Next Article in Journal
Game-Theoretic Dynamic Procedure for a Power Index under Relative Symmetry
Next Article in Special Issue
Ab Initio Computations of O and AO as well as ReO2, WO2 and BO2-Terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) Surfaces
Previous Article in Journal
On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter λ
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Symmetry
Volume 13
Issue 10
10.3390/sym13101920
symmetry-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Tendencies in ABO3 Perovskite and SrF2, BaF2 and CaF2 Bulk and Surface F-Center Ab Initio Computations at High Symmetry Cubic Structure

by
Roberts I. Eglitis
1,*,
Juris Purans
1,
Anatoli I. Popov
1 and
Ran Jia
1,2
1
Institute of Solid State Physics, University of Latvia, 8 Kengaraga Str., LV1063 Riga, Latvia
2
Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China
*
Author to whom correspondence should be addressed.
Symmetry 2021, 13(10), 1920; https://doi.org/10.3390/sym13101920
Submission received: 15 September 2021 / Revised: 4 October 2021 / Accepted: 8 October 2021 / Published: 12 October 2021
(This article belongs to the Special Issue Applied Surface Science)
Browse Figures
Versions Notes

Abstract

:
We computed the atomic shift sizes of the closest adjacent atoms adjoining the (001) surface F-center at ABO3 perovskites. They are significantly larger than the atomic shift sizes of the closest adjacent atoms adjoining the bulk F-center. In the ABO3 perovskite matrixes, the electron charge is significantly stronger confined in the interior of the bulk oxygen vacancy than in the interior of the (001) surface oxygen vacancy. The formation energy of the oxygen vacancy on the (001) surface is smaller than in the bulk. This microscopic energy distinction stimulates the oxygen vacancy segregation from the perovskite bulk to their (001) surfaces. The (001) surface F-center created defect level is nearer to the (001) surface conduction band (CB) bottom as the bulk F-center created defect level. On the contrary, the SrF2, BaF2 and CaF2 bulk and surface F-center charge is almost perfectly confined to the interior of the fluorine vacancy. The shift sizes of atoms adjoining the bulk and surface F-centers in SrF2, CaF2 and BaF2 matrixes are microscopic as compared to the case of ABO3 perovskites.

1. Introduction

In the last 50 years, great attention has been paid to an in-depth understanding of the radiation formation of lattice defects in alkali and alkaline earth metal halides, as well as in simple and complex oxides. Several review articles were published, where both the mechanisms of their creation and the properties of the main defects were described in detail [1,2,3,4,5]. Lattice-point defects in these materials are traditionally called color centers and are classified into several large groups, among which electron centers, hole centers and interstitial particles are the most noticeable primary point radiation defects. As for electronic centers, F-centers are among the most intensively studied point defects in alkali and alkaline–halides. An ordinary F-center consists of one electron captured by a halogen vacancy [1,2,5]. Such F (Farbe) centers in alkali halides and alkaline–earth halides and oxides have been studied for many decades [1,2,5,6,7,8,9,10,11,12]. Thus, F-centers are defects in ionic crystals in which an anion is replaced by one or more trapped electrons. These vacancy-trapped electrons, confined and screened by the surrounding crystal lattice, thus form gap states with unique optical, electrical and magnetic properties [7,8,9,10,11,12,13,14,15,16] that are relevant to different optoelectronic devices. How efficient the formation is of point defects, including F-centers, is also the determining factor of the material radiation resistance in nuclear applications [17,18,19,20,21]. F-centers at surfaces, along with other anionic defects, are also relevant in catalysis [22].
The F-center in ABO3 perovskites is the oxygen vacancy (V0), which catches 2 electrons. The V0 is the most frequent point defect in ABO3 perovskites [23,24,25,26,27]. Bearing in mind the technological relevance of ABO3 perovskite matrixes, as well as quantity of F-centers, which unavoidably exist in these materials and deteriorate their quality, the number of F-center studies is still insufficient [28,29,30,31,32,33,34,35]. In order to save the computer time, we performed bulk and (001) surface F-center ab initio computations in ABO3 perovskites in their high-symmetry cubic phase. The SrZrO3, PbTiO3, BaTiO3 and SrTiO3 cubic unit cells accommodate five atoms. The coordinates (0, 0, 0) have the A atom (A = Sr, Pb, Ba or Sr). It is placed at the corner position of the cube. The Ti atom is placed in the body center position of the cube, with the following coordinates (½, ½, ½). Finally, the three O atoms are placed in the face centered positions of the cube with the coordinates (½, ½, 0), (½, 0, ½) and (0, ½, ½). All our computed SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites at their high symmetry cubic structure belong to the space group Pm3m with the space group number 221. Our computed SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites exhibit a large variety of different structural phase transitions from the high temperature and symmetry cubic paraelectric phase as the temperature is reduced. For example, the SrZrO3 exhibits a cubic perovskite-type structure. The space group (Pm3m: 221) incorporates 48 symmetry operations. The Wyckoff positions for the atoms are as follows: Sr 1a (0.0, 0.0, 0.0), Zr 1b (0.5, 0.5, 0.5) and O 3c (0.0, 0.5, 0.5). The SrZrO3 perovskite undergoes three phase transitions: orthorhombic (Pnma), orthorhombic with another space group (Cmcm), tetragonal (I4/mcm) and cubic (Pm3m) at temperatures of approximately 970, 1100 and 1440 K, respectively. In contrast, the SrTiO3 crystal has a polar soft mode, but it does not exhibit a ferroelectric phase transition and always remains in its high symmetry cubic phase. Finally, BaTiO3 is a perovskite that undergoes a phase transition from a ferroelectric tetragonal phase to a paraelectric cubic phase due to heating above 403 K in temperature.
Taking into account the soaring industrial significance of SrF2, BaF2 and CaF2 matrixes, it is only logical that there exist a lot of studies devoted to those materials [36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57]. The SrF2, BaF2 and CaF2 unit cells are equal, and they contain three ions. The cation is located in the coordinate origin (0, 0, 0). The two anions are located at (¼, ¼, ¼) and (¾, ¾, ¾). The fluorites SrF2, BaF2 and CaF2 are the cubic Fm3m large-band-gap insulators. Their space group number is 225. The F-center in CaF2 has been observed experimentally by electron-spin-resonance techniques. The F-center resonance in CaF2 has been detected by Arends [58] in additively colored crystals and associated with the optical absorption band at 3.3 eV. Nepomnyashchikh et al. [59] experimentally detected that X-ray irradiation at 77 K of undoped BaF2 produces Vk and F-centers. They have absorption bands at 3.4 and 2.3 eV, respectively [59]. Finally, the experimentally measured F-center absorption energy at 4 K temperature in the SrF2 crystal is equal to 2.85 eV [60]. Present-day knowledge of defects in SrF2, BaF2 and CaF2 crystals has helped to generate the new area of high technology named defect engineering. SrF2, BaF2 and CaF2 crystals could be the important optical materials if we can manage the photo-induced defect process [61,62].
The aim of this contribution is to report our comprehensive ab initio computation results dealing with F-centers in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes, as well as SrF2, BaF2 and CaF2 fluorites. Next, we analyzed our ab initio computation results and created a unified theory, which describes systematic tendencies in ab initio computations dealing with F-centers in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskite matrixes, as well as SrF2, BaF2 and CaF2 fluorites.

