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Article

Computational Discovery of New Feasible Crystal Structures in Ce3O3N

by
Jelena Zagorac
1,2,*,
Johann Christian Schön
3,
Branko Matović
1,2,
Milan Pejić
1,2,
Marija Prekajski Đorđević
1,2 and
Dejan Zagorac
1,2
1
Institute of Nuclear Sciences Vinča, Materials Science Laboratory, Belgrade University, 11000 Belgrade, Serbia
2
Center for Synthesis, Processing and Characterization of Materials for Application in the Extreme Conditions-CextremeLab, 11000 Belgrade, Serbia
3
Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
*
Author to whom correspondence should be addressed.
Crystals 2023, 13(5), 774; https://doi.org/10.3390/cryst13050774
Submission received: 3 April 2023 / Revised: 25 April 2023 / Accepted: 4 May 2023 / Published: 6 May 2023
(This article belongs to the Special Issue Artificial Intelligence for Crystal Growth and Characterization (2nd Edition))
Browse Figures
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Abstract

Oxynitrides of cerium are expected to have many useful properties but have not been synthesized so far. We identified possible modifications of a not-yet-synthesized Ce3O3N compound, combining global search (GS) and data mining (DM) methods. Employing empirical potentials, structure candidates were obtained via global optimization on the energy landscape of Ce3O3N for different pressure values. Furthermore, additional feasible structure candidates were found using data mining of the ICSD database. The most promising structure candidates obtained were locally optimized at the ab initio level, and their E(V) curves were computed. The structure lowest in total energy, Ce3O3N-DM1, was found via local optimization starting from a data mining candidate and should be thermodynamically metastable up to high pressures.

1. Introduction

Mixed-anion compounds, such as oxynitrides, contain more than one anionic species in the structure. Such systems are of great interest since the introduction of two different anions in the structure adds new degrees of freedom to control the system and allows us to tune both the electronic and the atomic structures, thus achieving properties that are inaccessible to compounds containing only a single anion species. For example, oxynitrides can exhibit photocatalytic and magnetic properties [1,2,3] and can be used as dielectrics and non-toxic pigments [4,5]. Oxynitrides are expected to have smaller band gaps and better transport properties than the corresponding oxide. The band gap of oxide photocatalysts can be tuned by introducing nitrogen into the structure [6]. Furthermore, the oxides doped with nitrogen exhibit attractive elastic, catalytical, and optical properties and can be used as superionic conductors [7]. Usually, oxynitrides are more stable in air and moisture than pure nitrides [8].
In general, the structures of most mixed-anion compounds have been explored to a lesser degree than those of pure oxides or nitrides. Nevertheless, there are more than 7000 documents in the Scopus and WoS databases, which include oxynitride compounds, with a recent noticeable increase in the number of research papers; there are currently 612 oxynitride materials listed in the ICSD database according to Kageyama et al. [9]. Such mixed-anion systems have been the subject of recent studies [10,11,12], which mostly focus on property screening for known and hypothetical oxynitrides. In a recent work by Sharan et al. [13], a first-principles computational approach was used for the proposal of novel ternary oxide–nitride materials using the kinetically limited minimization (KLM) algorithm.
However, the preparation of nitrogen-doped oxides is not trivial. Considering the case of ceria, we find that inserting nonmetals in the CeO2 is uncommon, where successful doping significantly changes the physical and chemical properties of ceria [14,15,16]. Usually, ceria is doped with phosphorus, carbon, sulfur, europium, lanthanum, and praseodymium [17,18,19,20]. In this way, finding a stable ceramic compound with Ce3O3N composition would be attractive, both for science and technology, since this ceramic could have many intriguing properties.
Nevertheless, finding stable or metastable compounds with a Ce-O-N composition is not straightforward because cerium appears in its compounds with different oxidation numbers (+III) and (+IV), or even with both of the two valences. One of the most common compounds with Ce (+IV) is CeO2, showing cubic symmetry (Fm-3m) and fluorite structure type [21,22]. One more cerium oxide is Ce2O3, consisting of Ce in the (+III) oxidation state. Nevertheless, Ce2O3 can exhibit both valences, which depend on the temperature, number of vacancies, foreign ions, and oxygen pressure [23,24].
Our idea was to investigate the cerium–oxygen–nitride compound. Since cerium appears in two oxidation states, Ce4+ in Ce2ON2 and Ce3+ in Ce3O3N, it was necessary to investigate two completely different compositional subspaces of the Ce/O/N system. In our previous work, we identified possible modifications in Ce2ON2, combining structure prediction methods with local optimization [25]. We should emphasize the difference in global search settings for these two systems. Firstly, the ionic radius of Ce3+ is larger than Ce4+, and this should be considered during a global search. Additionally, Ce4+ usually builds compounds with coordination VI, while Ce3+ prefers coordination VIII. Furthermore, the anion distribution is quite different since, in Ce2ON2, one formula unit consists of five atoms (three anions and two cations), while in Ce3O3N, one formula unit contains seven atoms (four anions and three cations).
In this study, we investigate the hypothetical cerium oxynitride Ce3O3N composition, with Ce3+ cations, utilizing computational methods; so far, only one proposed candidate structure exists, exhibiting monoclinic P21 symmetry [13]. The candidates with different structures are generated using two approaches—the global optimization of the energy landscape and data mining search, followed by local optimization on the ab initio level of the most promising candidates. The two structure generation procedures find different sets of low-energy structures, which agrees with the general observation that employing a multi-method approach instead of using only a single tool to generate candidate structures is highly useful to efficiently increase the structural variety of the set of structure candidates.

