Contents I. Introduction
There are seven polymorphs of bismuth oxide, which are monoclinic α, tetragonal β, cubic centered on the body γ, cubic centered on the faces δ, orthorhombic ε, triclinic ω, and high-pressure hexagonal η [1]. Phase δ is particularly important because it is an excellent conductor of oxygen ions (O2-), with a conductivity of approximately 1 S • cm-1 at 750 °C. Because of its superb oxygen ion conductivity, δ-Bi2O3 has garnered attention as a potential electrolyte for intermediate-temperature solid oxide fuel cells, typically operating between 500-800 °C. This phase exhibits a defective fluorite-like structure, similar to CaF2, where bismuth atoms occupy face-centered cubic (fcc) sites. However, the exact arrangement of oxygen vacancies within this structure remains uncertain. The scientific community has proposed three feasible approaches to arrange these vacant positions within a unit cell, namely along the <100>, <110>, or <111> directions. However, no conclusive evidence supports any particular arrangement as the optimal solution. Based on stoichiometry, the reference [4] proposes that oxygen sites are average and random. Reference [5] proposes an orderly structure consisting of two oxygen vacancies along the direction <111>, whereas reference [6] suggests the disposition of vacancies along the direction <110>. A more complicated vacancy structure is revealed by neutron diffraction experiments, in which oxygen atoms also depart from their ideal positions within the fluorite structure [7]. According to the reference [8], the arrangement of vacancies in the <110> direction is influenced by the doping effect, while the orientation <111> is favored for the pure phases [9]. This has made it difficult to investigate the δ - Bi2O3 properties using DFT, as seen in [10]. The remarkably high ionic conductivity of the δ - Bi2O3 is believed to stem from the random distribution of oxygen vacancies, which are randomly distributed within the fluorite structure, and the high polarization of the fluorite ions Bi3+ from their lone electron pairs 6s2. Nevertheless, the δ phase is stable within the 730-825 °C temperature range. At lower temperatures, it is readily transformed into the β and/or γ phases that are much no less conductive [11]. However, it has recently been reported to stabilize at room temperature as a nanostructured material [12], [13], [14], [15], [16], [17]. To support this, [9] has proposed using a supercell that, using DFT, has obtained results that approximate the experimental results and explores its photocatalytic properties. These findings open the possibility of diversifying the application of δ - Bi2O3 as a gas sensor, especially an optical gas sensor. This is supported by the application of α phase proposed by [18], who has proven its application as an optical sensor of gases at room temperature. Nevertheless, to the best of our knowledge, no information regarding optical properties has been reported by DFT. This is necessary to serve as a basis for corroborating experimental results and/or to serve as a basis for designing active layers with nanostructures of δ - Bi2O3. This paper presents the outcomes of the calculations conducted using the DFT using CASTEP to compare the structural, electronic, and optical properties of the polymorphs α and δ of Bi2O3. The primary purpose has been to analyze the optical response of these phases to compare the region of light absorption and the behavior of the refractive index, since they are fundamental parameters in its application as an optical gas sensor. Given the difficulty in reproducing the semiconductor behavior of the phase δ, the supercell model proposed by [9]. For both phases, it has been observed that the conductivity function replicates the semiconductor behavior, that the light absorption range is located in the ultraviolet spectrum and a portion of the visible spectrum, and that the refractive index exhibits a similar behavior. This is even though the phase δ - Bi2O3 has a more significant band gap than the phase α - Bi2O3. This work focuses on the polymorphs α and δ of Bi2O3, for both describe their structural properties, indicate the crystallographic information used in the entire DFT calculations, and present the results of the electronic properties obtained. Finally, the optical properties are analyzed. This paper is structured as follows:
Section II, Computational Details, describes the DFT approach used in this study, including the software, pseudopotentials, and other computational settings.
Section III, Results and Discussion, is divided into three subsections. Subsection III-A focuses on the Structural Properties of the α and δ phases, including lattice parameters and atomic positions. Subsection III-B examines the Electronic Properties, discussing the band structures and density of states (DOS) for both polymorphs. Subsection III-C analyzes the Optical Properties, including the absorption spectra, refractive index, and optical conductivity.
Section IV, Conclusion, summarizes the findings of this study and discusses the potential applications of these materials in optical sensing technologies.
