Quaternary rare-earth selenides with closed cavities: Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu)

Abstract

New quaternary selenides, Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu), have been synthesized by high temperature solid state reactions of elements with a reactive CsCl flux. These compounds adopt the BaV₁₃O₁₈-structure type in the trigonal space group R3̄ (no. 148) with a = 17.4867(8)–17.263(2) Å, c = 9.7996(8)–9.681(2) Å and Z = 3. The major structure motif is the 3D network that is constructed by octahedra of MSe₆ (centered by disordered Mn and RE) and RESe₆, in which closed cavities of cuboctahedra Cs@Se₁₂ are embedded. This work extends the previously established empirical A/M-structure correlation in the ternary A/RE/Q system into quaternary A/RE/TM/Q, and A/M = 0.08 (A = the number of alkali metals, M = the sum of the numbers of RE and TM metals) represents the minimum ending value. The syntheses, properties, and theoretical analyses of the title compounds are also discussed.

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Introduction

Chalcogenides have attracted intense attention for not only their diverse structural chemistry,¹ but also their interesting properties, such as superconducting, thermoelectric, nonlinear optical, or magnetic properties.^2–5 The rich structural chemistry of ternary alkali metal/rare earth metal/chalcogenides (A/RE/Q) comes from the various linkages between the REQ₆ octahedral building units. Previously, based on 70 ternary channel chalcogenides, we have proposed an interesting empirical structure correlation, that is the size of the channel within the anionic moiety decreases as the A/M ratio decreases (A = the number of alkali metals, M = the number of rare earth metals).⁶ For instance, as the A/M ratio decreases from 0.43, 0.33 to 0.20 on going from Rb₃Yb₇Se₁₂,⁷ CsHo₃Te₅ ⁸ to RbSc₅Te₈,⁹ the number of A atoms accommodated per channel decreases monotonically from 4, 2, to 1 indicating the channel size reduction⁶ (Fig. 1, left). A/M = 1.0 is found in the infinite 2D layered structure, such as RbLaSe₂.¹⁰ From the conceptual point of view, such adjacent 2D layers can be considered to be separated by channels with infinite radius. Thus, A/M = 1.0 represents the maximum ending value of the A/M-structure correlation.

Fig. 1 Chart of the empirical A/M ratio–structure relationships in ternary A/RE/Q (left) and quaternary A/RE/TM/Q (right) systems. Red ball: A; yellow ball: Q; pink polyhedron: REQ₆; green polyhedron: TMQ₄; red polyhedron: a centering-close cavity. The A/M value is marked in the middle.

In this work, based on the systematic structure study of all available examples, we find that, in addition to ternary systems, the heterometallic anionic moiety in quaternary A/RE/TM/Q (TM = transition metals) systems also shows similar empirical A/M-correlation: as the A/M ratio decreases, the channel size decreases (note that M is now the sum of the numbers of RE and TM metals) (Fig. 1, right). Examples are ARETMQ₃,¹¹ ARE₂TM₃Q₅,¹ CsSc₃Cu₂Q₆,¹² K₂CeAg₃Te₄,¹³ A₃RE₄Cu₅Q₁₀,¹etc. On going from K₂CeAg₃Te₄,¹³ K₃Dy₄Cu₅Te₁₀,¹ to CsSc₃Cu₂Te₆,¹² as A/M decreases from 0.5, 0.33 to 0.2, the number of A atoms accommodated per channel drops from 4, 3 to 1 indicating the shrink of the channel. Note that TM and RE atoms usually have different local coordination behaviour, tetrahedron vs. octahedron, thus the corresponding monometallic and heterometallic anionic moieties differ in the structure considerably. Therefore, the A/M value may not be numerically equal for the corresponding ternary and quaternary structure-class (Fig. 1). For example, in the case of the 2D layered structure class, ternary compounds have an A/M of 1.0, but for quaternary it is 0.5. At A/M = 0.33, both ternary and quaternary compounds will be channel structures, but the former accommodates less A atoms per channel than the latter. Nevertheless, the principle A/M ratio–structure relationships coincide, and the channel size in both ternary and quaternary smoothly decreases until the A/M value drops to 0.2 (Fig. 1). Very interestingly, recent work shows that in the ternary system, when A/M = 0.14, the anionic moiety is no longer an open channel structure, instead it is a 3D network embedded with a closed cavity, such as in the CsLu₇Q₁₁ network, every two Cs atoms are captured into a dual-tricapped cube, Cs₂@Se₁₈.⁶ But if A/M in the quaternary system is further reduced, how the structure will change is yet unknown. Since low A/M ratio means low concentration of the reducing agent, it is also a great experimental challenge.

