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Synthesis, Crystal Structure, Optical, and Thermal Properties of a Novel Quaternary Selenide EuErAgSe3
1 University of Tyumen, Volodarskogo St., 6, Tyumen, Russia
2 Kurgan State University, Sovetskaya St., 63, Building 4, Kurgan, Russia
3 Kirensky Institute of Physics, Akademgorodok St., 50, Building 38, Krasnoyarsk, Russia
4 Far Eastern State Transport University, Seryshev St., 47, Khabarovsk, Russia
5 Siberian Federal University, Svobodny Pr., 79, Krasnoyarsk, Russia
6 Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Sciences, Pervomaiskaya St., 91, Ekaterinburg, Russia
* Corresponding Author: Navruzbek Habibullayev. Email:
Chalcogenide Letters 2026, 23(7), 3 https://doi.org/10.32604/cl.2026.085815
Received 19 May 2026; Accepted 29 June 2026; Issue published 07 August 2026
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A novel quaternary selenide, EuErAgSe3, has been synthesized for the first time. The phase forms upon annealing in the 1120–1800 K range and retains its crystal structure upon cooling to ambient conditions. The phase was prepared by the ampoule method from EuSe and AgErSe2 powders, followed by annealing at 1270 ± 10 K for up to 300 h. Powder X-ray diffraction revealed that EuErAgSe3 crystallizes in the AgBiS2 structure type (space group Fm-3m) with the lattice parameter a = 5.95322(14) Å. The microhardness of the phase is 340 ± 15 HV. The optical band gap for direct transitions is 1.78 eV, and for indirect transitions, it is 1.36 eV. The phase begins to form in the temperature range 1120–1170 K, likely due to diffusion processes, and melts incongruently at 1830 ± 30 K. The formation of EuLnAgSe3 phases was predicted for Ln = Gd–Lu, Y and confirmed experimentally for Gd, with a = 5.9906(4) Å, and for Yb, with a = 5.9312(5) Å. In the EuLnAgSe3 series, the unit cell parameter decreases linearly with the ionic radius of Ln3+.Keywords
Quaternary rare-earth chalcogenides with the general formula
No reports on the synthesis, structure, thermal stability, or properties of possible compounds of the EuLnAgSe3 series have been reported in the literature. Erbium (Er 4f126s2) is a typical rare-earth element of the yttrium subgroup and exhibits an oxidation state of +3. The synthesis and study of phases formed by erbium makes it possible to predict phase compositions for RE elements of the yttrium subgroup on the basis of the tetrad effect [9,10,11].
The composition of the quaternary compounds (0.5 Ag2Se + 0.5 Ln2Se3 + EuSe (Ln = Sm − Lu)) lies in the Ag2Se–AgLnSe2–EuSe system. The low-temperature modification α-Ag2Se transforms at 407 K into the β-Ag2Se modification [12], which melts at 1170 K [13]. The melting point of AgErSe2 is not reported in the literature; however, based on the available data for the related compounds AgHoSe2 and AgDyS2, it is estimated to lie in the range 1500–1600 K. The phase transition temperature of AgHoSe2 is 1050 K [7], while for AgDyS2 the phase transition temperature is 1280 K and the melting point is 1830 K [14]. EuSe melts at 2488 K [15]. According to [16], the EuSe2 phase crystallizes in the tetragonal system, space group I4/mcm, СТ CuAl2 structure type, and begins to decompose at 842 K with the formation of EuSe.
The formation of new phases or solid solutions between isostructural phases can be examined using the Hume-Rothery rule. The Hume-Rothery rule considers the conditions for the formation of solid solutions and new compounds [17]. The formation of solid solutions requires similarity of crystal lattices, a difference in atomic radii of no more than 15%, and the same valence of the elements. An electronegativity difference exceeding 0.4–0.5 favors the formation of a new phase.
In this work, we report the synthesis of EuErAgSe3, its crystallochemical characteristics, optical band gap, thermal properties, and a prediction of the formation of EuLnAgSe3 phases for yttrium-subgroup rare-earth elements.