2. Computational Details

Predicting feasible stable or metastable structures for the Ce3O3N system was performed using a two-step approach, integrating global optimization and data mining [26,27,28]. The global search (GS) of the energy landscape was performed in the first part of our study, and the results were supplemented by the outcome of a database search.
The enthalpy landscape of the Ce3O3N compound was explored for several pressures, utilizing simulated annealing [29] as an algorithm for the global search, combined with periodic local optimizations along the search trajectory. The standard stochastic simulated annealing based on (many) random Monte Carlo walks on the energy landscape was followed by periodic stochastic quenches, carried out with the G42+ code [30]. The global searches were accomplished for one, two, and three formula units and six different pressures in Gpa (0; 0.016; 0.16; 1.6; 16, and 160). The move class of the random walk included the following moves: shifts in all atoms only (20%); random shift in atoms within a box around a randomly specified atom (30%); shift in all atoms and change in the cell parameters together with atom movement (20%); change in all cell parameters with fixed atoms (10%); and change in all cell parameters with atom movement (20%). This is usually combined with a short stochastic quench. To perform the global searches with a rational computational effort, a fast computable empirical two-body potential consisting of Lennard–Jones and Coulomb terms was employed [31].
Next, we performed data-mining-based explorations of the ICSD database, Refs. [32,33] to find additional structure candidates in the Ce3O3N system via analogy to known crystallographic structures. This data mining search gave us additional structure candidates since a global search is not reliable to identify every possible candidate. When globally searching on empirical energy landscapes, some important candidates may not be identified, either because of computation time limitations or because of the inherent limitations of the empirical potential as an energy function, i.e., these missing structures may not correspond to local minima on the empirical landscape. On the other hand, performing the complete global search on the ab initio landscape for complex systems is often not feasible due to the several orders of magnitude larger computational effort compared to the search on the empirical potential landscape. Therefore, data mining is a very useful supplementary method for identifying potential structure candidates in not-yet-synthesized chemical systems.
For the database mining, we employed a systematic procedure known as KDD (knowledge discovery in databases), involving selection, pre-processing, transformation, and interpretation/evaluation (or post-processing), to identify a sufficiently large number of structure candidates for the Ce3O3N system from the ICSD database [32,33]. In our first run, we found 76,415 candidates belonging to the ternary systems in the ICSD database. The results were filtered by introducing the general formula AB3 × 3, resulting in 298 structure candidates. The candidates with the formula A3B3C occurring in the ICSD were extracted, followed by a prototype analysis to reduce the excess of candidates to a feasible number of different types of structures [27,34,35]. After eliminating duplicates, we obtained 19 structure candidates (see Supplementary Information).
Finally, ab initio calculations of the total energy and ab initio local optimizations of the structure candidates found after global search and data mining were accomplished with the CRYSTAL17 code [36], ground on linear combinations of atomic orbitals. Analytical gradients were used for the local optimization runs [37,38]. Local optimizations were performed at the DFT level by applying the local density approximation (LDA). For the Ce3+, a pseudopotential [39] was used with a [4s4p2d3f] basis set; for O2−, a [4s3p] basis set was used [40,41], and for N3− [3s2p], an all-electron basis set based on Gaussian-type orbitals was employed [42,43]. The symmetries of the analyzed structures were resolved using the program KPLOT [44]. Finally, structures were visualized using the Vesta software [45]. Here, we note that the local optimization of the data mining candidates often leads to quite substantial changes in the structure compared to the one originally extracted from the database, beyond just a simple rescaling of cell parameters.

