English

• 1. INTRODUCTION

  Silicophosphates, also named as phosphosilicates, specially refer to the compounds with bridging P−O−Si bonds between the moieties of phosphate and silicate^[1]. Non-crystalline silicophosphates have gained great industrial and academic interest for excellent chemical stability, mechanical property and photosensitivity, and can be used as optical fibers, biomaterials, luminescent materials and so on^[2-4]. However, crystalline silicophosphate compounds have been developed backwardly. Though there are a large number of synthetic compounds and natural minerals in the system containing P, Si, and O elements, most of them don't belong to silicophosphates for being without P–O–Si bonds. One case is that the anionic groups of phosphorous and silicon are isolated by metal cations, and they don't share any vertex oxygen atoms to form P–O–Si bonds^[5]. Another case is that phosphorous and silicon atoms disorderedly occupy the same lattice positions of crystal structure due to their close ionic radii^{[6, 7]}. By contrast, the proportion of silicophosphates, with bridging P–O–Si bonds, are not so much in the inorganic crystalline compounds containing P, Si and O.

  As we all know, the bonding between Si and O atoms are typically four-fold coordinated. The six-fold coordination of silicon usually exists in several high pressure materials, for example, MgSiO₃ ilmenite and SiO₂ stishovite^{[8, 9]}. The few oxides with SiO₆ that can stably exist at ambient pressure almost have P–O–Si bonds, for instance, SiP₂O₇^[10], Si₅O(PO₄)₆^[11], (Re₂O₅)Si₂[Si₂O(PO₄)₆]^[12], Rb₂SiP₄O₁₃ and BaH₂Si(P₂O₇)₂^[13]. So, the field of silicophosphate is distinctive from the view point of structural chemistry.

  The varieties of connection mode among PO₄, SiO₄ and SiO₆ by sharing vertex oxygen atoms would give rise for structure and property variations, thus more versatile applications could be foreseeing. For example, similar to aluminosilicates, silicophosphates with different frameworks and topologies may have an important place in various scientific applications, such as molecular sieves, absorbents, and ionic conductors^{[1, 14]}. Therefore, it is necessary to explore new silicophosphate compounds. Recently, the discoveries of Na₄Si₂PO₄F₉^[15], K₄Si₃P₂O₇F₁₂ and BaSiP₂O₈^[16] intensively catch the eyes of researchers for the six-fold coordinated Si and P–O–Si bonds. In this paper, we reported the synthesis and structure of a new silicophosphate K₂SiP₄O₁₃, and analyzed its structural features, and characterized it by IR and Raman spectroscopies, diffuse reflectance spectroscopy and thermal analysis.

  2. EXPERIMENTAL

  2.1 Synthesis

  Single crystals of K₂SiP₄O₁₃ were synthesized by the flux method in molten polyphosphoric acid. All the reagents used in synthesis were purchased from commercial sources without further treatment. K₂CO₃ (4.561 g, 33 mmol), SiO₂ (0.601 g, 10 mmol) and phosphoric acid (85 wt%, 8.6 mL, 126 mmol) were mixed by stirring in a Pt crucible at room temperature. The crucible was placed in a muffle furnace oven and then heated to 400 ℃ in 6 h. After having been kept at 400 ℃ for 2 days, the temperature of the furnace was gradually decreased to 30 ℃ in about 10 h. The resulting products in the crucible were washed by using hot water for eliminating polyphosphoric acid and its potassium salts, and the single crystals were separated and dried in air. Eventually, colorless and narrow crystal slices of K₂SiP₄O₁₃ were obtained with a yield of about 90% based on SiO₂.