The rare-earth metals (99.99 at.% La, Nd, Sm, Gd, Er, Yb) were used in the form of pieces, europium oxalate powder (99.98 wt.% EuC2O4·nH2O) (Toplus, Ltd., Guangzhou, China), silver (99.99 at.% Ag) as an ingot, and selenium granules (99.998 at.% Se) (JSC Khimreaktiv, Yekaterinburg, Russia). Hydrogen gas (99.999%) was obtained by electrolysis of deionized water in a generator (Spektr LLC, Dzerzhinsk, Russia). Crucibles were made of MG-1 grade graphite.
The EuErAgSe3 sample was synthesized by the ampoule method from EuSe and AgErSe2. EuSe was obtained by the action of an H2Se flow on europium oxalate powder at temperatures of 1120–1220 ± 10 K [18]. The product was a dark brown powder of phase-pure EuSe, which adopted the NaCl-type structure (Fm-3m, a = 6.1676 Å) [19].
AgErSe2 was synthesized from the elemental substances. Weighed portions of the substances (±0.0001 g) were placed in a graphite crucible inside a quartz ampoule. The ampoules were evacuated to 0.2 Pa and sealed. The ampoule with the substance was heated to 1170 ± 10 K at a rate of 5 K/h and then held at 1170 ± 10 K for 100 h. The sintered cake obtained in the crucible was annealed at 1500–1520 ± 20 K for 20 min by heating the crucible by induction with high-frequency currents. Subsequently, the ampoule containing the resulting cylindrical sample was annealed in a muffle furnace at 1170 ± 10 K for up to 300 h. A phase-pure AgErSe2 sample was obtained. It crystallizes in the orthorhombic structure (space group P212121) with unit cell parameters a = 4.1527 Å, b = 6.8041 Å, c = 13.6201 Å [7].
To synthesize EuErAgSe3 in an amount of 5 g, weighed portions of EuSe and AgErSe2 were ground together in an agate mortar and placed in a graphite crucible inside a quartz ampoule, which was evacuated and sealed. In a high-frequency current setup, the crucible was heated to 1620 ± 20 K and held for 20 min. Dense, partially melted sinters containing more than 90 mol.% EuErAgSe3 were obtained. Subsequently, the ampoule with the sample was annealed in a muffle furnace at 1270 ± 10 K for up to 500 h. The resulting sample contained 98 ± 2 mol.% EuErAgSe3. Afterwards, the sample was divided into two parts: one part was left for physicochemical study, the second part was annealed at 720 ± 10 K in a closed evacuated ampoule for up to 500 h.
Synthesis of EuLnAgSe3 samples (Ln = La, Nd, Sm, Gd, Yb) was carried out by the ampoule method from the binary metal selenides Ln2Se3, EuSe and Ag1.9Se [18]. The Ag1.9Se precursor was prepared in an evacuated and sealed quartz ampoule, which was heated to 1270 ± 10 K at a rate of 100 K/h and subsequently cooled in air. A polycrystalline silver-colored sample containing 100 mol% Ag1.9Se was obtained; its unit cell parameters are a = 4.1527 Å, b = 6.8041 Å, c = 13.6201 Å, space group P212121 [20]. Ln2Se3 compounds (Ln = La, Nd, Sm, Gd, Tb, Yb) were also synthesized by the ampoule method with the following main-component contents: 100 mol.% Ln2Se3 (Ln = Sm, Gd, Tb, Yb), 98 mol.% Nd2Se3 [21,22].
For the preparation of 3 g EuLnAgSe3 samples (Ln = La, Nd, Sm, Gd, Tb, Yb), the Ln2Se3, EuSe, and Ag1.9Se powders were ground together in an agate mortar and placed in a graphite crucible inside a quartz ampoule, which was then evacuated and sealed. Using a high-frequency induction furnace, the crucible was heated to 1750 ± 20 K, held at 1600 ± 20 K for one hour, and finally annealed at 1270 ± 10 K for 240 h. Dense, partially fused sinters were obtained.
Powder diffraction data for EuErAgSe3 for Rietveld analysis were collected at room temperature on a Haoyuan DX-2700BH powder diffractometer (Cu-Kα radiation) using the equipment of the Krasnoyarsk Shared Research Center of the Siberian Branch of the Russian Academy of Sciences. The step size in 2θ was 0.01°, and the counting time was 0.2 s per step. The structure of EuHoAgS3 was used as the starting model for the Rietveld refinement, which was carried out using TOPAS 4.2 [23,24].
