Synthesis of chiral high-entropy sulfides for non-linear optical applications

Abstract

Non-centrosymmetric semiconductors may exhibit non-linear optical (NLO) properties. For application-relevant materials, a careful balance of high second-harmonic generation (SHG) and high laser damage threshold (LDT) as well as phase-matchability are required. We have previously identified (A)₂Cu₂Ge₂S₁₄ (A = Y, La, Sm, and Gd) phases as promising NLO materials. Here, we developed a synthetic method to produce solid solution and high-entropy sulfides containing up to 9 elements. We report the synthesis, crystal structure, and NLO properties for solid solutions and high-entropy multi-metallic materials (HEMs) of the type (A)₆(TM)_xGe₂S₁₄ (A = La, Sm, Gd, mixture of (Y + La + Ce + Sm + Gd); TM = Mn, Cu; 1 ≤ x ≤ 2). In this work, we establish that nearly all phases are phase matchable and the HEA composition with Cu possesses a SHG signal enhancement of 1.5× as compared to the AgGaS₂ (AGS) standard for the largest particle size, as well as a LDT value of 2.8× of AGS.

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Introduction

Materials with non-linear optical (NLO) properties are widely used in a range of applications such as medicine, atmospheric sensing, telecommunications materials and biological imaging.^1,2 In order for a material to be suitable for NLO applications, several criteria must be met: the phase has to crystallize in a noncentrosymmetric space group, large crystals or bulk quantities of the material should be readily synthesizable, and lastly the material must possess an appropriate band gap.^3–10 In addition, the material must possess a good balance of high second-harmonic generation (SHG) and high laser damage threshold (LDT), as well as being phase-matchable.

For NLO oxide materials, considerable progress has been made, which can be seen in the plethora of new materials discovered in the past decade: Pb₁₇O₈Cl₈,¹¹ NaRb₃B₆O₉,¹² Sn₂B₅O₉Br,¹³ Na₄B₈O₉F₁₀,¹⁴ CaZn₂(BO₃)₂,¹⁵ and Rb₃B₅O₈F₂.¹⁶ For non-oxide/oxo-halide NLO materials, main progress has been made for chalcogenides: Li₂Cs₄Ge₂S₅(S₂)Cl₂,¹⁷ Zn₂HgP₂S₈,¹⁸ and Rb₂CdSi₄S₁₀.¹⁹

Among the different chalcogenides, quaternary sulfides of the type (RE)₆(TM)_x(Z)₂Q₁₄ (RE = rare-earth; TM = transition metals; Z = Si, Ge, Sn, Be, Fe, Zn, Sm, Yb, B, Al, Ga and In; Q = S and Se) stand out as an extremely large class of compounds which adopt the noncentrosymmetric, chiral, and polar space group P6₃.^20–22 Subscript x differs depending on the nature of the Z element and oxidation state of the TM used; for example for Z = Si, x = 2 (Li⁺, Cu⁺, Au⁺), x = 1 (Fe⁺, Mn²⁺), x = 0.67 (Cr³⁺, Rh³⁺), and x = 0.5 (Zr⁴⁺, Pt⁴⁺).²¹

We have previously identified La₃CuGeS₇ (La₆Cu₂Ge₂S₁₄) as a potential NLO material with good LDT and SHG properties.²¹ Then, following the principle of composition optimization within this prototype structure,²³ we attempted to synthesize phases with better NLO properties by changing La to other rare-earth metals: Y, Ce, Sm, and Gd.²⁴ Rare-earth cation variation caused changes to the bond lengths and angles of the underlying polyhedral structure. It was determined that Gd₃CuGeS₇ had the best combination of NLO properties with high LDT (3× AgGaS₂) and SHG (1.6× AgGaS₂ at 88–105 μm particle size) as well as being phase matchable.²⁴