2. Details of Ab Initio Computations of the F-Centers in ABO3 Perovskites, as Well as in SrF2, BaF2 and CaF2 Fluorites

We computed the F-centers in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, as well as SrF2, BaF2 and CaF2 fluorites, by means of the CRYSTAL computer program package [63]. For our ab initio F-center computations, we used the B3PW hybrid exchange-correlation functional [64]. On the contrary to the plane-wave program packages [65,66], the CRYSTAL brings into play Gaussian-type functions as the basis [63]. It is worth noting that Gaussian-type functions have been intensively investigated during the last years [67,68]. For our numerical computations of F-centers in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, we used the basis sets created by Piskunov et al. [69]. We bring into play the 8 × 8 × 8 extension of the Pack Monkhorst mesh [70]. The ABO3 perovskite F-center computations for bulk were performed employing 3 × 3 × 3 extended supercell with 134 atoms and one F-center (Figure 1). It is important to note that the generalized-gradient (GGA) and local-density (LDA) approximations to the density functional theory (DFT) strongly underestimate the band gap of insulators and complex oxide materials [46,71]. From another side, the Hartree–Fock (HF) method considerably overestimate the band gap of insulators and complex oxide materials [46,71]. In order to obtain as good as possible results for the band gaps of SrF2, BaF2 and CaF2 fluorites, as well as SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, we performed our ab initio computations by means of the B3PW hybrid exchange-correlation functional. The B3PW functional contain a portion of exact exchange energy density from the HF method (20%). The rest of the exchange-correlation part consisted of different approaches, including both exchange and correlation. Therefore, the B3PW functional, since it is a superposition of HF and DFT methods, is much better suited for our band gap and optical property (defect level positions in the band gap) ab initio computations in SrF2, BaF2, CaF2, SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes.
With aimed to compute the ABO3 perovskite; for example, for the the SrZrO3 (001) surface F-center, we selected a 3 × 3 × 1 times increase in the size of the surface supercells. Namely, with aim to compute the F-center situated on the ZrO2-terminated SrZrO3 (001) surface, we took away the arbitrary surface oxygen atom (Figure 2).
In order to maximally exact describe the F-center, we used an extra basis function [63]. Namely, we fixed inside the oxygen vacancy auxiliary basis function [63], identical to the commonly named “ghost atom”. The formation energy of the bulk oxygen vacancy in ABO3 perovskites was computed by us the using subsequent equation:
E(F)formation = E(oxygen) + E(F) − E(perfect)
where E(oxygen) is our computed total energy for an oxygen atom, and E(F) and E(perfect) are our computed total energies for the F-center containing and perfect ABO3 crystal, respectively.
We discuss our computational methodology for F-centers in SrF2, BaF2 and CaF2 matrixes by using the CaF2 case as an example. In our F-center computations in CaF2 matrix, we used a supercell consisting of 48 atoms (Figure 3). In order to produce the F-center, we removed one fluorine atom and kept the supercell charge neutral (Figure 3). To compute the fluorine vacancy with electron (F-center) formation energy in CaF2 matrix, we employed the subsequent expression:
E(F)formation = E(fluorine) + E(F) − E(perfect)
where E(fluorine) is our ab initio computed total energy for the isolated fluorine atom; and E(F) and E(perfect) are our ab initio computed total energies for the defective (F-center containing) CaF2 crystal and the perfect CaF2 crystal. We utilized the Mulliken representation for the elucidation of the bond populations and the effective atomic charges [72,73,74].

