Diffuse scattering in silver hypo­di­phos­phate, Ag4(P2O6), probed by 3D ED

Kinzhybalo, V.; Wojciechowski, J.; Kowalska, D.A.; Maliuzhenko, V.; Ślepokura, K.A.

doi:10.1107/S2053229626005012

electron diffraction

STRUCTURAL
CHEMISTRY

ISSN: 2053-2296

Volume 82| Part 6| June 2026| Pages 277-284

https://doi.org/10.1107/S2053229626005012

Open

access

Diffuse scattering in silver hypodiphosphate, Ag₄(P₂O₆), probed by 3D ED

Vasyl Kinzhybalo,^a ^* Jakub Wojciechowski,^b Dorota A. Kowalska,^a Vladyslav Maliuzhenko ^c and Katarzyna A. Ślepokura ^c

^aInstitute of Low Temperature and Structure Research, Polish Academy of Sciences, 2 Okólna, Wrocław, 50-422, Poland, ^bRigaku Europe SE, Hugenottenallee 167, Neu Isenburg, D-63263, Germany, and ^cFaculty of Chemistry, University of Wrocław, 14 F. Joliot-Curie, Wrocław, 50-383, Poland
^*Correspondence e-mail: [email protected]

Edited by E. Reinheimer, Rigaku Americas Corporation, USA (Received 6 August 2025; accepted 12 May 2026; online 26 May 2026)

This article is part of the collection Advances in electron diffraction for structural characterization.

The crystal structure of silver hypodiphosphate, Ag₄(P₂O₆), was determined using 3D ED. The average structure is hexagonal, described in the space group P6₃/mcm, and is isomorphous with the average structure of known Li₄(P₂S₆). The silver cations form hexagonal atomic ring layers and the hypodiphosphate anions occupy channels that centre every hexagonal ring, with the P—P bond oriented along the unique c axis. The hypodiphosphate P₂O₆⁴⁻ anions are disordered, with the P atoms occupying two positions having 50% occupancy each and with O atoms common for both positions of the anion. The O atoms form an octahedral coordination environment for the silver cations. The hypodiphosphate anions are stacked into columns along the unique axis direction. Neighbouring hypodiphosphate columns may have P—P bonds on the same (ferro-type) or on different (antiferro-type) levels. This correlated disorder manifests itself in diffuse scattering observed on hkl layers with uneven l values. Simulations based on an Ising-type model with geometric frustration align well with the experimental data, providing insight into the short-range antiferro-like arrangement of disordered hypodiphosphate anions.

Keywords: powder diffraction; electron diffraction; silver hypodiphosphate; diffuse scattering; real structure; geometric frustration.

CCDC references: 2553762; 2553761; 2553760

1. Introduction

Nowadays, the crystal structure determination of new materials has become routine for even sub-micron monocrystalline samples, largely thanks to the state-of-the-art electron diffractometers (Ito et al., 2021 ). Knowledge of the structure is important in terms of understanding the `composition–structure–properties' relationship, which is vital in the design of new materials with desired properties. However, sometimes the real structure differs from the average one, i.e. that determined by an analysis of Bragg diffraction. These differences may prove to be important and have a considerable effect on the properties of the material (Schmidt et al., 2023 ). One of the well-known examples of such structures are the triangular lattices with antiferro-type interactions between closest neighbours (Keen & Goodwin, 2015 ). The inability to completely satisfy the antiferro arrangement in the triangular lattice leads to disordered structures with eventual correlations in the disorder.

Since the first report on hypodiphosphoric acid, H₄P₂O₆ (Fig. 1), in 1877 by Theodor Salzer until nowadays, knowledge relating to the crystal structures of simple inorganic hypodiphosphates remains quite limited, especially in comparison with other common inorganic phosphates (Kinzhybalo et al., 2021 ). However, in recent years, there has been an increase in the number of reports of inorganic hypodiphosphates: lithium, sodium and ammonium salts have been systematically investigated for their crystal structures and properties, including ionic conductivity in Na₄(P₂O₆) (Szafranowska et al., 2012 ; Kinzhybalo et al., 2024 ; Ślepokura et al., 2025 ; Otręba et al., 2026 ), ferroelectricity in (NH₄)₂(H₂P₂O₆) (Szklarz et al., 2011 ), electron-density distribution in Li₄(P₂O₆)·6H₂O and bis(guanidinium) disodium heptahydrate, (CH₆N₃)₂Na₂(P₂O₆)·7H₂O (Kinzhybalo et al., 2013 ; Starynowicz et al., 2025 ), and thermal stability and spectroscopic properties of many inorganic salts have been reported (Gjikaj et al., 2012 ; Wu et al., 2012 ; Gjikaj & Wu, 2014 ; Gjikaj et al., 2014 ; Wu et al., 2015 ; Haase & Gjikaj, 2017 ; Haase & Gjikaj, 2018 ).

Figure 1
The structural formula of hypodiphosphoric acid.

