English

• 1. INTRODUCTION

  Phosphates have been pursued as nonlinear optical (NLO) material for a long time owing to their che-mical benignity, blue shifting ability of optical cutoff edges, and structural diversity^[1-4]. During the synthe-sis of phosphate materials with large SHG response, widely applied strategy is the involvement of NLO-active structural units, such as d⁰ ca-tions with second-order Jahn-Teller (SOJT) effects or stereo-active lone pair (SCALP) cations^[5-7], and d¹⁰ cations centered polyhedra with large polar displacement^[8- Recently, it is unanimously agreed that compounds with large alkaline and alkaline-earth metal cations are easy to form asymmetry and have short cut off edge. Meanwhile, the microscopic tetrahedral units like PO₄ perceived to conducive for ensuring short UV absorption edge^[11-13]. Assisted by the above ideas, during the past few years many pro-mising star NLO phosphates have been synthesized, such as single-metal phosphates Ba₃P₃O₁₀X (X = Cl, Br)^[14] and Ba₅P₆O₂₀^[15] and mixed-metal phosphates LiCs₂PO₄^[16-17], RbBa₂(PO₃)₅^[18], CsLiCdP₂O₇^[19], M₄Mg₄(P₂O₇)₃ (M = K, Rb)^[20], RbNaMgP₂O₇^[21], and CsNaMgP₂O₇^[22].

  By introducing a transition metal with a d¹⁰ elec-tron configuration and an alkali metal with a large radius into the borate system, Pan et al. synthesized a new beryllium-free Rb₃Al₃B₃O₁₀F^[23], which not only exhibits a large NLO response of 1.2 times that of KDP but also is transparent down to the deep-UV region (200 nm). As far as we know, few compounds have been reported in the alkali metals gallium phosphate pseudo-ternary system. In particular, there are only a few compounds in the Cs₂O–Ga₂O₃–P₂O₅ system, and only CsGa₂P₅O₁₆^[24], Cs₂GaP₃O₁₀^{[25, 26]} and CsGa(PO₃)₄^[27] have been reported.

  Our original aim was to search for the new compound within Cs₂O–Ga₂O₃–P₂O₅ system. Sur-prisingly, we obtained a new mixed metal phosphate Cs₂Ga₄(P₂O₇)₂(P₄O₁₃). Though it crystallizes in a centrosymmetric space group, we are deeply attracted by its amazing structure. In this paper, we report its synthesis and crystal structure and make some meaningful comparisons.

  2. EXPERIMENTAL

  2.1 Reagents

  All of the chemicals were purchased from com-mercial sources and used without further purification. NH₄H₂PO₄ (99.5%), TeO₂ (99.99%), Ga₂O₃ (99.99%), and Cs₂CO₃ (99.9%) were all purchased from the Shanghai Reagent Factory.

  2.2 Single crystal preparation

  2.2.1   Synthesis of Cs₂Ga₄P₈O₂₇

  Single crystals of Cs₂Ga₄P₈O₂₇ were initially pre-pared by the reaction of a mixture of 0.60 g (5.713 mmol) NH₄H₂PO₄, 0.20 g (1.253 mmol) TeO₂, 0.20 g (1.670 mmol) Ga₂O₃ and 0.22 g (0.675 mmol) Cs₂CO₃. The powder mixture was first grounded in an agate mortar and then transferred to a corundum crucible. The sample was gradually heated in air at 573 K for 10 h, and finally heated at 1123 for 48 h. The intermediate product was slowly cooled down to 873 K at a rate of 2 K/h where it was kept for 10 h and then cooled down to room temperature at a rate of 6 K/h. Some colorless crystals of different shapes were mechanically removed from the solidified flux dealing with the hot water.

  2.2.2   Single-crystal structure determination

  A single crystal of the title compound was selected for indexing and intensity data collection on a Rigaku Saturn70 diffractometer (2 × 2 bin mode) at 293 K. The structure was solved by direct methods and refined anisotropically by using SHELXS-97. Absorption correction by the multi-scan method was applied for the title compound^[35], and its structure was solved by direct methods and then refined on F² by full-matrix least-squares method, and performed in the Shelxl/PC program^[36]. All atoms were refined with anisotropic thermal parameters. The Cs(2) atoms in the unit cell are disordered and refined to four crystallographic positions (Cs(2A), Cs(2B), Cs(2C), Cs(2D)) to eliminate the high residual peaks. The occupancy factors of these positions were allowed to be refined to have a sum occupancy factor of 1 and equal displacement parameters for each position.