In this manuscript, we discover an even smaller A/M ratio of 0.08 in five new quaternary compounds, Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu), with Cs atoms being captured into a smaller closed cavity of the Se₁₂ cuboctahedron. The syntheses, crystal structure analyses, properties as well as theoretical analyses are reported.

Experimental section

Syntheses

Reactants were stored in an Ar-filled glovebox with controlled oxygen and moisture levels below 0.1 ppm. RE (99.95%) were purchased from Huhhot Jinrui Rare Earth Co., Ltd Se (99.999%) and Mn (99.99%) from Alfa Aesar, and CsCl (99.99%) from Sinopharm Chemical Reagent Co., Ltd.

After numerous explorations on the experimental conditions including the starting reactant, loading ratio, and annealing temperature, the optimal synthesis conditions were established as loading a mixture (about 300 mg in total) of CsCl, RE, Mn and Se in a molar ratio of 2 : 9 : 4 : 18 with a slight excess of CsCl as the reactive flux. The reactants were loaded in a fused-silica tube under vacuum, heated to 1223 K for 2 days, annealed at this temperature for 4 days, and then slowly cooled at 3 K h⁻¹ to 473 K before switching off the furnace. Crystals of good quality were subsequently selected for single crystal X-ray diffraction studies, e.g. Cs[Tm₉Mn₄Se₁₈] with a cuboctahedral crystal behaviour at room temperature (Fig. 2a). The EDX analyses carried out on several single crystals revealed the presence of Cs, RE, Mn, and Se in a ratio of 1 : 9 : 4 : 18. For example, CsTm_9.1(3)Mn_4.0(1)Se_18.1(2) (Fig. 2b) was close to CsTm_9.0(3)Mn_4.0(3)Se₁₈ as established by single-crystal diffraction data (Table 1 and Table S1 in ESI†). No other element was detected. The products were washed with distilled water to remove the excess CsCl and chloride by-products, and then dried with ethanol. After such a treatment, title compounds were obtained as pure phases according to the powder XRD patterns shown in Fig. 2c and Fig. S1 in ESI.† These compounds were stable in air for several months.

Fig. 2 (a) SEM photo, (b) EDX and ICP of Cs[Tm₉Mn₄Se₁₈] single crystals; (c) experimental (black) and simulated (blue) powder XRD patterns and (d) UV-Vis diffuse-reflectance spectrum of polycrystalline Cs[Tm₉Mn₄Se₁₈].

Table 1 Crystallographic data and refinement details for Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu)

