Syntheses, Structures and Properties of Alkali and Alkaline Earth Metal Diamond-Like Compounds Li2MgMSe4 (M = Ge, Sn)

Two new diamond-like (DL) chalcogenides, Li2MgGeSe4 and Li2MgSnSe4, have been successfully synthesized using a conventional high-temperature solid-state method. The two compounds crystallize in the non-centrosymmetric space group Pmn21 with a = 8.402 (14) Å, b = 7.181 (12) Å, c = 6.728 (11) Å, Z = 2 for Li2MgSnSe4, and a = 8.2961 (7) Å, b = 7.0069 (5) Å, c = 6.6116 (6) Å, Z = 2 for Li2MgGeSe4. The calculated results show that the second harmonic generation (SHG) coefficients of Li2MgSnSe4 (d33 = 12.19 pm/v) and Li2MgGeSe4 (d33 = −14.77 pm/v), mainly deriving from the [MSe4] (M = Ge, Sn) tetrahedral units, are close to the one in the benchmark AgGaS2 (d14 = 13.7 pm/V). The calculated band gaps for Li2MgSnSe4 and Li2MgGeSe4 are 2.42 and 2.44 eV, respectively. Moreover, the two compounds are the first series of alkali and alkaline-earth metal DL compounds in the I2-II-IV-VI4 family, enriching the structural diversity of DL compounds.

In a DL compound, the cation is coordinated with four anions, and follows the Pauling's electrostatic valency rule [19][20][21][22][23]. Hence, the optical properties including band gap and SHG response in the DL chalcogenide compounds could be effectively regulated by organizing proper tetrahedral units in the structure. On the basis of the statistical analyses, the DL chalcogenide compounds mainly consisted of univalent metal tetrahedral units, such as alkali metal tetrahedral LiQ 4 (Q = S, Se) and/or IB group metal tetrahedral M I Q 4 (M I = Cu, Ag; Q = S, Se), with IIB (Zn, Cd and Hg), IIIA (B, Al, Ga and In), IVA (Si, Ge and Sn) and VA (P and As) group element tetrahedral units [24][25][26][27]. Most recently, Pan and Li et al. [14] demonstrated that the alkaline-earth metal AQ 4 (A = Be, Mg; Q = S, Se) tetrahedral units, which without d-d and f -f electronic transitions, can be used to regulate the optical properties of DL chalcogenide compounds. By introducing alkaline-earth metal tetrahedral unit MgS 4 into the I 4 -II-IV 2 -Q 7 system, the first alkali and alkalineearth metal DL sulfide Li 4 MgGe 2 S 7 with excellent IR NLO optical performances was discovered. However, owing to the experimental challenges to obtain the four-coordinated alkaline-earth metal AQ 4 tetrahedral units in a crystal structure, the number of reported alkaline-earth metal containing DL compounds is very limited, and the exploration of new IR NLO materials, especially with excellent optical properties in alkali and alkaline-earth metal DL chalcogenide compounds, is just in the initial stage.
Considering the above discussions, the alkali metal tetrahedral LiS 4 and alkaline-earth metal tetrahedral MgSe 4 units were successfully introduced into the classical I 2 -II-IV-VI 4 family in this work. Two new alkali and alkaline-earth metal DL selenides Li 2 MgMSe 4 (M = Ge, Sn) were synthesized by conventional high temperature solid state reactions in sealed quartz tubes. Li