The first report on the synthesis of Ag₄(P₂O₆) (using phosphorus and a warm acidified solution of silver nitrate) dates back to 1883 (Philipp, 1883 ). It was also obtained by Joly in 1885 (Joly, 1885 ) and Salzer in 1886 (Salzer, 1877 ; Salzer, 1886 ) in double decomposition reactions. Silver hypodiphosphate was used to obtain organic esters of hypodiphosphoric acid (Sänger, 1886 ). It was also utilized in a quantitative determination of hypodiphosphate anions in the presence of phosphate and phosphite (Wolf & Jung, 1931 ). Solid-state ³¹P NMR spectroscopy was reported for Ag₄(P₂O₆) (Grimmer et al., 1978 ). Its diffraction pattern along with the unit-cell parameters and space group were deposited in the International Centre for Diffraction Data (Kabekkodu & Blanton, 2024 ; Kabekkodu et al., 2024 ) as PDF deposition number 00-047-0901 by H. Worzala in 1996, but a corresponding crystal structure has never been published in the literature. According to the deposited data, Ag₄(P₂O₆) crystallizes in the space group P6₃/mcm and is isostructural with the Li₄(P₂S₆) average structure (Mercier et al., 1982 ). Both are characterized by disorder of the hypodiphosphate anions within the ordered framework of metal cation positions. The structure of Li₄(P₂S₆) is still under debate in the literature, as there are several reports on its proper space-group determination. The models solved in the space groups P $[\overline 3]$ 1m, Pnnm and Pnma were considered by Hood et al. (2016 ), but none was given a preference. Dietrich et al. (2016 ) used synchrotron PXRD and PDF analysis and favoured the model in the space group P $[\overline 3]$ 1m. Refinement using NMR crystallography was reported in the space group P321 (Neuberger et al., 2018 ). The same noncentrosymmetric model was reported by Oxley et al. (2023 ) and confirmed by second and third harmonic generation measurements. Yahia et al. (2023 ) reported the twinned single-crystal structure solution in the space group P $[\overline 3]$ m1. The related selenium-containing material, Li₄(P₂Se₆), turned out to crystallize as a similar, but not isomorphous, form to the thio-analogue crystal form (Neuberger et al., 2025 ). The other related substance – effective sodium ionic conductor, sodium hexathiohypodiphosphate, Na₄(P₂S₆) – is known to exist in three polymorphic modifications, but none of them is isomorphous with Li₄(P₂S₆) (Scholz et al., 2021 ; Scholz et al., 2022 ). Similarly, the recently reported new ionic conductor Na₄(P₂O₆) crystallizes in its own structure type, different from the above-mentioned substances (Kinzhybalo et al., 2024). Knowledge of the proper crystal structure is crucial in understanding lithium and sodium ion conductivity mechanisms in these materials (Li et al., 2020 ; Stamminger et al., 2020 ; Hogrefe et al., 2025 ).

Considering the isomorphism of Li₄(P₂S₆) and Ag₄(P₂O₆), and the disorder of the anions in both compounds, it was interesting to perform detailed structural studies of the latter salt and record subtle diffraction effects that would allow the determination of its real crystal structure. Due to the limited solubility of silver hypodiphosphate in water, crystallization from aqueous solution gives a nanocrystalline material. Therefore, electron diffraction was employed to determine the crystal structure of Ag₄(P₂O₆), and to record and study the diffuse scattering that originates from the correlations in disorder of the hypodiphosphate anions.

2. Experimental

The obtained material was characterized using scanning electron microscopy (SEM) with energy dispersive X-ray analysis (EDX), three-dimensional electron diffraction (3D ED), powder X-ray diffraction (PXRD), variable-temperature PXRD (VT-PXRD), thermogravimetry–differential scanning calorimetry (TG–DSC) and variable-temperature optical microscopy.

2.1. Preparation

Hypodiphosphoric acid was obtained by red phosphorus oxidation with H₂O₂ and was further neutralized with NaOH to give crystalline Na₂(H₂P₂O₆)·6H₂O (Yoza & Ohashi, 1965 ). The title material was obtained by mixing stoichiometric amounts of Na₂(H₂P₂O₆)·6H₂O (314 mg, 1.00 mmol) and Ag₂SO₄ (624 mg, 2.00 mmol) dissolved in a minimum amount of distilled water. A white precipitate was formed immediately and gradually darkened over time. The precipitate was filtered off, washed with water and dried, yielding a slightly brownish grey powder.

2.2. Methods

2.2.1. Scanning electron microscopy (SEM) with energy dispersive X-ray analysis (EDX)

The electron microscopy imaging of the sample and its elemental composition were studied using the field-emission scanning electron microscope (FE-SEM) FEI Nova NanoSEM 230, along with an energy dispersive X-ray spectrometer (EDAX Genesis XM4).

2.2.2. Thermogravimetry–differential scanning calorimetry (TG–DSC)

TG–DSC analysis of Ag₄(P₂O₆) (12.57 mg) was performed using a Mettler–Toledo TGA/DSC 3+ instrument in the temperature range 303–1073 K with a ramp rate of 10 K min⁻¹. The scans were performed in flowing nitrogen (flow rate: 3 dm³ h⁻¹).

2.2.3. Variable-temperature microscopy

Optical observations were carried out on an Olympus BX53 microscope equipped with a Linkam THMS 600 temperature adapter and a CCD XC50 video camera in the temperature range 293–593 K.

2.2.4. Room-temperature and variable-temperature PXRD

The PXRD data for the Rietveld refinement of Ag₄(P₂O₆) were collected at room temperature on a PANalytical X'Pert Pro θ–2θ powder X-ray diffractometer using β-filtered Cu Kα radiation in the 2θ range 15–132°, with a scan step of 0.007°. The background was fitted as a 9-parameter polynomial. Peak shape was approximated with a pseudo-Voigt profile function. A scale factor and specimen displacement were refined. The coordinates (with special position restrains) and anisotropic B factors of all the atoms were refined.

Variable-temperature powder X-ray diffraction (VT-PXRD) analysis of the Ag₄(P₂O₆) sample was performed on the same PANalytical X'Pert Pro diffractometer with an Anton Paar HTK 1200N high-temperature chamber. Data were collected in the 2θ range 10–90° every 50 K in the temperature range 300–850 K. All Rietveld refinements were performed using the HighScore Plus program (Degen et al., 2014 ).

2.2.5. Electron diffraction data collection and refinement

The crystal structure was determined by 3D electron diffraction (3D ED) from a ca 400 nm single crystal rotated about one axis by 120° (scan width 0.5°, 240 images) and with a 0.5 s/° exposure time. The data were collected at ambient temperature in vacuo using a Rigaku Synergy-ED diffractometer equipped with a Rigaku HyPix-ED detector optimized for electron detection and an LaB₆ electron source at 200 kV (λ = 0.0251 Å) (Ito et al., 2021). Data collections, cell refinements, data reductions and analysis were carried out with CrysAlis PRO (Rigaku OD, 2022 ). Due to the high symmetry of the phase, this single scan resulted in 87% completeness (up to 0.6 Å resolution). The structure was solved with SHELXT (Sheldrick, 2015 ). Both kinematical and dynamical refinements were carried out in OLEX2 (Dolomanov et al., 2009 ). Anisotropic displacement parameters for all atoms were refined. The electron scattering atomic factors of UCLA were used (Saha et al., 2022 ). The average crystal structure model from dynamical 3D ED refinement (hexagonal crystal system, space group P6₃/mcm) was finally refined versus powder diffraction data.