Formula	Cs[Ho9Mn4Se18]	Cs[Er9Mn4Se18]	Cs[Tm9Mn4Se18]	Cs[Yb9Mn4Se18]	Cs[Lu9Mn4Se18]
a R 1 = ∑||Fo| − |Fc||/∑|Fo|, wR2 = [∑w(Fo^2 − Fc^2)^2/∑w(Fo^2)^2]^1/2.
fw	3258.31	3279.29	3294.32	3331.30	3348.64
Crystal system	Trigonal	Trigonal	Trigonal	Trigonal	Trigonal
Space group	R3̄ (no. 148)	R3̄ (no. 148)	R3̄ (no. 148)	R3̄ (no. 148)	R3̄ (no. 148)
a (Å)	17.4867(8)	17.441(4)	17.360(2)	17.3186(6)	17.263(2)
c (Å)	9.7996(8)	9.785(3)	9.724(2)	9.6972(5)	9.681(2)
V (Å^3)	2595.1(3)	2577.9(2)	2537.8(5)	2518.9(2)	2498.3(4)
Z	3	3	3	3	3
D c (g·cm^−3)	6.255	6.337	6.467	6.588	6.677
μ (mm^−1)	41.679	43.215	45.174	46.800	48.590
GOOF on F^2	1.036	1.093	1.086	1.057	1.091
R 1, wR2 (I > 2σ(I))^a	0.0285, 0.0653	0.0167, 0.0328	0.0411, 0.0868	0.0247, 0.0527	0.0305, 0.0768
R 1, wR2 (all data)	0.0305, 0.0663	0.0180, 0.0331	0.0459, 0.0888	0.0259, 0.0532	0.0308, 0.0770
Largest diff. peak and hole (e Å^−3)	2.319, −1.379	2.250, −1.134	4.376, −3.865	1.448, −3.361	2.259, −2.127

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Crystal structure determination

A Rigaku Mercury CCD diffractometer or a Rigaku Saturn724 CCD diffractometer equipped with graphite-monochromated Mo Kα radiation (λ = 0.71073 Å) was used for data collection at 293 K. The data were corrected for the Lorentz and polarization factor. Absorption corrections were based on the multiscan method.¹⁴ All structures were solved by direct methods and refined by the full-matrix least-squares fitting on F² by SHELX-97.¹⁵ Taking Cs[Tm₉Mn₄Se₁₈] as an example, the initial refinement generated one Cs, three Se, and three “Tm” atoms with R values of R₁ = 9.86% and wR₂ = 30.94%. Then, all three “Tm” sites were freely refined, after which the “Tm3” occupancy did not change, while those of the “Tm1” and “Tm2” sites decreased and the unbalanced formula “Cs₃Tm_25.37Se₅₄” was converged. According to the EDX results, the compound should consist of Mn as well. Subsequently, Tm and Mn atoms were constrained to the same site (with identical coordinates and temperature factors) in SHELX. Meanwhile, the Tm to Mn ratio was fixed as 2 : 1 to keep the charge balance, which is also in agreement with the EDX results. Finally, the structure refinement converged to R₁ = 3.94%, wR₂ = 8.54% with all atoms refined anisotropically and a formula of CsTm_9.0(3)Mn_4.0(3)Se₁₈. Crystallographic data and structural refinement details are summarized in Table 1, the positional coordinates and isotropic equivalent thermal parameters are given in Table 2, and important bond distances are listed in Table 3.

Table 2 Atomic coordinates and equivalent isotropic displacement parameters of Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu)