3. Results and Discussion

3.1. Candidates Generated via Global Exploration of the Energy Landscape at the Empirical Level

During the exploration of the enthalpy landscape using global optimization for different numbers of formula units (Z = 1, 2, 3), and six different pressures (0, 0.016, 0.16, 1, 6, 16, and 160 GPa), we found over 10,000 structure candidates. Initially, for each of these structure candidates, the symmetry was determined using the KPLOT code and the algorithms SFND [46] and RGS [47] implemented therein. In this way, we sorted the initial structures according to the space groups. They were then compared with each other using the CMPZ algorithm [48] to find duplicates with the same structure types. To identify the best candidates for local optimization, the crystallographic features of the obtained structures were investigated in detail.
The global search results for various pressures and one formula unit of Ce3O3N are presented in Table 1. One can observe that most of the local minima correspond to strongly distorted structures with space group P1. In addition to these candidates, the enthalpy landscape of Ce3O3N with Z = 1 contains many different structure candidates with non-trivial symmetry, i.e., a space group different from P1 or P-1, for the 0 to 160 GPa pressure range. Most of the structure candidates show relatively low symmetry (triclinic and monoclinic), but some high-symmetry candidates appear. For Z = 1, apart from the P1 structures, the most frequently observed structures appear in space groups Pm (no. 6) and Cm (no. 8) (Table 1). Among the candidates with orthorhombic symmetry, the most common ones exhibit space groups Pmm2 (no. 25) and Amm2 (no. 38), while most of the structures with cubic symmetry appear in space group Pm-3m (no. 221).
When the pressure increases, the number of distorted structures decreases. At the highest pressure in this study (160 GPa), only 332 structures with space group P1 for Z = 1 were obtained (Table 1).
For two formula units, Ce6O6N2, the number of structure candidates found with non-trivial symmetry is much smaller than for Z = 1. Thus, the subsequent statistical and crystallographic analysis of the enthalpy landscapes with Z = 2, at pressures up to 160 GPa, yielded only a few additional candidates with non-trivial symmetry, all of which were discarded after the local optimization step as being unstable and/or of too high energy.
For Z = 3, there are no new structure candidates with non-trivial symmetry among the 4800 minimum configurations. Quite generally, we note that with an increase in the formula unit number, many more local minima with quite low energy corresponding to defect structures or that exhibit several different coordination polyhedra of Ce atoms by O and N atoms appear. Since these polyhedra are usually distorted due to the different ionic radii of O2− and N3−, and there are many ways to arrange the anions around the cation, the number of symmetries of such a structure is greatly reduced compared to the case of the minimal number of formula units/simulation cells. In particular, the anion arrangements in the coordination polyhedra often do not differ by much in energy, and, thus, they are also found during the global search. This is expected since when the composition of the chemical system exceeds two types of atoms, the number of local minima that correspond to structures containing “defects” increases (where “defect” here refers to the non-optimal distribution of the two types of anions over the corners of the coordination polyhedra around the Ce ions, which is slightly higher in energy than the optimal distribution), and, in this way, most of the structure candidates show P1 (no. 1) symmetry, even though their energies are quite low.
Next, for each of the candidates with non-trivial symmetry from Table 1, a local optimization at the ab initio level was performed. After the local optimizations, we ranked the structures obtained according to the total energy values.