Details of the kinematical and dynamical crystal structure refinements, along with the PXRD Rietveld fit details, are given in Table 1.

Table 1
Crystallographic data for kinematical and dynamical refinement versus ED data, and Rietveld refinement versus PXRD data

Chemical formula	Ag₄P₂O₆
M_r (g mol⁻¹)	589.42
Crystal system, space group	Hexagonal, P6₃/mcm
Temperature (K)	293
a, c (Å)	5.39128 (7), 6.30229 (9)
V (Å³)	158.640 (5)
Z	1

3D ED refinement
Radiation type	200 kV electron beam (λ = 0.0251 Å)
θ range (°)	0.153–1.162
R₁ (kinematical/dynamical refinement)	0.116/0.122
wR₂ (kinematical/dynamical refinement)	0.400/0.281

Rietveld refinement
Radiation type	Cu Kα (λ = 1.5418 Å)
R (Bragg)	0.032
R (expected)	0.012
R (profile)	0.034
R (weighted profile)	0.051

The DIAMOND program (Brandenburg, 2022 ) was used to produce the figures. All diffraction patterns in this study were calculated using the program DIFFUSE (Proffen & Neder, 1997 ).

3. Results and discussion

3.1. Sample characterization

As mentioned above, the diffraction pattern, unit-cell parameters and space group, but not the atomic coordinates, for Ag₄(P₂O₆) were revealed in the database (ICDD, PDF deposition number 00-047-0901) (Kabekkodu & Blanton, 2024; Kabekkodu et al., 2024). We determined the crystal structure of the title compound by 3D ED and used the atomic model for the Rietveld refinement against the powder diffraction data (Fig. 2 and Fig. S1 in the supporting information). PXRD showed no signs of crystalline silver or any other impurities.

Figure 2
Rietveld fit of the PXRD data of the bulk sample using the average structure model from the dynamical refinement of the 3D ED data (room temperature, 2θ range 15–132°).

SEM images with EDX analysis of the sample of the title compound showed hexagonal plate- and rod-shaped crystals, and confirmed the Ag₄(P₂O₆) composition (Fig. 3 and Figs. S2 and S3 in the supporting information).

Figure 3
Representative electron microscopy images of the bulk sample (cf Figs. S2 and S3 in the supporting information).

3.2. Stability

Silver hypodiphosphate undergoes partial decomposition within a few minutes after its precipitation, and the snowy white material turns greyish. Despite that, powder diffraction of several months old samples does not reveal any reflections from additional crystalline phases. Thermogravimetric analysis combined with differential scanning calorimetry (TG–DSC, sample mass m = 12.57 mg, ramp rate = 10 K min⁻¹) does not reveal any considerable mass loss (Δm = 6.7 × 10⁻² mg, 0.5%) in the whole temperature range from 303 to 1073 K. However, the DSC curve shows several energetic processes in this range: three exothermic, around 500, 620 and 1020 K, and one endothermic, around 750 K (Fig. S4 in the supporting information). Variable-temperature optical microscopy performed in the temperature range 293–593 K (40 K min⁻¹), along with variable-temperature powder diffraction (VT-PXRD), were used for a better description and documentation of the processes. As seen in Fig. 4 (and Fig. S5 in the supporting information), the powder melts between 533 and 543 K, and transforms into semi-transparent glassy drops.

Figure 4
(a) Ag₄(P₂O₆) powder before heating from 293 to 593 K, (b) after cooling from 593 to 293 K, along with zoomed (c) blue and (d) red areas (cf Fig. S5 in the supporting information).

VT-PXRD experiments, collected every 50 K between 300 and 850 K, have confirmed that Ag₄(P₂O₆) is stable up to about 400 K (violet diffractograms in Fig. 5). At 450 K, decomposition begins and reflections from Ag appear (due to melting/decomposition and aggregation of the sample, the diffraction lines from the corundum sample holder also become visible; grey diffractograms in Fig. 5). On further heating, the intensities of the diffraction lines from metallic silver increase, and at 600 K, reflections from Ag(PO₃) appear (blue diffractograms in Fig. 5) (Terebilenko et al., 2011 ). This observation is consistent with the exothermic nature of the second peak on the DCS curve at about 620 K (crystallization). The crystalline Ag(PO₃) formed in this way is stable up to a temperature of 700 K. Then, at about 750 K, it melts (literature m.p. 755–761 K; Osterheld & Mozer, 1973 ), which is accompanied by the disappearance of the diffraction pattern in PXRD and the endothermic anomaly in the DSC curve at 750 K. The decomposition takes place as a redox process according to the equation:

Figure 5
The variable-temperature powder X-ray diffraction (VT-PXRD) patterns for the sample of Ag₄(P₂O₆) (2θ range 15–75°, recorded on heating every 50 K in the temperature range 350–700 K, shown from top to bottom). Calculated diffractograms are shown in black and experimental diffractograms are shown in violet, grey and blue.

Ag₄(P₂O₆) → 2Ag(PO₃) + 2Ag,

and is consistent with the observations of Philipp (1883).

3.3. Average crystal structure

The average structure is the time- and space-averaged model derived from diffraction (Rietveld refinement), providing a perfect periodic symmetry that lacks local detail. Real structure refers to the instantaneous, accurate and local atomic positions (obtained from PDF, EXAFS, diffuse scattering), capturing all disorder, defects and thermal vibrations.

The crystal structure of silver hypodiphosphate, Ag₄(P₂O₆), was determined using 3D ED. The average structural model obtained in this way was used for the Rietveld refinement of the PXRD data.