  2.3 Computational details

  The crystal and electronic structures of Cs₂Ga₄P₈O₂₇ were calculated by using density func-tional theory (DFT), as implemented in the Vienna Ab-initio Simulation Package (VASP). The pro-jector-augmented wave (PAW) potential^{[38, 39]} was used to describe the electron-ion interaction. The plane-wave basis-set with a cutoff energy of 520 eV, the Monkhorst-Pack scheme k-mesh of 3×3×6, and the Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation (GGA) exchange-correlation functional were adopted. The crystal structure was fully relaxed until the force on each atom is less than 10 meV/Å.

  3. RESULTS AND DISCUSSION

  Our exploration of the Cs-Ga-Te-P-O system by high temperature solid-state reaction afforded a new gallium phosphate, namely, Cs₂Ga₄P₈O₂₇. It features a 3D framework structure of {Ga₄P₈O₂₇}^2- formed by corner sharing of GaO₄, GaO₆, P₂O₇ and P₄O₁₃ groups, with the cesium cations balancing the charge (Fig. 1). It is amazing to find the coexistence of two kinds of coordination models (4 and 6) of Ga³⁺ cations in one single compound. Furthermore, the fundamental anionic group of Cs₂Ga₄P₈O₂₇ contains three non-condensed phosphoric anionic groups, two P₂O₇ and a P₄O₁₃, which represents the new topological type of phosphoric anionic groups within the family of phosphates.

  Figure 1

  

  Figure 1.  View the framework structure of Cs₂Ga₄P₈O₂₇ along the b axis

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  3.1 Structure discussion

  X-ray analysis revealed that the compound Cs₂Ga₄P₈O₂₇ crystallizes in monoclinic system with space group P2₁/c. There are two cesium atoms, four gallium atoms, eight phosphorus atoms and 27 oxygen atoms in its asymmetric unit. All of the oxygen atoms belong to the phosphoric groups and are two-coordinative to form P−O−P or P−O−Ga linkages. All of the atoms represent independent crystallographic sites except the Cs(2) atoms, which are disordered and were refined to four crystallo-graphy orientations (Cs(2A), Cs(2B), Cs(2C), Cs(2D)) to eliminate the high residual peaks.

  As is seen from Fig. 2, the 3D framework structure of the title compound can be regarded as further connected of the alternative layers of {Ga₂(P₄O₁₃)}_n and {Ga₂(P₂O₇)₂}_n^2n- via linkages of Ga(1)−O(5)−P(2) and Ga(4)−O(12)−P(4). The {Ga₂(P₄O₁₃)}_n layer parallel to the bc plane was formed by corner sharing Ga(1)O₆, Ga(4)O₆ and P₄O₁₃ groups, while the {Ga₂(P₂O₇)₂}_n^2n- layer parallel to the bc plane was formed by corner sharing Ga(2)O₆, Ga(3)O₄ and P₂O₇ groups, respectively.

  Figure 2

  

  Figure 2.  View the framework structure of {Ga₄P₈O₂₇}^2- along the b axis, and the layers of {Ga₂(P₄O₁₃)}_n and {Ga₂(P₂O₇)₂}_n^2n- along the a axis. Cs, Ga, O and P atoms are represented by green, blue, red and pink circles, respectively

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  There are four independent positions of Ga atoms in the asymmetric unit with two different coor-dination models. Among them, Ga(1), Ga(2) and Ga(4) were connected by six oxygen atoms to form GaO₆ distorted octahedra with the Ga–O distances ranging from 1.913(5) to 2.012(5) Å (Table 1), while Ga(3) atoms were connected by four oxygen atoms to form GaO₄ distorted tetrahedra with the Ga–O distances ranging from 1.786(5) to 1.798(5) Å (Table 1). Not only GaO₄ tetrahedra but also GaO₆ octahedra corner share all their oxygen atoms with PO₄ tetrahedra. In other words, all of the gallium atoms were separated by phosphorus atoms.