3. Ab Initio Computation Results for F-Centers in ABO3 Perovskites, as Well as in SrF2, BaF2 and CaF2

As an opener of our F-center computations in SrZrO3, PbTiO3, BaTiO3, SrTiO3, SrF2, BaF2 and CaF2 matrixes [36,42,75,76,77,78,79], we performed computations for the pristine crystal bulk lattice constants. Our B3PW approximation obtained bulk lattice constants for SrZrO3 (4.163 Å), PbTiO3 (3.936 Å), BaTiO3 (4.008 Å), SrTiO3 (3.904 Å), SrF2 (5.845 Å), BaF2 (6.26 Å) and CaF2 (5.50 Å), and these are in a fair correspondence with the literature’s experimental information [80,81,82,83,84,85,86,87,88,89,90,91,92,93,94] (Table 1). For example, our computed SrTiO3 bulk lattice constant (3.904 Å) is almost in perfect agreement with the experimentally detected SrTiO3 bulk lattice constant (3.89845 Å). Moreover, our ab initio B3PW computed SrF2 (5.845 Å), BaF2 (6.26 Å) and CaF2 (5.50 Å) bulk lattice constants are in a fair agreement with the respective experimental information (5.799, 6.20 and 5.46 Å).
Our computation data, dealing with the atomic shifts around the bulk and (001) surface F-centers in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes, are listed in Table 2. As we can see from Table 2, all B (Zr or Ti) atoms are repulsed from the bulk and (001) surface F-centers in all four our calculated perovskites. The repulsion magnitudes for the Zr atoms from the (001) surface F-center located on the ZrO2-terminated SrZrO3 (001) surface (+9.17% of a0), as well as for the Ti atoms from the F-centers located on the TiO2-terminated PbTiO3 and SrTiO3 (001) surfaces (+9.98 and +14.0% of a0), are considerably larger than the B atom repulsion magnitudes from the F-centers located in the bulk of SrZrO3, PbTiO3 and SrTiO3 matrixes (+3.68, +1.63 and 7.76% of a0, respectively). On the contrary, the Ti atom repulsion from the F-center located on the BaO-terminated BaTiO3 (001) surface (0.1% of a0) is smaller than the relevant Ti atom repulsion from the F-center located in the BaTiO3 bulk matrix (1.06% of a0) (Table 2).
The second nearest adjacent O atoms, both in the SrZrO3, PbTiO3, BaTiO3 and SrTiO3 bulk and on its (001) surfaces, always are shifted towards the F-center. Namely, the second nearest adjacent O atoms are attracted towards the bulk F-center in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes, by (−2.63, −0.88, −0.71 and −7.79% of a0, respectively). Even more strongly than in the bulk, the second nearest adjacent O atoms are shifted towards the (001) surface F-center in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites by (−4.16, −5.58, −1.4 and −8.0% of a0) (Table 2).
According to the ionic model, the net oxygen atom charge is equal to −2 e. In our B3PW computations, the oxygen atom charges in pristine SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes are considerably smaller than the classical ionic charges and equal to −1.351 e, −1.232 e, −1.388 e and −1.407 e (Table 3). Even less charge is localized inside the bulk oxygen vacancies in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, only −1.25 e, −0.85 e, −1.103 e and −1.10 e. Our B3PW computed oxygen vacancy formation energies are equal to 7.55, 7.82, 10.30 and 7.10 eV in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites (Table 3 and Figure 4). Our computed band-gap widths for the SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, containing the single bulk oxygen vacancy, at the Γ point are equal to 5.07, 2.87, 3.58 and 3.63 eV (Table 3). The oxygen-vacancy-induced defect levels are located inside the band gap, 1.12, 0.96, 0.23 and 0.69 eV below the conduction band (CB) bottom at the Γ-point (Table 3 and Figure 5).
Even less charge is confined in the (001) surface oxygen vacancies in SrZrO3 (−1.10 e) and BaTiO3 (−1.052 e) matrixes. The (001) surface oxygen vacancy formation energies in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes are equivalent to 7.52, 5.99, 10.20 and 6.22 eV (Table 3). Finally, the (001) surface-oxygen-vacancy-induced defect level is situated at the Γ-point 0.93, 0.71, 0.07 and 0.25 eV below the CB at SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes (Table 3).
In all three pristine SrF2, BaF2 and CaF2 fluorites, our B3PW computed fluorine atom effective charges (−0.954 e, −0.923 e and −0.902 e) are very close to the net ionic fluorine charge equivalent to −1.00 e (Table 4). According to our B3PW computations, even less charge is confined inside the bulk fluorine vacancy in the SrF2, BaF2 and CaF2 matrixes (−0.848 e, −0.801 e and −0.752 e) (Table 4). The nearest Sr atom is sifted towards the bulk fluorine vacancy in the SrF2 crystal by a very small displacement size (−0.02% of a0), whereas the nearest Ba and Ca atoms are repulsed from the bulk fluorine vacancy by (+0.03 and +0.15% of a0) in the BaF2 and CaF2 matrixes (Table 4).
The bulk fluorine vacancy formation energy in the SrF2, BaF2 and CaF2 matrixes is equal to 10.33, 7.82 and 7.87 eV, respectively (Table 4 and Figure 4). Our computed band-gap widths for the SrF2, BaF2 and CaF2 containing the single bulk fluorine vacancy at the Γ point are equal to 11.34, 11.28 and 10.99 eV, respectively (Table 4). The bulk-fluorine-vacancy-induced defect levels are located inside the band gap at 3.67, 4.27 and 4.24 eV, respectively, below the conduction band (CB) bottom at the Γ-point in the SrF2, BaF2 and CaF2 matrixes (Table 4 and Figure 5).
Finally, for the fluorine vacancy located on the BaF2 (111) surface, only the (−0.790 e) charge is localized inside it (Table 4). The nearest Ba atom is shifted towards the (111) surface fluorine vacancy in the BaF2 matrix by (−0.13% of a0), and the second nearest F atom is shifted towards the fluorine vacancy even more strongly, by (−0.37% of a0). The fluorine vacancy formation energy on the BaF2 (111) surface is equal to 7.48 eV (Table 4). The BaF2 (111) surface-fluorine-vacancy-induced defect level is located inside the BaF2 band gap, 4.11 eV below the conduction band (CB) bottom at the Γ-point (Table 4 and Figure 5).
It is worth noting that we observed in our ab initio B3PW computations strong increase of the chemical bond covalency between the F-center and its nearest neighbor cations in our calculated materials. For example, our B3PW computed chemical bond covalency between the Zr and O atoms in the pristine SrZrO3 perovskite is equal to 0.100 e, but the chemical bond covalency between the Zr atoms and bulk F-center in SrZrO3 is more than two times larger and equivalent to 0.244 e. The same situation, according to our B3PW computations, is also in the BaTiO3 perovskite. Namely, the Ti-O chemical bond covalency in the pure BaTiO3 bulk is equivalent to 0.100 e. We observed, according to our ab initio B3PW computations, the strong increase of the chemical bond covalency between the adjacent Ti atoms and the BaTiO3 bulk F-center equivalent to 0.320 e.

4. Conclusions

The shift magnitudes of the nearest-neighbor atoms around the (001) surface oxygen vacancy in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites (Table 3), in most cases, are larger than the respective shift magnitudes of the nearest atoms around the bulk oxygen vacancy. The atomic shift amplitudes around both (001) surface and bulk oxygen vacancies in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites (Table 3) almost always are significantly larger than the atomic shift magnitudes around the fluorine vacancy in SrF2, BaF2 and CaF2 fluorites (Table 4).
In the SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, the charge, as a rule, is much better localized inside the bulk oxygen vacancy than inside the (001) surface oxygen vacancy (Table 3). In ionic materials, such as, SrF2, BaF2 and CaF2, the charge is considerably better localized (Table 4) inside the fluorine vacancy than inside the oxygen vacancy of SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites (Table 3). More than 75% of charge is localized inside the bulk and (111) surface fluorine vacancy in the SrF2, BaF2 and CaF2 matrixes (Table 4). We obtained the strong increase of a chemical bond covalency among the F-center and its nearest adjoining cations, in comparison to the pristine crystals.
In the SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, as well as BaF2 fluorite, the surface-oxygen-induce or fluorine-vacancy-induced defect levels are located closer to the CB band bottom than in the bulk cases (Table 3 and Table 4). The B3PW computed energy difference between the SrZrO3, PbTiO3, BaTiO3, SrTiO3 and CaF2 bulk and surface oxygen or fluorine vacancies (Table 3 and Table 4) triggers the vacancy segregation from the bulk towards the surface.
Our computation results for the F-center defect ground state levels in CaF2, BaF2 and SrF2 fluorites, located at 4.24, 4.27 and 3.67 eV under the CB bottom, suggest a possible explanation of the optical absorption observed experimentally in CaF2, BaF2 and SrF2 fluorites at 3.3, 2.3 and 2.85 eV. According to our computations, the experimentally observed optical absorption may be due to an electron transition from the F-center ground state, located at 4.24, 4.27 and 3.67 eV under the CB, to the CB. Namely, rhe F-center defect band at CaF2, BaF2 and SrF2 is located 4.24, 4.27 and 3.67 eV under the CB, which is very close to the experimentally detected optical absorption energy equal to 3.3, 2.3 and 2.85 eV, respectively.

Author Contributions

R.I.E., J.P., A.I.P. and R.J. contributed equally to the writing of the manuscript. Calculations dealing with ABO3 perovskites were performed mostly by R.I.E., J.P. and A.I.P., whereas calculations dealing with SrF2, BaF2 and CaF2 fluorites were performed mostly by R.J. All authors, R.I.E., J.P., A.I.P. and R.J. contributed substantially to the funding acquisition. All authors have read and agreed to the published version of the manuscript.