  2.2 Crystal structure determination

  A single crystal of K₂SiP₄O₁₃ with the size of 0.30mm × 0.24mm × 0.05mm was selected for crystal structure determination. The single-crystal X-ray diffraction (XRD) data were collected on an Agilent Gemini E diffractometer with graphite-monochromated MoKα radiation (λ = 0.71073 Å) using the ω-scan technique. The crystal was kept around 106 K during data collection. In the range of 6.36≤2θ≤57.96°, a total of 3613 reflections were collected and 2415 were independent with R_int = 0.0265, of which 2095 were observed with I > 2σ(I). The absorption correction of multi-scan was performed. Using Olex2^[17], the structure was solved with the SHELXT^[18] structure solution program using intrinsic phasing, and was refined with the SHELXL^[19] refinement package using full-matrix least squares minimization on F². All atoms were refined with anisotropic thermal parameters. The final full-matrix least-squares refinement converged to R = 0.0352, wR = 0.0814 for the observed reflections with I > 2σ(I), and R = 0.0419, wR = 0.0863 for all data. The largest diffraction peak and hole are 0.52 and −0.56 e·Å⁻³, respectively. The structural data were checked by the PLATON program^[20], and no higher symmetries were found. Selected bond lengths and bond angles of K₂SiP₄O₁₃ are given in Table 1.

  Table 1

  

  Table 1.  Selected Bond Lengths (Å) and Bond Angles (°)

  DownLoad: CSV

  Bond	Dist.		Bond	Dist.		Bond	Dist.
  P(1)–O(1)	1.533(2)		Si(1)–O(1)ⅰ	1.799(2)		K(1)–O(1)ⅷ	3.457(2)
  P(1)–O(2)	1.541(2)		Si(1)–O(2)ⅱ	1.773(2)		K(2)–O(13)	2.676(2)
  P(1)–O(3)	1.473(2)		Si(1)–O(5)ⅱ	1.786(2)		K(2)–O(6)	2.701(2)
  P(1)–O(4)	1.631(2)		Si(1)–O(9)	1.780(2)		K(2)–O(13)ⅲ	2.750(2)
  P(2)–O(4)	1.579(2)		Si(1)–O(11)	1.766(2)		K(2)–O(5)ⅸ	2.827(2)
  P(2)–O(5)	1.525(3)		Si(1)–O(12)ⅲ	1.771(2)		K(2)–O(6)ⅹ	2.999(2)
  P(2)–O(6)	1.460(2)		K(1)–O(8)	2.742(2)		K(2)–O(12)ⅲ	3.151(2)
  P(2)–O(7)	1.596(2)		K(1)–O(3)ⅳ	2.794(3)		K(2)–O(11)ⅹⅰ	3.217(2)
  P(3)–O(7)	1.593(2)		K(1)–O(8)ⅵ	2.813(2)		K(2)–O(6)ⅸ	3.255(3)
  P(3)–O(8)	1.468(2)		K(1)–O(3)ⅵ	2.824(2)		K(2)–O(13)ⅸ	3.446(3)
  P(3)–O(9)	1.523(2)		K(1)–O(2)ⅰ	2.922(2)		K(2)–O(4)ⅹ	3.478(2)
  P(3)–O(10)	1.571(2)		K(1)–O(9)ⅴ	3.019(2)
  P(4)–O(10)	1.625(2)		K(1)–O(7)ⅵ	3.286(2)
  P(4)–O(11)	1.541(2)		K(1)–O(1)ⅳ	3.332(3)
  P(4)–O(12)	1.533(2)		K(1)–O(8)ⅴ	3.388(8)
  P(4)–O(13)	1.474(2)		K(1)–O(3)ⅶ	3.451(2)
  Angle	(°)		Angle	(°)		Angle	(°)
  O(1)ⅰ–Si(1)–O(2)ⅱ	87.91(10)		O(2)ⅱ–Si(1)–O(5)ⅱ	93.23(9)		O(5)ⅱ–Si(1)–O(11)	87.15(9)
  O(1)ⅰ–Si(1)–O(5)ⅱ	89.90(9)		O(2)ⅱ–Si(1)–O(9)	86.47(9)		O(5)ⅱ–Si(1)–O(12)ⅲ	89.81(9)
  O(1)ⅰ–Si(1)–O(9)	89.72(10)		O(2)ⅱ–Si(1)–O(11)	179.50(10)		O(9)–Si(1)–O(11)	93.15(9)
  O(1)ⅰ–Si(1)–O(11)	91.77(10)		O(2)ⅱ–Si(1)–O(12)ⅲ	91.56(9)		O(9)–Si(1)–O(12)ⅲ	90.57(9)
  O(1)ⅰ–Si(1)–O(12)ⅲ	179.38(9)		O(5)ⅱ–Si(1)–O(9)	179.52(10)		O(11)–Si(1)–O(12)ⅲ	88.76(10)
  Symmetry codes: (ⅰ) 1 + x, y − 1, z; (ⅱ) x, y − 1, z; (ⅲ) x − 1, y, z; (ⅳ) 1 − x, 1 − y, −z; (ⅴ) 1 + x, y, z; (ⅵ) 2 − x, 1 − y, −z; (ⅶ) 1 + x, y − 1, z; (ⅷ) 2 + x, y − 1, z; (ⅸ) 1 − x, 1 − y, 1 − z; (ⅹ) −x, 1 − y, 1 − z; (ⅹⅰ) 1 − x, − y, 1 – z