3.2. Candidates Generated via Data-Mining-Based Searches

The best structure candidates according to the total energy criterion are given in Table 2. The data mining search used the ICSD database [32], containing more than 200,000 inorganic structures. As a criterion for being chosen as structure candidates, we considered different structure prototypes in the ternary A3B3C system. After eliminating duplicate structures, we obtained 19 structure candidates: Al3ScC3 [49], Ba3FeN3 [50], Ca3PI3 [51], Ca3InP3 [52], Cu3SbS3 [53], Fe3TlTe3 [54], Fe3W3C [55], Gd3MnI3 [56], K3AlSe3 [57], K3BS3 [58], K6Sn2Te6 [59], KB3H3 [60], Na3AsS3 [61], Ni3SmGe3 [62], NiSc3Si3 [63], (proustite) [64], Rh4C12O12 [65], Tl3AsSe3 [66], and Ag3AsS3 (xanthoconite) [67].
Following local optimization at the ab initio level using LDA, most of the data mining structure candidates became unfavorable according to the total energy compared to the candidate structures obtained via the global search. Only one candidate, obtained starting from Ag3AsS3 (proustite) structure type after local optimization, yielded—after substantial rearrangements—the Ce3O3N-DM1 structure, which exhibited the lowest total energy among all structure candidates (Table 2). Among the structure candidates obtained during the global optimization, the one with the lowest total energy after the local optimization was Ce3O3N-GS1, adopting space group P2/m (no. 10), which is the same as the one found after the global search. Surprisingly, the Ce3O3N-GS1 structure candidate was not frequently observed during the global search on the empirical energy landscape (Table 1). Relative energies are also given in Table 2, showing the energy differences between the minima on the landscape. For further discussions, we considered all the structures with relative energies below 0.03 Eh/f.u. (corresponding to a temperature of ca. 1300 K) as the most favorable modification feasible for realistic experimental conditions.
In the next step, we computed the energy vs. volume curves (equations of state) at the ab initio level using the LDA functional for the six most relevant structure candidates in the Ce3O3N system (Figure 1). It appears that the Ce3O3N-DM1 modification is the global minimum with quite a dense structure, while all other local minima found after global search (GS1-GS5) appear in the low-density region with higher ab initio energies. As a consequence, the Ce3O3N-DM1 modification is expected to remain the thermodynamically preferred Ce3O3N phase at elevated pressures.