Atom	Symmetry	x	y	z	U (eq) ^b (Å^2)	Occu.
a The RE and Mn were restricted to sum up 100% occupancy at each of M1 and M2 sites. b U (eq) is defined as one-third of the trace of the orthogonalized Uij tensor.
CsHo9.0(3)Mn4.0(3)Se18 ^a
Cs1	3b	0	0	0.5	0.0437(3)	1
M1 = Ho1/Mn1	18f	0.24085(2)	0.27636(2)	0.33554(2)	0.0086(2)	0.84(2)/0.16(2)
M2 = Ho2/Mn2	18f	0.40509(2)	0.17719(2)	0.33403(3)	0.0107(2)	0.49(2)/0.51(2)
Ho3	3a	0	0	0	0.0090(2)	1
Se1	18f	0.26808(3)	0.15976(3)	0.49798(4)	0.0102(2)	1
Se2	18f	0.12506(3)	0.14042(3)	0.16153(4)	0.0100 (2)	1
Se3	18f	0.38269(3)	0.29806(3)	0.16872(4)	0.0080(2)	1
CsEr9.0(3)Mn4.0(3)Se18 ^a
Cs1	3b	0	0	0.5	0.0424(2)	1
M1 = Er1/Mn1	18f	0.05694(2)	0.42580(2)	0.00200(2)	0.0107(2)	0.84(2)/0.16(2)
M2 = Er2/Mn2	18f	0.15606(2)	0.26151(2)	0.00124(3)	0.0110(2)	0.49(2)/0.51(2)
Er3	3a	0	0	0	0.0102(2)	1
Se1	18f	0.01538(2)	0.14024(3)	0.16183(2)	0.0104(2)	1
Se2	18f	0.17362(2)	0.39874(3)	0.16483(2)	0.0100(2)	1
Se3	18f	0.28404(2)	0.24875(3)	0.16477(2)	0.0101(2)	1
CsTm9.0(3)Mn4.0(3)Se18 ^a
Cs1	3b	0	0	0.5	0.0434(5)	1
M1 = Tm1/Mn1	18f	0.05715(3)	0.42611(3)	0.00214(4)	0.0136(2)	0.82(2)/0.18(2)
M2 = Tm2/Mn2	18f	0.15598(4)	0.26149(4)	0.00124(6)	0.0159(2)	0.51(2)/0.49(2)
Tm3	3a	0	0	0	0.0155(3)	1
Se1	18f	0.01525(5)	0.13995(5)	0.16192(8)	0.0136(3)	1
Se2	18f	0.17349(5)	0.39881(5)	0.16504(8)	0.0140(3)	1
Se3	18f	0.28447(5)	0.24910(6)	0.16443(8)	0.0126(3)	1
CsYb9.0(3)Mn4.0(3)Se18 ^a
Cs1	3b	0	0	0.5	0.0352(2)	1
M1 = Yb1/Mn1	18f	0.05696(2)	0.42590(2)	0.00194(2)	0.0063(2)	0.81(2)/0.19(2)
M2 = Yb2/Mn2	18f	0.15606(2)	0.26151(2)	0.00124(3)	0.0078(2)	0.52(2)/0.48(2)
Yb3	3a	0	0	0	0.0078(2)	1
Se1	18f	0.01530(3)	0.13988(3)	0.16225(4)	0.0069(2)	1
Se2	18f	0.17347(3)	0.39897(3)	0.16543(4)	0.0070(2)	1
Se3	18f	0.28448(3)	0.24905(3)	0.16474(4)	0.0056(2)	1
CsLu9.0(3)Mn4.0(3)Se18 ^a
Cs1	3b	0	0	0.5	0.0377(3)	1
M1 = Lu1/Mn1	18f	0.05690(2)	0.42596(2)	0.00181(3)	0.0107(2)	0.82(2)/0.18(2)
M2 = Lu2/Mn2	18f	0.15601(2)	0.26155(2)	0.00132(3)	0.0120(2)	0.52(2)/0.48(2)
Lu3	3a	0	0	0	0.0118(2)	1
Se1	18f	0.01530(3)	0.13967(3)	0.16247(5)	0.0109 (2)	1
Se2	18f	0.17355(3)	0.39925(3)	0.16547(5)	0.0108(2)	1
Se3	18f	0.28436(3)	0.24904(4)	0.16480(5)	0.0093(2)	1

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Table 3 Selected bond lengths (Å) of Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu)

	RE = Ho	RE = Er	RE = Tm	RE = Yb	RE = Lu
M1–Se2	2.7782(5)	2.7727(6)	2.7556(9)	2.7508(4)	2.7437(6)
M1–Se1	2.8009(5)	2.7946(7)	2.7802(9)	2.7740(4)	2.7677(6)
M1–Se2	2.8087(5)	2.8042(6)	2.7874(9)	2.7827(4)	2.7761(6)
M1–Se3	2.8331(5)	2.8257(7)	2.8075(9)	2.7994(5)	2.7938(6)
M1–Se2	2.8358(5)	2.8282(7)	2.8126(9)	2.8020(5)	2.7944(6)
M1–Se3	2.8728(5)	2.8661(7)	2.8535(9)	2.8438(4)	2.8356(6)
M2–Se1	2.7650(6)	2.7616(7)	2.752(2)	2.7480(5)	2.7446(6)
M2–Se2	2.7720(6)	2.7693(7)	2.755(2)	2.7524(5)	2.7472(6)
M2–Se1	2.7961(6)	2.7903(7)	2.776(2)	2.7717(5)	2.7658(6)
M2–Se3	2.8413(5)	2.8366(7)	2.824(2)	2.8186(5)	2.8110(6)
M2–Se3	2.8516(5)	2.8459(7)	2.832(2)	2.8250(5)	2.8176(6)
M2–Se3	2.8538(5)	2.8484(7)	2.835(2)	2.8260(5)	2.8193(6)
RE3–Se1 × 6	2.8192(5)	2.8120(6)	2.7944(8)	2.7879(4)	2.7785(5)