The average structure is hexagonal, described by P6₃/mcm space-group symmetry, and isomorphous with the average structure of Li₄(P₂S₆) (Mercier et al., 1982). It should be noted that both known polymorphic modifications of Ag₄(P₂S₆) crystallize as non-isomorphous with the Ag₄(P₂O₆) structure types (Toffoli et al., 1982 ; Toffoli et al., 1983 ). The silver cations in Ag₄(P₂O₆) form a three-dimensional substructure, in which hexagonal atomic ring `layers' (perpendicular to [001]) can be distinguished. The `layers' are arranged one above the other, forming channels along the c-axis direction. The metal centres are in close contact (Ag⋯Ag distances within the layers are 3.11 Å and Ag⋯Ag distances between the layers = $[1 \over 2]$ c = 3.15 Å), which indicates argentophilic interactions (Schmidbaur & Schier, 2015 ). Hypodiphosphate anions, P₂O₆⁴⁻, occupy the channels, with the P—P bond oriented along the the unique c axis. P atoms are disordered into two positions, each of which is 50% occupied, which means that the whole hypodiphosphate anion occupies two positions [shown as violet and blue in Fig. 6(a)]. O-atom positions are common to both disorder components and create an octahedral coordination environment for the silver cations (Fig. S6). Hypodiphosphate anions are stacked into columns along the c-axis direction. Each column is chemically and structurally identical, but neighbouring columns may have P—P bonds on the same or on different levels [compare with the example arrangements of adjacent columns shown in Fig. 6(b)].

Figure 6
(a) Crystal structure packing views of Ag₄(P₂O₆) along with (b) possible different mutual arrangements of the hypodiphosphate anions shown in violet and blue colours. The Ag⋯Ag distances in part (a) are given in Å.

3.4. Diffuse scattering

The observed diffuse scattering (DS) lines on the hkl reciprocal planes shown in Fig. 7 (where l is odd, l = 2m + 1) appear midway between Bragg reflections along the a*, b* and a*–b* directions. This suggests short-range order in the crystal, with local doubling of the unit-cell parameters along the [100], [010] and [110] directions. The origin of this effect is in the occupational disorder at the P-site, which is half-occupied. However, along the c-axis direction, the P atoms are perfectly ordered due to the nature of the structure, resulting in the long-range order along this axis.

Figure 7
Ewald sphere reconstructions with diffuse scattering seen on hkl layers with l = 1 and l = 3, along with the schematic view of the diffuse streaks shown as red lines, Bragg reflections as small blue dots and the primary beam as a large blue dot (cf Fig. S7 in the supporting information).

In contrast, along the [100], [010] and [110] directions, the atomic arrangement allows for multiple configurations, but still tends toward a local ordering. This local ordering forms ordered layers perpendicular to these three directions, and the diffuse scattering lines observed between Bragg peaks are a direct consequence of these short-range atomic correlations. The overall structure retains long-range order in the c-axis direction, but exhibits short-range order along the other directions, providing insight into the atomic arrangements in the disordered regions.

To propose a model of short-range order, it is essential to consider the concept of `geometric frustration'. This well-established idea has been applied previously to explain diffuse scattering effects in various crystal systems (Welberry et al., 2011 ). We adopted a similar approach to investigate the spatial distribution of two distinct types of scatterers located on the triangular lattice of the ab plane in a hexagonal crystal. In our system, two possible anion configurations exist – designated as A and B (represented in blue and violet in Fig. 6). When an alternating arrangement of A and B is energetically favourable, such ordering is readily achievable on a square lattice but inherently frustrated on a triangular one. Specifically, when two sides of a triangle are occupied by alternating anions (A and B), the third must necessarily result in a like-pair (AA or BB), making perfect alternation geometrically impossible.

To implement such a model, Monte Carlo (MC) simulations based on the Ising model were employed. This approach has been used successfully in numerous studies to model various types of disorder in crystals (Welberry, 2004 ; Welberry et al., 2011; Komornicka et al., 2014 ; Bednarchuk et al., 2017 ; Kowalska et al., 2021 ). Simulations were performed for a series of cases using correlation parameters for both nearest-neighbour (J₁) and next-nearest-neighbour (J₂) interactions. The correlations were defined such that when J_i < 0, neighbouring sites tend to differ in type.

The calculated models consist only of P ions, as the remaining atoms in the structure are fully ordered and do not contribute to the observed diffuse scattering effects. Three examples are presented in Fig. 8. In these simulations, the value of J₁ was fixed at −5.0, while J₂ was varied. Figs. 8(a)–(c) show the lattice configurations corresponding to each model, providing an overview of the spatial arrangements. The associated diffraction patterns (hk1 section) calculated from these configurations, are shown in Figs. 8(d)–(f).

Figure 8
Example realizations of the Ising model with J₁ = −5.0 and varying values of J₂: (a) J₂ = 0.0, (b) J₂ = −0.3 and (c) J₂ = −3.0. Corresponding calculated hk1 sections of reciprocal space are shown in parts (d)–(f), respectively.

In Fig. 8(d), with J₂ = 0, the diffuse scattering appears as featureless diffuse rings. Introducing a small negative value for J₂ (−0.3) leads to narrowing of the diffuse features and the appearance of distinct intensity enhancements midway between pairs of Bragg peaks [Fig. 8(e)]. Further decreasing J₂ to −3.0 results in the weakening of diffuse streaks and a marked increase in additional intensity maxima [Fig. 8(f)]. Fig. 8(e) shows characteristics very similar to the observed patterns; therefore, the distribution in Fig. 8(b) can be considered the most representative of the short-range order present in the studied nanocrystal. Ewald sphere reconstructions based on the selected model, corresponding to those presented in Fig. 7, are shown in Fig. S8 in the supporting information.

4. Conclusions

The average crystal structure of silver hypodiphosphate, Ag₄(P₂O₆), was determined from 3D electron diffraction and Rietveld fitting against PXRD data. The hexagonal structure is characterized by the statistical disorder of hypodiphosphate anions, perfectly correlated along a unique axis direction and geometrically frustrated in the ab plane. Electron diffraction data revealed diffuse scattering between Bragg peaks on hkl layers with odd values of l, that originates from the presence of locally correlated anion arrangements, incompatible with long-range periodicity. Simulations using a frustrated Ising model reproduce the key features of the experimental data, providing insight into the nature of short-range order in the crystal.