Differential thermal analysis (DTA) was performed on a SETARAM SETSYS Evolution analyzer equipped with a PtRh-6/30 thermocouple. Powdered samples weighing 100 mg were placed in a cone-shaped quartz ampoule with a volume of 0.1 mL, which was evacuated to 0.2 Pa and sealed. Heating was conducted at a rate of 10 K/min. DTA results were processed using the SETSOFT 2000 software [25]. The baseline enclosing the peak area was obtained by approximating the baseline segments before and after the peak. The diffuse shape of the peak, or the presence of several overlapping components, resulted in a rather low accuracy of the integrated heat effect determination: ±17%.
Visual thermal analysis (VTA) was carried out on a VTA-T setup [26,27]. Samples weighing 50 mg were placed in cylindrical molybdenum crucibles 5 mm in diameter and 10 mm in height, which have a recess at the end face for the sample and a BP 5/25 thermocouple. The setup was evacuated to 0.3 Pa and filled with argon to a pressure of 1.1 bar. The heating rate ranged from 100 to 250 K/min. The condition of the sample in the crucible was recorded with an MC-HD-5 video camera. The setup was calibrated against the melting points of Cu, Ni, Pd, Pt, and white sapphire. The calibration curve was constructed with an approximation accuracy of 98%. The accuracy of temperature determination is 0.5% of the temperature value.
Reflectance spectra were recorded on a Shimadzu UV-2600 spectrophotometer (Kyoto, Japan) using a powdered sample [28]. The distribution of chemical elements and the quantitative composition in the near-surface layer of the samples at a depth of about 3 μm were determined on a Tescan Mira 3 scanning electron microscope equipped with an Oxford Instruments X-Max EDS attachment. EDS analysis was carried out at an accelerating voltage of 20 kV. Processing of the EDS data and mapping were performed using the Aztec software. The instrumental accuracy of the determination of major components (content >10 wt.%) by the EDS method is ~0.9 wt.%, which yields an absolute error of ±0.5 wt.% at an element content of ~50 wt.%. The detection limit of the method is ~0.1–0.3 wt.% [29].
Microhardness was measured on an HMV-G21DT microhardness tester by the Vickers method [30]. Indentations were made automatically at an indenter load of 98.07 mN. With the 40× objective used, the accuracy of the indentation area measurement is 0.09 μm.
Microstructural analysis (MSA) of polished sections of the samples from various stages of synthesis and after DTA was performed on a Zeiss Axio Vert.A1 MAT microscope using the AxioVision SE64 software [31]. After DTA, the ampoule was mechanically processed until the sample substance was exposed and then polished to a mirror finish.
The large language model DeepSeek-R1 was employed as an auxiliary analytical tool for the crystal-chemical prediction of the formation of cubic EuLnAgSe3 phases [32].
3.1 Crystal Structure of EuErAgSe3
Diffraction data for EuErAgSe3 were collected in the 2θ range of 10–100°. All peaks were indexed by the cubic cell (space group Fm-3m, AgBiS2 structure type [33]) with parameters a = 5.95322(14) Å, V = 210.987(15) Å3 close to those of EuHoAgS3 [8]. Therefore, this structure was taken as the starting model for Rietveld refinement, which was performed using TOPAS 4.2. The site of Eu/Ho/Ag ions was occupied by Eu/Er/Ag ions (Fig. 1a) with fixed occupancies of 1/3 each, according to the suggested chemical formula. However, conventional powder X-ray diffraction does not allow the occupancies to be refined reliably; therefore, they were kept fixed. Thus, the Eu2+/Er3+/Ag+ ions in EuErAgSe3 are statistically distributed in the cation sublattice and occupy the same positions as the Eu2+/Ho3+/Ag+ cations in the β-modification of EuHoAgS3 [8] (Fig. 1b). The refinements were stable and gave low R-factors: Rwp = 8.45%, Rp = 5.96%, χ2 = 3.75, RB = 1.53%. The atomic coordinates and the main bond lengths are listed in Table 1.
