научная статья по теме THEORETICAL STUDY OF ELECTRONIC STRUCTURE, CHEMICAL BONDING AND X-RAY ABSORPTION NEAR EDGE SPECTROSCOPY IN NIOBIUM AND NIOBIUM MONOXIDE Физика

Текст научной статьи на тему «THEORETICAL STUDY OF ELECTRONIC STRUCTURE, CHEMICAL BONDING AND X-RAY ABSORPTION NEAR EDGE SPECTROSCOPY IN NIOBIUM AND NIOBIUM MONOXIDE»

ОПТИКА И СПЕКТРОСКОПИЯ, 2013, том 115, № 2, с. 272-279

СПЕКТРОСКОПИЯ ^^^^^^^^^^

КОНДЕНСИРОВАННОГО СОСТОЯНИЯ

УДК 661.888.2

THEORETICAL STUDY OF ELECTRONIC STRUCTURE, CHEMICAL BONDING AND X-RAY ABSORPTION NEAR EDGE SPECTROSCOPY IN NIOBIUM AND NIOBIUM MONOXIDE © 2013 г. Nguyen Ngoc Ha

Department of Chemistry and Center for Computational Science, Hanoi National University of Education, Hanoi, Vietnam

E-mail: hann@hnue.edu.vn Received December 5, 2012

In this work, we calculate band structures, the density of state and chemical bonding of the metallic niobium (Nb) and its mono-oxide (NbO) crystals in their solid states using the Density Functional Theory and X-ray Absorption Near Edge Spectroscopy. The electronic properties of Nb and NbO are investigated using the Finite Difference Method. These theoretical results are found in good agreement with the most recent experimental data. Our calculations reveal that the NbO crystal behaves like a superconductor.

DOI: 10.7868/S003040341308014X

1. INTRODUCTION

Niobium metal is put right before and in the same column of tantalum in the periodic table and both exhibit similar chemical properties. This element is preferably used in producing the heat-resistant and stainless alloys (with smaller densities) for constructing nuclear reactors, aircraft, and missiles, etc. It has been well known that a small amount of niobium added into these alloys can make the mechanical properties of material (such as the resistances to sea water and atmospheric corrosion, the heat resistance, etc.) much better, compared to the mother material and alloys with other additive metals.

The 4 d transition metal niobium (Nb) in combination with oxygen is a key material system for a wide range of applications. Reacted with oxygen and upon changing their oxidation states, the electrical properties change from conducting (Nb and NbO) to semiconducting (NbO2) and further to insulating (Nb2O5).

In this work, the theoretical studies of these electronic structures, chemical bonding properties and the density of state of Nb and NbO crystals were performed in order to characterize and assess their properties in various material systems.

2. CALCULATION METHOD

All the Density Functional Theory (DFT) calculations were carried out using the SIESTA package [1] with numerical atomic basis sets. The Perdew-Burke-Ernzerhof (PBE) gradient-corrected functional [2] was used in the calculation of the exchange-correlation energy. All calculations were done using double zeta basis plus polarization (DZP) orbitals for valence electrons while the core electrons were "frozen" in their atomic states by employing standard norm-con-

serving pseudopotentials in their fully nonlocal (Kleinman-Bylander) forms. Troullier-Martins with a meshcutoff (the real energy) was defined to be the equivalent plane wave cutoff for the grid and was set to 1360 eV. The Broyden method was employed for achieving the geometry relaxation until the maximal force on each relaxed atom is less than 0.04 eV/A. The Monkhorst-Pack Brillouin-zone (BZ) sampling was set to be 8 x 8 x 8 (for Nb) and 6 x 6 x 6 (for NbO) for cell optimizations, relaxations and other calculations.

X-ray Absorption Near Edge Spectroscopy (XANES) was calculated using the Finite Difference Method (FDM) when the Schrodinger equation was solved [3]. In such way, the shape of the potential is flexible and capable of avoiding the muffin-tin approximation. This method was implemented in the FDMNES code.

In our calculations, the Methfessel-Paxton scheme [4] for Brillioun zone integration calculations of band structures, electronic density of states (DOS) and crystal orbital overlap populations (COOP) was employed. The Methfessel-Paxton scheme was chosen due to its advantages in, even for a quite large smearing temperature range, predicting the energy which is very close to the physical energy at zero Kelvin. Also, it allows for a much faster convergence process with respect to the ^-points, especially for metals. Moreover, the convergence procedure to the self-consistency was found having much improved (hence allowing for the use of larger mixing coefficients). The order of the corresponding Hermite polynomial expansion was chosen as 2 for all electronic calculations with the electronic temperature of 300 K.

3. RESULTS AND DISCUSSION 3.1. Cell Optimization

Nb crystallizes in a body-centered-cubic (bcc) lattice belonging to the Im3m space group [5] while NbO has the space group Pm3m. The optimized lattice parameters of the Nb and NbO are shown in Table 1. The calculated parameters are close to experimental data. The computed lattice parameters were used for further calculations.

3.2. Band Structure

The electronic band structure, one of the most important properties of crystal materials, can provide the information about electronic and optical properties. The electronic band structure of the material will change if the composition and atomic arrangement are modified.