  Table 1

  

  Table 1.  Selected Bond Lengths (Å) and Bond Valence Sums for Cs₂Ga₄P₈O₂₇

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  Bond	Dist.	BV	Bond	Dist.	BV
  Ga(1)–O(27)	1.932(5)	0.579	P(2)–O(4)	1.616(5)	1.003
  Ga(1)–O(17)	1.932(5)	0.579	P(2)–O(5)	1.494(5)	1.394
  Ga(1)–O(5)	1.943(5)	0.562			∑BVS = 4.989
  Ga(1)–O19)	1.945(5)	0.559	P(3)–O(10)	1.493(5)	1.398
  Ga(1)–O22)	1.972(5)	0.520	P(3)–O(8)	1.516(5)	1.314
  Ga(1)–O20)	2.001(5)	0.481	P(3)–O(9)	1.535(5)	1.248
  		∑BVS = 3.280	P(3)–O(11)	1.591(5)	1.073
  Ga(2)–O(10)	1.884(5)	0.660			∑BVS = 5.033
  Ga(2)–O(3)i	1.913(5)	0.610	P(4)–O(12)	1.492(5)	1.402
  Ga(2)–O(1)	1.918(5)	0.602	P(4)–O(14)	1.507(5)	1.346
  Ga(2)–O(8)	1.931(5)	0.581	P(4)–O(13)	1.535(5)	1.248
  Ga(2)–O(14)	1.995(5)	0.489	P(4)–O(11)	1.596(5)	1.058
  Ga(2)–O(6)1	2.012(5)	0.467			∑BVS = 5.054
  		∑BVS = 3.409	P(5)–O(16)	1.496(5)	1.387
  Ga(3)–O(2)	1.786(5)	0.860	P(5)–O(15)	1.505(5)	1.354
  Ga(3)–O(7)ii	1.789(5)	0.853	P(5)–O(17)	1.513(5)	1.325
  Ga(3)–O(13)	1.797(5)	0.834	P(5)–O(18)	1.627(5)	0.973
  Ga(3)–O(9)iii	1.798(5)	0.832			∑BVS = 5.039
  		∑BVS = 3.379	P(6)–O(20)	1.474(5)	1.472
  Ga(4)–O(12)iii	1.909(5)	0.616	P(6)–O(19)1	1.491(5)	1.406
  Ga(4)–O(26)iv	1.927(5)	0.587	P(6)–O(18)	1.549(5)	1.202
  Ga(4)–O(16)v	1.979(5)	0.510	P(6)–O(21)	1.593(5)	1.067
  Ga(4)–O(15)iv	2.002(5)	0.479			∑BVS = 5.147
  Ga(4)–O(25)	2.009(5)	0.470	P(7)–O(23)	1.471(5)	1.484
  Ga(4)–O(23)i	2.012(5)	0.467	P(7)–O(22)i	1.494(5)	1.394
  		∑BVS = 3.129	P(7)–O(24)	1.571(5)	1.132
  P(1)–O(3)	1.494(5)	1.394	P(7)–O(21)	1.615(5)	1.005
  P(1)–O(1)	1.509(5)	1.339			∑BVS = 5.015
  P(1)–O(2)	1.521(5)	1.296	P(8)–O(26)	1.507(5)	1.346
  P(1)–O(4)	1.597(5)	1.056	P(8)–O(25)	1.508(5)	1.343
  		∑BVS = 5.085	P(8)–O(27)	1.514(4)	1.321
  P(2)–O(6)	1.503(5)	1.361	P(8)–O(24)v	1.615(5)	1.005
  P(2)–O(7)	1.540(5)	1.231			∑BVS = 5.015
  Symmetry transformations used to generate the equivalent atoms: i x, 3/2–y, 1/2+z; ii –x, 1–y, –z; iii –x, 1–y, 1–z; iv1–x, 1–y, 1–z; v 1–x, –1/2+y, 1/2–z; vi x, 3/2–y, –1/2+z; vii1–x, 1/2+y, 1/2–z

  As shown in Fig. 3a and 3d, the (Ga(1)O₆) and (Ga(4)O₆) groups in the {Ga₂(P₄O₁₃)}_n layer use five of their oxygen atoms to corner share with three P₄O₁₃ groups, and use the last oxygen atoms to connect P(2) or P(4) atoms. The coordination models of two other gallium atoms Ga(2) and Ga(3) in the layer of {Ga₂(P₂O₇)₂}_n^2n- are quite different. The (Ga(2)O₆) group uses all its six oxygen atoms to connect with four P₂O₇ groups (Fig. 3b), while the (Ga(3)O₄) group is further connected to four P atoms from four different (P₂O₇) groups (Fig. 3c).

