 0.5937 Bohr magnetron.

� DOS

The ab-initio calculated Density of state (DOS) of bulk-nickel is shown in fig.2 & 3 with the corresponding ISMEAR value of 1 and -5 during the DOS calculations over the ground state calculations details as discussed in the calculations section. The figs. shows that the corresponding spin up and spin down DOS over energy. Among them fig. 3 with ISMEAR= -5 looks like the more opt one. Fig. 3 shows that there is no gap near the Fermi level @ 0 eV, which clearly shows that nickel is metallic.

-10 0 10 20 30 40 50-4

-3

-2

-1

0

1

2

3

4

D

OS

( n

o. o

f sta

tes/

unit

cell)

Energy (eV)

spin up spin down

ISMEAR=1 during DOS calc.

Fig.2. DOS of bulk-nickel with ISMEAR=1 in DOS calculations.

-10 0 10 20 30 40 50-3

-2

-1

0

1

2

3

DO

S (

no.

of s

tate

s/un

it ce

ll)

Energy (eV)

spin up spin down

ISMEAR = -5 during DOS calc.

Fig.3. DOS of bulk-Nickel with ISMEAR=-5 in the DOS calculations.

� Band Structure:

The band structure calculations carried out over the high symmetry lines as explained in the calculations section. Home-made utility being used to get the eigen values as a function of kpts from the output file EIGENVAL of the bandstructure calculations. Since, the interspacing of higher symmetry pts are not equal in this case, we have calculated the corresponding distance of the kpts from the Gamma point as shown in table.3 from the “k-points in reciprocal lattice” details from the OUTCAR of the calculation. The corresponding eigen value is plotted as shown in fig.4.

Kx Ky Kz Res.spa.dist. 0 0 0 0 0.05622 -0.05622 0.05622 0.097376364 0.112441 -0.11244 0.112441 0.194752745 0.168661 -0.16866 0.168661 0.292129109 0.224881 -0.22488 0.224881 0.389505474 0.281101 -0.2811 0.281101 0.486881855 0.337322 -0.33732 0.337322 0.584258219 0.393542 -0.39354 0.393542 0.681634583 0.449762 -0.44976 0.449762 0.779010947 0.505982 -0.50598 0.505982 0.876387328 0.505982 -0.50598 0.505982 0.876387328 0.477872 -0.42165 0.477872 0.969618107

0.449762 -0.33732 0.449762 1.062848885 0.421652 -0.25299 0.421652 1.156079657 0.393542 -0.16866 0.393542 1.249310435 0.365432 -0.08433 0.365432 1.342541207 0.337322 0 0.337322 1.435771985 0.309212 0.08433 0.309212 1.529002763 0.281101 0.168661 0.281101 1.622233535 0.252991 0.252991 0.252991 1.715464314 0.252991 0.252991 0.252991 1.715464314 0.252991 0.196771 0.309212 1.794971782 0.252991 0.140551 0.365432 1.874479264 0.252991 0.08433 0.421652 1.953986733 0.252991 0.02811 0.477872 2.033494201 0.252991 -0.02811 0.534093 2.113001676 0.252991 -0.08433 0.590313 2.192509152 0.252991 -0.14055 0.646533 2.27201662 0.252991 -0.19677 0.702753 2.351524095 0.252991 -0.25299 0.758974 2.431031571

Table.3. Kpt positions used for the band structure calculations and the corresponding reciprocal distance from the pt. Gamma. ( calculated from VASP output of the BS calculations).

-10

-5

0

5

10

15

20

25

30

35

40 SPINUP SPINDN

Ene

rgy

in e

V

G X L W

Fig.4. Spin polarized bandstructure of bulk-Ni along the high symmetry lines.

Fig.4. shows the spin polarized electronic bandstructure of bulk-Nickel. The Ef is @ 0 eV. The bandstructure clearly shows that the bands are available around the Fermi energy (Ef ) which indicate that Nickel is an metal. Close look at the bandstructure shows that there is no bands in the region of 2.248 eV- 6.213 eV, which is contrary to the DOS calculate with ISMEAR= -5 as shown in fig. 3 in our calculations. In the case of DOS calculated with ISMEAR= 1, we could find there is no DOS from 2.571 eV- 5.8373 eV regions. These contradiction of DOS & empty bands in the different energy position might be due to the lack of incorporating some other highsymmetry kpts like M, U & K in our band structure calculations which might significantly contribute to the DOS in that energy windows.

CONCLUSIONS:

We have carried out the ab-initio calculations to explore the electronic structure of bulk nickel using VASP- code. And thus found out the equilibrium lattice parameter to be 3.478 Å with the magnetic property having 0.5937 Bohr magnetron. We also found that nickel is an metal from the corresponding DOS and the electronic bandstructure.