Single Crystals of EuScCuSe₃: Synthesis, Experimental and DFT Investigations

Abstract

EuScCuSe₃ was synthesized from the elements for the first time by the method of cesium-iodide flux. The crystal belongs to the orthorhombic system (Cmcm) with the unit cell parameters a = 3.9883(3) Å, b = 13.2776(9) Å, c = 10.1728(7) Å, V = 538.70(7) ų. Density functional (DFT) methods were used to study the crystal structure stability of EuScCuSe₃ in the experimentally obtained Cmcm and the previously proposed Pnma space groups. It was shown that analysis of elastic properties as Raman and infrared spectroscopy are powerless for this particular task. The instability of EuScCuSe₃ in space group Pnma space group is shown on the basis of phonon dispersion curve simulation. The EuScCuSe₃ can be assigned to indirect wide-band gap semiconductors. It exhibits the properties of a soft ferromagnet at temperatures below 2 K.

1. Introduction

Copper-containing chalcogenides have recently attracted considerable interest due to their promising thermoelectric applications [1,2], owing to their low thermal conductivity [2,3]. The compounds can be used in solar cells [4], photocatalysts [5], and gas sensing [6,7].

The chemistry of trivalent scandium compounds is of particular interest in terms of crystal structure and properties [8]. Trivalent scandium differs from other trivalent cations of the first transition series due to the presence of a closed outer electron shell with an argon configuration. Scandium chalcogenides are p-type [2,4,9,10,11] and n-type [8] semiconductors. Doping with heavy metals results in n-type conduction with low resistivity [9] in compounds that exhibit metallic properties [12].

The band gap of scandium chalcogenides compounds varies over a wide range from 1.2–2.3 eV [6,7,13,14].

Scandium chalcogenides can be obtained in different ways:

-

In the form of single crystals by the methods of reactive flux or halide flux [15],

-

By chemical transport reaction with I₂ [9],

-

High-temperature alloying of elements with chalcogenides [12],

-

From the elements by the transport method at 1270 K,

-

By the interaction of binary chalcogenides at 1420 K [16],

-

As polycrystals by alloying the elements at 1420 K followed by annealing at 870 K for 240 h [17],

-

By sulfiding mixtures of oxides obtained by thermolysis of co-crystallized metal nitrates at 870–1170 K for 25 h [13].

For ternary scandium-copper chalcogenides ScCuCh₂, their structural stability, thermal lattice conductivity, transport, and thermoelectric properties were appreciated [2]. ScCuSe₂ has the highest Q factor of 0.65 at 1000 K among the chalcogenides. This makes it a potential candidate for high-temperature thermoelectric applications. [2]. Down the group of chalcogenides ScCuCh₂ (Ch = S, Se, and Te), there is a decrease in the elastic moduli and values of the Debye temperatures, the gap width [2,18]. Ternary compounds ScCuCh₂ are semiconductors with an indirect gap, with a minimum of the conduction band at the high symmetry L point and a maximum of the valence band at the Γ point [18]. ScCuCh₂ is considered for copper-based n-window applications [2].

Quaternary scandium chalcogenides exhibit a variety of magnetic properties. EuScCuS₃ shows a ferromagnetic transition at 3–9 K [13,14], SrScCuS₃ diamagnetic [13], and antiferromagnetic [14]. The replacement of Sr²⁺ by Eu²⁺ leads to a narrowing of the band gap due to the 4f–5d transition in the Eu²⁺ cations. This makes it possible to control the band gap of the chalcogenides by including europium. The activation energy of defects in the crystal structure, which is a source of additional absorption in the NIR spectral range, turned out to be 0.29 eV [13]. The EuScCuSe₃ compound should treat materials with excellent p-type semiconductor conductivity. The upper part of the valence band consists of Cu 3d states overlapping with S 3p states similar to Cu₂S [19] and ACuCh₂ materials [4,20].