  Figure 3

  

  Figure 3.  View of the linkages of [Ga1O₆], [Ga2O₆], [Ga3O₄] and [Ga4O₆] groups in the layer. Ga, P and O atoms are represented by light blue, pink, and red circles, respectively

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  The bond-valence sum calculation for gallium cations within the tetra- or hexa-coordinate options of 3.379 (Ga(3)), 3.280 (Ga(1)), 3.409 (Ga(2)), and 3.129 (Ga(4)) reveals that the oxidation states of gallium cations are +3. The Ga–O bond distances, coordination models and bond-valence sums are comparable to other cesium gallium phosphates^[24-27].

  As can be seen from Fig. 4, each P atom is coor-dinated with four oxygen atoms in a tetra-coor-dinated geometry with the P–O bond distances ranging from 1.471(5) to 1.616(5) Å (Table 1). PO₄ groups are further condensed via corner-sharing to form two P₂O₇ groups and one P₄O₁₃ tetraphosphate group. The shortest and longest P–O distances are found from the P(7)–O(23)–Ga(4) and P(1)–O(4)–P(2) linkages, respectively. These P–O bond lengths are comparable with those reported in cesium gallium phosphates^[24-27]. Two non-condensed (P(1)P(2)O₇) and (P(3)P(4)O₇) groups are built by corner sharing of P(1)O₄ and P(2)O₄ tetrahedra and P(3)O₄ and P(4)O₄ tetrahedra, respectively (Fig. 4a and 4b). The (P₄O₁₃) group is built from four crystallographically independent PO₄ groups (P(5)O₄, P(6)O₄, P(7)O₄, and P(8)O₄ groups) via corner sha-ring and features a horseshoe conformation (Fig. 4c). The bond-valence sum calculations for phosphorus within the tetra-coordinated options of 5.085 (P1), 4.989 (P(2)), 5.033 (P(3)), 5.054 (P(4)), 5.039 (P(5)), 5.147 (P(6)), 5.015 (P(7)), and 5.015 (P(8)), revealing that the oxidation states of phosphorus atoms are +5.

  Figure 4

  

  Figure 4.  View the linkages of (P1P2O₇), (P3P4O₇) and (P5P6P7P8O₁₃) groups in the title compound. Ga, P and O atoms are represented by light blue, pink and red circles, respectively

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  As shown in Fig. 1, the Cs⁺ cations are located in the free space between the layers of {Ga₂(P₄O₁₃)}_n and {Ga₂(P₂O₇)₂}_n^2n-. There are two unique Cs atoms in the asymmetric unit of the title compound. As mentioned above, Cs(1) atoms were refined with independent crystallographic sites and fully occupied, while Cs(2) atoms in the unit cell are disordered and were refined to four crystallographic positions (Cs(2A), Cs(2B), Cs(2C), Cs(2D)). As shown in Fig. S1, the Cs(1) atoms are surrounded by eleven oxygen atoms at the Cs–O distances less than 3.8 Å ranging from 2.970 to 3.767(7) Å with the calculated bond valence sums (BVS) of 1.121 for Cs1. The con-nection model of Cs(2) atoms is a little complicate, since it has been divided into four positions. If only the shortest connection of each oxygen atom surrounding of Cs(2A), Cs(2B), Cs(2C), Cs(2D) is remaining for simplification (Fig. S1), Cs(2) atoms are surrounded by twelve oxygen atoms with the Cs–O distances ranging from 3.241 to 3.714(7) Å with the calculated bond valence sums (BVS) of 0.790 for Cs(2). The BVS of Cs1 and Cs(2) are close to the oxidation state +1 of Cs. The Cs–O bond distances and connection models are comparable to those in other cesium phosphates^{[26, 27]}.