In this manuscript, we developed a synthetic method to produce multimetallic solid solution and high entropy phases. We explored the effect of solid-solution formation and high-entropy rare-earth cation mixing on the NLO properties of the resulting multinary sulfides. Solid-solutions between two phases of similar crystal structure are known to be beneficial not only for phase formation, often making the resulting composition more single phase by suppressing the formation of admixture phases, but also by enhancing mechanical (Vickers hardness and incompressibility) and optical properties.^23,25–29 By forming more complex solid solutions, we can achieve the high-entropy alloy (HEA) regime (containing 5 or more elements in a single crystallographic position in the structure). These phases may have additional thermodynamic stabilization owing to contributions from entropy and often have superior properties as compared to their parent non-HEA compounds.^30–33

Several studies have investigated the effects of solid-solution formation on the resulting NLO properties (mainly SHG). With substitution on the same crystallographic site by atoms with similar characteristics (e.g., charge and polarizability), an enhancement of the SHG signal relative to the standard was observed: Li_xAg_1−xGaSe₂ (x = 0.8, 5× SHG enhancement)³⁴ and Al_5−xGa_xBO₉ (x ≥ 0.4, 10× SHG enhancement).³⁵ In cases of solid solution formation with atoms of different polarizability, a decrease in the SHG signal was observed: Bi_2−xRE_xTeO₉ (RE = Y, Ce and Eu), Bi_4−xLa_xTi₃O₁₂ (x < 0.75), CsBi_1−xEu_xNb₂O₇ (x < 2), Ca₄Bi_6−xLn_xO₁₃ (Ln = La and Eu), and Na₂Mg_1−xZn_xSiO₄ (x < 1).³⁵ Finally, a decrease of the SHG signal was observed in Sb^IIISb^V_xM_1−xO₄ (M = Nb^V or Ta^V, x ≥ 0.6), caused by the fact that M^VO₆ octahedra and not the Sb^IIIO₄E unit were mainly responsible for the SHG response.³⁶

Herein, we report the synthesis, crystal structures, and NLO properties of several Mn/Cu solid solutions for (A)₆(TM)Ge₂S₁₄ (A = La, Sm, Gd, HEA = YLaCeSmGd, TM = Mn, Cu) as well as complex high-entropy alloy compositions, with one having 9 elements (nominal composition of (YLaCeSmGd)_1.2Mn_0.5CuGe₂S₁₄). We have shown the applicability of the method of atomic mixing of refractory components in the synthesis of single-phase homogeneous samples of complex high-entropy sulfides. High entropy materials synthesized in the current work exhibit NLO properties, SHG and LDT, which are on par with the single metal analogs.

Results and discussion

Fig. 1 shows the crystal structure of the mixed metal sulfide La₆Mn_0.5CuGe₂S₁₄. Detailed crystallographic information can be seen in Tables S1A and S1B.† This phase crystallizes in the noncentrosymmetric, chiral, and polar space group P6₃, making it a good candidate for non-linear optical (NLO) materials.^21,37,38 The crystal structure is composed of several types of space-filling polyhedra.^21,22,24 In analogy with the structures of the solid solution end members (containing only one transition metal), in the crystal structure of La₆Mn_0.5CuGe₂S₁₄, Mn and Cu occupy two distinct positions in face-sharing S₆ octahedra. Mn²⁺ atoms occupy the centers of the octahedra, forming [MnS₆] units, while Cu⁺ occupies the opposite faces of the octahedra, forming [CuS₃] trigonal planes (Fig. 1b and c). For a 50/50% solid solution, the octahedra will be occupied either by the Mn atom in the center or the Cu atoms on the faces, giving a “Mn_0.5Cu” composition. The tetrel atom, Ge, forms [GeS₄] tetrahedra, which fill the space around [LaS₈] units. The Ge1–S1 bond is shorter than the other three Ge–S bonds and points along the [001] direction (c-axis) (Fig. 1d and Tables S2A–C†). The lanthanide, in this case La, forms [LaS₈] dodecahedra, which arrange in spiral columns (Fig. 1e).

Fig. 1 (a) Crystal structure of La₆Mn_0.5CuGe₂S₁₄ (P6₃, no. 173) showing the connectivity of polyhedra; (b) green [MnS₆] octahedron; (c) pink [CuS₃] trigonal planes shown occupying opposite faces of a hypothetical octahedron; (d) blue [GeS₄] tetrahedron; and (e) red [LaS₈] dodecahedron.