The crystallographic data we obtained have been deposited at the Cambridge Crystallographic Data Centre and assigned the deposition number CSD-2466594. These data can be downloaded from the website—http://www.ccdc.cam.ac.uk/data_request/cif.
The EuErAgSe3 powder obtained by grinding the annealed sample is dark brown in color. The phase particles exhibit faceting typical of substances crystallizing in the cubic system: angles of 60° and 90°, edges, and faces (Fig. 1c).
Figure 1: Rietveld difference plot (a), crystal structure (b), and image of particles (c) of the EuErAgSe3 sample annealed at 1273 K.
Table 1: Fractional atomic coordinates, isotropic displacement parameters (Å2), and selected bond lengths (Å) for EuErAgSe3.
| Atom | x | y | z | Biso | Occupancy | Bond | Distance |
|---|---|---|---|---|---|---|---|
| Eu | 0.5 | 0.5 | 0.5 | 2.02(7) | 1/3 | Eu–Sei | 2.9700(1) |
| Er | 0.5 | 0.5 | 0.5 | 2.02(7) | 1/3 | Er–Sei | 2.9700(1) |
| Ag | 0.5 | 0.5 | 0.5 | 2.02(7) | 1/3 | Ag–Sei | 2.9700(1) |
| Se | 0 | 0 | 0 | 1.35(7) | 1 | - | - |
3.2 Microstructure and Microhardness of the EuErAgSe3
In the EuErAgSe3 sample obtained by annealing at 1270 ± 10 K, SEM data reveal a uniform distribution of the chemical elements constituting the main phase. The elemental composition measured at points 1 and 2 (Fig. 2, Table 2) corresponds to stoichiometric EuErAgSe3. The presence of individual grains of impurity phases was also detected; these were identified as Er2O2Se, Er2Si2O7, Ag2−xSe. The chemical composition of these phases indicates a tendency of erbium (III) selenide compounds to oxidize and form silicate compounds, which has also been noted in Refs. [18,34]. The involvement of erbium ions in side reactions leads to incomplete interaction between the components of the sample. The microhardness of the EuErAgSe3 phase was measured on well-formed crystals, and at least 20 clear indentations were made. The median microhardness value is 340 ± 15 HV.
Figure 2: SEM image of the surface of a polished cross-section of the EuErAgSe3 sample annealed at 1270 ± 10 K. Points 1 and 2 mark the spots where elemental analysis of the main phase was performed; the corresponding chemical composition is indicated in the figure.
Table 2: Content of chemical elements (at.%) at points 1, 2 (see Fig. 2) in a thin section of the EuErAgSe3.
| Theor. (at.%) | Point 1 (at.%) | Point 2 (at.%) | |
|---|---|---|---|
| Eu | 16.6 (6) | 18.1 | 18.3 |
| Er | 16.6 (6) | 15.1 | 15 |
| Ag | 16.6 (6) | 21.5 | 19.6 |
| Se | 50 | 45.3 | 47.1 |
| Compound | EuErAgSe3 | Eu1.2Er1.0Ag1.4Se3.0 | Eu1.2Er1.0Ag1.3Se3.1 |
The evaluation of the bandgap was conducted via the Tauc-like modified Kubelka-Munk treatment as described in [35]. Values p = 1/2 for dipole-allowed transitions occurring at a direct band gap, while p = 2 for dipole-allowed transitions near an indirect gap were used. EuErAgSe3, as Fig. 3 illustrates, is featured by narrower bandgap in comparison with EuErCuSe3: the bandgap for direct interband transition Eg direct = 1.78 ± 0.01 eV (energy range for fitting 1.818–2.023 eV, Pearson R = 0.9989), and the bandgap for indirect transition Eg indirect = 1.36 ± 0.05 eV (energy range for fitting 1.888–2.119 eV, Pearson R = 0.99889). The ion packing in the crystal structure of EuErAgSe3 is less dense than for EuErCuSe3. As XRD results show, for EuErAgSe3 (Eu1.33Er1.33Ag1.33Se4) the cell volume per one formula unit is 210.99(1) Å3. Ratio of the cell volume to the number of formula units equals to 141 Å3 for EuErCuSe3, while the unit cell volume of EuErAgSe3 divided by 1.33 is equal to 157 Å3, that indicates a denser packing in case of EuErCuSe3. However, despite a denser packing in EuErCuSe3, the Eu–Se distance is equal to 2.977 Å in EuErAgSe3, while in EuErCuSe3 it is equal to 3.066 Å.