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Powder X-ray diffraction

The powder XRD patterns were obtained at room temperature on a Rigaku DMAX 2500 powder X-ray diffractometer by using Cu Kα radiation (λ = 1.5418 Å) at room temperature. The purity and homogeneity of all phases were confirmed by comparison of the results from powder XRD with those calculated from single-crystal data.

Elemental analysis

The semiquantitative microprobe elemental analysis was performed using a field emission scanning electron microscope (JSM6700F) equipped with an energy-dispersive X-ray (EDX) spectroscope (Oxford INCA) on clean single crystal surfaces. The Ultima-2 inductively coupled plasma (ICP) optimal emission spectrometer was used to quantitatively determine the composition of the hand-picked single crystals. The mass percentage of 46.3(2)% Tm, 6.5(3)% Mn and 43.4(2)% Se is also in good agreement with the single-crystal refinement stoichiometry (CsTm₉Mn₄Se₁₈ mass percentage: 46.2% Tm, 6.7% Mn and 43.1% Se).

UV-Vis-near IR spectroscopy

The optical diffuse reflectance spectra of powder samples were measured at room temperature using a Perkin-Elmer Lambda 900 UV-Vis spectrophotometer equipped with an integrating sphere attachment and BaSO₄ as a reference in the range of 0.19–2.5 μm. The absorption spectrum was calculated from the reflection spectrum via the Kubelka–Munk function: α/S = (1 − R)²/2R, in which α is the absorption coefficient, S is the scattering coefficient, and R is the reflectance.¹⁶

Magnetic susceptibility

The direct current magnetic susceptibility was measured using a Quantum Design PPMS-9 T magnetometer at a field of 1000 Oe in the temperature range of 2–300 K. The handpicked single crystals were ground to fine powder to minimize possible anisotropic effects and loaded into a gelatin capsule. The data were corrected for the susceptibility of the container and for the diamagnetic contribution from the ion core.

Electronic structure calculations

The geometry optimization, band structure and density of states (DOS) were calculated by the Vienna ab initio simulation package (VASP).^17a The generalized gradient approximation (GGA)^17b was chosen as the exchange–correlation functional and a plane wave basis with the projector augmented wave (PAW)^17c,d potentials was used. The plane-wave cut-off energy of 270 eV, and a threshold of 10⁻⁶ eV were set for the self-consistent-field convergence of the total electronic energy. The k integration over the Brillouin zone was performed by the tetrahedron method^17e using total 172 k-points in the irreducible Brillouin zone (IBZ) and the Fermi level (E_F = 0 eV) was selected as the reference of the energy. During the geometry optimization, an energy cutoff of 385 eV and a 3 × 3 × 3 Monkhorst–Pack k-point grid and the quasi-Newton minimization method were employed to make sure that the force on each atom is less than 0.02 eV Å⁻¹. The results suggested that model-b5 is the most energetically favorable configuration (from Fig. 7 and Table S2†). To understand the distribution of Mn atoms in Cs[Tm₉Mn₄Se₁₈], VASP calculations were carried out. As shown in Fig. 7 and Table S2,† 18 models of possible Mn-distribution were calculated. All models were constructed in a P1 primitive cell (a_init = b_init = c_init = 10.538 Å, α = β = γ = 110.97°) instead of R3̄. The optimal structural parameters were a_opt ≈ b_opt ≈ c_opt ≈ 10.565 Å, and α ≈ β ≈ γ ≈ 110.61°.