4. Crystal Structure Analysis

Structure details, including unit cell parameters and atomic positions for the most relevant structure candidates, are given in Table 3. Bond lengths inside the different coordination polyhedra for the most relevant Ce3O3N modifications are presented in the Supplementary Material (Table S1). Furthermore, structure details for the structurally interesting but energetically not favorable structure candidates (Ce3O3N-GS6, Ce3O3N-GS7, Ce3O3N-DM2, and Ce3O3N-DM3) are also shown in Tables S1–S3 and Figure 5.
The Ce3O3N-DM1 modification exhibits the trigonal space group R3c (no. 161). Cerium is 8-fold coordinated with six oxygen and two nitrogen atoms, with a mean distance of about 2.48 Å. As remarked above, the structure of the Ce3O3N-DM1 (Figure 2a) modification noticeably differs from the initial Ag3AsS3 (proustite) structure type shown in Figure 2b: starting from the initial proustite [64] structure type, the local optimization resulted in a completely different arrangement of atoms while keeping the space group R3c (161).
It is noteworthy that the Ce3O3N-DM1 modification was only found via an intermediary structure candidate using data mining, and that, in compliance with the E(V) curves, the Ce3O3N-DM1 modification is a distinctive equilibrium structure type and global minimum up to high pressures.
The Ce3O3N-GS1 structure candidate is in the space group P2/m (no. 10) and was found after the global optimization. The structure is shown in Figure 3a where the unit cell parameters are: a = 5.89 Å; b = 3.62 Å; c = 5.04 Å, and β = 113.3°. Cerium is in 7-fold coordination (with atom–atom distances of 2 × 2.37 Å—O, 2 × 2.44 Å—N, 1 × 2.30 Å—O, 1 × 2.39 Å—O, 1 × 2.75 Å—O), where the mean distance is 2.53 Å, and 6-fold coordination (with atom–atom distances of 4 × 2.34 Å—O, 2 × 2.52 Å—N), where the mean distance is 2.40 Å. However, the one 6-fold coordinated cerium atom resides inside a nice octahedral polyhedron, while the other Ce atom is surrounded by a distorted octahedron since it has one longer bond to an oxygen atom (1 × 2.75 Å—O), and it might be regarded as a 6 + 1 coordination. This structure is the most stable candidate from the global search output and is ranked second in Figure 1. Inspecting the E(V) curves, one can expect this modification to be the preferred one in the effective negative pressure region where a phase transformation from Ce3O3N-DM1 to Ce3O3N-GS1 may occur. This could indicate a possible synthesis route via, e.g., crystallization from an amorphous phase deposited from the gas phase, as was recently used in the synthesis of a new gallium modification (β’-gallium) [68].
Among the many candidates with orthorhombic symmetry, the Ce3O3N-GS2 modification is the most stable one and is ranked as the third one in total energy (Figure 1 and Figure 3b). This structure type is characterized by Ce atoms in distorted octahedral coordination. In the first type of octahedra, with a mean Ce-anion distance of 2.36 Å, there is only one nitrogen atom, while in the second type of octahedra, with a mean distance of 2.42 Å, two nitrogen atoms are present. Nevertheless, these polyhedra are strongly deformed where the distances from the Ce ions to the oxygen and nitrogen anions range from 2.23 to 2.61 Å (Figure 3b).
There are four candidates with orthorhombic symmetry among the top five GS modifications according to the total energy ranking (Table 1). In addition to the above-mentioned Ce3O3N-GS2 modification with orthorhombic Amm2 (sg. 38) symmetry, there are Ce3O3N-GS3, Ce3O3N-GS4, and Ce3O3N-GS5 with Imm2 (sg. 44), Pmmm (sg. 47), Amm2 (sg. 38) space groups, respectively.
Next, the orthorhombic modifications (especially with sg. 38 and 44) were found to be favorable modifications at high pressures during global optimization with empirical potential (Table 1). After DFT local optimization, these structures appeared to belong to the high-temperature region as metastable phases, which would indicate the need for elevated pressures and temperatures during their synthesis.
In the Ce3O3N-GS3 structure, there are two kinds of polyhedra, building two different alternating layers (Figure 4a). In the first layer, where oxygen prevails, there is a Ce cation coordinated with six oxygen atoms and one nitrogen atom. Another layer is made from octahedra with four nitrogen atoms with the same bond length Ce−N of 2.39 Å, and two oxygen atoms at approximately the same distance of 2.28 Å. This structure is interesting since we, for the first time, have a candidate where the oxygen and nitrogen atoms tend to separate and arrange themselves in layers. This kind of arrangement is not as energetically favorable as those of structures DM1, GS1, and GS2, where the distribution of the anions is more random.
Only the octahedral coordination of cerium is present in the Ce3O3N-GS4 structure candidate (Figure 4b), in contrast to the Ce3O3N-GS1 and Ce3O3N-GS3 structures where we also had a seven-fold coordination of cerium. One should emphasize the difference in the mean Ce-anion distances of the octahedra: there are octahedra with a mean Ce-anion distance of 2.30 Å, and another one with an average Ce-anion distance of 2.42 Å. Interestingly, both octahedra include four oxygen and two nitrogen atoms.