Funding

This research was partly funded by the Latvian Councel of Science project No. LZP-2020/2-0009 (for R. Eglitis), as well as the ERAF Project No. 1.1.1.1/18/A/073. We express our gratitude for the financial support from Latvian–Ukraine cooperation Project No. Latvia–Ukraine LV-UA/2021/5.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Acknowledgments

The Institute of Solid State Physics, University of Latvia (Latvia), as the Centre of Excellence has received funding from the European Unions Horizon 2020 Framework Programme H2020-WIDESPREAD01-2016-2017-Teaming Phase2 under Grant Agreement No. 739508, project CAMART2.

Conflicts of Interest

The authors declare no conflict of interests.

References

  1. Kotomin, E.A.; Popov, A.I. Radiation-induced point defects in simple oxides. Nucl. Instrum. Methods Phys. Res. Sect. B 1998, 141, 1–15. [Google Scholar] [CrossRef]
  2. Popov, A.I.; Kotomin, E.A.; Maier, J. Basic properties of the F-type centers in halides, oxides and perovskites. Nucl. Instrum. Methods Phys. Res. Sect. B 2010, 268, 3084–3089. [Google Scholar] [CrossRef]
  3. Itoh, N. Creation of lattice defects by electronic excitation in alkali halides. Adv. Phys. 1982, 31, 491–551. [Google Scholar] [CrossRef]
  4. Itoh, N.; Tanimura, K. Formation of interstitial-vacancy pairs by electronic excitation in pure ionic-crystals. J. Phys. Chem. Solids 1990, 51, 717–735. [Google Scholar] [CrossRef]
  5. Lushchik, C.; Lushchik, A. Evolution of Anion and Cation Excitons in Alkali Halide Crystals. Phys. Solid State 2018, 60, 1487–1505. [Google Scholar] [CrossRef]
  6. Dauletbekova, A.; Akilbekov, A.; Elango, A. Thermo-and Photostimulated Recombinations of F-HA and α-IA Centres in KBr with Large Na Concentration. Phys. Stat. Sol. B 1982, 112, 445–452. [Google Scholar] [CrossRef]
  7. Kirm, M.; Lushchik, A.; Lushchik, C.; Martinson, I.; Nagirnyi, V.; Vasil’chenko, E. Creation of groups of spatially correlated defects in a KBr crystal at 8 K. J. Phys. Condens. Matter 1998, 10, 3509–3521. [Google Scholar] [CrossRef]
  8. Weinstein, I.A.; Kortov, V.S.; Vohmintsev, A.S. The compensation effect during luminescence of anion centers in aluminum oxide. J. Lumin. 2007, 122, 342–344. [Google Scholar] [CrossRef]
  9. Feldbach, E.; Toldsepp, E.; Kirm, M.; Lushchik, A.; Mizohata, K.; Raisanen, J. Radiation resistance diagnostics of wide-gap optical materials. Opt. Mater. 2016, 55, 164–167. [Google Scholar] [CrossRef]
  10. Ananchenko, D.V.; Nikiforov, S.V.; Konev, S.F.; Ramazanova, G.R. ESR and luminescent properties of anion-deficient α-Al2O3 single crystals after high-dose irradiation by a pulsed electron beam. Opt. Mater. 2019, 90, 118–122. [Google Scholar] [CrossRef]
  11. Lushchik, A.; Karner, T.; Lushchik, C.; Vasilchenko, E.; Dolgov, S.; Issahanyan, V.; Liblik, P. Dependence of long-lived defect creation on exciton density in MgO single crystals. Phys. Stat. Sol. C 2007, 4, 1084–1087. [Google Scholar]
  12. Myasnikova, L.; Shunkeyev, K.; Zhanturina, N.; Ubaev, Z.; Barmina, A.; Sagimbaeva, S.; Aimaganbetova, Z. Luminescence of self-trapped excitons in alkali halide crystals at low temperature uniaxial deformation. Nucl. Instrum. Methods Phys. Res. Sect. B 2020, 464, 95–99. [Google Scholar] [CrossRef]
  13. Schweizer, S.; Secu, M.; Spaeth, J.M.; Hobs, L.W.; Edgar, A.; Williams, G.V.M. New developments in X-ray storage phosphors. Radiat. Meas. 2004, 38, 633–638. [Google Scholar] [CrossRef]
  14. Elango, A.; Sagimbaeva, S.; Sarmukhanov, E.; Savikhina, T.; Shunkeev, K. Effect of uniaxial stree on luminescence of X- and VUV-irradiated NaCl and NaBr crystals. Radiat. Meas. 2001, 33, 823–827. [Google Scholar] [CrossRef]
  15. Kortov, V.; Lushchik, A.; Nagirnyi, V.; Ananchenko, D.; Romet, I. Spectrally resolved thermally stimulated luminescence of irradiated anion-defective alumina single crystals. J. Lumin. 2017, 186, 189–193. [Google Scholar] [CrossRef]
  16. Koyama, T.; Suemoto, T. Dynamics of nuclear wave packets at the F center in alkali halides. Rep. Prog. Phys. 2011, 74, 076502. [Google Scholar] [CrossRef]
  17. Skuratov, V.A.; O’Connell, J.; Kirilkin, N.S.; Neethling, J. On the threshold of damage formation in aluminium oxide via electronic excitations. Nucl. Instrum. Methods Phys. Res. Sect. B 2014, 326, 223–227. [Google Scholar] [CrossRef]
  18. Van Vuuren, J.A.; Saifulin, M.M.; Skuratov, V.A.; O’Connell, J.H.; Aralbayeva, G.; Dauletbekova, A.; Zdorovets, M. The influence of stopping power and temperature on latent track formation in YAP and YAG. Nucl. Instrum. Methods Phys. Res. Sect. B 2019, 460, 67–73. [Google Scholar] [CrossRef]
  19. Mota, F.; Ortiz, C.J.; Vila, R.; Casal, N.; Garcia, A.; Ibarra, A. Calculation of damage function of Al2O3 in irradiation facilities for fusion reactor applications. J. Nucl. Mater. 2013, 442, S699–S704. [Google Scholar] [CrossRef]
  20. Dukenbayev, K.; Kozlovskiy, A.; Kenzhina, I.; Berguzinov, A.; Zdorovets, M. Study of the effect of irradiation with Fe7+ ions on the structural properties of thin TiO2 foils. Mater. Res. Express 2019, 6, 046309. [Google Scholar] [CrossRef]
  21. Zdorovets, M.; Dukenbayev, K.; Kozlovskiy, A.; Kenzhina, I. Defect formation in AlN after irradiation with He2+ ions. Ceram. Int. 2019, 45, 8130–8137. [Google Scholar] [CrossRef]