Results and discussion

Structure description

Compounds Cs[RE₉Mn₄Se₁₈] crystallize in the BaV₁₃O₁₈ structure type¹⁸ in the trigonal space group R3̄ (no. 148) (Fig. 3). In the unit cell, M1 and M2 sites are disordered by RE1/Mn1 and RE2/Mn2 atoms with occupancies of 0.83/0.17 and 0.50/0.50, respectively. As usual, on going from Ho to Lu as indicated in Fig. 4, the lattice parameters of these compounds contract monotonically with the increase of the atomic number of the rare earth metal. In the structure, Cs and Se ions form a cubic close-packed arrangement along the c axis. Each M (or RE) is coordinated by 6 Se atoms forming an MSe₆ (or RESe₆) octahedron that is propagated by sharing edges and corners. Alternatively, the major structure motif can be described as the 3D framework condensed by MSe₆ octahedra and RESe₆ octahedra, in which the closed cavities, Cs centering Se₁₂ cuboctahedra, are embedded (Fig. 5). As shown in Fig. 3b, the asymmetric unit, REM₁₂Se₄₂, is fused by 6 M1Se₆, 6 M2Se₆ and 1 RE3Se₆ octahedra via edge-sharing with the normal M–Se or RE–Se bond distance (Table 3). Each REM₁₂Se₄₂ asymmetric unit is interconnected with other 6 neighbouring units into a 2D single layer parallel to the ab plane (Fig. 3b). Such layers connect to each other along the c direction via strong M–Se or RE–Se covalent bonding interactions into a trigonal 3D structure.

Fig. 3 (a) Structure of Cs[RE₉Mn₄Se₁₈] viewed down the b-direction with the unit cell marked. (b) A single layer in the ab plane, the asymmetric unit, REM₁₂Se₄₂, is outlined by the blue dotted line. Cyan: (RE/Mn)Se₆ octahedron; pink: RESe₆ octahedron.

Fig. 4 Plots of the unit cell parameters vs. the atomic number for Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu) and the red lines represent the least-square fitting.

Fig. 5 The structure comparison (up), A/M ratio (middle), and Cs-centering polyhedron (bottom) of Cs[RE₉Mn₄Se₁₈] (left) and Cs[Lu₇Se₁₁] (right).

Selected bond distances of Cs[RE₉Mn₄Se₁₈] are shown in Table 3. All metal atoms (RE and M) are octahedrally coordinated by six Se atoms with distances of 2.7785(5)–2.8192(5) Å and 2.7437(6) Å–2.8661(5) Å for RE–Se and M–Se, respectively. These bond distances are consistent with those in CsREMnSe₃ (RE–Se: 2.8360(5)–2.9325(5) Å and Mn–Se: 2.4996(8)–2.5898(7) Å),¹⁹ CsLu₇Se₁₁ (Lu–Se: 2.701(2)–2.911(1) Å),⁶ and Cs₂Mn₃Se₄ (Mn–Se: 2.540(2)–2.576(3) Å).²⁰ The Se–M–Se angles deviate from the ideal values (90° and 180°), ranging from 86.84(7)–94.71(9)°, and 175.9(2)–179.6(2)°, respectively. The Cs centering-cuboctahedron exhibits a 12-fold site symmetry with Cs–Se distances ranging from 3.9904(6) to 4.0846(5) Å, in comparison with those in CsLu₇Se₁₁ (3.634–4.133 Å),⁶ CsTaSe₃ (3.996–4.004 Å),²¹ and CsRe₆I₃Se₈ (3.955–4.076 Å).²² The same Se₁₂ cuboctahedron is also observed in KCd₄Ga₅S₁₂-type compounds.^4b,23