Chemical Syntheses
High purity (99.99%) raw materials (Li, Mg, Sn, Ge and Se) were obtained from Aladdin Industrial Corporation (Fengxian District, Shanghai, China) and utilized without extra purification.
Li 2 MgMSe 4 (M = Ge, Sn) single crystals for structural determination were prepared using a melting method in sealed quartz tubes. The starting mixture samples (Li:Mg:Ge:Se = 2:1:1:4; Li:Mg:Sn:Se = 2:1:1:4) were packaged in graphite crucibles in a glove box. After that the graphite crucibles were moved into quartz tubes, and the quartz tubes were sealed by flame under a vacuum atmosphere (about 10 −3 Pa). Then, the samples were heated to 880 • C in 46 h, and kept at 880 • C for 50 h, then cooled to room temperature in 48 h. Breaking the tubes, the yellow Li 2 MgGeSe 4 and Li 2 MgSnSe 4 single crystals were harvested in the graphite crucibles. It is worth mentioning that the two crystals show strong moisture absorptions in air.
The syntheses of Li 2 MgMSe 4 (M = Ge, Sn) powder samples for performance characterization were tried at a higher temperature. The mixtures of Li, Mg, Ge/Sn and Se elements with an atomic stoichiometric ratio were first weighed, ground and sealed in quartz tubes. The sealed samples were slowly heated to 900 • C (in 60 h) in a muffle furnace, and kept at this temperature for 100 h, then cooled to room temperature in 100 h.

Single-Crystal X-ray Diffractions
Li 2 MgMSe 4 (M = Ge, Sn) single crystals were manually picked out and utilized for structural determinations. The X-ray diffraction data of Li 2 MgMSe 4 (M = Ge, Sn) single crystals were collected in a Bruker D8 Venture diffractometer that was equipped with monochromatic Mo-Kα radiation (λ = 0.71073 Å) operating at 50 kV and 40 mA. The structure refinements of the two compounds were carried out in the SHELX-97 crystallography software package. The XPREP program was used for the absorption correction (multiscan), the structures of Li 2 MgMSe 4 (M = Sn, Ge) were checked by PLATON in case of additional symmetry elements [29][30][31]. The detailed processes can be found in previous works [9,14,32,33]. It is worth noting that the initial Li/Mg occupation from refinement was 0.53715:0.462850 for Li 2 MgSnSe 4 , and 0.48933:0.51067 for Li 2 MgGeSe 4 , which is close to 1:1.
To maintain the charge balance in the whole structures, the atomic ratio of Li/Mg in both title compounds was set to 1:1. The crystal data and structural refinements of Li 2 MgMSe 4 (M = Ge, Sn) are listed in Table 1. Meanwhile, the corresponding atomic coordinates, bond distances and angles, isotropic displacement parameters and atomic parameters are shown in Tables S1-S7. Since Li 2 MgGeSe 4 deliquesces quickly in air, the data collection for Li 2 MgGeSe 4 was repeated several times using different single crystals. However, the data integrity of Li 2 MgGeSe 4 is still lower than Li 2 MgSnSe 4 .

Powder X-ray Diffraction (PXRD)
The Powder X-ray diffraction (PXRD) pattern of Li 2 MgSnSe 4 was characterized using a Bruker D2 Phaser diffractometer (Bruker Corporation, Karlsruhe, Germany) under Cu-Kα radiation (λ = 1.5418 Å) with a metal holder. Meanwhile, the experimental XRD pattern of Li 2 MgSnSe 4 ( Figure S1) was recorded from 10 to 70 • (2θ) with a scan step width of 0.02 • . The experimental and calculated PXRD patterns of Li 2 MgSnSe 4 are shown in Figure S1. Owing to the experimental challenge in synthesizing and characterizing the moisture-sensitive compounds, impurities such as SnSe 2 and SnSe were observed in the synthesized Li 2 MgSnSe 4 powder samples. However, based on the XRD patterns, the main phase can be determined to be Li 2 MgSnSe 4 . Meanwhile, compared with Li 2 MgSnSe 4 , Li 2 MgGeSe 4 powder samples exhibit more serious moisture absorption. It was deliquesced too fast in air (the samples were deliquesced in 1 min at room temperature) to finish the PXRD measurement. GSAS was used to fit and refine the powder diffraction data of Li 2 MgSnSe 4 . The main phase Li 2 MgSnSe 4 and impurity phases SnSe and SnSe 2 were refined. A certain peak function was fitted with experimental intensity data, and the values of peaks and structural parameters (including background function, lattice parameters, peak parameters, atomic position, preference orientation, etc.) were constantly adjusted during the fitting process until the difference between calculated intensity and experimental intensity stabilized [34]. The multi-phase Rietveld refinement yielded tiny impurities contents such as SnSe 2 and SnSe (total 9.7%) remaining from the staring materials, and a weight fraction of 90.3% of target Li 2 MgSnSe 4 ( Figure S2). The refined structural parameters are provided in Table S8. The large difference in the refinement can be attributed to the experimental challenge to obtain long time and high quality PXRD data for the moisturesensitive Li 2 MgSnSe 4 . However, the refined results are helpful in judging the purity of the product.