  22. Janesco, B.G.; Jones, S.I. Quantifying the delocalization of surface and bulk F-centers. Surf. Sci. 2017, 659, 9–15. [Google Scholar] [CrossRef] [Green Version]
  23. Eglitis, R.I.; Christensen, N.E.; Kotomin, E.A.; Postnikov, A.V.; Borstel, G. First-principles and semiempirical calculations for F center in KNbO3. Phys. Rev. B 1997, 56, 8599–8604. [Google Scholar] [CrossRef] [Green Version]
  24. Carballo-Cordova, D.A.; Ochoa-Lara, M.T.; Olive-Mendez, S.F.; Espinosa-Magana, F. First-principles calculations and Bader analysis of oxygen-deficient induced magnetism in cubic BaTiO3-x and SrTiO3-x. Philos. Mag. 2019, 99, 181–187. [Google Scholar] [CrossRef]
  25. Ojha, S.K.; Gogoi, S.K.; Mandal, P.; Kaushik, S.D.; Freeland, J.W.; Jain, M.; Middey, S. Oxygen vacancy induced electronic structure modification of KTaO3. Phys. Rev. B 2021, 103, 085102. [Google Scholar] [CrossRef]
  26. Osinkin, D.A.; Khodimchuk, A.V.; Porotnikova, N.M.; Bogdanovich, N.M.; Fetisov, A.V.; Ananyev, M.V. Rate-Determining Steps of Oxygen Surface Exchange Kinetics on Sr2Fe1.5Mo0.5O6−δ. Energies 2020, 13, 250. [Google Scholar] [CrossRef] [Green Version]
  27. Farlenkov, A.S.; Ananyev, M.V.; Eremin, V.A.; Porotnikova, N.M.; Kurumchin, E.K.; Melehov, B.T. Oxygen isotope exchange in doped calcium and barium zirconates. Solid State Ion. 2016, 290, 108–115. [Google Scholar] [CrossRef]
  28. Mueller, D.N.; Machala, M.L.; Bluhm, H.; Chuech, W.C. Redox activity of surface oxygen anions in oxygen-deficient perovskite oxides during electrochemical reactions. Nat. Commun. 2015, 6, 6097. [Google Scholar] [CrossRef] [Green Version]
  29. Ji, Q.; Bi, L.; Zhang, J.; Cao, H.; Zhao, X.S. The role of oxygen vacancies of ABO3 perovskite oxydes in the oxygen reduction reaction. Energy Environ. Sci. 2020, 13, 1408–1428. [Google Scholar] [CrossRef]
  30. Su, H.Y.; Sun, K. DFT study of the stability of oxygen vacancy in cubic ABO3 perovskites. J. Mater. Sci. 2015, 50, 1701–1709. [Google Scholar] [CrossRef]
  31. Eglitis, R.I. Ab initio calculations of SrTiO3, BaTiO3, PbTiO3, CaTiO3, SrZrO3, PbZrO3 and BaZrO3 (001), (011) and (111) surfaces as well as F centers, polarons, KTN solid solutions and Nb impurities therein. Int. J. Mod. Phys. B 2014, 28, 1430009. [Google Scholar] [CrossRef] [Green Version]
  32. Crespillo, M.L.; Graham, J.T.; Agullo-Lopez, F.; Zhang, Y.W.; Weber, W.J. Real-Time Identification of Oxygen Vacancy Centers in LiNbO3 and SrTiO3 during Irradiation with High Energy Particles. Crystals 2021, 11, 315. [Google Scholar] [CrossRef]
  33. Jiao, X.P.; Liu, T.Y.; Lu, Y.Z.; Li, Q.Y.; Guo, R.; Wang, X.L.; Xu, X. Optical Properties of the Oxygen Vacancy in KNbO3 Crystal. J. Electron. Mater. 2020, 49, 2137–2143. [Google Scholar] [CrossRef]
  34. Eglitis, R.I.; Popov, A.I.; Purans, J.; Jia, R. First principles hybrid Hartree-Fock-DFT calculations of bulk and (001) surface F centers in oxide perovskites and alkali-earth fluorides. Low Temp. Phys. 2020, 46, 1206–1212. [Google Scholar] [CrossRef]
  35. Gu, X.K.; Samira, S.; Nikolla, E. Oxygen Sponges for Electrocatalysis: Oxygen Reduction/Evolution on Nonstoichiometric, Mixed Metal Oxides. Chem. Mater. 2018, 30, 2860–2872. [Google Scholar] [CrossRef]
  36. Shi, H.; Eglitis, R.I.; Borstel, G. Ab initio calculations of the CaF2 electronic structure and F centers. Phys. Rev. B 2005, 72, 045109. [Google Scholar] [CrossRef]
  37. Wen, C.; Lanza, M. Calcium fluoride as high-k dielectric for 2D electronics. Appl. Phys. Reviews 2021, 8, 021307. [Google Scholar]
  38. Laanaiya, M.; Bouibes, A.; Zaoui, A. Ground state properties of fluorine from DFT-hybrid functional. Vacuum 2021, 187, 110118. [Google Scholar] [CrossRef]
  39. Weng, J.P.; Gao, S.P. Layer-dependent band gaps and dielectric constants of ultrathin fluorite crystals. J. Phys. Chem. Solids 2021, 148, 109738. [Google Scholar] [CrossRef]
  40. Liebig, A.; Hapala, P.; Weymouth, A.J.; Giessibl, F.J. Quantifying the evolution of atomic interaction of a complex surface with a functionalized atomic force microscopy tip. Sci. Rep. 2020, 10, 14104. [Google Scholar] [CrossRef]
  41. Ryabochkina, P.A.; Krushchalina, S.A.; Yurlov, I.A.; Egorysheva, A.V.; Atanova, A.V.; Veselova, V.O.; Kyashkin, V.M. Blackbody emission from CaF2 and ZrO2 nanosized electric particles doped with Er3+ ions. RSC Adv. 2020, 10, 26288–26297. [Google Scholar] [CrossRef]
  42. Shi, H.; Eglitis, R.I.; Borstel, G. Ab initio calculations of the BaF2 bulk and surface F centres. J. Phys. Condens. Matter 2006, 18, 8367–8381. [Google Scholar] [CrossRef]
  43. Cappellini, G.; Bosin, A.; Serra, G.; Furthmüller, J.; Bechstedt, F.; Botti, S. Electronic and Optical Properties of Small Metal Fluoride Clusters. ACS Omega 2020, 5, 13268–13277. [Google Scholar] [CrossRef] [PubMed]
  44. Pawlik, N.; Szpikowska-Sroka, B.; Goryczka, T.; Pisarski, W.A. Spectroscopic Properties of Eu3+ Ions in Sol-Gel Materials Containing Calcium Fluoride Nanocrystals. Phys. Stat. Sol. B 2020, 257, 1900478. [Google Scholar] [CrossRef]
  45. Matusalem, F.; Marques, M.; Teles, L.K.; Filippetti, A.; Cappellini, G. Electronic properties of fluorides by efficient approximated quasiparticle DFT-1/2 and PSIC methods. J. Phys. Condens. Matter 2018, 30, 365501. [Google Scholar] [CrossRef] [PubMed]