Narrower bandgap of EuErAgSe3 in comparison to EuErCuSe3 correlates with the smaller Eu–Se distance, since at smaller Eu-Se distance a stronger crystal field at a separate Eu2+ ion must be expected. Stronger crystal field in case of a solitary Eu2+ ion in a lattice, as it is well-known, leads to a stronger red shift of a part of 5d energy levels of Eu2+, which are responsible for the formation of the bottom of conduction band upon the formation of the band structure, and consequently, for the formation of fundamental absorption edge. Similar behavior of Eu2+ energy levels is demonstrated, e.g., in [36] where stronger crystal field results in the red shift of the absorption bands.
Figure 3: Kubelka-Munk Function for EuErAgSe3 crystal modified for indirect (left) and for direct (right) interband transitions.
It is extremely interesting to note that Kubelka-Munk Function modified for indirect transition, aside from an evident region of the fundamental absorption onset, exhibits a minor step corresponding to 1.11 eV bandgap. Contrarily, for Kubelka-Munk Function modified for direct transition, aside from an evident region of the fundamental absorption onset, the higher lying linear region at 3.31 eV is pronounced. These features indicate onto a complicated band structure of EuErAgSe3.
The diffraction characteristics of the EuErAgSe3 phase did not noticeably change after the sample had been kept under ambient conditions for six months. During heating in the course of DTA, the EuErAgSe3 phase begins to decompose. The DTA trace exhibits a peak at 798 K with a distinct linear portion in the endothermic temperature range of the sample (Fig. 4a). The enthalpy of the peak increases during thermal cycling and reaches its maximum value for the multi-phase sample obtained by annealing EuErAgSe3 at 720 ± 10 K for 300 h. The peak is reproducible over heating and cooling cycles. The temperature closest to this peak is the decomposition temperature of the EuSe2 phase, 842 K [16], however, the formation peak of EuSe2 upon cooling is not detected by DTA.
Figure 4: DTA curves of the high-temperature phase of EuErAgSe3: 1 and 2—first and second heating–cooling cycles (a); DSC of the multiphase sample obtained by annealing EuErAgSe3 at 720 ± 10 K (b).
The presence of a linear segment in the first half of the peak at 798 K indicates that the observed melting process corresponds to an invariant phase equilibrium on the phase diagram. It was established, by analogy with Cu2S−EuS [37], that in the Ag2−xSe−EuSe system a eutectic forms at 10 ± 1.5 mol% EuSe and 930 ± 10 K. Several samples of a possible ternary eutectic were studied; however, the recorded temperatures of the onset of heat absorption fell within the range 850–870 K.
Microstructural analysis was performed on approximately 15 mg of the molten (sweated) portion of the sample after DTA (Fig. 4a). On the polished section, Ag2−xSe grains form a continuous phase, in which very small amounts of at least three types of grains were identified. Fine needle-shaped crystals exhibited the same morphology as EuSe crystals in their eutectic with Ag2−xSe. Small crystals forming chains were identified as Er2Se3. Several other crystals up to 2–3 μm in size remained unidentified. The grain morphology of the sample indicates the formation of a multicomponent eutectic. The peak at 798 K is caused by the melting of a eutectic situated close to the low-melting Ag2−xSe phase. The enthalpy of the peak at 798 K indirectly indicates the degree of decomposition of the EuErAgSe3 phase during heating; this decomposition increases upon thermal cycling (Fig. 4a,b).
Anosov [38] links the formation of a phase that exists only at elevated temperatures with the appearance of an endothermic effect in the reaction of its synthesis from equilibrium phases. For instance, the formation of the high-temperature phase CuSb3Se5 is accompanied by a pronounced peak at 718 K, which increases the enthalpy of the phase by ΔH = 17.7 kJ/mol [39]. No peak corresponding to the heat effect of the formation of EuErAgSe3 was detected by DTA. Prolonged annealing is required to achieve a high content of the EuErAgSe3 phase in the samples. Most probably, EuErAgSe3 is formed as a result of diffusion processes that start at temperatures of 1120–1170 K (Fig. 4a,b).