  3.2 Phosphoric anion comparison

  As we know, P atoms are always coordinated by four oxygen atoms to form the PO₄ group, and then they further connect through corner sharing to form various condensed phosphoric anions. The pho-sphoric anions P₂O₇ and P₄O₁₃ in the title compound both belong to the non-condensed linear oligo-phosphates with the general formula of (P_nO_3n+1)^(n+2)-. Phosphates containing two or more types of discrete phosphoric anions are rare because such structures were once believed to be beyond Pauling's fifth rule^[40]. However, some of phosphates containing two types of separated phosphoric anions are presently well characterized. For example, the PO₄ and P₂O₇ anions coexist in compounds Na₄Ni₅(PO₄)₂(P₂O₇)₂^[41], Na₄M₃(PO₄)₂(P₂O₇) (M = Mn, Co, Ni)^[42], and Na₇V₄(PO₄)(P₂O₇)₄^[43]. The PO₄ and P₄O₁₃ anions coexist in Li₆[(UO₂)₁₂(PO₄)₈(P₄O₁₃)]^[44]. S.L Pan reported that Rb₃Sr₂(PO₃)₃ was the first example of two kinds of [PO₃]_∞ linear chains coexisting in one phosphate and Cs₃Sr₂(PO₃)₃(P₄O₁₂) was a rare example of the non-condensed [P₄O₁₂] ring and the 1D [PO₃]_∞ chain^[45].

  The title compound Cs₂Ga₄(P₂O₇)₂(P₄O₁₃) com-posed of the P₂O₇ and P₄O₁₃ phosphoric anions belongs to the tetrapoly-dipolyphosphates (Fig. 4). As far as we know, tetrapoly-dipolyphosphates are rarely reported. CaNb₂O(P₄O₁₃)(P₂O₇) is the first example of a tetrapoly-dipolyphosphate featuring a stacking of alternating rows of P₄O₁₃ and P₂O₇ groups (Fig. 5a)^[46]. Pb₁₂[Li₂(P₂O₇)₂(P₄O₁₃)₂](P₄O₁₃) containing the isolation of P₂O₇ and two types of P₄O₁₃ with different symmetries has been synthesized by using Li₂O as dimensional reduction agent to dismantle Pb₃P₄O₁₃ by S.L Pan' group (Fig. 5b)^[47], as well as Pb_9−xBa_x[Li₂(P₂O₇)₂(P₄O₁₃)₂] (x = 0, 2, 6, 7), which exhibits 0D [Li₂(P₂O₇)₂(P₄O₁₃)₂]¹⁸⁻ anionic clusters constructed by LiO₄, P₂O₇ and P₄O₁₃ groups (Fig. 5c)^[48]. KV₄(PO₄)(P₂O₇)(P₄O₁₃) contains three different types of phosphoric anions, PO₄, P₂O₇, and P₄O₁₃ groups (Fig. 5d)^[49].

  Figure 5

  

  Figure 5.  Configuration of the phosphoric anions; (a) in CaNb₂O(P₄O₁₃)(P₂O₇), (b) in Pb_9−xBa_x[Li₂(P₂O₇)₂(P₄O₁₃)₂] (x = 0, 2, 6, 7), (c) in Pb₁₂[Li₂(P₂O₇)₂(P₄O₁₃)₂](P₄O₁₃), and (d) in KV₄(PO₄)(P₂O₇)(P₄O₁₃)

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  As shown in Table 2, the comparisons of the condensed phosphoric anions of the title compound (compound 1) with these reported tetrapoly-dipoly-phosphates (compound 2~5) have been summarized. Though, all phosphoric anions (P₂O₇ and P₄O₁₃) in these compounds are non-condensed without further connecting to form infinite chain or ring, we found some interesting differences among them.

  Table 2

  

  Table 2.  Comparison of the Corresponding Condensed Phosphates

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  	Compounds	P/O ratio	Types of anion	Phosphoric anions	P2O7/P4O13 ratio	Structure of P4O13	References
  1	Cs2Ga4(P2O7)2(P4O13)	8:27	Two	(P2O7)2(P4O13)	2:1	Horseshoe-shaped	This paper
  2	CaNb2O (P2O7) (P4O13)	6:21	Three	(P2O7) (P4O13)	1:1	S-shaped	[46]
  3	Pb12[Li2(P2O7)2(P4O13)2](P4O13)	16:53	Three	[(P2O7)2(P4O13)2](P4O13)	2:3	S-shaped	[47]
  4	Pb9−xBax[Li2(P2O7)2(P4O13)2] (x = 0, 2, 6, 7)	12:40	Two	(P2O7)2(P4O13)2	2:2	S-shaped	[48]
  5	KV4(PO4)(P2O7)(P4O13)	7:24	Three	(PO4)(P2O7)(P4O13)	1:1	S-shaped	[49]
  6	K2V2O2(P4O13)	4:15	Two	(P4O13)		Horseshoe-shaped	[50]
  7	Cs2Cr3[B(P2O7)2](P4O13)	8:27	Two	[B(P2O7)2](P4O13)	2:1`	Horseshoe-shaped	[51]