The structure type of NaCuTiS₃ was predicted for EuScCuSe₃, and quantum mechanical calculations were performed using the PBE functional, according to which the band gap of this selenide was 0.82 eV [3]. The NaCuTiS₃ compound crystallizes in the orthorhombic system (space group $Pnma$) with the lattice parameters a = 12.738 Å, b = 3.554 Å, and c = 9.529 Å [21]. The structure is represented by layers 2D-[CuTiS₃]^– consisting of alternating pairs of distorted tetrahedra [CuS₄]^7– and octahedra [TiS₆]^8– in the direction [001], which are separated by single-capped trigonal prisms [NaS₇]^13– [21]. However, previously synthesized quaternary scandium chalcogenides EuScCuS₃ [11], SrScCuS₃ [11,22], SrScCuSe₃ [1,23], BaScCuS₃ [24] crystallize in the space group Cmcm with structure type of KZrCuS₃. Since the ionic radius of Eu²⁺ (r_i(Eu²⁺) = 1.17 Å, C.N. = 6 [25]) is close to the ionic radius of Sr²⁺ (r_i(Sr²⁺) = 1.18 Å, C.N. = 6 [25]), it is expected that the EuScCuSe₃ compound will crystallize in the same structure type as and SrScCuSe₃ [1,23].

There are no data in the literature on the synthesis, crystal structure, or any properties of EuScCuSe₃. In this work, we describe the synthesis of EuScCuSe₃ for the first time, the studies of its crystal structure, as experimentally as well as using theoretical methods, and the investigation of its magnetic properties. Simultaneously, taking into account that most of the photonic media are single crystals, it has been decided to synthesize EuScCuSe₃ in that form.

2. Materials and Methods

2.1. Materials and Synthesis

The following chemical reagents were used: Eu (99.3%), Sc (99.9%), CsI (99.9%), Se (99.9%) were procured from ChemPur (Karlsruhe, Germany), and Cu (99.999%) stemmed from Aldrich (Milwaukee, WI, USA). EuScCuSe₃ was synthesized by the halide-flux method. The work was carried out in a glove box under an argon gas inert atmosphere. The stoichiometric ratio of the elements of europium (76.39 mg), scandium (22.60 mg), copper (31.94 mg), and selenium (119.07 mg) in the presence of CsI (800 mg) was loaded into silica ampoules. These ampoules were evacuated to a pressure of 2 × 10⁻³ mbar, sealed, and then heated in a resistant furnace. A temperature of 1120 K was reached within 30 h and kept for 96 h. Afterward, it was cooled to 570 K at a rate of 4 K h⁻¹ and then to room temperature within 3 h. The reaction proceeded according to the equation: Eu + Cu + Sc + 3 Se → EuScCuSe₃. The reaction product was purified from flux residues with demineralized water. The synthesized samples were dark red, needle-shaped single crystals of EuScCuSe₃ (Figure 1).

2.2. Methods

A selected single crystal of EuScCuSe₃ 0.05 × 0.05 × 0.45 mm³ in size was sealed into a thin-walled glass capillary (Figure 1) for X-ray diffraction experiments. The capillary was subsequently mounted on a Bruker-Nonius κ-CCD single-crystal diffractometer (Bruker, Billerica, MA, USA) equipped with a Mo-K_α radiation source, a graphite monochromator, and a CCD detector. The unit cell of this compound belongs to the orthorhombic crystal system. The space group was determined from a statistical analysis of the intensities of all reflections. The DENZO program [26] was used to process the collected intensity data. The HABITUS program [27] was used to numerically correct the absorption. The crystal structure was solved and refined by means of the SHELX-2013 software package [28,29]. CSD 2,239,558 contains supplementary crystallographic data. These data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures (accessed on 11 February 2023) or from the Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: (+44)1223-336-033; or e-mail: [email protected]. Crystal structures were visualized in the program package VESTA 3.5.7 [30].