EuErAgSe3 was heated in a Visual Thermal Analysis (VTA) setup from room temperature to 1270 ± 10 K at 250 K/min and subsequently to 1670 ± 30 K at 150 K/min; the sample remained polycrystalline throughout the process (Fig. 5a). After holding at this temperature for 5 min and cooling to ambient temperature within 4–5 min, the resulting product contained 95 mol.% EuErAgSe3 with a = 5.9532 Å.
In a parallel experiment, a polycrystalline sample of EuErAgSe3 was heated at the same rate to 1830 ± 30 K (Fig. 5b). A melt appeared in various parts of the sample, and intensive melting of the whole sample occurred. At 1970 ± 30 K, no crystals remained in the crucible, and the melt formed was transparent (Fig. 5c). According to XRD and microstructure examination, the phase samples that were rapidly heated to melting and crystallized from the melt predominantly contain the EuSe, Ag2−xSe, Er2O2Se, and Er2Se3 phases, as well as up to several mol.% EuErAgSe3. The phase compositions of the cooled samples and the transformation of EuErAgSe3 into the melt indicate incongruent melting with the formation of a melt and crystals of the EuSe phase. The incongruent melting temperature of EuErAgSe3 is estimated as 1830 ± 30 K.
Figure 5: Appearance of the EuErAgSe3 sample at the following temperatures: 1670 ± 30 K—polycrystalline state (a), 1830 ±30 K—bulk melting (b), 1970 ± 30 K—complete melt (c).
The formation of the EuErAgSe3 phase at high temperatures (1120–1170 K) should be related to an increase in entropy due to the statistical distribution of three metal ions in the cation sublattice. The incongruent melting further confirms that at still higher temperatures (above 1830 K) the entropy contribution is no longer sufficient to stabilize the phase.
3.5 Prediction and Experimental Verification of the Formation of EuLnAgSe3 Phases
The EuErAgSe3 phase should be regarded as a chemical compound formed by isomorphic substitution in the EuSe phase of formal composition (EuSe)3, where two Eu2+ cations are simultaneously replaced by Ag+ and Er3+ cations. The formation of the phase is governed by several factors: size factor (ionic radii ratio), energetic factor (electronegativity ratio). The difference between the cation radius r(Eu2+, CN = 6) = 1.17 Å and the average radius of the substituting cations r(Ag+, CN = 6) = 1.15 Å and r(Er3+, CN = 6) = 0.89 Å (rav. = 0.5(r(Ag+) + r(Er3+)) = 1.02 Å) amounts to 12.8% [40]. According to the Hume-Rothery rules, the size factor (12.8%) does not exceed the threshold value of 15%, which makes substitution in the cation sublattice possible. The smaller rav. value accounts for the decrease in the unit cell parameters: EuSe a = 6.1676 Å, EuErAgSe3 a = 5.95322(14) Å.
According to the Hume-Rothery rules for the formation of continuous solid solutions, the electronegativity difference Δχ must not exceed 0.4–0.5. In the system under consideration, the electronegativity differences are Δχ(Eu–Ag) = |1.2 − 1.93| = 0.73, Δχ(Ag–Er) = |1.93 − 1.24| = 0.67 [41,42]; these values noticeably exceed the indicated threshold. This precludes the formation of an extended solid solution between EuSe and EuErAgSe3 and, on the contrary, promotes cation ordering and the formation of an individual compound. Application of the size and energy factors showed that EuLnAgSe3 compounds should form for the entire rare-earth series except Sc. Literature data on EuLnAgX3 phases and the proposed criteria for the formation of EuLnAgSe3 were communicated to the DeepSeek-R1 large language model [32], which also noted that “EuLnAgSe3 compounds form for La–Lu, while the formation is more favorable for cerium-subgroup rare-earth elements”.
Compositions with the ratio Ag1.9Se:1.9EuSe:0.95Ln2Se3 (Ln = La, Nd, Sm, Gd) were synthesized. The samples containing the rare-earth elements La, Nd, and Sm exhibit a similar phase composition: EuSe, Ag2−xSe and also phases with the Th3P4 structure type, EuLn2Se4 (Ln = La, Nd, Sm) (Fig. 6). The sample with Gd contains 97 mol% EuGdAgSe3, which crystallizes in the AgBiS2 structure type with a = 5.9906(4) Å (Fig. 7a).
