Structural, Elastic, and Electronic Properties of Y(1-xSrxTiO3 (x=0.01, 0.10, 0.50, 0.99) by Means of Density Functional Theory

1. Introduction

The perovskite crystal structure has garnered significant attention due to its unique properties and potential applications. One of the key compounds within this family is Yttrium titanate (YTiO₃) which has been a subject of interest, with studies focusing on the use of molecular dynamics simulations to explore the crystal symmetry and oxygen-ion transport in perovskite materials, shedding light on their behavior at different temperatures [1] .  YTiO₃ is a ferromagnetic Mott insulator with strong electron correlation effects and orbital ordering [2,3] . High-quality epitaxial YTiO₃ thin films have been synthesized using pulsed laser deposition and molecular beam epitaxy [2,4] . The electronic structure of YTiO₃ is characterized by a Mott-Hubbard band gap of ~1.5 eV and a lower Hubbard band at 1.1 eV below the Fermi level [2] . Both structural distortions and multiorbital electron interactions contribute to orbital polarization in YTiO₃ [3] . Doping with La or Ca significantly affects the electronic and optical properties of YTiO₃, including spectral weight transfer and changes in the band structure and optical conductivity [3,5] . Furthermore, YTiO₃ has been studied for its potential applications in energy storage, electronic devices, and sensors [6] One study investigated the metal-insulator transition at YTiO₃/LaTiO₃ interfaces grown by the soft chemical method [7] . The researchers aimed to understand the behavior of the interface between YTiO₃ and LaTiO₃, shedding light on potential applications in electronics and optoelectronics. Additionally, a computational study explored the use of YTiO₃±δ as cathode materials in solid oxide fuel cells (SOFCs) [8] . This study delved into the native defects and oxygen diffusion within YTiO₃, providing valuable insights for the development of advanced SOFC technologies. In another study, Yttrium-doped SrTiO3 (SYT) demonstrated high electrical conductivity, structural stability, and chemical compatibility with YSZ and LSGM, making it a promising anode material for solid oxide fuel cells, achieving a maximum power density of 58 mW/cm² at 900 °C [9] . Furthermore, investigations on functional properties of Al_0.8Eu_yLa_0.2-yTiO₃ (y = 0.01 - 0.04) nanoparticles synthesized by the hydrothermal method have also been conducted [10] . The research focused on the potential applications of these nanoparticles and their unique properties for specific electronic or optical devices. The effect of high-temperature annealing on the phase transformations of the perovskite YTiO_3−x system was also explored, providing important insights into the structural characteristics of YTiO₃-based materials [11] . Measurement of elastic modulus in YTiO₃ suggests the appearance of the magnetostriction effect [12] .

Additionally, the magnetic properties of YTiO₃ have been studied extensively in the literature, revealing several intriguing phenomena. Gossling et al. [13] investigated optical excitations in Mott-Hubbard insulators YTiO₃ and SmTiO₃, observing absorption bands and peak anomalies attributed to charge-neutral quasibound states. Akimitsu et al. [14] used the polarized neutron diffraction technique to directly observe the orbital ordering in ferromagnetic YTiO₃. Additionally, a study by Zhou et al. [15] explored the magnetic properties and electronic structures of YTiO₃-based superlattices, revealing unexpected magnetic orders and electronic behavior at the interfaces. In a different approach, a joint refinement model for the spin-resolved one-electron reduced density matrix of YTiO₃ was proposed by Gueddida et al. [16] , which provided insights into the magnetic properties of YTiO₃ using magnetic structure factors and magnetic Compton profiles data. Chae et al. [17] investigated epitaxial growth and the magnetic properties of orthorhombic YTiO₃ thin films, revealing ferromagnetic transitions and the influence of substrate-induced atomic arrangements. Moreover, the transition from orbital liquid to the Jahn-Teller insulator in orthorhombic perovskites RTiO₃, including YTiO₃, was examined by Cheng et al. [18] , demonstrating a spin/orbital transition at a magnetic transition temperature. Furthermore, a first-principles study by Weng et al. [19] investigated electron doping of SmNiO₃ / YTiO₃ via interfacial charge transfer and its effects on the electronic and magnetic properties, highlighting the complex interplay between different materials. An interesting work by An et al. [20] explored the possibility of ferrimagnetism and ferroelectricity in half-substituted rare-earth titanates, including Y_0.5La_0.5TiO₃.

In this study, we investigate the effect of doping Sr into YTiO₃ with different ratios (0.01, 0.10, 0.50, 0.99). Our investigation covers elastic and electronic properties. The outline of this article is as follows. In the next section, the main methods are explained. The investigation results are given in the Results and Discussion section. Lastly, the outcomes of this research are given in the conclusion.

2. Materials and Methods

Y_1-xSr_xTiO₃ in Pm$\overline{3}$m space group is doped by Sr by various ratios (x=0.01, 0.10, 0.50, 0.99). In Figure 1, the initial structure of YTiO₃ is given with the lattice constant a=3.88Å. The geometry computation is completed with GGA-PBE, and cutoff energy is 630 eV which is defined based on used pseudopotentials and finite basis set correction [21] . The Monkhorst–Pack scheme was utilized to perform special k-points sampling integration across the Brillouin zone with the 6×6×6 mesh [22] .