Considering RE and Mn having the same coordination environment, the formula of title compounds can be written as [CsRE₉Mn₄Se₁₈] ≡ “CsM₁₃Se₁₈”. As shown in Fig. 5, the title compounds and Cs[Lu₇Se₁₁]⁶ are 3D network structures made by metal–Se octahedra, within which cavities of either small cuboctahedra Cs@Se₁₂ or large dual-tricapped cubes Cs₂@Se₁₈ are embedded. As the A/M ratio decreases from 0.14 to 0.08, the cavity size decreases from Se₁₈ atoms to Se₁₂. Previous studies suggest that when the A/M ratio drops from 1 to 0.2 (Fig. 1), the anionic moiety varies from infinite 2D layers to open channel structures, of which, the channel size gradually narrows and reaches the minimum at A/M = 0.2.⁶ The Cs[Lu₇Q₁₁] example illustrates that at A/M = 0.14, the open channel has been closed up into individual closed cavities.⁶ Here, we demonstrate nicely that the cavity size also reduces with the A/M decrease.

Optical and magnetic properties

According to the diffuse-reflectance spectra at room temperature, the band gaps were estimated to be 1.90 eV showing semiconducting behavior (Fig. 2d and S2†), which are in agreement with the color of the title compounds. These values are similar to those of CsYbMnSe₃ (1.60 eV)¹⁹ and CsLu₇Se₁₁ (1.78 eV).⁶

The magnetic susceptibility was measured at an applied field of 1000 Oe in the temperature range 2–300 K and shown as χ⁻¹–T plots in Fig. 6. The susceptibility data in the temperature range 40–300 K were fit by a least-squares method to the Curie–Weiss equation χ = C/(T − θ), where χ is the magnetic susceptibility, C is the Curie constant and θ is the Weiss constant. The theoretical total effective magnetic moment can be calculated by the equation μ_eff(cal.) = [9μ_eff(RE)² + 4μ_eff(Mn)²]^1/2μ_B, and the experimental effective magnetic moment was calculated from the equation μ_eff(obsd.) = (7.997C)^1/2μ_B.²⁴ The resulting values for C, θ, and μ_eff are summarized in Table 4. The negative θ value suggests significant antiferromagnetic interactions existing between the magnetic ions. Furthermore, the experimental value of μ_eff for Cs[Ho₉Mn₄Se₁₈] is smaller than the theoretical value calculated for Ho³⁺ and Mn²⁺. This presumably is attributed to that the 3d electrons of Mn lie in the outermost shell and are responsible for the magnetic behavior of Cs[Ho₉Mn₄Se₁₈], whereas the electrons of the 4f shell of Ho lie deep inside the ion, within the 5s and 5p shells. Such a result is similar to that in CsTmMnSe₃.¹⁹ The magnetic interactions should occur mainly between the centers M–M or RE–M (the nearest distance is around 3.90 Å).

Fig. 6 Temperature dependence of the inverse molar magnetic susceptibility (χ⁻¹) of Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu).

Table 4 Magnetic properties of Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu)

	C (emu K mol^−1)	θ (K)	μ eff (μB) obsd	μ eff (μB) cal.
Cs[Ho9Mn4Se18]	133.52	−10.05	32.91	33.93
Cs[Er9Mn4Se18]	118.34	−9.20	30.77	31.11
Cs[Tm9Mn4Se18]	79.43	−18.29	25.20	25.61
Cs[Yb9Mn4Se18]	39.14	−54.22	17.71	18.05
Cs[Lu9Mn4Se18]	16.06	−6.28	11.53	11.84

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Electronic structure

According to the single crystal structure refinement results, Mn and Tm atoms share each of the two sites (M1: blue and M2: black sites as shown in Fig. 7) with Mn occupancies of about 1/6 and 1/2, respectively. All the equivalent blue M1 sites are numbered by 1–6, of which only one can be occupied by Mn. Meanwhile, half of the six black M2 sites will be occupied by Mn according to one of the patterns of a, b, c. Consequently, total 18 possible configurations of the Mn-distribution had been designed and donated as model-ij (i = a, b and c; j = 1, 2, 3, 4, 5, 6) to probe the site preference of Mn atoms (Fig. 7a–c). The energy difference between each model and model-a1, ΔE (ΔE = E_tol − E_a1), is calculated and listed in Table S2.† And the results reveal that the more the Mn ions are dispersed, the lower ΔE of the compound is (Fig. 7d), such as model-b5 and model-cj are the most energetically favorable configurations.