Supporting information

CCDC references: 2553762; 2553761; 2553760

Crystal structure: contains datablocks exp_7626_kinem, exp_7626_dynam, Ag4P2O6_5-140_17h_p_01, global. DOI: https://doi.org/10.1107/S2053229626005012/eq3025sup1.cif

Structure factors: contains datablock exp_7626_dynam. DOI: https://doi.org/10.1107/S2053229626005012/eq3025exp_7626_dynamsup2.hkl

Structure factors: contains datablock exp_7626_kinem. DOI: https://doi.org/10.1107/S2053229626005012/eq3025exp_7626_kinemsup3.hkl

Rietveld powder data: contains datablock Ag4P2O6_5-140_17h_p_01. DOI: https://doi.org/10.1107/S2053229626005012/eq3025Ag4P2O6_5-140_17h_p_01sup4.rtv

Additional figures. DOI: https://doi.org/10.1107/S2053229626005012/eq3025sup5.pdf

Computing details top

Tetrasilver hypodiphosphate (exp_7626_kinem) top

Crystal data top

Ag₄(P₂O₆)	Z = 1
M_r = 589.42	F(000) = -29
Hexagonal, P6₃/mcm	D_x = 6.170 Mg m⁻³
a = 5.39128 (7) Å	µ = 0.000 mm⁻¹
c = 6.30229 (9) Å	T = 298 K
V = 158.64 (1) Å³

Data collection top

725 measured reflections	θ_max = 0.9°, θ_min = 0.2°
64 independent reflections	h = −6→6
60 reflections with I > 2σ(I)	k = −6→6
R_int = 0.128	l = −7→6

Refinement top

Refinement on F²	Primary atom site location: iterative
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.160P)² + 0.050P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.116	(Δ/σ)_max < 0.001
wR(F²) = 0.400	Δρ_max = 0.33 e Å⁻³
S = 2.09	Δρ_min = −0.29 e Å⁻³
64 reflections	Extinction correction: SHELXL2014 (Sheldrick, 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
11 parameters	Extinction coefficient: 35470 (58)
0 restraints

Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ag1	0.6667	0.3333	0.0000	0.045 (4)
P1	0.0000	0.0000	0.171 (9)	0.032 (12)	0.5
O1	0.276 (3)	0.0000	0.2500	0.040 (8)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ag1	0.039 (4)	0.039 (4)	0.057 (9)	0.019 (2)	0.000	0.000
P1	0.020 (9)	0.020 (9)	0.05 (4)	0.010 (5)	0.000	0.000
O1	0.012 (6)	0.024 (10)	0.09 (2)	0.012 (5)	0.000	0.000

Geometric parameters (Å, º) top

P1—P1ⁱ	0.99 (11)	P1—O1^iv	1.57 (2)
P1—P1ⁱⁱ	2.16 (11)	P1—O1^v	1.57 (2)
P1—O1ⁱⁱⁱ	1.57 (2)	P1—O1ⁱ	1.57 (2)
P1—O1	1.57 (2)	O1—P1ⁱ	1.57 (2)

P1ⁱ—P1—P1ⁱⁱ	180.000 (13)	O1^v—P1—O1	110.5 (19)
P1ⁱ—P1—O1^iv	71.6 (19)	O1^iv—P1—O1ⁱⁱⁱ	110.5 (19)
P1ⁱ—P1—O1ⁱⁱⁱ	71.6 (19)	O1ⁱ—P1—O1ⁱⁱⁱ	0.0
P1ⁱ—P1—O1^v	71.6 (19)	O1^iv—P1—O1^v	110.5 (19)
P1ⁱ—P1—O1ⁱ	71.6 (19)	O1^v—P1—O1ⁱⁱⁱ	110.5 (19)
P1ⁱ—P1—O1	71.6 (19)	O1ⁱⁱⁱ—P1—O1	0.0
O1ⁱⁱⁱ—P1—P1ⁱⁱ	108.4 (19)	O1^iv—P1—O1	110.5 (19)
O1^v—P1—P1ⁱⁱ	108.4 (19)	O1^iv—P1—O1ⁱ	110.5 (19)
O1ⁱ—P1—P1ⁱⁱ	108.4 (19)	O1^v—P1—O1ⁱ	110.5 (19)
O1^iv—P1—P1ⁱⁱ	108.4 (19)	O1ⁱ—P1—O1	0.0
O1—P1—P1ⁱⁱ	108.4 (19)	P1—O1—P1ⁱ	37 (4)

P1ⁱⁱ—P1—O1—P1ⁱ	180.000 (5)	O1^v—P1—O1—P1ⁱ	61 (2)
O1^iv—P1—O1—P1ⁱ	−61 (2)	O1ⁱ—P1—O1—P1ⁱ	0 (100)
O1ⁱⁱⁱ—P1—O1—P1ⁱ	0 (100)

Symmetry codes: (i) x, y, −z+1/2; (ii) −x, −y, −z; (iii) x−y, −y, −z+1/2; (iv) −x+y, −x, z; (v) −y, x−y, z.