Figure 6: Difference X-ray diffraction pattern obtained by the Rietveld method for the sample with the initial phase ratio Ag1.9Se:1.9EuSe:0.95Nd2Se3.
The phase composition data of the synthesized samples for La, Nd, Sm, Gd, and Er were analyzed using a language model. Based on these experimental results and several literature sources [6,7], the model proposed a new crystal-chemical factor (ρ). For ternary AgLnSe2 selenides, the cubic AgBiS2-type structure, which is a derivative of the NaCl-type, is stable only when the geometric criterion ρ = r(Ln3+)/r(Ag+) ≤ 0.82 is satisfied; this condition is met for Ln = Gd–Lu, Y. Exceeding this threshold ratio causes strong distortions of the octahedral polyhedron (see Section 3.1, Fig. 1b) that accommodates the cations, making it impossible to retain the cubic NaCl-type lattice. In the case of Cu-containing analogues, the r(Ln3+)/r(Cu+) ratio even for the smallest rare-earth cation Lu3+ amounts to 0.861/0.77 ≈ 1.12, which significantly exceeds the indicated threshold. This explains why cubic CuLnSe2 phases are unknown. The prompts will be provided in the Supplementary Materials.
Figure 7: Difference X-ray diffraction pattern obtained by the Rietveld method for the sample EuGdAgSe3 (a) and EuYbAgSe3 (b).
The application of three criteria (Δr ≤ 15%, Δχ ≥ 0.4 and ρ ≤ 0.82) to assess the formation of EuLnAgSe3 phases showed that the cubic phase may appear exclusively for heavy rare-earth elements—Ln = Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, as well as for Y. For experimental verification of the above prediction, an additional EuYbAgSe3 sample was synthesized; it contained 95 mol% EuYbAgSe3 with a = 5.9312(5) Å and crystallized in the AgBiS2 structure type (Fig. 7b). The decrease in the unit cell parameters in the EuLnAgSe3 series is fully consistent with the lanthanide contraction along the series of Ln3+ ionic radii: Gd, Er, Yb (Fig. 8a). The SEM/EDS results for the EuYbAgSe3 compound (Fig. 8b, Table 3) fully confirm the XRD data: the average elemental ratio for EuYbAgSe3 over three spectra was 1.00 Eu:1.00 Yb:1.05 Ag:3.05 Se, which is in good agreement with the expected 1:1:1:3 stoichiometry.
Figure 8: Plot of the unit cell parameters of EuLnAgSe3 compounds (Ln = Gd, Er, Yb) as a function of the ionic radius of Ln3+ (CN = 6) (a); SEM image of the surface of a polished cross-section of the EuYbAgSe3 sample annealed at 1270 ± 10 K, points 1–3 mark the spots where elemental analysis of the main phase was performed; the corresponding chemical composition is indicated in the figure (b).
Table 3: Content of chemical elements (at.%) at points 1–3 (see Fig. 8b) in a thin section of the EuYbAgSe3.
| Elements | Theoretical (at.%) | Point 1 (at.%) | Point 2 (at.%) | Point 3 (at.%) |
|---|---|---|---|---|
| Eu | 16.6 (6) | 16.4 | 16.5 | 16.1 |
| Yb | 16.6 (6) | 16.9 | 16.7 | 16.6 |
| Ag | 16.6 (6) | 17.7 | 17.1 | 17.1 |
| Se | 50 | 49.1 | 49.7 | 50.2 |
| Compound | EuYbAgSe3 | Eu1.0Yb1.0Ag1.1Se3.0 | Eu1.0Yb1.0Ag1.0Se3.0 | Eu1.0Yb1.0Ag1.1Se3.1 |
The band gap of EuGdAgSe3 was determined: an indirect transition at 1.42 eV and direct transitions at 1.72 and 4.05 eV (Fig. 9). The corresponding values for EuErAgSe3 are 1.36 eV (indirect) and 1.78, 3.31 eV (direct). The decrease in the transition energies from Gd to Er is caused by the lanthanide contraction: the smaller ionic radius of Er3+ (0.890 Å vs. 0.938 Å for Gd3+) leads to a reduction of the lattice parameter, which enhances the hybridization of Ln 5d and Se 4p states and, consequently, narrows the band gap.