The synthesis of high-entropy alloys is a challenge,^39–42 and the synthesis of sulfides is complicated by the high vapor pressure of sulfur at elevated temperatures. For synthesis from elements or binary sulfides for multi-metal phases, it is difficult to achieve proper mixing and distribution of metals. Our solution was to use the method of atomic mixing of the refractory components.^12,31 By reacting homogenized arc-melted precursors of the nominal composition (A)₆(TM)Ge₂ with sulfur, we can achieve significantly better atomic mixing and produce bulk powder samples with high enough purity and homogeneity to be suitable for NLO measurements, as well as grow large single crystals (see the ESI† for details). This method was used to produce Mn/Cu solid solution phases for La, Sm and Gd, as well as the high-entropy alloy (Y + La + Ce + Sm + Gd) phases for Mn, Cu and Mn/Cu – the last having 9 elements in the composition.

The powder X-ray diffraction (PXRD) data for the synthesized phases are shown in Fig. 2. The common feature is that the compositions with only Mn often have secondary admixture phases (which can affect the optical properties), while compositions with Cu or mixed Mn/Cu systems are in single-phase. The high-entropy alloy (HEA) composition phases, including the nonary (YLaCeSmGd)_1.2Mn_0.5CuGe₂S₁₄ sample, show very clean powder patterns without substantial peak broadening, suggesting a homogeneous single-phase product, which can be ascribed to the favorable nature of solid-solution and HEA formation for a given system.

Fig. 2 PXRD data for the phase formation of the (A)₆(TM)Ge₂S₁₄ compositions (A = La, Sm, Gd, HEA = YLaCeSmGd, TM = Mn, Cu). Nominal compositions are given in quotation marks (“ ”). The pattern in black is calculated from the single crystal (SC) structural solution. Diffraction peaks corresponding to admixtures are labeled as (*) and re-crystallized grease as (#).

Elemental compositions were verified using energy dispersive spectroscopy (EDS), which showed good agreement of the nominal and EDS compositions, even for the high-entropy alloy compositions (Tables 1 and 2). Deviations from the nominal compositions can be attributed to the fact that the emission lines for the lanthanides, Cu, and Ge have partial overlap. The atomic percentage of light elements, sulfur in this case, is often underestimated by EDS. HEA materials with Cu and Mn/Cu show good agreement between the nominal and actual contents of rare-earth (RE) metals (Table 2). In turn, HEA materials with Mn only, in line with the observed broad and split peaks in the PXRD pattern, have a rare-earth metal content which is different from the nominal content (Y-poor and Ce-rich).

Table 1 EDS compositions for powder samples of (A)₆(TM)Ge₂S₁₄ composition (A = La, Sm, Gd, TM = Mn, Cu) phases when normalized to 6 A atoms. For each sample, 10–20 sites were probed and averaged to determine the average composition. Standard deviations are given in parentheses. To test the reproducibility, two different synthesized batches of samples were studied

Nominal composition	EDS composition from batch 1	EDS composition from batch 2
La6MnGe2S14	La6Mn0.93(6)Ge2.12(11)S12.6(4)	La6Mn0.94(3)Ge2.1(1)S12.8(2)
La6Mn0.5CuGe2S14	La6Mn0.53(3)Cu1.0(1)Ge1.78(3)S13.14(5)	La6Mn0.53(2)Cu0.94(5)Ge1.77(4)S13.09(7)
Sm6MnGe2S14	Sm6Mn0.7(1)Ge1.94(9)S13.1(2)	Sm6Mn0.71(9)Ge1.94(4)S12.9(1)
Sm6Mn0.5CuGe2S14	Sm6Mn0.30(5)Cu1.4(1)Ge2.00(9)S13.17(2)	Sm6Mn0.29(4)Cu1.4(1)Ge1.9(2)S13.1(1)
Gd6MnGe2S14	Gd6Mn0.81(6)Ge2.0(2)S13.27(9)	Gd6Mn0.77(6)Ge2.0(2)S13.2(2)
Gd6Mn0.5CuGe2S14	Gd6Mn0.40(5)Cu1.09(5)Ge1.20(7)S13.6(2)	Gd6Mn0.38(5)Cu0.9(2)Ge1.1(2)S13.7(1)