  2.3 Characterization of K₂SiP₄O₁₃

  The powder XRD patterns were collected on a Bruker D8 Advance diffractometer with CuKα radiation (λ = 1.5418 Å) at room temperature in the 2θ range of 5~70° with a step size of 0.02°. The IR spectrum was recorded on a Bruker TENSOR Ⅱ FTIR spectrophotometer in the range of 400~4000 cm⁻¹ with KBr pressed pellet. The Raman spectrum was measured at room temperature in the range from 100 to 3000 cm⁻¹, using a Renishaw in via spectrometer under the excitation of an argon ion laser with the wavelength of 785 nm. The UV-vis diffuse reflectance spectrum was scanned in the range of 200~800 nm at room temperature on a Hitachi U-4100 spectrophotometer, with a powder pellet of BaSO₄ as a standard (100% reflectance). The thermogravimetric (TG) and differential scanning (DSC) calorimetric analyses were carried out on a Setaram Setsys Evolution thermal analyzer from METTLER TOLEDO, and the samples were placed in alumina crucibles and heated at a rate of 10 ℃/min from room temperature to 1000 ℃ under an atmosphere of Ar.

  3. RESULTS AND DISCUSSION

  3.1 Crystal structure description

  K₂SiP₄O₁₃ crystallizes in the triclinic system, P$ \overline 1 $ (No. 2) space group with a = 4.8327(10), b = 7.7403(15), c = 14.485(3) Å, α = 82.29(3)°, β = 83.31(3)°, γ = 81.95°, V = 529.02(19) ų and Z = 2. Its asymmetric unit comprises of two K, one Si, four P, and thirteen O atoms, and all of them locate on general lattice positions. K₂SiP₄O₁₃ crystal features 2D layers of [SiP₄O₁₃]_∞ along the c axis, and counter cations K⁺ reside among the layers.

  Each P atom in K₂SiP₄O₁₃ is covalently bonded with four O atoms to form basic PO₄ tetrahedron, and the four unique tetrahedra are linked by sharing three vertex O atoms to build a short zigzag chain, i.e. tetraphosphate anion group [P₄O₁₃]⁶⁻, which is quite comparable to a fragment of a long-chain polyphosphate^{[21, 22]}. The [P₄O₁₃]⁶⁻ groups are isolated from each other, and are linked by Si atoms. Each [P₄O₁₃]⁶⁻ interconnects with four Si atoms, and vice versa, which leads to the formation of a 2D layer of [SiP₄O₁₃]_∞ polyanion in the ab plane, as shown in Fig. 1(a). The Si atom in K₂SiP₄O₁₃ is in an octahedral coordination with the O atoms from six adjacent PO₄. The six O atoms almost uniformly surround around Si with nearly identical distances. The distortion index of SiO₆ was calculated based on the methodology proposed by Halasyamani^[23], and its value was 0.04, which means that the SiO₆ octahedron is basically undistorted. The layers of [SiP₄O₁₃]_∞ stack along the c axis, and K(1) and K(2) atoms occupy the void among the layers. Not only do they balance the electronic charges, but also join the layers by the electrostatic force between themselves and O²⁻ to build the 3D framework of K₂SiP₄O₁₃, as shown in Fig. 1(b). The coordination environments around the K atoms are rather irregular, and the K–O distances vary in a rather wide range of 2.676(2)~3.478(2) Å.