Our DFT calculations are performed using the projector-augmented wave approach as implemented in the CASTEP [23,24] . We described the exchange and correlation potential using the GGA-PW91 functional, and the electron-core interactions with the ultrasoft pseudopotential [25] . The energy convergence tolerance was set at $5.0\times {10}^{-6}eV/atom$, the maximum force was set at $0.01eV/Å$, the maximum stress was set at $0.02GPa$, and the maximum displacement was set at $5.0\times {10}^{-4}Å.$ The Perdew-Burke-Ernzorhof generalized gradient approximation was used to solve the Kohn-Sham equations [26] . The crystal structures underwent complete relaxation using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization method [27] .

The elastic properties are determined by the CASTEP through the application of the finite strain theory [28] . This theory allows for the calculation of elastic constants, which are the coefficients that relate the applied strain to the resulting stress, ${\sigma }_i=c_{ij}{\epsilon }_j$. The polycrystalline bulk modulus B and shearmodulus G are then evaluated using the Voigt-Reuss-Hill approximation based on the obtained $c_{ij}$ values [29] .

3. Results and Discussion

In this study, we investigated the structural, elastic, and electronic properties of Y_1-xSr_xTiO₃ (x=0, 0.01, 0.1, 0.5, 0.99) perovskites using density functional theory (DFT). The materials exhibit a cubic structure (Pm$\overline{3}$m) with optimized lattice constants. Elastic properties, including bulk modulus, shear modulus, and Young's modulus, confirm mechanical stability in accordance with the Born-Huang criteria. Electronic properties, examined through band structure and partial density of states (PDOS), reveal significant alterations in band structure due to Sr doping; however, no bandgap is observed, and the metallic nature of the materials is retained, with notable contributions from p and d orbitals.

3.1. Structural Properties

The structural properties and geometries of Y_1-xSr_xTiO₃ (x=0, 0.01, 0.1, 0.5, and 0.99) perovskites were examined using density functional theory (DFT) (See Figure 1). The materials were found to have cubic structures with the space group Pm$\overline{3}$m (no. 221). The states of complete relaxation in the structures are achieved through the optimization of its geometry, taking into account the lattice constants and internal atomic positions. This process involves adjusting the arrangement of atoms within the structure to minimize any residual stress or strain. By optimizing these parameters, the structure can achieve a more stable and energetically favorable configuration. Wyckoff spaces of Y, Ti, and O are respectively (0, 0, 0), (1/2, 1/2, 1/2), and (1/2, 1/2, 0). The optimized lattice constants, obtained from the unit cell optimization for the ground state stable atomic configuration, are presented in Table 1 . To ascertain the stability of perovskite materials, we employ a computational approach to calculate and present the elastic constants in the subsequent sections, providing comprehensive details.

3.2. Elastic Properties

The study of the elastic properties of materials is essential prior to their practical use, as many device features depend on the elastic properties of the materials used in their manufacturing. Therefore, materials with superior elastic properties are highly valuable for incorporation into various devices. The elastic constant serves as a mathematical link between the mechanical and dynamical characteristics of materials, playing a crucial role in determining their properties and how they respond to external forces. Based on the principles of cubic symmetry, the elastic tensor consists of three distinct elastic components, namely $c_{11}$, $c_{12}$, and $c_{44}$. The bulk modulus (BM) calculates the stress needed to change a material's volume, whereas the shear modulus (SM) describes how resistant a material is to shear stress-induced deformation. The forces per unit cross sectional area needed for an elongation or shortening dimensional change are measured by the Young modulus (YM).

The obtained values for these elastic constants are presented in Table 2 and are evaluated against the Born-Huang generalized stability criteria [31] as defined in equation (1) for the Pm$\overline{3}$m structure. Therefore, it can be concluded that compounds exhibit mechanical stability.

$$c_{44}>0,c_{11}>\left|c_{12}\right|,c_{11}+2c_{12}>0$$

(1)

Table 2 displays the findings of our study on the elastic properties under no pressure conditions. Based on the computation results, elastic stability is confirmed.

3.3. Electronic Properties

Figure 2 illustrates the band arrangement and PDOS of Y_1-xSr_xTiO₃ (x=0, 0.01, 0.1, 0.5, and 0.99), where the lattice parameters have been optimized along the high symmetry directions within the first Brillouin zone. The electronic band structure helps to identify the valence band and the area empty of electrons. The possible energies of electrons are explained by the conduction band. The conduction and valence bands are distinguished by the E_F. The valence bands are seen behind the E_F, while the conduction band is located above it. The findings indicate that, despite a considerable alteration in band structures due to Sr doping, there is no bandgap. The valence and conduction band spacing is expanding in doped crystals, but the metal nature of the crystals is preserved. In the band structure, p and d orbitals are particularly stronger than s orbitals.

4. Conclusion

In conclusion, the structural, elastic, and electronic properties of Y_1-xSr_xTiO₃ (x=0.01, 0.10, 0.50, 0.99) perovskites within the Pm$\overline{3}$m space group were thoroughly investigated using density functional theory (DFT). The initial geometry optimizations, performed with the GGA-PBE functional, revealed stable configurations with varying Sr doping levels. Detailed elastic property calculations confirmed the mechanical stability of these compounds, with significant variations in elastic constants attributed to Sr doping. The electronic structure analysis, including band structure and partial density of states (PDOS), indicated that despite changes in the band structures, the materials retained their metallic nature, dominated by p and d orbitals. These findings underscore the potential of Sr-doped YTiO₃ perovskites for applications that demand superior mechanical properties and highlight the influence of Sr doping on the materials' structural and electronic characteristics.