UV-Vis-NIR Diffuse Reflectance Spectroscopy
The diffuse reflectance spectrum of the synthesized Li 2 MgSnSe 4 powder samples was characterized using a DUV spectrophotometer (Shimadzu SolidSpec-3700, Shimadzu Corporation, Shanghai, China) at room temperature in air. Based on the reflection spectrum, the corresponding absorption spectrum was obtained using the Kubelka-Munk formula [35,36]. The process was completed in 5-10 min.

Raman Spectroscopy
The Raman spectrum of Li 2 MgSnSe 4 was characterized on a single crystal in a LABRAM HR Evolution spectrometer.
The Li 2 MgSnSe 4 single crystal was firstly placed onto a transparent glass slide. Then, a suitable objective lens was used to select the measured area on the crystal. The maximum power of the used laser beam was about 60 mW with a spot size of~35 µm.

Theoretical Calculations
Based on the density functional theory (DFT) and CASTEP program, the plane wave pseudopotential was applied to calculate the electronic structures of Li 2 MgMSe 4 (M = Ge, Sn) [37]. Meanwhile, the exchange-correlation effects of the compounds were analyzed by using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) function [38,39]. Under the norm conserving pseudopotentials for wave function expansion, the kinetic energy cutoff of the models was set to 450 eV. Moreover, the Brillouin zone [40] contained 2 × 2 × 2 Monkhorst-pack k-point sampling [41]. The virtual unit cells were used to process the occupancy [42,43].

Crystal Structure
As shown in Figure 1a,f, the two compounds are isomorphic structures. Herein, Li 2 MgSnSe 4 is taken as an example of the structure description. Li 2 MgSnSe 4 crystallizes in the noncentrosymmetric space group Pmn2 1 with a = 8.402 (14) Å, b = 7.181 (12) Å, c = 6.728 (11) Å and Z = 2. In the asymmetric unit of Li 2 MgSnSe 4 , there are two Li, one Mg, one Sn and three Se atoms that are crystallographically independent. In Li 2 MgSnSe 4 , the Li2 and Sn1 atoms are bonded to four Se atoms to build up the [LiSe 4 ] and [SnSe 4 ] tetrahedra with Li-Se bond lengths ranging from 2.50 Å-2.65 Å and Sn-Se bond lengths ranging from 2.505 Å-2.528 Å, respectively. The Li1 and Mg1 atoms are set to share the same sites with the atomic ratio of 1:1 in the initial refinements with the identical anisotropic displacement parameters, which can help to obtain better R values and reasonable temperature factors, similar to the situation of Cu/Mg atomic co-occupation in Cu 2 MgSiS 4 [44], Cu 2 MgGeS 4 [44] and Cu 2 MgSiSe 4 [44]. Furthermore, Li/Mg atomic co-occupation is very common, which can be found in the LiMg(IO 3 ) 3 [45] and Li 0.8 Mg 2.1 B 2 O 5 F [46]. Similar to the Li2 and Sn1 atoms, the co-occupied Li1 and Mg1 atoms are bonded to four Se atoms to construct the [(Li/Mg) Se 4 ] tetrahedra units at the Wyckoff position 4b (Table S7). Furthermore, the formed tetrahedra groups are connected with each other by sharing Se atoms to constitute the final DL structure. For both compounds, there is a similar channel-like structure with a channel diameter of about 6 Ångstrom on the ab plane, as shown in Figure 1e