  Figure 1

  

  Figure 1.  (a) View of the [SiP₄O₁₃]_∞ layer in the ab plane and the K⁺ ions in the cavities, (b) Projection of the K₂SiP₄O₁₃ crystallographic structure along the a axis

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  The bond valences (BV)^[24] and bond valence sums (BVS) of all atoms in K₂SiP₄O₁₃ were calculated, with the results listed in Table 2. The calculated BVS value of each atom is in good agreement with its corresponding oxidation number. It should be noted that thirteen independent O atoms can be divided into three groups according to their bonding characters. The first group consists of the bridge oxygen atoms of P–O–P, i.e., O(4), O(7) and O(10), which have the longest bond lengths of P–O in each PO₄ tetrahedron. The second one includes the bridging O atoms bonding with P and Si: O(1), O(2), O(5), O(9), O(11), and O(12). Finally, the terminal oxygen atoms of PO₄ tetrahedra, i.e. O(3), O(6), O(8) and O(13), belong to the third group, which has the shortest distances of P–O and correspondingly, the highest BV values in each tetrahedron. The average values of BVS for these three groups are 2.13, 2.03, and 1.88, respectively, which reflects well the differences of O atoms on the bonding environments in K₂SiP₄O₁₃ that brings rich stretching vibrations in the IR and Raman spectra.

  Table 2

  

  Table 2.  Bond Valences (BV) and Bond Valence Sums (BVS) in K₂SiP₄O₁₃

  DownLoad: CSV

  BV	P(1)	P(2)	P(3)	P(4)	Si(1)	K(1)	K(2)	BVS
  O(4)	0.964	1.110					0.026	2.10
  O(7)		1.059	1.067			0.044		2.17
  O(10)			1.133	0.979				2.11
  O(1)	1.253				0.651	0.039 0.028		1.97
  O(2)	1.227				0.699	0.118		2.04
  O(5)		1.282			0.673		0.153	2.11
  O(9)			1.289		0.685	0.091		2.06
  O(11)				1.228	0.711		0.053	1.99
  O(12)				1.255	0.702		0.064	2.02
  O(3)	1.476					0.167 0.154 0.028		1.83
  O(6)		1.528					0.215 0.096 0.048	1.89
  O(8)			1.494			0.192 0.159 0.034		1.88
  O(13)				1.471			0.230 0.188 0.029	1.92
  BVS	4.92	4.98	4.98	4.93	4.12	1.05	1.10

  K₂SiP₄O₁₃ crystal is isostructural with its homologue, Rb₂SiP₄O₁₃^[13], of which cell parameters are a = 4.8327(10), b = 7.7403(15) and c = 14.485(3) Å. In comparison to those of Rb₂SiP₄O₁₃, the dimensions of a and b axes of K₂SiP₄O₁₃ don't generate obvious changes (less than 0.5%) though the ion radius of K⁺ (1.51 Å) is obviously smaller than that of Rb⁺ (1.61 Å). Meanwhile, the dimension of the c axis decreases 4%, which implies that the 2D network of [SiP₄O₁₃]_∞ is rigid parallel to the ab plane and the size of the cavities along the c axis occupied by the alkali metal cations is delimited by it. When Na⁺ with smaller size (1.18 Å) residing the cavities, the long distances of Na–O would make the structure instable. On the contrary, the cavities could not accommodate bigger cation, such as Cs⁺ (1.74 Å). It may be the reason that the isostructural silicophosphates of Na⁺ and Cs⁺ have not been successfully synthesized. With the substitution of Si⁴⁺ (0.40 Å) by Ge⁴⁺ (0.53 Å) or Ti⁴⁺ (0.61 Å), the sizes of the cavities would increase and could hold bigger alkali metal cation. Therefore, Cs₂GeP₄O₁₃^[25] and Cs₂TiP₄O₁₃^[26] that are isostructural with K₂SiP₄O₁₃ and Rb₂SiP₄O₁₃ can stably exist.