The last promising GS modification considered in the energy vs. volume, E(V), curves (Figure 1) for Ce3O3N-GS5, as shown in Figure 4c. We note that Ce3O3N-GS3 and Ce3O3N-GS5 are related: they are close in energy, both designate high-pressure and high-temperature synthesis conditions, and both appear in orthorhombic symmetry (Figure 3a,c). Furthermore, they have similar structures, with the same coordination polyhedra (6- and 7-fold). The main difference is in the way the polyhedra are connected. They appear as polytypes, similar to what we found in our previous studies [69,70,71]. The separation of layers where oxygen dominates from the layers with mostly nitrogen anions is pronounced.
There is one more GS candidate that should be mentioned, even if it is energetically not as favorable as the modifications included in Figure 1. This structure is mentioned in Table 1 as Ce3O3N-GS7 with Pm-3m (221) symmetry and shown in Figure 5b. Interestingly, local optimizations of various configurations initially exhibiting space groups R3 (sg. 146), R3m (sg. 160), P4mm (sg. 99), P432 (sg. 207), and R32 (sg. 155) all resulted in the conversion of the starting structures into a modification with cubic Pm-3m (sg. 221) symmetry. This suggests that this candidate represents a large local multi-minimum basin at an empirical potential level. Additionally, since structures with space groups 160 and 99 are only found in the high-pressure regime (160 Gpa) during the global search (Table 2), structures with this cubic Pm-3m (221) symmetry can be expected to be of relevance at extremely high pressures in the Ce3O3N system.
Regarding other structures we obtained after the local DFT optimization, starting from either the global search minima or the data mining results, we will not discuss them in detail since we consider them energetically unfavorable. Figure 5 shows the visualization of predicted non-favorable structures of Ce3O3N: the Ce3O3N-GS6 in the orthorhombic space group Pmmm (Figure 5a); the Ce3O3N-GS7 in the cubic space group Pm-3m (Figure 5b); the Ce3O3N-DM2 in the hexagonal space group P63/m (Figure 5c); and Ce3O3N-DM3 in the cubic space group I-43m (Figure 5d). Tables with their full structural details are given in the Supplementary Material (Tables S2 and S3). Specifically, the data mining candidates, except the Ce3O3N-DM1 modification, are very high in total energy (Table 1) and are, thus, not of interest for further analysis.
Finally, it is interesting to record that in the five relevant GS structure candidates, the cerium cations are seven- or six-fold coordinated by the anions, where the only difference is the coordination polyhedra shape and the connection between them. On the other hand, the energetically most favorable modification, Ce3O3N-DM1, comprises eight-fold coordinated polyhedra around Ce cations. This suggests that the ratio of the ionic radii between Ce3+ and O2− and N3− might be too small in the parameters of the empirical potential employed, which had been fitted originally to the binary Ce2O3 and CeN structures. Furthermore, it demonstrates the general observation that not a single exploration method but a combination of several, such as global search and data mining for the Ce3O3N system studied here, is most effective for finding sets of suitable candidates of a not-yet-synthesized chemical compound [72].
In the literature, there was a recent proposal of a structure candidate for the Ce3O3N system in the space group P21 (no. 4) [13]. We optimized the proposed structure candidate together with the best candidates from the global and data mining search (Ce3O3N-DM1 and Ce3O3N-GS1) using the VASP code and the LDA functional for comparison, since the optimization in the literature structure was not possible with the CRYSTAL17 code. According to the VASP calculations, the proposed structure candidate from the literature has a higher energy than the present Ce3O3N-DM1 and Ce3O3N-GS1 candidates (see Supplementary Information, Table S4). Of course, there is a possibility for changes in the total energy ranking by using a different functional (e.g., GGA), basis set, etc., and, thus, the corresponding predicted structure in the space group P21 (no. 4) [13] should be included as a potential structure candidate for experimental synthesis in the Ce/O/N system with Ce in the oxidation stage III.
While this study focuses on the single ternary system Ce3O3N and the determination of possible candidate modifications of this composition, it is interesting to know whether these candidates would be thermodynamically stable or metastable with regard to the decomposition into the boundary phases Ce2O3 and CeN, Ce3O3N => Ce2O3 + CeN. After computing the ab initio energies of Ce2O3 and CeN at the same level of accuracy as for Ce3O3N, we found that the total energy of Ce3O3N-DM1 was higher than the sum of total energies for Ce2O3 + CeN. The difference is 0.62 eV per formula unit, i.e., about 0.09 eV/atom, which indicates that, at low temperatures, Ce3O3N-DM1 would be thermodynamically unstable against such a decomposition. Nevertheless, this does not mean that this mixed cerium oxynitride compound could not be kinetically stable at low temperatures, i.e., once such a modification has been synthesized, it might well be stable for long periods at sufficiently low temperatures and, thus, could be employed in applications.