(exp_7626_dynam) top

Crystal data top

Ag₄O₆P₂	Z = 1
M_r = 589.42	F(000) = 298.006
Hexagonal, P6₃/mcm	D_x = 6.170 Mg m⁻³
a = 5.39128 (7) Å	Synchrotron radiation, λ = 0.02510 Å
c = 6.30229 (9) Å	µ = 0.05 mm⁻¹
V = 158.64 (1) Å³	T = 298 K

Data collection top

1500 measured reflections	θ_max = 0.9°, θ_min = 0.2°
725 independent reflections	h = −8→8
479 reflections with I ≥ 2u(I)	k = −8→8
R_int = 0.155	l = −9→9

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	0 constraints
R[F² > 2σ(F²)] = 0.122	Primary atom site location: iterative
wR(F²) = 0.281	w = 1/[σ²(F_o²) + (0.050P)²] where P = (F_o² + 2F_c²)/3
S = 1.61	(Δ/σ)_max = −0.0003
64 reflections	Δρ_max = 16.02 e Å⁻³
10 parameters	Δρ_min = −9.94 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ag1	0.666667	0.333333	0.0	0.0389 (10)
P1	0.0	0.0	0.1784 (19)	0.022 (5)	0.500000
O1	0.2706 (10)	0.0	0.25	0.028 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ag1	0.0402 (10)	0.0402 (10)	0.036 (3)	0.0201 (5)	−0.000000	0.000000
P1	0.013 (2)	0.013 (2)	0.041 (14)	0.0064 (11)	−0.000000	0.000000
O1	0.020 (2)	0.014 (3)	0.048 (8)	0.0068 (14)	−0.000000	0.000000

Geometric parameters (Å, º) top

Ag1—Ag1ⁱ	3.1127 (1)	Ag1—O1^ix	2.536 (3)
Ag1—Ag1ⁱⁱ	3.1512 (1)	Ag1—O1	2.536 (3)
Ag1—Ag1ⁱⁱⁱ	3.1127 (1)	Ag1—O1^x	2.536 (3)
Ag1—Ag1^iv	3.1512 (1)	O1—P1	1.527 (7)
Ag1—Ag1^v	3.1127 (1)	O1—P1^xi	1.527 (7)
Ag1—O1^vi	2.536 (3)	P1—P1^xi	0.90 (2)
Ag1—O1^vii	2.536 (3)	P1—P1^xii	2.25 (2)
Ag1—O1^viii	2.536 (3)

Ag1ⁱⁱⁱ—Ag1—Ag1^v	120.0	O1^ix—Ag1—O1^vii	104.30 (10)
Ag1ⁱⁱⁱ—Ag1—Ag1ⁱⁱ	90.0	O1^vii—Ag1—O1^viii	85.48 (7)
O1^vii—Ag1—Ag1^v	83.37 (10)	O1^vi—Ag1—O1	104.30 (10)
O1^ix—Ag1—Ag1ⁱⁱ	51.60 (5)	O1^ix—Ag1—O1	85.48 (7)
O1^ix—Ag1—Ag1^v	136.80 (9)	O1^x—Ag1—O1^viii	104.30 (10)
O1^x—Ag1—Ag1ⁱⁱ	51.60 (5)	Ag1ⁱ—O1—Ag1	75.70 (10)
O1^x—Ag1—Ag1ⁱⁱⁱ	83.37 (10)	Ag1ⁱⁱ—O1—Ag1	76.80 (10)
O1^ix—Ag1—Ag1ⁱⁱⁱ	52.15 (5)	Ag1ⁱ—O1—Ag1^xiii	76.80 (10)
O1^vi—Ag1—Ag1ⁱⁱ	128.40 (5)	Ag1^xiii—O1—Ag1	121.6 (2)
O1^vii—Ag1—Ag1ⁱⁱ	128.40 (5)	Ag1ⁱⁱ—O1—Ag1ⁱ	121.6 (2)
O1^viii—Ag1—Ag1^v	52.15 (5)	Ag1ⁱⁱ—O1—Ag1^xiii	75.70 (10)
O1—Ag1—Ag1^v	83.37 (10)	P1—O1—Ag1ⁱⁱ	130.5 (3)
O1^viii—Ag1—Ag1ⁱⁱⁱ	136.80 (9)	P1^xi—O1—Ag1^xiii	106.4 (3)
O1^x—Ag1—Ag1^v	52.15 (5)	P1—O1—Ag1^xiii	130.5 (3)
O1^viii—Ag1—Ag1ⁱⁱ	128.40 (5)	P1^xi—O1—Ag1	130.5 (3)
O1—Ag1—Ag1ⁱⁱⁱ	136.80 (9)	P1^xi—O1—Ag1ⁱⁱ	106.4 (3)
O1^vii—Ag1—Ag1ⁱⁱⁱ	52.15 (5)	P1^xi—O1—Ag1ⁱ	130.5 (3)
O1^vi—Ag1—Ag1ⁱⁱⁱ	83.37 (10)	P1—O1—Ag1	106.4 (3)
O1—Ag1—Ag1ⁱⁱ	51.60 (5)	P1—O1—Ag1ⁱ	106.4 (3)
O1^vi—Ag1—Ag1^v	136.80 (9)	P1^xi—O1—P1	34.4 (9)
O1^viii—Ag1—O1	86.40 (19)	O1^xiv—P1—O1	111.7 (4)
O1^vi—Ag1—O1^viii	85.48 (7)	O1^xv—P1—O1	111.7 (4)
O1^x—Ag1—O1^ix	85.48 (7)	O1^xiv—P1—O1^xv	111.7 (4)
O1^ix—Ag1—O1^viii	166.7 (2)	P1^xi—P1—O1	72.8 (4)
O1^x—Ag1—O1^vii	86.40 (19)	P1^xii—P1—O1^xiv	107.2 (4)
O1^vi—Ag1—O1^x	166.7 (2)	P1^xii—P1—O1^xv	107.2 (4)
O1^x—Ag1—O1	85.48 (7)	P1^xi—P1—O1^xiv	72.8 (4)
O1^vii—Ag1—O1	166.7 (2)	P1^xi—P1—O1^xv	72.8 (4)
O1^vi—Ag1—O1^ix	86.40 (19)	P1^xii—P1—O1	107.2 (4)
O1^vi—Ag1—O1^vii	85.48 (7)