The temperature dependence of the EuScCuSe₃ magnetization was measured using a helium-cooled magnetic property measurement system (MPMS3, Quantum Design, San Diego, CA, USA) in the temperature range from 2 to 300 K in zero-field cooling (ZFC) modus and heating in an external magnetic field (FC). The field value was 500 kOe (39.8 mA m⁻¹). The field-dependent magnetic moments were measured at room temperature (300 K) and at 2 K.

The ab-initio calculations of the EuScCuSe₃ were carried out in the framework of density functional theory (DFT) using the PBE0 exchange-correlation functional [18], which takes into account both local and nonlocal Hartree–Fock exchanges. The calculations were performed in the CRYSTAL17 program designed to simulate periodic structures [31,32]. For Eu²⁺, the ECP53MWB quasi-relativistic pseudopotential was used to describe the inner shells of this lanthanoid cation. Thus, the inner shells, including 4, were replaced by a pseudopotential. To describe the outer shells (5s²5p⁶) involved in chemical bonds, a valence basis set of TZVP type was used. The pseudopotential and the valence basis set are available on the site [4].

For scandium, copper, and selenium, the full-electron basis sets were used. The basis sets are available on the CRYSTAL program site as «Sc_864–11G*_harrison_2006», «Cu_86–4111(41D)G_doll_2000» and «Se_976–311d51G_towler_1995» [32]. Gaussian primitives with orbital exponent values less than 0.1 were removed from the basis sets since these calculations are periodic. The exponent in the outer orbital of selenium was set to 0.14. The accuracy of calculating the self-consistent field was set to 10⁻⁹ a.u. The accuracy of the calculation of the two-electron integrals was set to at least 10⁻⁸. Integration over the Brillouin zone was carried out according to the Monkhorst-Pack scheme with a grid of k-points equal to 8 × 8 × 8. The sequence of calculations was as follows. The optimization of the crystal structure was carried out first. After that, the phonon spectrum was calculated at the Г point, or the elastic constants were calculated for the crystal structure corresponding to the minimum energy.

3. Results and Discussion

3.1. Crystal Structure

The crystal structure was determined from single-crystal X-ray diffraction data. Crystallographic and structural data are described in

Table 1. Crystallographic data for EuScCuSe₃ and their determination.

Compound	EuScCuSe3
Space group	Cmcm (no. 63)
Structure type	KZrCuS3
a (Å)	3.9883 (3)
b (Å)	13.2776 (9)
c (Å)	10.1728 (7)
Z	4
ρcal (g cm−3)	6.132
Vu.c. (Å3)	538.70 (7)
Measuring range, ±h/±k/±l	±5/±16/±13
F(000)	860
Absorption coefficient μ (mm−1)	36.73
Measured reflections	5112
Symmetry-independent reflections	367
Rint/Rσ	0.089/0.041
R1 for n reflections with ∣Fo∣ ≥ 4σ(Fo)	0.055
n	294
R1/wR2 for all reflections	0.042/0.091
GooF	1.087
Extinction coefficient, ε	0.0016 (4)
Residual electron density, ρmax/min (e− 106 pm−3)	2.318/−2.273
CSD-number	2239558

and

Table 2. Fractional atomic coordinates of EuScCuSe₃.

Atom	Site	Symmetry	x/a	y/b	z/c	Ueq (Å2)
Eu	4c	m2m	0	0.75168 (9)	1/4	0.0232 (5)
Sc	4a	2/m..	0	0	0	0.0147 (7)
Cu	4c	m2m	0	0.4697 (2)	1/4	0.0242 (7)
Se1	4c	m2m	0	0.07683 (17)	1/4	0.0191 (6)
Se2	8f	m..	0	0.36312 (11)	0.05610 (16)	0.0199 (5)

as well as Tables S1–S3 of the Supplementary Materials (SM).

