Using the plane-wave ultrasoft pseudopotential technique based on the first-principles density functional theory (DFT), we have studied the structural, electronic, chemical bonding, and optical properties of tetragonal PbMoO4. The obtained structural parameters are in good agreement with experiments. Band structure, density of states, and chemical bonding are calculated and shown. It is found that tetragonal PbMoO4 is an indirect band gap. The dielectric function, refractive index, extinction coefficient, reflectivity, absorption coefficient, loss function, and conductivity function are calculated for radiation up to 20 eV.
PbMoO4 has been the subject of great research interest both experimentally [
The crystal structure of tetragonal PbMoO4 belongs to the space group
Hence, we study the structural parameters, electronic structure, chemical bonding, and optical properties of tetragonal PbMoO4 using the plane-wave ultrasoft pseudopotential technique based on the first-principles density functional theory. The rest of the work is organized as follows. In Section
Density functional theory calculations are performed with plane-wave ultrasoft pseudopotential using the generalized gradient approximation (GGA) with the Perdew-Wang 1991 (PW91) functional [
The crystal structure of tetragonal PbMoO4 is shown in Figure
Calculated equilibrium lattice parameters
This work | ||||
Castep | Expt. [ | Expt. [ | Expt. [ | |
5.5173 | 5.424–5.4360 | 5.433 | 5.418–5.464 | |
12.3305 | 12.076–12.1107 | 12.110 | 12.065–12.088 | |
2.2349 | 2.226–2.229 | — | — |
The crystal structure of tetragonal PbMoO4.
The calculations of the electronic band structure along the symmetry lines of the Brillouin zone, the total and the partial density of states (DOSs and PDOSs) are shown in Figures
Band structure of tetragonal PbMoO4 along with the high-symmetry points of the Brillouin zone.
Total and partial density of states of tetragonal PbMoO4.
In order to further elucidate the nature of the electronic band structure, we have calculated and explained the DOSs and PDOSs. From the PDOSs, we can identify the angular momentum character of the different structures. Structure (1) is mainly due to Mo-4 s electrons, structure (2) due to Mo-4p electrons, structure (3) due to O-2 s electrons, structure (4) due to Pb-5d electrons, structure (5) due to Pb-6 s electrons, structures (6) and (7) due to O-2p electrons with hybridization of Mo-4d electrons, and structure (8) due to O-2p electrons. The conduction bands are composed of Mo-4d and show the hybridization with O-2p, as well as the hybridization between Pb-6p and O-2p.
To understand the chemical bonding of this material, we have poltted the charge density of (112) plane corresponding to the (1)–(8) located at Figure
Calculated results of population analysis.
Atom | s | p | d | Total | Charge (e) |
---|---|---|---|---|---|
O | 1.89 | 4.78 | 0 | 6.68 | −0.68 |
Mo | 2.24 | 6.51 | 4.01 | 12.76 | 1.24 |
Pb | 1.71 | 0.81 | 10 | 12.52 | 1.48 |
Total charge densities of (112) plane and charge densities located (1)–(8) in the (112) plane of tetragonal PbMoO4.
Charge densities in the (220) plane of tetragonal PbMoO4.
We need to calculate two dielectric tensor components to completely characterize the linear optical properties due to the tetragonal symmetry of PbMoO4. The imaginary and the real parts of the dielectric function are calculated using (
Figures
Calculated imaginary parts of complex dielectric function of tetragonal PbMoO4 as well as calculated results from experimental data [
Calculated real parts of complex dielectric function of tetragonal PbMoO4 as well as calculated results from experimental data [
The refractive index and the extinction coefficient are displayed in Figure
Calculated refractive index and extinction coefficient of tetragonal PbMoO4 from (100) and (001).
Calculated reflectivity, absorption coefficient, loss function and complex conductivity function of tetragonal PbMoO4 from (100) and (001).
The paper reports detailed investigations on the structural, electronic, chemical bonding, and optical properties of tetragonal PbMoO4 using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT). The calculated equilibrium lattice parameters are in agreement with experiments. Our calculated results of the band structure and DOSs show that this compound is an indirect band gap of 2.838 eV. The charge densities and population analysis are obtained and analyzed, which show that Mo and O are mainly covalent, whereas Pb and O are mainly ionic. The complex dielectric function has been shown, and the peaks position distributions of imaginary parts of complex dielectric function have been explained, which show electron transitions in the electronic bands.
This work was financially supported by the National Natural Science Foundation of China (Contract no. 50902110), the Doctorate Foundation of Northwestern Polytechnical University (Contract no. cx201005), the 111 Project (Contract no. B08040), and the Research Fund of the State Key Laboratory of Solidification Processing (NWPU), China (Contract no. 58-TZ-2011).