The valence configuration of Nb is 4d45s15p0 of which the band structure shown in Fig. 1 indicates the typical conductivity of metal without a band gap, due to the overlap between its valence band and conduction band (the reciprocal space of the bcc Nb is Fm3m). There is the lowest-energy band around —5 eV at the r point. This energy band can be characterized by calculating the Total Density of States (TDOS) and Partial Density of States (PDOS) of Nb bulk.

NbO has the crystal lattice belonging to the space group Pm3m. In the first Brillouin Zone (BZ), the special ^-points to be considered are r, R, M and X (Fig. 2a).

In general, the metals in 0 K all exhibit their superconductivities, when the band gap of the metal becomes very small. For example, the band gaps of Al, Cd, Ga, and Nb are 3.4 x 10-4, 1.5 x 10-4, 3.3 x 10-4 and 30.5 x 10-4 eV, respectively [6]. In the similar way, the band gap of a superconductor (either pure ele-

Table 1. Lattice parameters of Nb and NbO, cell vector modules in A

Nb NbO

Present work 3.3124 4.226

Experiment 3.3004 [20] 4.240 [21]

ments or chemical compounds) will be very small, especially in very low temperatures.

In the BCS (John Bardeen, Leon Cooper, and Robert Schrieffer) theory [7], the evidence of the existence of a small band gap at the Fermi level is a key indicator. The BCS theory predicts the band gap of a superconductor to be about (7/2)kBTc, where kB is the Boltzmann constant.

The band structure of NbO, in Fig. 2b, shows that there is a nearly zero band gap at the Fermi level (between M and X points). This does not always happen for metal oxides and is in agreement with the fact that NbO is a conducting material. Besides, J.K. Hulm and C.K. Jones [8] reported that the superconductivity was observed in NbO at 1.38 K while Schulz et al. [9] found the superconducting transition temperature of Tc = 1.5 K is consistent with the measured magnitude of the linear resistivity of NbO at room temperature.

In Fig. 2b, the region below the Fermi level consists of 12 bands which can be divided into 2 sub-regions: the bottom valence band and the top valence band. The top-valence-band region contains 9 bands and among those bands there is one broad band which crosses the Fermi level and is distinctly different from the others.

The bottom-valence-band region is around —21.5 eV below the Fermi level and contains three bands arising from oxygen 2s with the niobium 4d, 5s, 5p states (see COOP below). In these band structures, the lowest energy level is at r point for both Nb and NbO.

Energy. 4

eV

Fig. 1. (a) The special ^-points in Brillouin zone and (b) band structure of the Nb bulk. 7 ОПТИКА И СПЕКТРОСКОПИЯ том 115 № 2 2013

(a)

Energy, eV

(b)

epol^'vx

^_

zi //K / A V T\

C

E

-5

-10

-15

-20

r R M X r

Fig. 2. (a) The spécial ^-points in the Brillouin zone and (b) band structure of NbO.

States, eV-1 2

Ef

PDOS 5p 1

-10 -5 0 PDOS 55 1

10 15 20 25

______,-vwA.

-10 -5 0 2

PDOS 4d

10 15 20 25

A_

-10 -5 0 TDOS

5 10 15 20 25

5

5

-10 -5 0 5 10 15 20 25

Energy, eV

Fig. 3. TDOS and PDOS for valence states of Nb on the Nb bulk (EF = 0.0 eV).

3.3. Chemical Bonding

Using the pseudo-potential method, only the valence states were explicitly treated, such as 4d, 5s, 5p

for niobium and 2s, 2p for oxygen, respectively. Figure 3 illustrates the TDOS and PDOS of the valence states of Nb in a pure Nb bulk crystal. The energy region from —10 to 25 eV around the Fermi level relating to

States, eV-1 0.6

0.3

Nb PDOS 5p

(a)

j_i_i_i_l.

-10 -5 0 5 10 15 20 Nb PDOS 55

-10 -5 0 5 10 15 20 Nb PDOS 4d

-10 -5 0 5 10 15 20 Nb TDOS

-10 -5 0 5 10 15 20

States, eV-1 0.9 I

Energy, eV

15 20 Energy, eV

Fig. 4. TDOS and PDOS for states of Nb (a) and O (b) on the NbO bulk (EF = 0.0 eV).

bonding was investigated. This figure shows clearly that the 4d states have the highest contribution in bonding. This behavior is very typical for a transition metal.

The PDOS decomposes the total density of states into contributions due to different angular momentum components Xj (s orpx, py, pz, ...) and is defined as

gjb r) = Xl< X j k(r))|2 8(s;.-s),

(1)

where e; is the Kohn-Sham eigenvalue, corresponding to the individual Kohn-Sham orbital y,(r) and S(s;- - s) is the delta Dirac function.

The PDOS of the Nb bulk crystal shows that only these 5s states are occupied around the region of —5 eV. This is consistent with the band structure shown in Fig. 1b where the energy band around —5 eV is observable. Therefore, the energy band around —5 eV is of these 5s states of Nb.

The number of electrons N of each state on the specific energy region at 0 K can be calculated from the electronic density of states:

N =

= 2 J g(s)d s.

(2)

Applying this expression, we can calculate the number of electrons on each state for a single Nb atom from —5 eV to its Fermi level EF (—3.85 eV):

Ntdos = 4.86e, NPDOS4d = 3.77e, Npdos55 = 0.64e and Npdos5p = 0.45e.

(3)

Normally,

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