  The sample for powder XRD was prepared by pulverizing and grinding the synthesized crystals, and Fig. 2 presents the experimental XRD pattern accompanied with the simulated one by Powder Cell^[27] based on the single-crystal structure. The positions of diffraction peaks between them are completely identical with each other, and so do the intensities basically except for the multiple diffraction of (001), whose experimental peaks are greatly stronger than the simulated ones. This shows a strong preferred orientation in the tested powder XRD sample. The [SiP₄O₁₃]_∞ layer is fully composed of strong covalent interactions of Si–O and P–O in the ab plane. By contrast, the layers are interconnected along the c axis only by weak electrostatic forces between K⁺ and O²⁻. So, K₂SiP₄O₁₃ is very apt to cleavage parallel to the (001) crystal face. The slice-like crystallization habit of K₂SiP₄O₁₃ is also related to its special layered structure.

  Figure 2

  

  Figure 2.  Experimental XRD pattern of the pulverized K₂SiP₄O₁₃ crystals

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  3.2 IR and Raman spectra

  IR and Raman spectra of K₂SiP₄O₁₃ are presented in Fig. 3. On the basis of literature reports^{[3, 4, 7, 28-32]}, the stretching vibrations in the IR spectrum could be divided mainly to four regions. The broad band in region Ⅰ is attributed to the O–P–O stretching vibrations of the terminal oxygen atoms, which are sometimes called as doubly bonded oxygen vibrations. The intensive band around 1060 cm⁻¹ in region Ⅱ is assigned to the O–P–O stretching vibrations of the bridging oxygen atoms in PO₄ tetrahedra while the band around 940 cm⁻¹ (region Ⅲ) to the O–Si–O stretching vibrations in the SiO₆ octahedron. The bands in region Ⅳ are attributed to the stretching vibrations of P–O–P and P–O–Si. The assignments of the stretching vibrations in the Raman spectrum are principally identical with those in the IR spectrum. The bands below 600 cm⁻¹ are attributed to the bending vibrations of PO₄ and SiO₆ structural units and the harmonics of stretching vibrations.

  Figure 3

  

  Figure 3.  IR and Raman spectra of K₂SiP₄O₁₃

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  3.3 UV-vis diffuse reflectance spectrum

  Fig. 4 shows the UV-vis diffuse reflectance spectrum of K₂SiP₄O₁₃. The absorption spectrum was calculated from the diffuse reflectance spectrum using the Kubelka-Munk function: F(R) = (1 − R)²/2R = K/S, where R represents the reflectance, K the absorption, and S the scattering. In a F(R) versus E(eV) plot, extrapolating the linear part of the rising curve to zero provides the onset of absorption. Based on the inset of Fig. 4, the optical band gap of K₂SiP₄O₁₃ is estimated to be 4.85 eV, which is much wider than that of Cs₂GeP₄O₁₃ (4.07 eV)^[25]. However, the band gap of K₂SiP₄O₁₃ is narrow by contrast with the phosphates of alkali metals or alkali earth metals^{[33, 34]}, which should be related to the electronic transition of the Si–O bonds^[35].