The octahedral [ScSe₆]⁹⁻ units in the EuScCuSe₃ structure are interconnected to each other through the (Se1)²⁻ ions along the z axis, as shown in Figure 2a, and though the (Se2)²⁻ anions along a axis (see Figure 2b). The [CuSe₄]⁷⁻ tetrahedra are linked via common (Se1)²⁻ anions along a axis. The [ScSe₆]⁹⁻ and [CuSe₄]⁷⁻ units have common Se1 and Se2 vertices. The nearest neighbors around Eu²⁺ cations form trigonal prisms [EuSe₆]¹⁰⁻ (Figure S1). The four Eu–Se1 bond lengths are equal to 3.0605 Å, while the remaining two Eu–Se2 bonds are 3.1711 Å long (Table S2).

3.2. Density Functional Theory Calculations

As has been mentioned above, a crystal structure prediction was previously made for EuScCuSe₃, and the space group Pnma was supposed [3]. Due to the fact that the sample experimentally synthesized in our work was solved in space group Cmcm, we did a comprehensive investigation of the EuScCuSe₃ crystal structure stability in both space groups, Pnma and Cmcm.

At the first step of density functional theory calculations, crystal structures of EuScCuSe₃ in Pnma and Cmcm space groups were totally optimized, and the obtained lattice parameters are presented in

Table 3. Lattice parameters of EuScCuSe₃ obtained using PBE0 calculations.

Compound		Space Group	Structure Type	Lattice Constants (Å)			V (Å3)	ρ (g cm−3)
EuScCuSe3	Calc.	Pnma	Eu2CuS3	4.01674	13.38926	10.03507	539.698	6.160
EuScCuSe3	Calc.	Cmcm	KZrCuS3	4.02028	13.38869	10.02436	539.574	6.162
EuScCuSe3	Exp.	Cmcm	KZrCuS3	3.9883(3)	13.2776(9)	10.1728(7)	538.70(7)	6.132

. The simulated structural data get close to the experiments in both cases. It should be noted that the energy per formula unit is almost the same for both structure types and differs only in the fifth decimal place: −9634.327521165 at. un (Pnma), −9634.327541515 at. un (Cmcm).

The next mandatory part of the crystal structure stability investigation is the simulation of elastic properties [33]. Calculations of the elastic constants were performed using the built-in functionality of CRYSTAL17 code. The obtained data for EuScCuSe₃ in Cmcm and Pnma structures are presented in

Table 4. Elastic constants (GPa) for EuScCuSe₃.

Compound	Space Group	Structure Type	C11	C12	C13	C22	C23	C33	C44	C55	C66	B	HVcal
EuScCuSe3	Pnma	Eu2CuS3	122	33	38	150	44	99	46	21	33	66	5.7
EuScCuSe3	Cmcm	KZrCuS3	151	43	27	98	37	128	13	33	45	65	4.8

. The necessary and sufficient Born criteria [34] for the orthorhombic crystal-system stability are C₁₁ > 0, C₁₁C₂₂ > C₁₂, C₁₁C₂₂C₃₃ + 2C₁₂C₁₃C₂₃ − C₁₁C₂₃² − C₂₂C₁₃² − C₃₃C₁₂² > 0, C₄₄ > 0, C₅₅ > 0, C₆₆ > 0. All the above conditions are satisfied both for the real Cmcm and predicted Pnma-structure of EuScCuSe3 previously.

As any data on elastic properties of EuScCuSe₃ are absent at this time in databases or articles, we present calculation of the bulk modulus, Young’s modulus, and shear modulus in the Voigt, Reuss, and Hill approximations (

Table 5. Bulk (B), shear (G), and Young’s modulus (GPa) of EuScCuSe₃.

Compound	Space Group	Structure Type	Averaging Scheme	B	G	Young’s Modulus	Poisson Ratio
EuScCuSe3	Pnma	Eu2CuS3	Voigt	67	37	94	0.263
			Reuss	65	34	86	0.278
			Hill	66	36	90	0.271
EuScCuSe3	Cmcm	KZrCuS3	Voigt	66	36	92	0.267
			Reuss	64	28	74	0.309
			Hill	65	32	82	0.287

). The dependence of Young’s modulus on the crystal directions demonstrates a significant anisotropy of the elastic properties in both the Cmcm and the Pnma structure (Figure S2).