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Table 2 EDS compositions for powder samples of (HEA)₆(TM)Ge₂S₁₄ composition (HEA = YLaCeSmGd, TM = Mn, Cu) phases when normalized to 6 HEA atoms. For each of the three compositions, the high-entropy composition is given in the second row. For each sample, 10–20 sites were probed and averaged to determine the average composition. Standard deviation is given in parentheses. To test the reproducibility, two different synthesized batches of samples were studied

Nominal composition	EDS composition from batch 1	EDS composition from batch 2
(YLaCeSmGd)1.2Cu2Ge2S14	(HEA1)6Cu1.87(4)Ge1.83(6)S13.1(1)	(HEA1)6Cu1.83(6)Ge1.8(1)S12.9(2)
HEA1	Y1.1(1)La1.4(2)Ce1.1(2)Sm1.3(2)Gd1.1(2)	Y1.2(2)La1.3(3)Ce1.1(2)Sm1.3(3)Gd1.1(2)
(YLaCeSmGd)1.2MnGe2S14	(HEA2)6Mn0.93(4)Ge1.70(6)S12.8(2)	(HEA2)6Mn0.93(3)Ge1.74(7)S12.9(2)
HEA2	Y0.5(1)La1.1(3)Ce2.2(3)Sm1.3(2)Gd0.8(4)	Y0.6(1)La1.0(2)Ce2.2(3)Sm1.5(2)Gd0.71(8)
(YLaCeSmGd)1.2Mn0.5CuGe2S14	(HEA3)6Mn0.43(3)Cu1.10(5)Ge1.74(9)S13.1(2)	(HEA3)6Mn0.37(4)Cu1.07(5)Ge1.78(8)S13.2(2)
HEA3	Y1.18(9)La1.2(1)Ce1.25(6)Sm1.14(7)Gd1.19(7)	Y1.13(9)La1.3(2)Ce1.27(4)Sm1.13(8)Gd1.13(7)

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A suitable band gap is another crucial requirement for infrared (IR) NLO materials. The Tauc plots for the (A)₆(TM)Ge₂S₁₄ samples are shown in Fig. 3. Optical images of the crystals of the sulfides can be seen in Fig. S1.† All compositions are semiconducting phases with visible range direct bandgaps of 1.75–2.31 eV, which are slightly smaller than the bandgap of the standard AgGaS₂ (2.5 eV).²² The insets in Fig. 3 show the optical images of the powders for these sulfide phases. It can be noted that compositions with Mn are more red-brown in color (which could be due to the presence of a small amount of admixture phases), while the compositions with Cu or Mn/Cu are more yellow. We have previously reported (RE)₆CuGe₂S₁₄ compositions with good NLO properties, having larger band gaps of 2.1–2.7 eV.²⁴ However, another member of the same sulfide family, La₆PdSi₂S₁₄, possesses very good NLO properties while having a much smaller band gap of 1.4 eV.²² IrSi₃As₃ is another example of a compound with a smaller band gap and good NLO properties.⁴³

Fig. 3 Tauc plots showing direct band gaps (αhν)² for the (A)₆(TM)Ge₂S₁₄ compositions (A = La, Sm, Gd, HEA = YLaCeSmGd, TM = Mn, Cu) measured using diffuse reflectance UV-Vis spectroscopy. Insets: optical images of powdered samples showing the colors of the phases.

The second-harmonic generation (SHG) signal data for these phases are shown in Fig. 4 (top and middle) and Table S3.† The compositions with pure Mn contain admixtures which can have an effect on the NLO properties measured. All the compositions analyzed (except for Gd₆Mn_0.5CuGe₂S₁₄), including the HEAs, are phase matchable, which means that they show an increase in the SHG signal with increasing particle size. This is very important for NLO applications as it signifies that the bulk material possesses good NLO properties.