  Firstly, all of the oxygen atoms in these com-pounds belong to the phosphoric groups except CaNb₂O(P₄O₁₃)(P₂O₇), which contains one free oxy-gen atom and should be called tetraphosphate dipho-sphate oxide instead of tetrapoly-dipoly-pho-sphate.

  Secondly, the ratios of P/O in compound 1~5 are 8/27, 6/21, 15/53, 12/40, and 7/24, respectively, as well as the ratios of P₂O₇ to P₄O₁₃ groups are 2/1, 1/1, 2/3, 2/2 and 1/1, respectively. Among them, the highest ratio of P/O is in 2 (CaNb₂O(P₄O₁₃)(P₂O₇)), which has the lowest ratio of P₂O₇ to P₄O₁₃ groups (1:1) and an additional O atom beyond of phosphoric groups, while compound 5 (KV₄(PO₄)(P₂O₇)(P₄O₁₃)) has the lowest P/O ratio owing to the coexistence of threetypes of phosphoric groups (PO₄, P₂O₇, and P₄O₁₃) and the ratio of PO₄/P₂O₇/P₄O₁₃ is 1/1/1 (Table 2).

  Thirdly, the horseshoe conformation of the P₄O₁₃ group in the title compound is different from those observed in compounds 2~5, which are principally S-shaped (Fig. 4c). As far as we know, there are only two cases containing horseshoe shaped conformation of the P₄O₁₃ group before, K₂V₂O₂(P₄O₁₃)^[50] and Cs₂Cr₃[B(P₂O₇)₂](P₄O₁₃)^[51]. Both of these two compounds are not tetraphosphate-diphosphates. K₂V₂O₂(P₄O₁₃) has only one condensed phosphoric group P₄O₁₃ and two other oxygen atoms beyond the phosphoric group, and its P₄O₁₃ group is charac-terized as horseshoe-shaped with two bridging P(1)–P(2)–P(3) and P(2)–P(3)–P(4) angles of 112.07° and 99.45° (Fig. S2a). Cs₂Cr₃[B(P₂O₇)₂](P₄O₁₃) contains two types of complex anionic groups, (P₄O₁₃)⁶⁻ and [B(P₂O₇)₂]⁵⁻, which were better to be called as boro-phosphate-phosphate. The P₄O₁₃ group in Cs₂Cr₃[B(P₂O₇)₂]-(P₄O₁₃) is also characterized as horseshoe-shaped with two bridging P(1)–P(2)–P(3) and P(2)–P(3)–P(4) angles of 112.42° and 103.89°, respectively (Fig. S2b). The horseshoe-shaped P₄O₁₃ groups K₂V₂O₂(P₄O₁₃) and Cs₂Cr₃[B(P₂O₇)₂](P₄O₁₃) are comparable to that of the title compound Cs₂Ga₄-(P₂O₇)₂(P₄O₁₃), of which two bridging P(5)–P(6)–P(7) and P(6)–P(7)–P(8) angles are 117.71° and 106.31°, respectively (Fig. S2c).

  3.3 Theoretical studies

  The fully relaxed lattice constants by PBE functional are a = 15.147, b = 16.454, c = 9.804 Å and β = 92.30°, which agree with the experimental values. Electronic structure calculations are performed based on the relaxed structure. The calculated band structures along the high-symmetry points of the first Brillouin zone are plotted in Fig. 6. It is clear that Cs₂Ga₄P₈O₂₇ is a direct band gap insulator with the conduction band minima (CBM) and valence band maximum (VBM) located at the Γ-point. The PBE calculated band gap is 4.13 eV, which is likely to be underestimated due to the shortages of the semilocal functionals. However, the unit cell size of the title compound is too large to go beyond the semilocal functionals. The valence bands are very flat and the conduction bands are highly dispersive around the Γ point. The orbital contribution of each atom to the energy band can be clearly seen from the corresponding partial density of states (PDOS) and band decomposed charge density. The flat valence band is mainly from the O 2p orbitals and the more dispersive conduction band is mainly from the more extended 4s orbitals of Ga³⁺, as shown in Fig. S3.

