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ARTICLE

Phase-Dependent Structural, Optical, and Thermodynamic Behavior of BaTiO₃: Insights from First-Principles Calculations

Yasemin O. Ciftci¹, İlknur K. Durukan¹, Upasana Rani², Peeyush Kumar Kamlesh^3,*

1 Physics Department, Science Faculty, Gazi University, Ankara, Turkey
2 Department of Applied Sciences & Humanities, IIMT College of Engineering, Greater Noida, Uttar Pradesh, India
3 Department of Physics, Poornima University, Jaipur, Rajasthan, India

* Corresponding Author: Peeyush Kumar Kamlesh. Email:

Computers, Materials & Continua 2026, 87(3), 35 https://doi.org/10.32604/cmc.2026.078722

Received 06 January 2026; Accepted 26 February 2026; Issue published 09 April 2026

Abstract

This study examines the phase-dependent structural, electronic, optical, and thermodynamic characteristics of the cubic, tetragonal, and orthorhombic phases of BaTiO₃ using DFT simulations. Lattice parameters and bulk moduli computed through structural optimizations within the GGA-PBE framework are in good agreement with existing experimental and theoretical studies. All phases exhibit negative formation energies, indicating thermodynamic stability, with the orthorhombic phase being the most stable. Electronic structure calculations reveal indirect band gaps of 2.86, 2.96, and 3.43 eV for the cubic, tetragonal, and orthorhombic phases, respectively. The density of states analysis indicates that O-p states dominate the valence band, and Ti-d states are the primary source of the conduction band. The optical properties of BaTiO₃ have been evaluated using the frequency-dependent dielectric function over 0–15 eV, showing strong optical absorption in both the visible and ultraviolet regions. The optical band gap is consistent with the electronic results. The dielectric constants for all three phases of BaTiO₃ are calculated to be 4.7, 4.4, and 4.5, while the refractive indices are 2.18, 2.09, and 2.12, respectively. In the infrared and visible regions (below ~3.1 eV), the refractive index exhibits relatively high, weakly dispersive behavior for all phases, indicating strong polarization and low optical losses. The thermodynamic properties of BaTiO₃ were evaluated using the quasi-harmonic Debye model in the temperature range 0–1000 K and pressure range 0–30 GPa. The calculated thermodynamic parameters suggest that the bulk modulus decreases with increasing temperature but increases with increasing pressure. At very high temperatures, the heat capacity approaches the Dulong-Petit limit. This study suggests that BaTiO₃ shows potential for optoelectronic and high-temperature applications.

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