Fig. 7 (a)–(c) The total 18 possible Mn sites in Cs[Tm₉Mn₄Se₁₈], where 1/6 of M1 (blue, denoted as j = 1, 2, 3, 4, 5 and 6) and 3/6 of M2 (black, denoted as i = a, b and c) are occupied by Mn atoms. The total energy of each model is labelled as E_ij (i; j). Taking E_a1 as the reference, we define energy ΔE_ij = E_tol − E_a1, the curve of ΔE varies with the j site as shown in (d).

To check the influence of the strong correlation effect at Mn sites, additionally GGA + U calculations were performed. The analyses indicated that the band gap of Cs[Tm₉Mn₄Se₁₈] can be significantly widened by increasing U from 2 to 4 eV (see Fig. 8). Further increasing the effective Hubbard parameter does not alter significantly the calculated band gap value, which reaches a constant value of 1.68 eV. Consequently, the effective U (U_eff) of 5.0 eV was used for Mn in all the calculations carried out in this work. Similar U_eff was utilized in previous work.²⁵

Fig. 8 The Hubbard U effect on the band gap of Cs[Tm₉Mn₄Se₁₈], calculated by the GGA + U method. The Hubbard correction is made to the Mn 3d states.

The on-site Coulomb correction was only applied to the Mn 3d electrons, which mostly increase the energy of empty 3d states, and widen the optical band gap. In order to simplify the calculation, the Tm 4f electrons were treated as core electrons. The total and partial DOSs of CsTm₉Mn₄Se₁₈ were calculated, and the results revealed the semiconducting behavior and a band gap of about 1.67 eV (Fig. 9). The E_cal value is slightly smaller than E_exp (1.89 eV).

Fig. 9 Total and partial DOSs of Cs[Tm₉Mn₄Se₁₈] (dashed line, E_F).

The valence band (VB) maximum near the Fermi level is mostly Se 4p states mixed with small contributions from Tm 5d and Mn 3d states, whereas the conduction band (CB) minimum is dominated by Tm 5d and Mn 3d states with minor contributions from Se 4p states. Cs atoms almost make no contribution around E_F and act as electron donors to stabilize the structure. Accordingly, the optical absorptions are mainly assigned the charge transfer from Se 4p to Tm 5d and Mn 3d states.

Conclusion

In summary, new quaternary selenides, Cs[RE₉Mn₄Se₁₈] (RE = Ho–Lu), have been synthesized by high temperature solid state reactions of elements with the reactive CsCl flux. They adopt the BaV₁₃O₁₈-structure type and the major structure motif is the 3D network that is constructed by octahedra of RESe₆ and MSe₆ (with disordered Mn and RE center), within which long-range ordered closed cavities of cuboctahedra Cs@Se₁₂ are embedded. The Mn distribution on the anionic network (on M1 and M2 sites) is probed using single crystal diffraction data and is further discussed with the aid of VASP calculations. This work extends the empirical A/M-structure correlation established in the ternary A/RE/Q system into quaternary A/RE/TM/Q, and demonstrates that as the A/M ratio decreases from 0.14 to 0.08 (the minimum ending value to date), the cavity size decreases from Se₁₈ atoms to Se₁₂. To sum up, the A/M-structure correlation for chalcogenides can be better described as follows: when the A/M ratio drops from 1 to 0.2, the anionic moiety varies from infinite 2D layered to open channel structures with a gradually reduced channel size; at A/M = 0.14 for ternary, and 0.08 for quaternary, the anionic moiety is no longer an open channel structure, instead it is a 3D network embedded with individual closed cavities, of which the size also reduces with the A/M decrease. More examples to support such a regulation are in anticipation.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (21225104, 21233009, 91422303, 21301175 and 21171168).

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Footnote

† Electronic supplementary information (ESI) available: The cif file, experimental and theoretical methods, and additional tables and figures. CCDC 1044644–1044648. See DOI: 10.1039/c4qi00202d

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