  46. Vassilyeva, A.F.; Eglitis, R.I.; Kotomin, E.A.; Dauletbekova, A.K. Ab initio calculations of MgF2 (001) and (011) surface structure. Physica B 2010, 405, 2125–2127. [Google Scholar] [CrossRef]
  47. Shi, H.; Chang, L.; Jia, R.; Eglitis, R.I. Ab initio calculations of the charge transfer and aggregation of F centers in CaF2. J. Phys. Chem. C 2012, 116, 4832–4839. [Google Scholar] [CrossRef]
  48. Häfner, M.; Bredow, T. Mobility of F Centers in Alkali Halides. J. Phys. Chem. C 2021, 125, 9085–9095. [Google Scholar] [CrossRef]
  49. Mir, A.; Zaoui, A.; Bensaid, D. The displacement effect of a fluorine atom in CaF2 on the band structure. Appl. Surf. Sci. 2018, 439, 1180–1185. [Google Scholar] [CrossRef]
  50. Ibraheem, A.M.; Khalafalla, M.A.H.; Eisa, M.H. First principle calculation of accurate native defect levels in CaF2. Eur. Phys. J. B 2017, 90, 42. [Google Scholar] [CrossRef]
  51. Shi, H.; Jia, R.; Eglitis, R.I. First-principles calculations of surface H centers in BaF2. Phys. Rev. B 2010, 81, 195101. [Google Scholar] [CrossRef]
  52. Andrade, A.B.; Ferreira, N.S.; Valerio, M.E.G. Particle size effects on structural and optical properties of BaF2 nanoparticles. RSC Adv. 2017, 7, 26839–26848. [Google Scholar] [CrossRef] [Green Version]
  53. Watanabe, M.; Azuma, J.; Asaka, S.; Tsujibayashi, T.; Arimoto, O.; Nakanishi, S.; Itoh, H.; Kamada, M. Photostimulated detection of defect formation in BaF2 under irradiation of synchrotron radiation. Phys. Stat. Sol. B 2013, 250, 396–401. [Google Scholar] [CrossRef]
  54. Shi, H.; Jia, R.; Eglitis, R.I. First-principles simulations on the aggregation of F centers in BaF2: R centers. Solid State Ion. 2011, 187, 1–7. [Google Scholar] [CrossRef]
  55. Hoya, J.; Laborde, J.I.; Richard, D.; Renteria, M. Ab initio study of F-centers in alkali halides. Comput. Mater. Sci. 2017, 139, 1–7. [Google Scholar]
  56. Shi, H.; Chang, L.; Jia, R.; Eglitis, R.I. Ab initio calculations of hydroxyl impurities in CaF2. J. Phys. Chem. C 2012, 116, 6392–6400. [Google Scholar] [CrossRef]
  57. Cen, J.; Liang, F.; Chen, D.L.; Zhang, L.L.; Yang, N.; Zhu, W.D. Adsorption of water molecule on calcium fluoride and magnesium fluoride surfaces: A combined Theoretical and experimental study. J. Phys. Chem. C 2020, 124, 7853–7859. [Google Scholar] [CrossRef]
  58. Arends, J. Color centers in additively colored CaF2 and BaF2. Phys. Stat. Sol. B 1964, 7, 805–815. [Google Scholar] [CrossRef]
  59. Nepomnyashchikh, A.I.; Radzhabov, E.A.; Egranov, A.V.; Ivashechkin, V.F.; Istomin, A.S. Defect formation and VUV luminescence in BaF2. Radiat. Eff. Defects Solids 2002, 157, 715–719. [Google Scholar] [CrossRef]
  60. Cavenett, B.C.; Hayes, W.; Hunter, I.C.; Stoneham, A.M. Magneto optical properties of F centres in alkaline earth fluorides. Proc. R. Soc. Lond. Ser. A 1969, 309, 53–68. [Google Scholar]
  61. Assylbayev, R.; Lushchik, A.; Lushchik, C.; Kudryavtseva, I.; Shablonin, E.; Vasilchenko, E.; Akilbekov, A.; Zdorovets, M. Structural defects caused by swift ions in fluorite single crystals. Opt. Mater. 2018, 75, 196–203. [Google Scholar] [CrossRef]
  62. Batool, A.; Izerrouken, M.; Aisida, S.O.; Hussain, J.; Ahmad, I.; Afzal, M.Q. Effect of Ca colloids on in-situ ionoluminescence of CaF2 sigle crystals. Nucl. Instrum. Methods Phys. Res. Sect. B 2020, 476, 40–43. [Google Scholar] [CrossRef]
  63. Saunders, V.R.; Dovesi, R.; Roetti, C.; Causa, N.; Harrison, N.M.; Orlando, R.; Zicovich-Wilson, C.M. Crystal-2009 User Manual; University of Torino: Torino, Italy, 2009. [Google Scholar]
  64. Perdew, J.P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 1992, 45, 13244–13249. [Google Scholar] [CrossRef] [PubMed]
  65. Cohen, R.E. Surface effects in ferroelectrics: Periodic slab computations for BaTiO3. Ferroelectrics 1997, 194, 323–342. [Google Scholar] [CrossRef]
  66. Cohen, R.E. Periodic slab LAPW computations for ferroelectric BaTiO3. J. Phys. Chem. Solids 1996, 57, 1393–1396. [Google Scholar] [CrossRef] [Green Version]
  67. Shang, Y. Lower bounds for Gaussian Estrada index of graphs. Symmetry 2018, 10, 325. [Google Scholar] [CrossRef] [Green Version]
  68. Alhevaz, A.; Baghipur, M.; Shang, Y. On generalized distance Gaussian Estrada index of graps. Symmetry 2019, 11, 1276. [Google Scholar] [CrossRef] [Green Version]
  69. Piskunov, S.; Heifets, E.; Eglitis, R.I.; Borstel, G. Bulk properties and electronic structure of SrTiO3, BaTiO3, PbTiO3 perovskites: An ab initio HF/DFT study. Comput. Mater. Sci. 2004, 29, 165–178. [Google Scholar] [CrossRef]
  70. Monkhorst, H.J. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188. [Google Scholar] [CrossRef]
  71. Eglitis, R.I. Ab initio calculations of the atomic and electronic structure of BaZrO3 (111) surfaces. Solid State Ion. 2013, 230, 43–47. [Google Scholar] [CrossRef]
  72. Mesquita, W.D.; Oliveira, M.C.; Assis, M.; Ribeiro, R.A.P.; Eduardo, A.C.; Teordoro, M.D.; Marques, G.E.; Júnior, M.G.; Longo, E.; Gurgel, M.F.C. Unraveling the relationship between bulk structure and exposed surfaces and its effect on the electronic structure and photoluminescent properties of Ba0.5Sr0.5TiO3: A joint experimental and theoretical approach. Mater. Res. Bull. 2021, 143, 111442. [Google Scholar] [CrossRef]