Ag1—O1—P1—O1^xv	−77.34 (18)	O1—P1—O1^xiv—Ag1^xli	−156.9 (5)
Ag1^ix—O1—P1—O1^xv	−77.34 (18)	O1—P1^xi—O1^xxix—Ag1^xlii	116.7 (3)
Ag1^x—O1—P1—O1^xv	−77.34 (18)	O1—P1—O1^xv—Ag1^xliii	−116.7 (3)
Ag1—O1^ix—P1^xvi—O1^xvii	−9.12 (6)	O1—P1^xi—O1^xxvi—Ag1^xliv	−116.7 (3)
Ag1^xviii—O1—P1—O1^xv	116.7 (6)	O1^xxix—P1—O1—Ag1	−77.3 (6)
Ag1—O1^vi—P1^xix—O1^xx	156.9 (3)	O1—P1—O1^xv—Ag1^xlv	77.3 (6)
Ag1—O1^ix—P1^xvi—O1^xxi	116.7 (6)	O1—P1^xi—O1^xxix—Ag1^xlvi	−156.9 (5)
Ag1—O1—P1—O1^xiv	156.9 (3)	O1—P1^xi—O1^xxix—Ag1^xlvii	9.1 (9)
Ag1—O1^x—P1^xxii—O1^xxiii	116.7 (6)	O1^xxvi—P1—O1—Ag1	156.9 (5)
Ag1—O1^x—P1^xxii—O1^xxiv	−9.12 (6)	O1—P1—O1^xiv—Ag1^xiv	−77.3 (6)
Ag1—O1^vi—P1^xix—O1^xxv	−77.34 (18)	O1—P1^xi—O1^xxvi—Ag1^xlviii	77.3 (6)
Ag1—O1—P1^xi—O1^xxvi	116.7 (6)	O1—P1—O1^xv—Ag1^xlix	−9.1 (9)
Ag1—O1^viii—P1^xxvii—O1^xii	−77.34 (18)	O1—P1^xi—O1^xxvi—P1	−62.9 (6)
Ag1^x—O1—P1—O1^xiv	156.9 (3)	O1—P1—O1^xv—P1^xxix	−62.9 (6)
Ag1—O1^viii—P1^xxvii—O1^xxviii	156.9 (3)	O1—P1^xi—O1^xxix—P1	62.9 (6)
Ag1—O1—P1^xi—O1^xxix	−9.12 (6)	O1—P1—O1^xiv—P1^xxvi	62.9 (6)
Ag1^xiii—O1—P1—O1^xv	116.7 (6)	O1—P1—P1^xi—O1^xxix	120.0
Ag1^ix—O1—P1—O1^xiv	156.9 (3)	O1—P1^xi—P1—O1^xv	−120.0
Ag1^xiii—O1—P1—O1^xiv	−9.12 (6)	O1—P1—P1^xi—O1^xxvi	−120.0
Ag1^xxx—O1—P1—O1^xv	116.7 (6)	O1—P1^xi—P1—O1^xiv	120.0
Ag1—O1^vii—P1^xxxi—O1^xxxii	−77.34 (18)	P1—O1—P1^xi—O1^xxix	−62.9 (3)
Ag1^xviii—O1—P1—O1^xiv	−9.12 (6)	P1—O1—P1^xi—O1^xxvi	62.9 (3)
Ag1^xxx—O1—P1—O1^xiv	−9.12 (6)	P1—O1^xv—P1^xxix—O1^xxvi	−62.9 (3)
Ag1—O1^vii—P1^xxxi—O1^xxxiii	156.9 (3)	P1—O1^xiv—P1^xxvi—O1	−62.9 (3)
Ag1—O1—P1^xi—P1^xxxiv	−126.2 (3)	P1—O1^xiv—P1^xxvi—O1^xxix	62.9 (3)
Ag1^xiii—O1—P1—P1^xi	53.8 (3)	P1—O1^xv—P1^xxix—O1	62.9 (3)
Ag1^x—O1—P1^xi—P1	53.8 (3)	P1—O1^xv—P1^xxix—P1^l	180.0
Ag1—O1—P1^xi—P1	53.8 (3)	P1—O1—P1^xi—P1^xxxiv	180.0
Ag1^xiii—O1—P1^xi—P1	−140.24 (9)	P1—O1^xiv—P1^xxvi—P1^xxx	180.0
Ag1^xxx—O1—P1—P1^xi	53.8 (3)	P1^xi—P1—O1—Ag1ⁱⁱ	−53.8 (3)
Ag1—O1—P1—P1^xii	39.76 (9)	P1—P1^xii—O1^xxvii—Ag1^li	126.2 (3)
Ag1^xxx—O1—P1^xi—P1	−140.24 (9)	P1—P1^xi—O1^xxix—Ag1^xlii	53.8 (3)
Ag1^ix—O1—P1—P1^xi	−140.24 (9)	P1—P1^xi—O1^xxix—Ag1^xlvii	−53.8 (3)
Ag1^ix—O1—P1—P1^xii	39.76 (9)	P1^xxix—P1—O1—Ag1	−140.24 (8)
Ag1—O1^ix—P1^xvi—P1^xviii	−126.2 (3)	P1—P1^xii—O1^xxviii—Ag1^lii	126.2 (3)
Ag1^x—O1—P1—P1^xi	−140.24 (9)	P1—P1^xii—O1^xxvii—Ag1^liii	−126.2 (3)
Ag1^xxx—O1—P1—P1^xii	−126.2 (3)	P1^xii—P1—O1—Ag1ⁱⁱ	126.2 (3)
Ag1—O1^x—P1^xxii—P1^xxxv	−126.2 (3)	P1^xxviii—P1—O1—Ag1	39.76 (8)
Ag1^xviii—O1—P1—P1^xi	53.8 (3)	P1—P1^xi—O1^xxvi—Ag1^xl	53.8 (3)
Ag1^xviii—O1—P1—P1^xii	−126.2 (3)	P1—P1^xii—O1^xxviii—Ag1^xliv	−39.76 (8)
Ag1—O1^vi—P1^xix—P1^xxxvi	39.76 (9)	P1^xxvii—P1—O1—Ag1	39.76 (8)
Ag1—O1^viii—P1^xxvii—P1	39.76 (9)	P1—P1^xi—O1^xxix—Ag1^xlvi	140.24 (8)
Ag1^xviii—O1—P1^xi—P1	−140.24 (9)	P1—P1^xi—O1^xxvi—Ag1^xlviii	140.24 (8)
Ag1^xiii—O1—P1—P1^xii	−126.2 (3)	P1^xi—P1—O1—Ag1ⁱ	140.24 (8)
Ag1—O1^vii—P1^xxxi—P1^xxxvii	39.76 (9)	P1^xii—P1—O1—Ag1ⁱ	−39.76 (8)
Ag1—O1—P1—P1^xi	−140.24 (9)	P1—P1^xi—O1^xxvi—Ag1^xliv	−53.8 (3)
Ag1^ix—O1—P1^xi—P1	53.8 (3)	P1^xxvi—P1—O1—Ag1	−140.24 (8)
Ag1^x—O1—P1—P1^xii	39.76 (9)	P1—P1^xii—O1^xxvii—Ag1^xlvii	−39.76 (8)
O1—P1—O1^xv—Ag1^xv	156.9 (5)	P1—P1^xii—O1^xxviii—Ag1^liv	−126.2 (3)
O1—P1—O1^xiv—Ag1^xxxviii	116.7 (3)	P1—P1^xii—O1^xxviii—P1^lv	180.0
O1—P1—O1^xiv—Ag1^xxxix	9.1 (9)	P1—P1^xii—O1^xxvii—P1^viii	−180.0
O1—P1^xi—O1^xxvi—Ag1^xl	−9.1 (9)	P1^xii—P1—O1—P1^xi	180.0