  Figure 6

  

  Figure 6.  Band structure and partial density of states (PDOS) of Cs₂Ga₄P₈O₂₇

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  4. CONCLUSION

  In summary, our original aim was to search for new NLO materials within the A^I–Ga^Ⅲ–TeO₂–P₂O₅ system. Luckily, we afforded a new alkali metal gallium phosphate, Cs₂Ga₄P₈O₂₇. It features a 3D framework structure of {Ga₄P₈O₂₇}^2- formed by corner sharing GaO₄, GaO₆, P₂O₇ and P₄O₁₃ groups with the cesium cations balancing the charge. With the synthesis of Cs₂Ga₄P₈O₂₇, we have now found the coexistence of two kinds of coordination models (4 and 6) of Ga³⁺ cations in one single compound. In particular, the main outstanding feature of this compound rests on the coexistence of two kinds of phosphoric anions with different degree of con-densation: a horseshoe-shaped P₄O₁₃ and linear dimer of P₂O₇. Furthermore, the density functional theory calculations indicate that Cs₂Ga₄P₈O₂₇ is a direct insulator with the band gap of 4.13 eV. Our work provides useful information on the design and search for novel phosphates, largely enriching the current classification system and full fill expanding the family of condensed phosphoric anions, which is helpful to strengthen the exploring and understan-ding of the investigation of phosphates or condensed phosphates.

  
  
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• 

  Figure 1  View the framework structure of Cs₂Ga₄P₈O₂₇ along the b axis

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  Figure 2  View the framework structure of {Ga₄P₈O₂₇}^2- along the b axis, and the layers of {Ga₂(P₄O₁₃)}_n and {Ga₂(P₂O₇)₂}_n^2n- along the a axis. Cs, Ga, O and P atoms are represented by green, blue, red and pink circles, respectively

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  Figure 3  View of the linkages of [Ga1O₆], [Ga2O₆], [Ga3O₄] and [Ga4O₆] groups in the layer. Ga, P and O atoms are represented by light blue, pink, and red circles, respectively

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  Figure 4  View the linkages of (P1P2O₇), (P3P4O₇) and (P5P6P7P8O₁₃) groups in the title compound. Ga, P and O atoms are represented by light blue, pink and red circles, respectively

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  Figure 5  Configuration of the phosphoric anions; (a) in CaNb₂O(P₄O₁₃)(P₂O₇), (b) in Pb_9−xBa_x[Li₂(P₂O₇)₂(P₄O₁₃)₂] (x = 0, 2, 6, 7), (c) in Pb₁₂[Li₂(P₂O₇)₂(P₄O₁₃)₂](P₄O₁₃), and (d) in KV₄(PO₄)(P₂O₇)(P₄O₁₃)

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  Figure 6  Band structure and partial density of states (PDOS) of Cs₂Ga₄P₈O₂₇

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  Table 1.  Selected Bond Lengths (Å) and Bond Valence Sums for Cs₂Ga₄P₈O₂₇