  73. Eglitis, R.I.; Kleperis, J.; Purans, J.; Popov, A.I.; Jia, R. Ab initio calculations of CaZrO3 (011) surfaces: Systematic trends in polar (011) surface calculations of ABO3 perovskites. J. Mater. Sci. 2020, 55, 203–217. [Google Scholar] [CrossRef]
  74. Eglitis, R.I.; Purans, J.; Gabrusenoks, J.; Popov, A.I.; Jia, R. Comparative ab initio calculations of ReO3, SrZrO3, BaZrO3, PbZrO3 and CaZrO3 (001) surfaces. Crystals 2020, 10, 745. [Google Scholar] [CrossRef]
  75. Eglitis, R.I.; Piskunov, S. First principles calculations of SrZrO3 bulk and ZrO2-terminated (001) surface F centers. Comput. Condens. Matter 2016, 7, 1–6. [Google Scholar] [CrossRef] [Green Version]
  76. Zhukovskii, Y.F.; Kotomin, E.A.; Piskunov, S.; Ellis, D.E. A comparative ab initio study of bulk and surface oxygen vacancies in PbTiO3, PbZrO3 and SrTiO3 perovskites. Solid State Commun. 2009, 149, 1359–1362. [Google Scholar] [CrossRef]
  77. Sokolov, M.; Eglitis, R.I.; Piskunov, S.; Zhukovskii, Y.F. Ab initio hybrid DFT calculations of BaTiO3 bulk and BaO-terminated (001) surface F-centers. Int. J. Mod. Phys. B 2017, 31, 1750251. [Google Scholar] [CrossRef] [Green Version]
  78. Carrasco, J.; Illas, F.; Lopez, N.; Kotomin, E.A.; Zhukovskii, Y.F.; Evarestov, R.A.; Mastrikov, Y.A.; Piskunov, S.; Maier, J. First-principles calculations of the atomic and electronic structure of F centers in the bulk and on the the (001) surface of SrTiO3. Phys. Rev. B 2006, 73, 064106. [Google Scholar] [CrossRef] [Green Version]
  79. Jia, R.; Shi, H.; Borstel, G. Ab initio calculations for SrF2 with F and M centers. Comput. Mater. Sci. 2008, 43, 980–988. [Google Scholar] [CrossRef]
  80. Lee, Y.S.; Lee, J.S.; Noh, T.W.; Byun, D.Y.; Yoo, K.S.; Yamaura, K.; Takayama-Muromachi, E. Systematic trends in the electronic structure parameters of the 4d transition-metal oxides SrMO3 (M = Zr, Ru and Rh). Phys. Rev. B 2003, 67, 113101. [Google Scholar] [CrossRef] [Green Version]
  81. Yoshino, M.; Yukawa, H.; Morinaga, M. Modification of local electronic structures due to phase transition in perovskite-type oxides, SrBO3 (B = Zr, Ru, Hf). Mater. Trans. 2004, 45, 2056–2061. [Google Scholar] [CrossRef] [Green Version]
  82. Kennedy, B.J.; Howard, C.J.; Chakoumakos, B.C. High-temperature phase transitions in SrZrO3. Phys. Rev. B 1999, 59, 4023–4027. [Google Scholar] [CrossRef]
  83. Robertson, J. Band offsets of wide-band-gap oxides and implications for future electronic devices. J. Vacuum Sci. Technol. 2000, 18, 1785–1791. [Google Scholar] [CrossRef]
  84. Nelmes, R.J.; Kuhs, W.F. The crystal structure of tetragonal PbTiO3 at room temperature and at 700 K. Solid State Commun. 1985, 54, 721–723. [Google Scholar] [CrossRef]
  85. Mabud, S.A.; Glazer, A.M. Lattice parameters and birefringence in PbTiO3 single crystals. J. Appl. Cryst. 1979, 12, 49–53. [Google Scholar] [CrossRef]
  86. Wemple, S.H. Polarization fluctuations and the optical-absorption edge in BaTiO3. Phys. Rev. B 1970, 2, 2679–2689. [Google Scholar] [CrossRef]
  87. Meyer, B.; Padilla, J.; Vanderbilt, D. Theory of PbTiO3, BaTiO3 and SrTiO3 surfaces. Faraday Discuss. 1999, 114, 395–405. [Google Scholar] [CrossRef] [Green Version]
  88. Edwards, J.W.; Speiser, R.; Johnston, H.L. Structure of barium titanate at elevated temperatures. J. Amer. Chem. Soc. 1951, 73, 2934–2935. [Google Scholar] [CrossRef]
  89. van Benthem, K.; Elsasser, C.; French, R.H. Bulk electronic structure of SrTiO3: Experiment and theory. J. Appl. Phys. 2001, 90, 6156–6164. [Google Scholar] [CrossRef] [Green Version]
  90. Sato, M.; Soejima, Y.; Ohama, N.; Okazaki, A.; Scheel, H.J.; Müller, K.A. The lattice constant vs temperature relation around the 105 K transition of a flux-grown SrTiO3 crystal. Phase Trans. 1985, 5, 207–218. [Google Scholar] [CrossRef]
  91. Rubloff, G.W. Far-Ultraviolet Reflectence Spectra and the Electronic Structure of Ionic Crystals. Phys. Rev. B 1972, 5, 662–684. [Google Scholar] [CrossRef]
  92. Hayes, W. Crystals with the Fluorite Structure; Clarendon Press: Oxford, UK, 1974. [Google Scholar]
  93. Leger, J.M.; Haines, J.; Atouf, A.; Schulte, O. High-pressure x-ray and neutron-diffraction studies of BaF2: An example of a coordination number of 11 in AX2 compounds. Phys. Rev. B 1995, 52, 13247. [Google Scholar] [CrossRef] [PubMed]
  94. Nicolav, M. Shaped single crystals of CaF2. J. Cryst. Growth 2000, 218, 62–66. [Google Scholar] [CrossRef]
Symmetry 13 01920 g001 550
Figure 1. F-center in the SrZrO3 bulk, computed by using 3 × 3 × 3 extended supercell.
Figure 1. F-center in the SrZrO3 bulk, computed by using 3 × 3 × 3 extended supercell.
Symmetry 13 01920 g001
Symmetry 13 01920 g002 550
Figure 2. Our ab initio computed F-center situated on the 3 × 3 × 1 times increased in size ZrO2-terminated SrZrO3 (001) surface.
Figure 2. Our ab initio computed F-center situated on the 3 × 3 × 1 times increased in size ZrO2-terminated SrZrO3 (001) surface.
Symmetry 13 01920 g002
Symmetry 13 01920 g003 550
Figure 3. F-center (XX) in the CaF2 bulk matrix, computed by using 48-atom supercell.
Figure 3. F-center (XX) in the CaF2 bulk matrix, computed by using 48-atom supercell.
