Ab initiostudy for the IR spectroscopy of PbTiO₃and PbZrO₃, primary blocks of PbZr_1−xTi_xO₃

Abstract

PbTiO (PT) and PbZrO (PZ) are the two primary blocks of the solid solution PbZr Ti O (PZT). They can be modelled in different ways; but, in order to do comparable DFT calculations on PZT, with different values of x, one must find a unique method that can be used for both PT and PZ. In particular, we want to evaluate their vibrational properties to compare them with experimental data. Density functional theory (DFT) is used to perform structure geometry optimizations and electronic structure calculations, both on low- and high-temperature phase. Then, harmonic vibrational frequencies of their low-temperature phase are determined for transverse and longitudinal optical (TO & LO) phonons. Moreover, a detailed study of the eigenvectors shows that accurate calculations are necessary to correctly interpret and understand the IR spectra. In the end, the comparison of our theoretical results with previous experimental and theoretical data confirm the strong potential of the SOGGA (second-order generalized gradient approximation) functional to correctly describe PT, PZ and, hopefully, PZT; especially their structural and vibrational properties.

IR Spectroscopy of PbZr1–xTixO3 Material: A Complementary Experimental/Ab Initio Calculations Approach of a Solid Solution

“…In a previous study, some of us developed a model for the two pure compounds, PT and PZ, within the framework of Density Functional Theory (DFT). 17 We showed that the SOGGA functional 18 is a reliable choice for describing these materials' properties. Here, we use this functional for calculating the IR absorption spectra of pure PT and PZ, as well as PZT of various compositions (x ≥ 0.5) in both the cubic and tetragonal phases.…”

“…Calculated Infrared and THz Spectra of PZ (PbZrO 3 ) and PT (PbTiO 3 ). In a previous article, 17 we highlighted the need to carry out precise modeling to interpret the IR spectra of perovskites such as PT and PZ. The use of the SOGGA functional, 18 implemented in the 2014 version of the CRYSTAL computer code, 30 permitted the determination of a good description of the structural and electronic structure of the two compounds.…”

“…2,16,36 The DFT calculations for all configurations were done using the 2014 version of the CRYSTAL code, 30 based on the linear combination of Gaussian-type functions method for the crystalline orbitals' expansion. The basis sets and the functional (SOGGA) chosen for this study are the same than those used in our previous study on PT and PZ 17 (details can also be found at the end of the Computation section). The spectra made from the TO phonon modes for each of the five tetragonal configurations of PZT 75 are presented Figure 5a, while equivalent results for other compositions can be found in the SI.…”

“…and by using the Boltzmann occupation probability, P i (V, T), given by 37 Infrared spectra obtained by ab initio calculations for the two primary building blocks of PZT, 17 that is, tetragonal PT and orthorhombic PZ, each TO mode is convoluted at a bandwidth (fwhm) of 30 cm −1 . Because of the large number of PZ modes (presented in Table 1), only the PT modes are identified.…”

“…Such dead-layer phenomenon could explain the lack of the most polar modes in the presented IR spectra for 5 and 10 nm samples. 41 In order to exclude the occurrence of islands of pure PT (or less likely of pure PZ) domains in the present films, a comparison of the IR spectrum of the PT and PZ films 17 with PZT 75 films is presented in Figure 7. The resemblance of these spectra is unmistakable.…”