Optical Properties
Based on the UV-Vis-NIR diffuse-reflectance spectrum, the experimental band gap of Li2MgSnSe4 was determined to be 2.62 eV (Figure 2a). To confirm chemical bonding, the Raman spectrum of Li2MgSnSe4 was characterized on a single crystal. As shown in Figure 2b, the peaks below 193 cm −1 are related to the vibrations of Li-Se and Mg-Se bonding, matched with the previous results [47][48][49]. The peak at 193 cm −1 and the overlapping peaks around 235 cm −1 could be assigned to the asymmetric and symmetric stretching vibrations of Sn-Se bonding in SnSe4 tetrahedral groups [49,50].

Theoretical Calculations
To study the linear and nonlinear optical properties of Li2MgMSe4 (M = Ge, Sn), DFT calculations were implemented. Considering the Li/Mg atomic co-occupation at the

Optical Properties
Based on the UV-Vis-NIR diffuse-reflectance spectrum, the experimental band gap of Li 2 MgSnSe 4 was determined to be 2.62 eV (Figure 2a). To confirm chemical bonding, the Raman spectrum of Li 2 MgSnSe 4 was characterized on a single crystal. As shown in Figure 2b, the peaks below 193 cm −1 are related to the vibrations of Li-Se and Mg-Se bonding, matched with the previous results [47][48][49]. The peak at 193 cm −1 and the overlapping peaks around 235 cm −1 could be assigned to the asymmetric and symmetric stretching vibrations of Sn-Se bonding in SnSe 4 tetrahedral groups [49,50].

Optical Properties
Based on the UV-Vis-NIR diffuse-reflectance spectrum, the experimental band gap of Li2MgSnSe4 was determined to be 2.62 eV (Figure 2a). To confirm chemical bonding, the Raman spectrum of Li2MgSnSe4 was characterized on a single crystal. As shown in Figure 2b, the peaks below 193 cm −1 are related to the vibrations of Li-Se and Mg-Se bonding, matched with the previous results [47][48][49]. The peak at 193 cm −1 and the overlapping peaks around 235 cm −1 could be assigned to the asymmetric and symmetric stretching vibrations of Sn-Se bonding in SnSe4 tetrahedral groups [49,50].

Theoretical Calculations
To study the linear and nonlinear optical properties of Li2MgMSe4 (M = Ge, Sn), DFT calculations were implemented. Considering the Li/Mg atomic co-occupation at the

Theoretical Calculations
To study the linear and nonlinear optical properties of Li 2 MgMSe 4 (M = Ge, Sn), DFT calculations were implemented. Considering the Li/Mg atomic co-occupation at the Wyckoff position 4b in the structures, the virtual unit cells were built for the calculations, as shown in Table S9 and Figure S3. The calculated theoretical band gaps, SHG coefficients and birefringences of the two compounds are shown in Table 2  To detect the origin of the optical properties, the electronic structures, SHG densities and band-resolved NLO susceptibilities of Li 2 MgMSe 4 (M = Ge, Sn) were further investigated. Figure 3 shows the calculated band structures, total and partial density of states and the band-resolved NLO susceptibility χ (2) of the two compounds. The band structures (Figure 3a Figure 4 shows the calculated SHG densities for the two compounds. Combined with the band-resolved NLO susceptibility χ (2) in Figure 3c

Conclusions
In summary, the first series of DL selenides in the I2-II-IV-VI4 family, Li2MgGeSe4 and Li2MgSnSe4, have been rationally designed and synthesized. Their crystal structures were determined using single crystal X-ray diffractions, and the optical properties were studied using experimental spectra and DFT calculations.  Table S1: Atomic coordinates and equivalent isotropic displacement parameters of Li2MgSnSe4, Table S2: Anisotropic displacement parameters (Å 2 × 10 3 ) of Li2MgSnSe4, Table S3: Symmetry, selected bond lengths and angles of crystal data and structural refinements of Li2MgSnSe4, Table S4: Atomic coordinates and equivalent isotropic displacement parameters of Li2MgGeSe4, Table S5: Anisotropic