Symmetry codes: (i) −x+1, −y, −z; (ii) −x+y+1, −x+1, −z+1/2; (iii) −x+2, −y+1, −z; (iv) −x+y+1, −x+1, −z−1/2; (v) −x+1, −y+1, −z; (vi) −x+1, −y, z−1/2; (vii) y+1, −x+y+1, z−1/2; (viii) x−y, x, z−1/2; (ix) −y+1, x−y, z; (x) −x+y+1, −x+1, z; (xi) x−y, −y, −z+1/2; (xii) −y, −x, −z; (xiii) x−y, x−1, z+1/2; (xiv) −x+y, −x, z; (xv) −y, x−y, z; (xvi) y+1, x, −z+1/2; (xvii) −x+1, −x+y, −z+1/2; (xviii) −x+1, −y, z+1/2; (xix) −x+y+1, y, −z; (xx) −y+1, −x, −z; (xxi) x−y+1, −y, −z+1/2; (xxii) −x+1, −x+y+1, −z+1/2; (xxiii) y+1, x+1, −z+1/2; (xxiv) x−y+1, −y+1, −z+1/2; (xxv) x+1, x−y, −z; (xxvi) −x, −x+y, −z+1/2; (xxvii) x, x−y, −z; (xxviii) −x+y, y, −z; (xxix) y, x, −z+1/2; (xxx) y, −x+y, z+1/2; (xxxi) −y+1, −x+1, −z; (xxxii) −x+y+1, y+1, −z; (xxxiii) x+1, x−y+1, −z; (xxxiv) x−y, x, z+1/2; (xxxv) y+1, −x+y+1, z+1/2; (xxxvi) −x+y+1, −x, z; (xxxvii) x+1, y+1, z; (xxxviii) y−1, −x+y, z+1/2; (xxxix) −y, x−y−1, −z+1/2; (xl) −x+y, y−1, −z; (xli) x−y−1, x−1, −z; (xlii) x−1, x−y, −z; (xliii) x−1, y, −z+1/2; (xliv) x−y−1, −y, z; (xlv) y, −x+y+1, −z; (xlvi) −y, −x+1, z+1/2; (xlvii) −x+1, −x+y+1, z; (xlviii) x−1, x−y−1, z+1/2; (xlix) −x+1, −y+1, z+1/2; (l) −x, −y, z+1/2; (li) −x+y+1, y, z−1/2; (lii) −y, −x+1, z−1/2; (liii) x−y, −y+1, −z−1/2; (liv) y−1, x−1, −z−1/2; (lv) −x, −y, z−1/2.

(Ag4P2O6_5-140_17h_p_01) top

Crystal data top

Ag₄P₂O₆	α = 90°
P6₃/mcm	β = 90°
a = 5.39128 (7) Å	γ = 120°
b = 5.39128 (7) Å	Cu Kα₁₊₂ radiation
c = 6.30229 (9) Å

Data collection top

2θ_min = 15.006°, 2θ_max = 131.997°, 2θ_step = 0.007°

Refinement top

R(F) = 0.032

16714 data points

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ag1	0.666670	0.333330	0.000000	0.04093 (7)*
P1	0.000000	0.000000	0.161226	0.022000*	0.500000
O1	0.266569	0.000000	0.250000	0.028000*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ag1	0.0483 (4)	0.0483 (4)	0.0317 (4)	0.0283 (4)	0.000000	0.000000
P1	0.012999	0.012999	0.040998	0.006300	0.000000	0.000000
O1	0.019999	0.012999	0.046998	0.006700	0.000000	0.000000

Crystallographic data for kinematical and dynamical refinement versus ED data, and Rietveld refinement versus PXRD data top

Chemical formula	Ag₄P₂O₆
M_r (g mol^-1)	589.42
Crystal system, space group	Hexagonal, P6₃/mcm
Temperature (K)	293
a, c (Å)	5.39128 (7), 6.30229 (9)
V (Å³)	158.640 (5)
Z	1

3D ED refinement
Radiation type	200 kV electron beam (λ = 0.0251 Å)
θ range (°)	0.153–1.162
R₁ (kinematical/dynamical refinement)	0.116/0.122
wR₂ (kinematical/dynamical refinement)	0.400/0.281

Rietveld refinement
Radiation type	Cu Kα (λ = 1.5418 Å)
R (Bragg)	0.032
R (expected)	0.012
R (profile)	0.034
R (weighted profile)	0.051

Acknowledgements

This research was performed under a cooperation agreement between Rigaku Polska Sp. z o.o. and the University of Wrocław (agreement No. 1/2021).

Conflict of interest

There are no conflicts of interest.

Data availability

The published raw data, along with any supporting information not included in the article, is available from the authors upon reasonable request.

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Volume 82| Part 6| June 2026| Pages 277-284

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