The calculated values of the shear modulus and bulk modulus make it possible to estimate the Vickers hardness for EuScCuSe₃ (Table 5). To estimate the Vickers hardness, the empirical formula (3.3.1) from work [1] was used.

H_v = 0.92(G/B)^1.137G^0.708

(1)

This formula well describes the hardness of a row of compounds with an ionic and covalent type of chemical bond (about 40 compounds were considered in work [1]). In Formula (1), G and B are the shear modulus, and bulk modulus by Hill is estimated. The experimental values of hardness are absent from research papers. According to calculations, the elastic constants and hardness of EuScCuSe₃ differ significantly for the Cmcm and Pnma structures (Table 4).

As vibrational spectroscopy is a powerful tool for the determination of crystal structure details, simulation of Raman and infrared spectra for the experimentally obtained data in this work (Cmcm structure) and possibly earlier predicted Pnma structure [1] were done. The results for the infrared-active modes, Raman modes, and “silent” modes at the Г point are given in Tables S4 and S5 of the SM. The degree of participation of each ion in a particular mode is estimated from the analysis of displacement vectors obtained from these ab-initio calculations. The ions that are shifted significantly in the mode are listed in the column “participants” (Tables S4 and S5). The values of ion displacements for vibrational modes are shown in Figure S3.

The number of formula units in the Pnma structure is equal to 4 (Z = 4), and this value is the same for the Cmcm structure, see Table 1. However, the primitive cell of the Cmcm structure contains only two formula units (Figure S4). Thus, the number of vibrational modes should be larger in the Pnma case. The Raman-active modes for Pnma and Cmcm structures should be listed as 12 A_g + 6 B_1g +12 B_2g + 6 B_3g and 5 A_g + 4 B_1g + B_2g + 5 B_3g, correspondingly [35]. The result of Raman and infrared spectra simulations for both structures are presented in Figure 3. Despite the fact that the number of vibrational modes is different for the structures in Cmcm and Pnma, the simulated Raman and infrared spectra are quite similar. Thus, we suppose that the definition of the correct space group (Cmcm or Pnma) using experimental vibrational spectroscopy is almost impossible in this case.

The only possible indicator for the Pnma structure is the low-lying weak band in the Raman spectrum (Figure 3a) which is associated with very strong movements of all ions except for Cu⁺ (Figure S3). However, the wavenumber value of this vibrational mode is the lowest in both structures. In this regard, the calculation of phonon dispersion curves was done for the Pnma structure, and the results of the simulation in Γ–X direction are shown in Figure 4a. The key factor of the dynamical stability of crystal lattice is the absence of imaginary (unstable) phonon modes and this approach works in for the case of experimentally observed crystal structures [36] as for crystal structure stability prediction [37,38]. According to the obtained data (Figure 4a), we can say that the crystal structure of EuScCuSe₃ in the previously supposed space group Pnma should be unstable. This fact, among other things, is consistent with the experimentally obtained space group Cmcm obtained for the real EuScCuSe₃ in this work. At the same time, simulated phonon dispersion for the Cmcm structure do not contain unstable phonon modes over all of the high-symmetric Brillouin zone points (Cmcm).