All the experimental results fully confirm the proposed criteria for the formation of cubic EuLnAgSe3 phases (Δr ≤ 15% and ρ ≤ 0.82 for Ag) and demonstrate the feasibility of the targeted prediction of new quaternary selenides with a cubic structure.
Figure 9: Kubelka-Munk Function for EuGdAgSe3 crystal modified for indirect (left) and for direct (right) interband transitions.
The EuErAgSe3 phase was synthesized from samples of the EuSe and AgErSe2 phases by annealing at 1270 ± 10 K and retains its structure upon cooling to ambient conditions. The EuErAgSe3 crystallizes in the cubic system, space group Fm-3m, AgBiS2 structure type, with a = 5.95322(14) Å. The Eu2+/Er3+/Ag+ ions are statistically distributed over the cation sites. According to the Hume-Rothery rules, the formation of the phase became possible owing to a size factor of 12.8%, which lies below the 15% threshold. The considerable electronegativity differences, Δχ(Eu–Ag) = 0.73 and Δχ(Ag–Er) = 0.69, exceed the Hume-Rothery limit of 0.4–0.5 and account for the individuality of the EuErAgSe3 phase, which does not form a solid solution with EuSe. The phase particles exhibit faceting, with angles of 60° and 90°. The direct optical band gap for direct transitions is 1.78 eV, and the indirect one is 1.36 eV. The EuErAgSe3 phase begins to form at approximately 1120–1170 K, probably as a result of diffusion processes. The phase melts incongruently at a temperature of 1830 ± 30 K.
The possibility of the formation of EuLnAgSe3 compounds (Ln = La–Lu) was predicted on the basis of geometric, energetic, and crystal-chemical factors. The decisive factor proved to be the crystal-chemical criterion: the cubic NaCl-type structure is stable only when the condition ρ = r(Ln3+)/r(Ag+) ≤ 0.82 is satisfied, which is met for Ln = Gd–Lu and Y. The phases EuGdAgSe3 a = 5.9906(4) Å and EuYbAgSe3 a = 5.9312(5) Å were synthesized. For EuGdAgSe3, the band gap was determined: an indirect transition at 1.42 eV and direct transitions at 1.72 and 4.05 eV. Quantitative EDS analysis confirmed the stoichiometric elemental ratio in EuYbAgSe3. The unit cell parameters vary linearly along the EuLnAgSe3 series (Ln = Gd, Er, Yb). No quaternary compound forms for cerium-subgroup rare-earth elements.
The approach employing several types of criteria to predict the formation of cubic EuLnAgSe3 phases can be effective in the search for new quaternary selenides with a cubic structure. The EuLnAgSe3 phases are of potential interest owing to the presence of three cations statistically distributed over the cation sublattice.
Acknowledgement:
Funding Statement: State Assignment No. FEWZ-2024-0052 for University of Tyumen from the Ministry of Science and Higher Education of the Russian Federation funded the large language model (LLM)-based phase prediction employed in this study.
Author Contributions: Conceptualization, Oleg Andreev, Navruzbek Habibullayev; methodology, Oleg Andreev, Navruzbek Habibullayev; investigation, Navruzbek Habibullayev, Ilya Yurev, Maxim Molokeev, Aleksandr Aleksandrovsky, Nikita Shulaev, Svetlana Volkova; data curation, Navruzbek Habibullayev; writing—original draft preparation, Oleg Andreev, Navruzbek Habibullayev, Maxim Molokeev, Aleksandr Aleksandrovsky; writing—review and editing, Olga Trofimova; visualization, Navruzbek Habibullayev, Maxim Molokeev, Aleksandr Aleksandrovsky; supervision, Oleg Andreev. All authors reviewed and approved the final version of the manuscript.
Availability of Data and Materials: Data available on request from the authors.
Ethics Approval: Not applicable.
Conflicts of Interest: The authors declare no conflicts of interest.
Supplementary Materials: The supplementary material is available online at https://www.techscience.com/doi/10.32604/cl.2026.085815/s1.
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