  Figure 4

  

  Figure 4.  UV-vis diffuse reflectance spectrum of K₂SiP₄O₁₃

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  3.4 Thermal properties

  Fig. 5 presents the TG-DSC curves of K₂SiP₄O₁₃. A sharp endothermic peak was observed at 730 ℃ while the sample weight didn't show a representative change in the whole temperature range. The isostructural compound Rb₂SiP₄O₁₃ was reported to decompose at 723 ℃, however, no more information was mentioned^[13]. In order to clarify whether the title compound melts or decomposes at high temperature, a sample of pulverized K₂SiP₄O₁₃ crystal was heated at 800 ℃ for two hours, and then the sample was very quickly decreased to room temperature. White solidified polycrys-talline substances mixed glassy things were observed. The sample after heat-treating was analyzed by powder XRD. As shown in the inset of Fig. 5, K₂SiP₄O₁₃ should decompose in accordance with the reaction: K₂SiP₄O₁₃ → Si₅O(PO₄)₆ + amorphous phase. The amorphous phase probably contained phosphorus and potassium oxides since the sample weight remained roughly constant. The approximate decomposition temperature of K₂SiP₄O₁₃ and Rb₂SiP₄O₁₃ indicates that the rigid 2D network of [SiP₄O₁₃]_∞ could play a crucial role in their thermal stability. After comparing with the structure of Si₅O(PO₄)₆^[11], it should be mentioned that the majority of Si atoms originally in K₂SiP₄O₁₃ still kept an octahedron coordination after heat decomposition while the short zigzag chain of [P₄O₁₃]⁶⁻ was broken.

  Figure 5

  

  Figure 5.  TG and DSC curves of the K₂SiP₄O₁₃ pulverized crystals and the powder XRD pattern of their thermal decomposition products (inset)

  DownLoad: Full-Size Img PowerPoint

  4. CONCLUSION

  In summary, we have synthesized a new silicophosphate compound, K₂SiP₄O₁₃, by the flux method. The crystallo-graphic structure features a 2D network of [SiP₄O₁₃]_∞ stacking along the c axis, which is composed of tetraphosphate anions interconnected by Si atoms in a hardly distorted octahedral coordination. The IR and Raman vibration spectra reflect the structural characteristics of K₂SiP₄O₁₃. The compound is thermally stable up to 730 ℃, and then decomposes to Si₅O(PO₄)₆. Its optical band gap was estimated to be about 4.85 eV by diffuse reflectance spectroscopy.

  
  
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  Figure 1  (a) View of the [SiP₄O₁₃]_∞ layer in the ab plane and the K⁺ ions in the cavities, (b) Projection of the K₂SiP₄O₁₃ crystallographic structure along the a axis

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  Figure 2  Experimental XRD pattern of the pulverized K₂SiP₄O₁₃ crystals

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  Figure 3  IR and Raman spectra of K₂SiP₄O₁₃

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  Figure 4  UV-vis diffuse reflectance spectrum of K₂SiP₄O₁₃

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  Figure 5  TG and DSC curves of the K₂SiP₄O₁₃ pulverized crystals and the powder XRD pattern of their thermal decomposition products (inset)

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  Table 1.  Selected Bond Lengths (Å) and Bond Angles (°)

