Zhanhong Lei(雷展宏), Weiliang Wang(王偉良),?, and Juncong She(佘峻聰)

1State Key Laboratory of Optoelectronic Materials and Technologies,Guangdong Province Key Laboratory of Display Material and Technology,School of Physics,Sun Yat-sen University,Guangzhou 510275,China

2State Key Laboratory of Optoelectronic Materials and Technologies,Guangdong Province Key Laboratory of Display Material and Technology,School of Electronics and Information Technology,Sun Yat-sen University,Guangzhou 510275,China

Keywords: Raman tensor,DFT,α-PtO2

1. Introduction

In recent years, the versatility of platinum oxides has attracted extensive attention in different fields. Known as Adams’ catalyst, platinum oxides play an important role in industry.[1,2]Abundant researches on the catalytic behavior of platinum oxides have been conducted, such as the oxidation of ammonia,[3]CO oxidation,[4]hydrosilylation reaction[5]and oxidation of ethanol to acetic acid.[6,7]In electrochemistry, the oxidation on the surface of platinum electrodes remarkably influence the reaction processes.[8,9]In electronics,platinum oxides find applications for memory capacitors as electrode materials,[10]as well as nanoscale and molecular electronics.[11]

Compared with conventional evaporation or sputtering methods of producing α-PtO2, new approaches such as oxygen plasma treatment to produce ultra-thin platinumoxide films[11]and hydrolytic reaction to synthesize α-PtO2nanocrystals[15]have greatly improved the material’s performance and facilitated their applications. However, there exists a problem that α-PtO2needs to be characterized from the experimental product PtOx, where 1

2. Calculation method

The structural optimization and calculation of dielectric tensor was performed using the Vienna ab initio simulation package within the framework of density functional theory.[21]The exchange-correlation potential was described by generalized gradient approximation using Perdew–Burke–Ernzerhof type functional.[22]The projected augmented-wave method was used to construct plane-wave basis set,and the energy cutoff is 400 eV for structural optimization and 500 eV for force constant calculation.[23]Brillouin zone was sampled on a Γ centered grid of 4×4×4 k-mesh for structural optimization and force constant calculation and a Γ centered 40×40×40 k-mesh for dielectric tensor calculation. The convergence of the total energy was set to 10?8eV.The phonon dispersion of α-PtO2was calculated using the density functional perturbation theory and Phonopy code for a 3×3×3 supercell.[24]

The Raman intensity of the j-th mode can be obtained by[25]

3. Results and discussion

The crystal structure of α-PtO2is composed of stacked O–Pt–O trilayers,with 3 atoms in each unit cell(Fig.1). The lattice constants are found to be a=b=3.164 ?A,c=4.728 ?A,which are larger than the XRD results a = b = 3.113 ?A,c=4.342 ?A.[20]There are nine phonon modes in the phonon dispersion of α-PtO2(Fig.2),including six optical modes and three acoustic modes. The six optical modes are A1g, 2Eg,2Euand A2u. The two oxygen atoms vibrate relatively in z,y and x directions in A1g(Fig.3(a)), Eg,1(Fig.3(b))and Eg,2(Fig.3(c)) modes, respectively. The platinum atom and oxygen atoms vibrate relatively in x, y and z directions in Eu,1(Fig.3(d)),Eu,2(Fig.3(e))and A2u(Fig.3(f))modes,respectively.

Fig.1. The crystal structure of α-PtO2. The gray (red) balls refer to platinum(oxygen)atoms. The solid lines indicate a unit cell. The x,y and z axes are along[10ˉ10],[1ˉ210]and[0001]directions,respectively.

The α-PtO2belongs to D3dpoint group and Pˉ3m1 space group. According to group theory, the Raman-active modes of α-PtO2are A1gand Eg. The vibrational frequency is 15.14 THz for mode A1gand 15.92 THz for mode Eg(double degenerate), which means that we can observe two peaks at 505 cm?1and 531 cm?1in the Raman spectra of α-PtO2.This is close to the experimental results of 514 cm?1and 560 cm?1.[20]

Fig.2. Phonon dispersion of α-PtO2.

Fig.3. Atomic movement of the six optical modes at the Γ point.

We also obtain the eigenvectors of A1gmode and Egmodes at the Γ point. Then we calculate the dielectric function variation. The Raman tensor in agreement with the group theory is obtained as follows:

Table 1. Raman tensor elements.

When the wave vector of the incident light is along y direction([1ˉ210]direction),the polarization direction of the incident light can be written as(sinθ,0,cosθ).The polarization directions of the scattered light in parallel configuration and perpendicular configuration are(sinθ,0,cosθ)and(cosθ,0,?sinθ),respectively. Therefore,

When the wave vector of the incident light is along z direction([0001]direction),the polarization direction of the incident light can be written as(cosθ,sinθ,0).The polarization directions of the scattered light in parallel configuration and perpendicular configuration are (cosθ, sinθ, 0) and (?sinθ,cosθ,0),respectively. Therefore,

Fig.4. The polarization-resolved Raman intensities of A1g mode (top panels) and Eg (bottom panels) in parallel polarization configuration.The incident light wave vector is along[10ˉ10](left panels),[1ˉ210](middle panels)and[0001](right panels)crystal direction,respectively.

Fig.5. The polarization-resolved Raman intensities of A1g mode(top panels)and Eg (bottom panels)in perpendicular polarization configuration. The incident light wave vector is along[10ˉ10](left panels),[1ˉ210](middle panels)and[0001](right panels)crystal direction,respectively.

The Raman intensity does not depend on θ when the wave vector of the incident light is in z direction.

Comparing the magnitudes of the polar plots,the Raman intensity of the Egmode is about five times stronger than that of the A1gmode,due to larger value of elements in Raman tensor. The Raman intensity is about three times stronger when the wave vector of the incident light is in x or y direction than in z direction because|b|>|a|and|d|>|c|.

4. Conclusion

We have investigated the vibrational properties of α-PtO2and calculated the Raman tensor of two Raman-active modes A1gand Eg. The polarization-resolved Raman intensities in parallel polarization configuration and perpendicular polarization configuration are obtained for the cases that the wave vector of incident light is in x,y and z directions.The polar plot of A1gmode in parallel polarization configuration is found to be useful in identifying the orientation of the crystal. The Raman intensity of the Egmode is about five times stronger than that of the A1gmode. The Raman intensity is about three times stronger when the wave vector of the incident light is in x or y direction than in z direction. Our work will help material scientists to characterize α-PtO2and identify its orientation by comparing the experimental spectra with our result.