Fig. 4 (Top) Second-harmonic generation (SHG) intensity for (A)₆(TM)Ge₂S₁₄ compositions (A = La, Sm, Gd, HEA = YLaCeSmGd, TM = Mn, Cu). The solid lines are drawn to guide the eye. All compositions are phase matchable except Gd₆Mn_0.5CuGe₂S₁₄ (shown with a dashed pink line). (Bottom Left) Laser damage threshold (LDT) intensities for (A)₆(TM)Ge₂S₁₄ compositions. Numbers above the columns indicate the value of LDT relative to the standard AgGaS₂. Standard AgGaS₂ is shown in black in all panels. (Bottom right) SHG/LDT diagram showing SHG values at the maximum studied particle size and LDT values normalized to those for the AGS standard. Data for single RE–Cu compositions are taken from ref. 24.

The SHG signals for the largest particle size (200–250 μm) are comparable or better than those of the AgGaS₂ standard, with the two HEA compositions having values of almost 1.5 times the standard (Fig. 4). All compositions show an enhancement of LDT over the AgGaS₂ standard with values ranging from 1.5× to 3.4×. The trends shown in the Fig. 4 bottom right panel allow us to compare HEA compositions with single RE compositions. For the cases of TM = Mn no clear trends are obtained which may be partially due to the non-single phase nature of the samples. However, for TM = Cu or Cu/Mn there is a clear trend that HEA mixing of the rare-earth cations enhances the SHG response while only slightly decreasing LDT, suggesting that this technique may be a viable strategy to enhance the NLO performance in reported materials.^44,45

To understand the trends in the NLO data, it is important to analyze the bonding within and between the different polyhedral units (Tables S2A–C† and Fig. 5). As expected, the unit cell volumes decrease for both Mn and Cu end members going from La to Gd (Mn: from 539.77 to 488.54 ų, Cu: from 537.95 to 493.07 ų)²⁴ because the size of the lanthanide decreases.⁴⁶ The HEA compositions have unit cell volumes between those of the pure lanthanide parent phases (514.70–521.19 ų). For the dodecahedral [(RE)S₈] units, the polyhedral volumes (46.97–42.13 ų) and the mean RE–S bond lengths (3.004–2.899 Å) decrease going from La to Gd, as expected. There is no obvious correlation between the rare-earth and [GeS₄] tetrahedron volume (∼5.5 ų) or Ge–S bond lengths (mean lengths: ∼2.21 Å). However, the Ge1–S1 bond length is noticeably shorter than the Ge1–S3 bond length in all cases, leading to a local C_3v (3mm) symmetry, with the greatest difference in bond lengths observed in the case of Gd and HEA compositions with Mn. This in turn causes the S–Ge–S angles to deviate from the ideal 109.5° angle (Fig. 5a).

Fig. 5 (a) [GeS₄] tetrahedral unit showing ∠S3–Ge–S1 and ∠S3–Ge1–S3 angles; (b) [MnS₆] octahedral unit showing ∠S2–Mn–S2-axial and ∠S2–Mn1–S2-equatorial angles; (c) two [CuS₃] trigonal planar units showing angle α (∠Cu1–Cu1–S2) indicating the co-planarity of these two units (perfect co-planarity having α = 90°), and angle β (∠S2–Cu1–S2) indicating the deviation from the planar D_3h (6̄m2) symmetry for [CuS₃] (in planar β = 120°).