5. Conclusions

In this study, we explored the energy landscape of the not-yet-synthesized c cerium oxynitride Ce3O3N ceramic and predicted several feasible modifications for this compound. The prediction of new modifications with the composition Ce3O3N was performed by combining global optimization at the empirical potential level with a data mining procedure, where the energy landscape was explored for different pressure values and various numbers of formula units in the simulation cell. In the second step, local structure optimizations of the candidates obtained during the global search and the data mining prototyping approach were performed at the ab initio level, and the structures of the various candidates were analyzed. This analysis showed that by combining global search and data mining, we obtained six low-energy modifications that could be realized as (meta)stable modifications, thus emphasizing the importance of combining different methods in the search for feasible structure candidates, especially in hypothetical systems.
For the fixed composition Ce3O3N, i.e., without considering a possible decomposition into the boundary phases Ce2O3 and CeN, the Ce3O3N-DM1 modification, with an Ag3AsS3 (proustite) structure, is predicted to be the thermodynamically stable modification in standard conditions. The stability of Ce3O3N-DM1 also extends to high pressures, while at effective negative pressures, the Ce3O3N-GS1 modification should be synthetically accessible. Four predicted orthorhombic modifications, Ce3O3N-DM2, 3, 4, and 5, might be stable at high temperatures. Following on from our earlier study of the feasible modifications of composition Ce2ON2 [25], this work provides a further glimpse into the potential structural richness of the Ce-O-N system and supports attempts to synthesize the predicted modifications of Ce3O3N, guided by our analysis of the energy landscape of this chemical system.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/cryst13050774/s1. Table S1: Bond lengths inside of different coordination polyhedra for various Ce3O3N modifications; Table S2: Space group, unit cell parameters (Å), atomic positions, and total energy values in Hartrees (Eh) for eight optimized modifications found using the global search method; Table S3: Space group, unit cell parameters (Å), atomic positions, and total energy values in Hartrees (Eh) for three optimized modifications found using the data mining method; Table S4: Total energy ranking in eV for the best candidates from the global energy landscape and data-mining searches (Ce3O3N-DM1, and Ce3O3N-GS1) and literature data calculated using the VASP code and the LDA functional.