  Bond	Dist.	BV	Bond	Dist.	BV
  Ga(1)–O(27)	1.932(5)	0.579	P(2)–O(4)	1.616(5)	1.003
  Ga(1)–O(17)	1.932(5)	0.579	P(2)–O(5)	1.494(5)	1.394
  Ga(1)–O(5)	1.943(5)	0.562			∑BVS = 4.989
  Ga(1)–O19)	1.945(5)	0.559	P(3)–O(10)	1.493(5)	1.398
  Ga(1)–O22)	1.972(5)	0.520	P(3)–O(8)	1.516(5)	1.314
  Ga(1)–O20)	2.001(5)	0.481	P(3)–O(9)	1.535(5)	1.248
  		∑BVS = 3.280	P(3)–O(11)	1.591(5)	1.073
  Ga(2)–O(10)	1.884(5)	0.660			∑BVS = 5.033
  Ga(2)–O(3)i	1.913(5)	0.610	P(4)–O(12)	1.492(5)	1.402
  Ga(2)–O(1)	1.918(5)	0.602	P(4)–O(14)	1.507(5)	1.346
  Ga(2)–O(8)	1.931(5)	0.581	P(4)–O(13)	1.535(5)	1.248
  Ga(2)–O(14)	1.995(5)	0.489	P(4)–O(11)	1.596(5)	1.058
  Ga(2)–O(6)1	2.012(5)	0.467			∑BVS = 5.054
  		∑BVS = 3.409	P(5)–O(16)	1.496(5)	1.387
  Ga(3)–O(2)	1.786(5)	0.860	P(5)–O(15)	1.505(5)	1.354
  Ga(3)–O(7)ii	1.789(5)	0.853	P(5)–O(17)	1.513(5)	1.325
  Ga(3)–O(13)	1.797(5)	0.834	P(5)–O(18)	1.627(5)	0.973
  Ga(3)–O(9)iii	1.798(5)	0.832			∑BVS = 5.039
  		∑BVS = 3.379	P(6)–O(20)	1.474(5)	1.472
  Ga(4)–O(12)iii	1.909(5)	0.616	P(6)–O(19)1	1.491(5)	1.406
  Ga(4)–O(26)iv	1.927(5)	0.587	P(6)–O(18)	1.549(5)	1.202
  Ga(4)–O(16)v	1.979(5)	0.510	P(6)–O(21)	1.593(5)	1.067
  Ga(4)–O(15)iv	2.002(5)	0.479			∑BVS = 5.147
  Ga(4)–O(25)	2.009(5)	0.470	P(7)–O(23)	1.471(5)	1.484
  Ga(4)–O(23)i	2.012(5)	0.467	P(7)–O(22)i	1.494(5)	1.394
  		∑BVS = 3.129	P(7)–O(24)	1.571(5)	1.132
  P(1)–O(3)	1.494(5)	1.394	P(7)–O(21)	1.615(5)	1.005
  P(1)–O(1)	1.509(5)	1.339			∑BVS = 5.015
  P(1)–O(2)	1.521(5)	1.296	P(8)–O(26)	1.507(5)	1.346
  P(1)–O(4)	1.597(5)	1.056	P(8)–O(25)	1.508(5)	1.343
  		∑BVS = 5.085	P(8)–O(27)	1.514(4)	1.321
  P(2)–O(6)	1.503(5)	1.361	P(8)–O(24)v	1.615(5)	1.005
  P(2)–O(7)	1.540(5)	1.231			∑BVS = 5.015
  Symmetry transformations used to generate the equivalent atoms: i x, 3/2–y, 1/2+z; ii –x, 1–y, –z; iii –x, 1–y, 1–z; iv1–x, 1–y, 1–z; v 1–x, –1/2+y, 1/2–z; vi x, 3/2–y, –1/2+z; vii1–x, 1/2+y, 1/2–z

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  Table 2.  Comparison of the Corresponding Condensed Phosphates

  	Compounds	P/O ratio	Types of anion	Phosphoric anions	P2O7/P4O13 ratio	Structure of P4O13	References
  1	Cs2Ga4(P2O7)2(P4O13)	8:27	Two	(P2O7)2(P4O13)	2:1	Horseshoe-shaped	This paper
  2	CaNb2O (P2O7) (P4O13)	6:21	Three	(P2O7) (P4O13)	1:1	S-shaped	[46]
  3	Pb12[Li2(P2O7)2(P4O13)2](P4O13)	16:53	Three	[(P2O7)2(P4O13)2](P4O13)	2:3	S-shaped	[47]
  4	Pb9−xBax[Li2(P2O7)2(P4O13)2] (x = 0, 2, 6, 7)	12:40	Two	(P2O7)2(P4O13)2	2:2	S-shaped	[48]
  5	KV4(PO4)(P2O7)(P4O13)	7:24	Three	(PO4)(P2O7)(P4O13)	1:1	S-shaped	[49]
  6	K2V2O2(P4O13)	4:15	Two	(P4O13)		Horseshoe-shaped	[50]
  7	Cs2Cr3[B(P2O7)2](P4O13)	8:27	Two	[B(P2O7)2](P4O13)	2:1`	Horseshoe-shaped	[51]

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