The band structure and the density of states for EuScCuSe₃ calculated using hybrid PBE0 functional are shown in Figure 5. The path in the Brillouin zone is plotted through the most highly symmetric points. For the space group Cmcm, the path is made along Г–Y–T–Z–S–R–Г. The coordinates of the points are (0,0,0,), (¹/₂,¹/₂,0), (¹/₂,¹/₂,¹/₂), (0,0,¹/₂), (0,¹/₂,0), (0,¹/₂,¹/₂), (0,0,0) respectively. The Bilbao crystallographic server was used [35]. Since for europium pseudopotential that replaced their core shells, the 4f inclusive was used, the band structure does not include 4f states. For the Eu²⁺ cations, only outer shells (5s²5p⁶) were taken into account by means of valence basis sets [39]. The projected DOS onto the whole set of atomic orbitals of Eu, Sc, Cu, and Se atoms was calculated near the band gap. According to these calculations, the DOS of copper and selenium are located near the top of the valence band. The DOS of scandium and europium are located near the bottom of the conduction band. The band gap value is defined as the difference in energy between the top of the valence band and the bottom of the conduction band. Calculations predict for EuScCuSe₃ the indirect electronic transition with a band gap value of 3.27 eV. It should be noted, that in the case of the dynamically unstable Pnma structure, the band gap value is the same, but the calculated electronic transition is direct (Figure S5).

3.3. Magnetic Properties

The temperature dependence of the specific magnetization was measured in the temperature range from 2 to 300 K (Figure 6). Based on it, the temperature dependences of the direct and reciprocal values of the molar magnetic susceptibility are calculated.

The main contribution to the magnetic properties of EuScCuSe₃ is made by the Eu²⁺ cations with unfilled f-shells. There is no significant effect of the crystal field on the magnetic moment since, in the ground state (⁸S_7/2), this cation has a zero-orbital momentum. Its temperature dependence of magnetic susceptibility in the paramagnetic region should be well described by the Curie-Weiss law: $\chi ={\chi }_{\mathrm{TIP}}+\frac{C}{T-{\theta }_W}$ considering the temperature-independent term χ_TIP. Approximation of the experimental dependence by this formula gives the following values: χ_TIP = 1.04·10⁻⁵ m³ kmol⁻¹, C = 0.0977 K m³ kmol⁻¹, θ_W = 6.0 K. The deviations of the experimental points from the approximating curve in the temperature ranging from 40 to 300 K are no more than 1%, and from 10 to 40 K about 2.5%. A comparison of the characteristics obtained with those calculated for non-interacting Eu²⁺ cations is given in

Table 6. Magnetic characteristics for EuScCuSe₃.

Magnetic Characteristics	Calculated	M(H) at 300 K	M(T) at 500 kOe
C (K m3 kmol−1)	0.098999	0.0995	0.0977
μ (μB)	7.9373	7.96	7.89
θW (K)	-	-	6.0
Tc (K)	-	-	4.5

.

There is a sharp deviation from the Curie-Weiss law at temperatures below 5 K. This deviation is obviously due to the ferromagnetic transition, although there is no noticeable discrepancy in the data for the FC and ZFC

The experimental curve of magnetization at a temperature of 2 K (Figure 7b) has the form characteristic of magnetically soft ferromagnets. The coercive force is less than 2 kA m⁻¹, and saturation occurs in a field of about 500 kA m⁻¹. The magnetization in a field of 4 MA m⁻¹ per formula unit is 6.5 μ_B, which is close to the theoretical value of about 7 μ_B for a free Eu²⁺ cation.

4. Conclusions

In summary, we report on the new quaternary scandium selenide EuScCuSe₃, which was synthesized from a mixture of the elements with CsI as a flux in sealed silica ampoules at elevated temperatures. The structural, vibrational, and elastic-property calculations have been performed for EuScCuSe₃ in the framework of the density functional theory (DFT) by using the PBE0 hybrid functional and LCAO-MO approach. The calculation results predict the Cmcm structure, which agrees very well with the obtained crystallographic data (a = 3.9883(3), b = 13.2776(9), c = 10.1728(7) Å). The calculation results can be used to interpret the Raman and infrared spectra.

The crystal structure, according to single-crystal data, showed that EuScCuSe₃ belongs to the orthorhombic crystal system with the space group Cmcm. The structure type corresponds to KZrCuS_3, and thus the structure includes trigonal prisms [EuSe₆]¹⁰⁻, octahedra [ScSe₆]⁹⁻, and tetrahedra [CuSe₄]⁷⁻. The title compound is paramagnetic above 4.5 K and soft ferromagnetic at lower temperatures.