Author Contributions

D.Z., B.M. and J.C.S. conceived the idea; the global search and ab initio structure optimizations were performed by D.Z. and J.Z.; M.P.Đ. collected and analyzed the literature and computational data, M.P. collected and analyzed the literature and computational data. All authors contributed to the discussion and writing of the paper. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through Contract No. 451-03-47/2023-01/200017.

Data Availability Statement

Not applicable.

Acknowledgments

The authors are grateful to R. Dovesi, K. Doll, and Crystal Solutions for software support with CRYSTAL code.

Conflicts of Interest

The authors declare no conflict of interest.

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Crystals 13 00774 g001
Figure 1. Energy vs. volume, E(V), curves for the six most stable and energetically favorable structure candidates of Ce3O3N obtained using the LDA functional. Energies per formula unit are given in Hartree (Eh).
Figure 1. Energy vs. volume, E(V), curves for the six most stable and energetically favorable structure candidates of Ce3O3N obtained using the LDA functional. Energies per formula unit are given in Hartree (Eh).
Crystals 13 00774 g001
Crystals 13 00774 g002
Figure 2. Visualization of structure for (a) Ce3O3N-DM1 modification in space group R3c (161); (b) initial Ag3AsS3 (proustite) structure type. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Figure 2. Visualization of structure for (a) Ce3O3N-DM1 modification in space group R3c (161); (b) initial Ag3AsS3 (proustite) structure type. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Crystals 13 00774 g002
Crystals 13 00774 g003
Figure 3. Visualization of the structure for (a) Ce3O3N-GS1 in monoclinic space group P2/m; (b) Ce3O3N-GS2 in orthorhombic space group Amm2. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Figure 3. Visualization of the structure for (a) Ce3O3N-GS1 in monoclinic space group P2/m; (b) Ce3O3N-GS2 in orthorhombic space group Amm2. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Crystals 13 00774 g003
Crystals 13 00774 g004
Figure 4. Visualization of structure for three orthorhombic global search candidates: (a) Ce3O3N-GS3 in space group Imm2; (b) Ce3O3N-GS4 in space group Pmmm; and (c) Ce3O3N-GS5 in space group Amm2. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Figure 4. Visualization of structure for three orthorhombic global search candidates: (a) Ce3O3N-GS3 in space group Imm2; (b) Ce3O3N-GS4 in space group Pmmm; and (c) Ce3O3N-GS5 in space group Amm2. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Crystals 13 00774 g004
Crystals 13 00774 g005
Figure 5. Visualization of the structure for (a) Ce3O3N-GS6 in space group Pmmm; (b) Ce3O3N-GS7 in space group Pm-3m; (c) Ce3O3N-DM2 in space group P63/m; and (d) Ce3O3N-DM3 in space group I-43m. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Figure 5. Visualization of the structure for (a) Ce3O3N-GS6 in space group Pmmm; (b) Ce3O3N-GS7 in space group Pm-3m; (c) Ce3O3N-DM2 in space group P63/m; and (d) Ce3O3N-DM3 in space group I-43m. Cerium, oxygen, and nitrogen atoms are shown as violet, red, and grey spheres, respectively.
Crystals 13 00774 g005
Table 1. Frequency of the space groups obtained for the results of the search at a global level performed at different pressures for Z = 1 of Ce3O3N.
Table 1. Frequency of the space groups obtained for the results of the search at a global level performed at different pressures for Z = 1 of Ce3O3N.
Pressure
(GPa)		Space Group No.
1356810162538444799115146155160207221
0379--3211--7-2-1------
0.01637621277--102--11-1-13
0.16368--383115-111----310
1.637312269--73--1--1-27
16370232510---72------67
160332-3362011516111--4-2--
Σ21985918460223428612414221227
Table 2. Energy ranking of the structure candidates from the global search (GS) and data mining (DM) after ab initio optimization. The total energy (in Eh) and relative energy values (in Eh and kcal/mol) per formula unit (f.u.) compared to the global minimum (Ce3O3N-DM1 structure taken as the zero of energy), computed using the LDA-PZ functional.
Table 2. Energy ranking of the structure candidates from the global search (GS) and data mining (DM) after ab initio optimization. The total energy (in Eh) and relative energy values (in Eh and kcal/mol) per formula unit (f.u.) compared to the global minimum (Ce3O3N-DM1 structure taken as the zero of energy), computed using the LDA-PZ functional.
ModificationSpace Group (No.)Total Energy (Eh)Relative Energy
in Eh (kcal/mol)
Ce3O3N-DM1R3c (161)−1702.48750
Ce3O3N-GS1P2/m (10)−1702.48130.0062 (3.89)
Ce3O3N-GS2Amm2 (38)−1702.46850.0190 (11.92)
Ce3O3N-GS3Imm2 (44)−1702.46270.0248 (15.56)
Ce3O3N-GS4Pmmm (47)−1702.45880.0287 (18.01)
Ce3O3N-GS5Amm2 (38)−1702.45760.0299 (18.76)
Ce3O3N-GS6Pmmm (47)−1702.45090.0366 (22.97)
Ce3O3N-GS7Pm-3m (221)−1702.43940.0481 (30.18)
Ce3O3N-DM2P63/m (176)−1702.40070.0868 (54.47)
Ce3O3N-DM3I-43m (217)−1702.28370.2038 (127.89)
Table 3. Space group, unit cell parameters (Å), and atomic positions for the most relevant Ce3O3N modifications.
Table 3. Space group, unit cell parameters (Å), and atomic positions for the most relevant Ce3O3N modifications.
ModificationSpace Group (No.)Cell Parameters (Å) and Fractional Coordinates
Ce3O3N-DM1R3c (161)a = 10.17; c = 6.15
Ce (−0.1996 −0.0378 0.2416)
O (−0.0656 0.2200 0.3762)
N (0 0 0.0066)
Ce3O3N-GS1P2/m (10)a = 5.89; b = 3.62; c = 5.04; β = 113.2°
Ce (0 0 0)
Ce (0.3017 1/2 0.6238)
O (0.2702 1/2 0.0652)
O (1/2 0/2)
N (0 0 1/2)
Ce3O3N-GS2Amm2 (38)a = 3.59; b = 9.83; c = 5.78
Ce (1/2 0.1729 0.8911)
Ce (0 0 0.3964)
Ce (1/2 0 0.8038)
O (0.5 0 0.1402)
O (0 0.7712 0.1681)
N (1/2 0 0.6528)
Ce3O3N-GS3Imm2 (44)a = 3.38; b = 3.39; c = 17.39
Ce (0 0 0.7735)
Ce (0 0 0.4276)
Ce (0 0 0.0814)
O (0 0 0.5589)
O (0 0 0.2961)
O (0 1/2 0.1775)
N (0 0 0.9277)
Ce3O3N-GS4Pmmm (47)a = 6.86; b = 3.53; c = 4.62
Ce (1/2 0 0)
Ce (0.7607 1/2 1/2)
O (0.2869 1/2 0)
O (0 0 1/2)
N (1/2 0 1/2)
Ce3O3N-GS5Amm2 (38)a = 3.49; b = 3.32; c = 17.93
Ce (1/2 0 0.0970)
Ce (0 0 0.4475)
Ce (1/2 0 0.8038)
O (0 0 0.5730)
O (0 0 0.3143)
O (1/2 0 0.6850)
N (1/2 0 0.9444)
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Zagorac, J.; Schön, J.C.; Matović, B.; Pejić, M.; Prekajski Đorđević, M.; Zagorac, D. Computational Discovery of New Feasible Crystal Structures in Ce3O3N. Crystals 2023, 13, 774. https://doi.org/10.3390/cryst13050774

AMA Style

Zagorac J, Schön JC, Matović B, Pejić M, Prekajski Đorđević M, Zagorac D. Computational Discovery of New Feasible Crystal Structures in Ce3O3N. Crystals. 2023; 13(5):774. https://doi.org/10.3390/cryst13050774

Chicago/Turabian Style

Zagorac, Jelena, Johann Christian Schön, Branko Matović, Milan Pejić, Marija Prekajski Đorđević, and Dejan Zagorac. 2023. "Computational Discovery of New Feasible Crystal Structures in Ce3O3N" Crystals 13, no. 5: 774. https://doi.org/10.3390/cryst13050774

APA Style

Zagorac, J., Schön, J. C., Matović, B., Pejić, M., Prekajski Đorđević, M., & Zagorac, D. (2023). Computational Discovery of New Feasible Crystal Structures in Ce3O3N. Crystals, 13(5), 774. https://doi.org/10.3390/cryst13050774

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