  Bond	Dist.		Bond	Dist.		Bond	Dist.
  P(1)–O(1)	1.533(2)		Si(1)–O(1)ⅰ	1.799(2)		K(1)–O(1)ⅷ	3.457(2)
  P(1)–O(2)	1.541(2)		Si(1)–O(2)ⅱ	1.773(2)		K(2)–O(13)	2.676(2)
  P(1)–O(3)	1.473(2)		Si(1)–O(5)ⅱ	1.786(2)		K(2)–O(6)	2.701(2)
  P(1)–O(4)	1.631(2)		Si(1)–O(9)	1.780(2)		K(2)–O(13)ⅲ	2.750(2)
  P(2)–O(4)	1.579(2)		Si(1)–O(11)	1.766(2)		K(2)–O(5)ⅸ	2.827(2)
  P(2)–O(5)	1.525(3)		Si(1)–O(12)ⅲ	1.771(2)		K(2)–O(6)ⅹ	2.999(2)
  P(2)–O(6)	1.460(2)		K(1)–O(8)	2.742(2)		K(2)–O(12)ⅲ	3.151(2)
  P(2)–O(7)	1.596(2)		K(1)–O(3)ⅳ	2.794(3)		K(2)–O(11)ⅹⅰ	3.217(2)
  P(3)–O(7)	1.593(2)		K(1)–O(8)ⅵ	2.813(2)		K(2)–O(6)ⅸ	3.255(3)
  P(3)–O(8)	1.468(2)		K(1)–O(3)ⅵ	2.824(2)		K(2)–O(13)ⅸ	3.446(3)
  P(3)–O(9)	1.523(2)		K(1)–O(2)ⅰ	2.922(2)		K(2)–O(4)ⅹ	3.478(2)
  P(3)–O(10)	1.571(2)		K(1)–O(9)ⅴ	3.019(2)
  P(4)–O(10)	1.625(2)		K(1)–O(7)ⅵ	3.286(2)
  P(4)–O(11)	1.541(2)		K(1)–O(1)ⅳ	3.332(3)
  P(4)–O(12)	1.533(2)		K(1)–O(8)ⅴ	3.388(8)
  P(4)–O(13)	1.474(2)		K(1)–O(3)ⅶ	3.451(2)
  Angle	(°)		Angle	(°)		Angle	(°)
  O(1)ⅰ–Si(1)–O(2)ⅱ	87.91(10)		O(2)ⅱ–Si(1)–O(5)ⅱ	93.23(9)		O(5)ⅱ–Si(1)–O(11)	87.15(9)
  O(1)ⅰ–Si(1)–O(5)ⅱ	89.90(9)		O(2)ⅱ–Si(1)–O(9)	86.47(9)		O(5)ⅱ–Si(1)–O(12)ⅲ	89.81(9)
  O(1)ⅰ–Si(1)–O(9)	89.72(10)		O(2)ⅱ–Si(1)–O(11)	179.50(10)		O(9)–Si(1)–O(11)	93.15(9)
  O(1)ⅰ–Si(1)–O(11)	91.77(10)		O(2)ⅱ–Si(1)–O(12)ⅲ	91.56(9)		O(9)–Si(1)–O(12)ⅲ	90.57(9)
  O(1)ⅰ–Si(1)–O(12)ⅲ	179.38(9)		O(5)ⅱ–Si(1)–O(9)	179.52(10)		O(11)–Si(1)–O(12)ⅲ	88.76(10)
  Symmetry codes: (ⅰ) 1 + x, y − 1, z; (ⅱ) x, y − 1, z; (ⅲ) x − 1, y, z; (ⅳ) 1 − x, 1 − y, −z; (ⅴ) 1 + x, y, z; (ⅵ) 2 − x, 1 − y, −z; (ⅶ) 1 + x, y − 1, z; (ⅷ) 2 + x, y − 1, z; (ⅸ) 1 − x, 1 − y, 1 − z; (ⅹ) −x, 1 − y, 1 − z; (ⅹⅰ) 1 − x, − y, 1 – z

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  Table 2.  Bond Valences (BV) and Bond Valence Sums (BVS) in K₂SiP₄O₁₃

  BV	P(1)	P(2)	P(3)	P(4)	Si(1)	K(1)	K(2)	BVS
  O(4)	0.964	1.110					0.026	2.10
  O(7)		1.059	1.067			0.044		2.17
  O(10)			1.133	0.979				2.11
  O(1)	1.253				0.651	0.039 0.028		1.97
  O(2)	1.227				0.699	0.118		2.04
  O(5)		1.282			0.673		0.153	2.11
  O(9)			1.289		0.685	0.091		2.06
  O(11)				1.228	0.711		0.053	1.99
  O(12)				1.255	0.702		0.064	2.02
  O(3)	1.476					0.167 0.154 0.028		1.83
  O(6)		1.528					0.215 0.096 0.048	1.89
  O(8)			1.494			0.192 0.159 0.034		1.88
  O(13)				1.471			0.230 0.188 0.029	1.92
  BVS	4.92	4.98	4.98	4.93	4.12	1.05	1.10

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