For the octahedral [MnS₆] units, the polyhedral volumes (26.05–23.76 ų) and Mn–S mean bond length (2.698–2.615 Å) somewhat follow a similar trend – both decrease upon going from La to Gd. The axial S2–Mn1–S2 angles (Fig. 5b) are all very close to 180°; however the equatorial angles (86.559–87.032°) differ from the ideal 90° showing that the octahedra are slightly distorted. Finally, for the trigonal planar [CuS₃] units (Fig. 5c), the Cu–S bonds (2.269–2.222 Å) decrease going from La to Gd as expected. In all cases, the [CuS₃] units lack coplanarity as is evident from the values of angle α (88.391–92.351°) which deviates from the ideal 90°. At the same time, within each CuS₃ unit, atoms are nearly planar as is evident from the β angles (119.833–119.898°) being close to 120°. Comparing the data for RE–Cu compositions²⁴ and (HEA)–Cu, as well as RE–Mn with (HEA)–Mn, it can be noted that the formation of HEAs does not seem to induce additional significant long range distortions. However, it is possible that alternation of larger and smaller rare-earth cations may induce local perturbations which affect the SHG and LDT properties. Further studies using X-ray total scattering and EXAFS will be required to clarify these local distortions.

In summary, it can be shown that LDT and SHG responses have different trends with respect to TM solid solution formation. The mixing of Mn and Cu was beneficial for enhancing LDT relative to not only the standard AgGaS₂, but also most of their single transition metal counterparts. LDT enhancement can be attributed to the added crystallographic disorder due to Mn and Cu partially occupying different crystallographic positions in the structure (Mn at the center of the octahedron, while Cu being on the faces of the octahedron) (Fig. 1), as well as the stability and relatively small anisotropy of the Ge–S bonds in [GeS₄] tetrahedral units (which can be seen from a 2.02–2.39% bond length difference, Table S2†). This is similar to the decrease of the SHG signal observed in Sb^IIISb^V_xM_1−xO₄ (M = Nb^V or Ta^V, x ≥ 0.6), caused by the fact that M^VO₆ octahedra are mainly responsible for the SHG effect.³⁶ In turn, HEA phases with multiple rare-earth cations show performance on par or better than the corresponding single RE compounds. Analyses of the crystal structures do not reveal any special long-range structural deformations for HEA compounds, yet one can assume that the optimization of chemical bonding may occur on the local scale. These results together, along with the reported method of synthesis for complex HEA sulfides, open ways to use mixtures of rare-earth metals (such as mischmetal), rather than purified single RE metals, to synthesize efficient NLO compounds with properties benefiting from the high-entropy nature of the materials.

Conclusions

The effects of structural peculiarities on NLO properties are a complex problem. To analyze the effect of solid-solutions and structural entropy on NLO properties, several compositions within the (A)₆(TM)_xGe₂S₁₄ family of compounds (A = La, Sm, Gd, HEA = YLaCeSmGd, TM = Mn, Cu) were synthesized by a simple reaction of arc-melted precursors with elemental sulfur. The compositions resembling those of Mn/Cu solid solutions or HEAs not only showed SHG signals comparable to or better than the AgGaS₂ standard but are also phase matchable and show an enhancement of LDT relative to the standard. The best NLO properties were achieved for the HEA compound (YLaCeSmGd)_1.2Cu₂Ge₂S₁₄, showing an SHG enhancement of almost 1.5× AgGaS₂ at the largest particle size (200–250 μm), together with an LDT enhancement of 2.8× the standard.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

G. A. is grateful to the Rutgers University – Newark new faculty start-up fund and to the Ames National Laboratory Spedding Postdoctoral Fellowship for financial support. This work was supported by the Ames National Laboratory's Laboratory Directed Research and Development (LDRD) program (G. A., N. W. H., G. V., and K. K.). N. W. H. was supported by the U.S. Department of Energy Office of Science, Science Undergraduate Laboratory Internships (SULI). The Ames National Laboratory is operated for the U.S. DOE by Iowa State University under contract #DE-AC02-07CH11358. We thank Prof. V. Pecharsky (deceased) (ISU and Ames National Laboratory) for access to the arc-melting setup and Professor Javier Vela (ISU) for the use of the diffuse-reflectance setup. This manuscript is dedicated in loving memory of Dina Akopova, the grandmother of Dr. Georgiy Akopov.

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Footnote

† Electronic supplementary information (ESI) available: Details of synthesis^21,47–50 and characterization by single and powder X-ray diffraction, scanning electron microscopy and energy dispersive spectroscopy, UV-Vis diffuse reflectance and non-linear optical properties measurements. CCDC 2266451–2266460. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3qi01214j

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