Symmetry 13 01920 g003
Symmetry 13 01920 g004 550
Figure 4. B3PW computed surface (1) and bulk (2) F-center formation energies (in eV) in SrZrO3, PbTiO3, BaTiO3, SrTiO3 and BaF2 matrixes.
Figure 4. B3PW computed surface (1) and bulk (2) F-center formation energies (in eV) in SrZrO3, PbTiO3, BaTiO3, SrTiO3 and BaF2 matrixes.
Symmetry 13 01920 g004
Symmetry 13 01920 g005 550
Figure 5. B3PW computed valence band (VB) top (1), conduction band (CB) bottom (3) as well as F-center-induced levels (2) between the VB top and CB bottom in the SrZrO3, PbTiO3, BaTiO3, SrTiO3, SrF2, BaF2 and CaF2 bulk matrixes.
Figure 5. B3PW computed valence band (VB) top (1), conduction band (CB) bottom (3) as well as F-center-induced levels (2) between the VB top and CB bottom in the SrZrO3, PbTiO3, BaTiO3, SrTiO3, SrF2, BaF2 and CaF2 bulk matrixes.
Symmetry 13 01920 g005
Table
Table 1. Experimental details for pristine SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, as well as SrF2, BaF2 and CaF2 matrixes [80,81,82,83,84,85,86,87,88,89,90,91,92,93,94].
Table 1. Experimental details for pristine SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites, as well as SrF2, BaF2 and CaF2 matrixes [80,81,82,83,84,85,86,87,88,89,90,91,92,93,94].
SubstanceStructure at Room TemperatureBand Gap (eV), Room TemperatureTransition T to Cubic Phase (K)Experimental Lattice Constant at Cubic Phase (Å)
SrZrO3Orthorhombic5.6 [80]1433 [81]4.154 [82]
PbTiO3Tetragonal3.4 [83]763 [84]3.970 [85]
BaTiO3Tetragonal to
orthorhombic		3.38 (// c); 3.27 (⊥ c) [86]403 [87]4.0037 [88]
SrTiO3Cubic3.75 [89]110 [87]3.89845 [90]
SrF2Cubic11.25 [91]-5.799 [92]
BaF2Cubic11.00 [91]-6.20 [93]
CaF2Cubic12.1 [91]-5.46 [94]
Table
Table 2. B3PW computed 3 closest adjacent atom shifts around the bulk and (001) surface F-center (in% of the a0).
Table 2. B3PW computed 3 closest adjacent atom shifts around the bulk and (001) surface F-center (in% of the a0).
Computed CharacteristicsSrZrO3PbTiO3BaTiO3SrTiO3
Bulk lattice constant (Å)4.1633.9364.0083.904
Bulk oxygen vacancy in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites
B atom shift (% of a0)+3.68+1.63+1.06+7.76
O atom shift (% of a0)−2.63−0.88−0.71−7.79
A atom shift (% of a0)+0.46−2.58−0.08+3.94
Oxygen vacancy on SrZrO3, PbTiO3, BaTiO3 and SrTiO3 (001) surface
B atom shift (% of a0)+9.17+9.98+0.1+14.0
O atom shift (% of a0)−4.16−5.58−1.4−8.0
A atom shift (% of a0)+7.68-+1.0-
Table
Table 3. B3PW computed electronic structure of the bulk and (001) surface oxygen vacancy in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes.
Table 3. B3PW computed electronic structure of the bulk and (001) surface oxygen vacancy in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 matrixes.
Computed CharacteristicsSrZrO3PbTiO3BaTiO3SrTiO3
Bulk oxygen vacancy in SrZrO3, PbTiO3, BaTiO3 and SrTiO3 perovskites
O atom net charge (e)−2.0−2.0−2.0−2.0
O atom charge (e) in ABO3−1.351−1.232−1.388−1.407
F-center charge (e)−1.25−0.85−1.103−1.10
F-cent. format. energy (eV)7.557.8210.307.10
Band gap with F-cent. (eV)5.072.873.583.63
F-center under CB (eV)1.120.960.230.69
Oxygen vacancy on SrZrO3, PbTiO3, BaTiO3 and SrTiO3 (001) surface
F-center charge (e)−1.10-−1.052-
F-cent. format. energy (eV)7.525.9910.206.22
F-center under CB (eV)0.930.710.070.25
Table
Table 4. B3PW computed atomic and electronic structure of the fluorine vacancy in SrF2, BaF2 and CaF2 matrixes.
Table 4. B3PW computed atomic and electronic structure of the fluorine vacancy in SrF2, BaF2 and CaF2 matrixes.
Computed Bulk Fluorine Vacancy PropertiesSrF2BaF2CaF2
B3PW computed lattice constant a0 (Å)5.8456.265.50
F atom net charge (e)−1.0−1.0−1.0
F atom charge (e) in SrF2, BaF2 and CaF2−0.954−0.923−0.902
Charge inside the fluorine vacancy (e)−0.848−0.801−0.752
A atom shift (% of a0)−0.02+0.03+0.15
F atom shift (% of a0)−0.27−0.23+0.28
Fluorine vacancy formation energy (eV)10.337.827.87
B3PW calc. band gap, perfect crystal (eV)11.3111.3010.96
B3PW calc. band gap with F-center (eV)11.3411.2810.99
Fluorine vacancy ind. level under CB (eV)3.674.274.24
Computed (111) surface fluorine vacancy
Ba atom shift (% of a0)-−0.13-
F atom shift (% of a0)-−0.37-
Charge inside the fluorine vacancy (e)-−0.790-
Fluorine vacancy formation energy (eV)-7.48-
Fluorine vacancy ind. level under CB (eV)-4.11-
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Eglitis, R.I.; Purans, J.; Popov, A.I.; Jia, R. Tendencies in ABO3 Perovskite and SrF2, BaF2 and CaF2 Bulk and Surface F-Center Ab Initio Computations at High Symmetry Cubic Structure. Symmetry 2021, 13, 1920. https://doi.org/10.3390/sym13101920

AMA Style

Eglitis RI, Purans J, Popov AI, Jia R. Tendencies in ABO3 Perovskite and SrF2, BaF2 and CaF2 Bulk and Surface F-Center Ab Initio Computations at High Symmetry Cubic Structure. Symmetry. 2021; 13(10):1920. https://doi.org/10.3390/sym13101920

Chicago/Turabian Style

Eglitis, Roberts I., Juris Purans, Anatoli I. Popov, and Ran Jia. 2021. "Tendencies in ABO3 Perovskite and SrF2, BaF2 and CaF2 Bulk and Surface F-Center Ab Initio Computations at High Symmetry Cubic Structure" Symmetry 13, no. 10: 1920. https://doi.org/10.3390/sym13101920

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop