Structures and thermal stability of the α-LiNH4SO4 polytypes doped with Er3+ and Yb3+

Sabalisck, N.P.; Guzmán-Afonso, C.; González-Silgo, C.; Torres, M.E.; Pasán, J.; del-Castillo, J.; Ramos-Hernández, D.; Hernández-Suárez, A.; Mestres, L.

doi:10.1107/S2052520616019028

research papers

STRUCTURAL SCIENCE
CRYSTAL ENGINEERING
MATERIALS

ISSN: 2052-5206

Volume 73| Part 1| February 2017| Pages 122-133

https://doi.org/10.1107/S2052520616019028

Structures and thermal stability of the α-LiNH₄SO₄ polytypes doped with Er³⁺ and Yb³⁺

N. P. Sabalisck,^a ^* C. Guzmán-Afonso,^a C. González-Silgo,^a M. E. Torres,^a J. Pasán,^a,^b J. del-Castillo,^a D. Ramos-Hernández,^a A. Hernández-Suárez ^a and L. Mestres ^c

^aDepartamento de Física, Facultad de Ciencias, Sección Física, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain, ^bInstitut de Ciencia Molecular (ICMol), C/ Catedrático José Beltrán 2, 46980 Paterna, Valencia, Spain, and ^cGrup de Química de l'Estat Sòlid, Departament de Química Inorgànica, Universitat de Barcelona, 08028 Barcelona, Spain
^*Correspondence e-mail: nanprado@ull.edu.es

Edited by P. Bordet, Institut Néel, France (Received 29 April 2016; accepted 28 November 2016; online 31 January 2017)

In order to clarify the polymorphism in the lithium sulfate family, LiRE_x(NH₄)_1 − xSO₄ (0.5 ≤ x ≤ 4.0 mol%, nominal value; RE = Er³⁺, Yb³⁺ and Dy³⁺) crystals were grown from aqueous solution by slow evaporation between 298 and 313 K. The doping of the samples allowed us to obtain two polymorphic forms, α and β, of LiNH₄SO₄ (LAS). By means of X-ray diffraction (XRD) in single crystals, we determined the crystal structures of two new α-polytypes, which we have named α₁- and α₂-LAS. They present the same space group P2₁/c and the following relation among their lattice parameters: a₂ = −c₁, b₂ = −b₁, c₂ = −2a₁ − c₁. In order to evaluate the stability of the new α-polytypes, we performed thermal analysis, X-ray diffraction and dielectric spectroscopy on single crystals and polycrystalline samples over the cyclic temperature range: 190 → 575 → 190 K. The results obtained by all the techniques used in this study demonstrate that α-polytypes are stable across a wide range of temperatures and they show an irreversible phase transition to the paraelectric β-phase above 500 K. In addition, a comparative study of α- and β-polytypes shows that both polymorphic structures have a common axis, with a possible intergrowth that facilitates their coexistence and promotes the reconstructive α → β transition. This intergrowth was related to small anomalies detected between 240 and 260 K, in crystals with an α-habit.

Keywords: polytypism; polymorphism; phase transitions; lithium ammonium sulfate.

CCDC references: 1519626; 1530426

1. Introduction

In the last few years, considerable attention has been devoted to the lithium sulfate family with the chemical formula ALiSO₄ (A = Li, Na, K, Rb, Cs, NH₄ or Tl) and related compounds. These materials present open lattices, which provide them with a great flexibility that makes possible thermal rearrangements of their LiO₄ and SO₄ tetrahedra, involving phase transitions (Tomaszewski, 1992b ; Połomska, 2001 ; Mata-Ramírez, 2002 ; Lim et al., 2013 , and references cited therein). This ability to generate polymorphism allows a large number of different crystal structures to be obtained, which display interesting nonlinear physical properties of current interest such as ferroelectricity (Połomska et al., 2005 ; Shamshin, 2010 ), ferroelasticity (Czaja, 2013 ; Lim & Kim, 2012 ) and second harmonic generation (Palmero et al., 2008 ; Closser et al., 2013 ); as well as fast-ion conduction at higher temperatures (Lv et al., 2015 ; Xiao et al., 2015 ). In the case of the lithium ammonium sulfate (LAS), its varied polymorphism and its phase transition sequence (which depend on the synthesis conditions, i.e. thermal treatment, doping of the ammonium ion etc.), have been the subject of more than 200 articles in the last 50 years, which were not exempt from controversy (for instance, see Solans et al., 1999 ; Tomaszewski, 2000 ). Still nowadays some phases are being revised and referenced (Komornicka et al., 2014 ; Rudysh et al., 2015 ; Lim, 2016 ). Moreover, a variety of phases in this family is largely influenced by the chemical pressure, which can be changed by the replacement of cations and anions (Połomska, 2001; Lim et al., 2013; Czaja, 2013; Rousse & Tarascon, 2014 ).

The three polymorphic phases and thermal stability of β-LiNH₄SO₄ (β-LAS) have been described as: ferroelectric β-LAS, from 285 to 460 K (P2₁cn space group; Połomska, 2001). Above 460 K the corresponding ferroelectric–paraelectric transition to a crystal structure with the space group Pmcn takes place (Itoh et al., 1981 ). Below 285 K, it undergoes a ferroelectric–ferroelastic phase transition with a final monoclinic phase (P2₁/c; Mashiyama & Kasano, 1993 ). Very recently, this non-polar and ferroelastic phase has been identified as a ferroaxial crystal structure (Hlinka et al., 2016 ). There is also the so-called α-LiNH₄SO₄ (α-LAS) or α-modification. It has been described as an orthorhombic structure with the space group Pbc2₁ and the following lattice parameters: a = 4.991, b = 10.196 and c = 17.010 Å (Z = 8; Pietraszko & Lukaszewicz, 1992 ; Tomaszewski, 1992a ). The α-modification presents a complex correlated structural disorder that can be represented by, at least, three different polytypes and whose lattice parameters c follow the conditions: c₁ = c, c₂ = 2c and c₃ = 3c (Tomaszewski, 1992a). Recently, Komornicka et al. (2014) have studied the polytypism in α-LAS. They have simulated the X-ray diffuse scattering by the Monte Carlo technique, using a two-spin like Ising model of disorder. This model incorporates correlations into the α-polytypism, described as a `domainized' sequence of layers.

Several authors have studied the growth conditions, thermal stability and phase transitions of both modifications: α- and β-LAS. The crystallization above and at room temperature favors the ferroelectric β-phase, whereas the α-polytype is obtained below room temperature (Solans et al., 1999; Połomska, 2001; Mel'nikova et al., 2003 ). According to the literature, the α-LAS modification has an unstable structure and undergoes a reversible phase transition to β-LAS at 250 K and a non-reversible phase transition to the ferroelectric phase of β-LAS, at ∼ 350 K (Połomska, 2001). Another study of crystal growth conditions of α- and β-LAS performed by Mel'nikova et al. (2003) showed that there are two temperature intervals where the crystal may experience a reconstructive $[\alpha\rightarrow\beta]$ phase transition. In the first temperature interval (340–350 K) a reconstructive phase transition causes the fast destruction of the sample. In the second temperature interval (440–450 K) the crystal structure undergoes a slow transformation (recrystallization) without significant distortions. Using XRD, Komornicka et al. (2014) confirmed the reconstructive and irreversible α → β phase transition between 431 and 457 K.

In this work we present two new crystal structures of Yb³⁺-doped LiNH₄SO₄, obtained from XRD of single crystals, which are new polytypes of the α-LAS modification. In addition, from DSC and dielectric spectroscopy of single crystals and XRD of polycrystalline samples, we study the thermal stability, the reconstructive α → β phase transition and the possible coexistence of both α and β polymorphs for different Yb³⁺ and Er³⁺ doped samples with α modification. In this study we try to clarify most of the controversy given in the literature and to contribute to future research which correlate physical properties with new structural distortions.

2. Experimental

2.1. Sample preparation and selection of crystals

Pure and doped LiNH₄SO₄ (LAS) crystals, with different concentrations of Er³⁺, Yb³⁺ and Dy³⁺, were grown at 298, 308 and 313 K from aqueous solutions by slow evaporation (see Table 1). Pure LAS was obtained at equimolar quantities of Li₂SO₄ and (NH₄)₂SO₄; whereas for the doped compounds, the molar ratio was 1:1:x, where x is the concentration of the corresponding rare earth sulfate [RE₂(SO₄)₃]. All reagents had a purity grade of 99.99%. At least four syntheses were performed for each temperature and concentration, for all compounds studied.

Table 1
Concentrations of Er³⁺, Yb³⁺ and Dy³⁺ used to obtain doped LiNH₄SO₄ crystals

Rare earth	Nominal concentration (mol%)
Er³⁺	–	0.6	–	0.8	–	1.0	1.2	1.4	2.0	–
Yb³⁺	0.5	0.6	0.7	0.8	0.9	1.0	1.2	1.4	2.0	4.0
Dy³⁺	–	0.6	–	0.8	–	1.0	1.2	–	–	–

Although α-LAS usually crystallizes below 293 K and β-LAS grows above this temperature (Mel'nikova et al., 2003), by visual and microscopic analysis, a marked difference was observed in the crystalline habits of obtained single crystals under our conditions. According to Mel'nikova et al. (2003) and Mata-Ramírez (2002), the samples with polyhedral and cylindrical shapes were classified as β-habit (see Figs. 1a and b). While the very thin (millimetric thickness), flat and transparent layers, with rectangular or square shapes, of the samples were classified as α-habit (Fig. 1c). After the classification of the crystals obtained from experiments, they were counted and divided into two parts: one for the analysis of single crystals and the other one to grind for the analysis of polycrystalline samples.

Figure 1
Samples of LiNH₄SO₄ with different crystalline habits: (a), (b) β-habit, and (c) α-habit for doped with Yb³⁺ crystal.

2.2. Thermal analysis

Differential scanning calorimeter (DSC) analysis was performed in order to study the stability of all selected, doped and pure, single crystals with different habits. DSC measurements were carried out on a Perkin–Elmer differential scanning calorimeter Pyris I-DSC, under nitrogen gas in a sequential cycle: 298 → 190 → 575 →190 K, using a heating and cooling rate of 10 K min⁻¹.

2.3. X-ray diffraction

XRD data were obtained by using three different experimental protocols. Two of them related to single crystals and the third one for powder samples.

(i) Two single crystals of Yb-doped LAS with 2 and 4 mol% (nominal concentrations), and α-habit were selected. Diffraction data at 293 K were collected on a MARS345 automated diffractometer, with an image-plate detector and using monochromatic Mo Kα radiation by reflection from a graphite crystal. The structures were solved by Patterson's method, using SHELXS (Sheldrick, 2015 ), and refined by full-matrix least-squares using SHELXL (Sheldrick, 2015). For details of the data collection and the structure determination see Table 2 and the CIF files in the supporting information.

Table 2
Single crystal and refinement data for the α₁-LAS and α₂-LAS polytypes

Identification code	α₁-LAS Yb 2 mol%	α₂-LAS Yb 4 mol%
Crystal data
Empirical formula	H_3.940LiN_0.984O₄SYb_0.005	H_3.843LiN_0.961O₄SYb_0.013
M_r	121.54	122.51
Crystal system, space group	Monoclinic, P2₁/c	Monoclinic, P2₁/c
Temperature (K)	293	293
Wavelength (Å)	0.71073	0.71073
a, b, c (Å)	17.856 (8), 5.008 (3), 10.264 (13)	10.177 (15), 5.106 (4), 34.234 (16)
β (°)	106.46 (5)	90.20 (10)
V (Å³)	880.2 (13)	1779 (3)
Z	8	16
F(000)	497	1000.0
D_x (Mg m⁻³)	1.836	1.831
Radiation type	Mo Kα	Mo Kα
μ (mm⁻¹)	0.73	0.89
Crystal size (mm³)	0.18 × 0.14 × 0.09	0.17 × 0.11 × 0.09

Data collection
Diffractometer	Enraf–Nonius CAD4	Enraf–Nonius CAD4
Absorption correction	–	–
No. of measured, independent and observed [I > 2σ(I)] reflections	4811, 2549, 2020	9573, 5071, 3231
R_int	0.0905	0.068
(sin θ/λ)_max (Å⁻¹)	0.705	0.704
Range of h, k, l	h = −25 → 0, k = −7 → 7, l = −13 → 14	h = −14 → 14, k = −7 → 7, l = −48 → 0
Completeness to θ (%)	99.90 (θ = 25.242°)	100 (θ = 25.242°)

Refinement
Refinement method	Full-matrix least-squares on F²	Full-matrix least-squares on F²
Final R indices [I > 2σ(I)]	R₁ = 0.0535, wR₂ = 0.1354	R₁ = 0.0603, wR₂ = 0.1333
R indices (all data)	R₁ = 0.0671, wR₂ = 0.1434	R₁ = 0.1029, wR₂ = 0.1632
Goodness-of-fit on F²	1.173	1.197
No. of reflections, restraints, parameters	2549, 74, 153	5071, 0, 256
Δρ_max, Δρ_min (e Å⁻³)	1.05, −0.68	1.89, −1.04

(ii) On the other hand, single crystals with an α-habit were measured with the Agilent SuperNova diffractometer, in order to study the thermal dependence of their reciprocal space images and lattice parameters at low temperatures (from 200 to 295 K). The CrysAlisPro computer software (Agilent, 2014 ) was used during the data analysis and also for diffractometer control and data collection.

(iii) Powder diffraction measurements were performed for all doped and pure LAS samples, using a PANalytical X'Pert Pro diffractometer (Bragg–Brentano mode) equipped with an X'Celerator detector using Cu Kα₁ radiation. The angular range 5 > 2θ > 100° was scanned at a step size of 0.02° and 200 s step time. Divergence and anti-scatter slits were set at 1 and 0.5°, respectively, and the detector was used in a scanning mode with an active length of 2.14°. A 0.02 rad Soller slit was used in the diffraction beam. Measurements at different temperatures were carried out during a cyclic process of heating and cooling: 298 $[\rightarrow]$ 548 $[\rightarrow]$ 298 K using an Anton Paar HTK–2000 chamber and under air atmosphere. The heating and cooling rate was 10 K min⁻¹ and the sample kept at the selected temperature for 5 min to stabilize before the scan. Whole pattern fits were performed using the FullProf computer program (Rodríguez-Carvajal, 1993 ). In addition, to compare the obtained crystal structures, we performed a symmetry-mode analysis of the more distorted structure with respect to the more symmetric one, by using the AMPLIMODES program (Orobengoa et al., 2009 ), available on the Bilbao Crystallographic Server (Aroyo et al., 2011 ).

2.4. Dielectric spectroscopy

Dielectric measurements (real $[\varepsilon _{r}^{\prime}]$ and imaginary $[\varepsilon _{r}^{\prime\prime}]$ parts of complex permittivity) were performed on single crystals, using an HP 4192A impedance analyzer in the frequency range from 0.1 kHz to 1 MHz with an AC signal amplitude of 1 V. Three single crystals were selected: one β-LAS with cylindrical shape (height 2.0 mm and diameter 3.0 mm) was cut with the c-axis (pseudo-hexagonal axis) parallel to the axis of the cylinder, and two single crystals with thin plate shapes: one pure α-LAS (obtained at room temperature), and one doped α-LAS Yb 1.4 mol%. After, the plane parallel faces for all crystal samples were coated with silver paste and then placed into the cell (parallel plate capacitor). The measurements were recorded in two different runs: (1) heating from 190 until 290 K, using a homemade cryostat, and (2) above room temperature, following the cycle: 298 $[\rightarrow]$ 520 $[\rightarrow]$ 298 K using a resistance furnace, with a warming and cooling rate of 0.8 K min⁻¹. In both experiments, the temperature was monitored using a thermocouple within an accuracy of approximately 0.1 K. In order to gain a deeper knowledge of the dielectric behavior, we performed a conductivity spectra analysis. It is based on the Universal Dielectric Response (UDR; Jonscher (1977 ; Ngai et al., 1979 ; Dissado & Hill, 1979 ). According to this model, the real part of the conductivity spectra $[\sigma^{{\prime}}]$ tends towards the DC conductivity ( $[\sigma _{\rm dc}]$ ) as the frequency (ν) decreases and shows a dispersive regime where the conductivity strongly increases with the frequency. A slightly different version of the more typical Jonscher equation is given by León et al. (1997 )

$[{\sigma^{{\prime}}(\nu) = \sigma _{\rm dc}\left[1+\cos\left({{s\pi} \over {2}}\right)\left({{\nu} \over {\nu _{\rm p}}}\right)^{s}\right]}, \eqno(1)]$

where s is a fractional exponent with values between 0 and 1, depending on the many-body interactions among charge carriers, and $[\nu _{\rm p}]$ is crossover frequency.

3. Results and discussion

3.1. Effect of the doping in the LAS single crystals

Taking into account the crystals identified as α- and β-habits, obtained from each experiment, we found for pure compounds at 298, 308 and 313 K only 5% of an α-habit. However, by doping the compounds with rare earth ions (Er³⁺ and Yb³⁺), at the same evaporation temperatures, it was possible to obtain a bigger proportion of crystals with the α-habit; reaching a percentage of 15%. The crystals with better quality were obtained for concentrations of Er³⁺ ions between 0.6 and 1.2 mol% and for concentrations of Yb³⁺ ions from 0.7 mol% thereafter. In the cases where we used Dy³⁺ as a dopant, with the concentrations given in Table 1, we did not obtain the α-habit. Therefore, as a first result, when we doped the samples with the Er³⁺ and Yb³⁺ ions above and at room temperature the α-habit is favored.

In order to evaluate the thermal stability of the doped LAS crystals, we have compared the DSC curves of single crystals with both α- and β-habits. The results obtained for pure β-LAS crystals (Fig. 2a) are comparable to those found in the literature (Połomska, 2001; Połomska et al., 1994 ). The curve shows two characteristic peaks: the ferroelastic–ferroelectric phase transition at 287 K and the ferroelectric–paraelectric one at 461 K.

Figure 2
DSC curves correspond to single crystals: (a) for the pure compound with the β-habit (reference sample) and (b) for the α-LAS Yb³⁺ 0.7 mol%.

In the case of the α-LAS Yb 0.7 mol% (nominal value; Fig. 2b), the phase transition at low temperature seems precluded. At high temperature, the ferroelectric–paraelectric transition takes place at 484 K and it is accompanied by a post-transition around 500 K. This more complex transition adds an enthalpy change almost one order of magnitude greater than the ferroelectric–paraelectric transition observed for β-LAS. However, in the case of α-LAS Yb 0.7 mol%, as the temperature decreases, the paraelectric–ferroelectric transition was recovered, although the low-temperature transition was not well distinguished. In this process, the crystal recovered the β-habit. Very similar behavior was observed in other single crystals with α-LAS habit. Thermal analysis has revealed that the α $[\rightarrow]$ β transition takes place at high temperature and it must be the reconstructive and irreversible transition observed by Komornicka et al. (2014).

3.2. Structural characterization of two new polytypes

Two different polytypes, with an α-habit, were solved in the same space group P2₁/c for ytterbium-doped LAS crystals with 2 and 4 mol% (nominal concentrations) and these phases were named $[\alpha _{{1}}]$ - and $[\alpha _{{2}}]$ -LAS, respectively (see Table 2). The atomic coordinates, equivalent thermal displacement and occupation factor are shown in Tables 3 and 4; including the atomic coordinates of the H atoms, which were calculated only for $[\alpha _{{1}}]$ -LAS. The bond lengths as well as the angles are given as CIF files attached as supporting information. The refinement of the ammonium sites indicates that NH₄⁺ and Yb³⁺ are located at the same position, in agreement with the electron density residuals found in the difference Fourier maps (see Table 2). Note that the substitution of ammonium by ytterbium is not homogeneous and the experimental concentrations, calculated from the occupation factors, are 0.5 and 1.3 mol% for the $[\alpha _{{1}}]$ -LAS, and the $[\alpha _{{2}}]$ -LAS, respectively. These values are less than the nominal concentrations: 2 and 4 mol%.

Table 3
Atomic coordinates, equivalent isotropic displacement parameters and occupation factors for the α₁-LAS polytype

U_eq is defined as one third of the trace of the orthogonalized U^ij tensor.

Atom	x	y	z	U_eq (10⁻³ Å²)	Occ. factor
S1	0.4019 (1)	0.7881 (1)	0.3501 (1)	16 (1)	1.0
O11	0.4075 (1)	0.7062 (5)	0.4897 (2)	28 (1)	1.0
O12	0.4109 (1)	1.0821 (4)	0.3465 (2)	31 (1)	1.0
O13	0.3261 (1)	0.7155 (5)	0.2583 (2)	36 (1)	1.0
O14	0.4649 (1)	0.6618 (4)	0.3038 (2)	24 (1)	1.0
S2	0.0981 (1)	0.2884 (1)	0.4473 (1)	15 (1)	1.0
O21	0.0925 (1)	0.2049 (5)	0.5819 (2)	26 (1)	1.0
O22	0.0894 (1)	0.5822 (4)	0.4341 (2)	29 (1)	1.0
O23	0.0349 (1)	0.1605 (4)	0.3389 (2)	22 (1)	1.0
O24	0.1740 (1)	0.2124 (5)	0.4303 (2)	34 (1)	1.0
Yb1	0.3329 (1)	0.2738 (5)	0.0677 (2)	31 (1)	0.0051 (12)
N1	0.3329 (1)	0.2738 (5)	0.0677 (2)	31 (1)	0.985 (4)
Yb2	0.1673 (1)	0.7751 (5)	0.2335 (3)	31 (1)	0.0054 (12)
N2	0.1673 (1)	0.7751 (5)	0.2335 (3)	31 (1)	0.984 (4)
Li1	0.0011 (2)	0.2967 (9)	0.1505 (4)	20 (1)	1.0
Li2	0.5016 (2)	0.2965 (10)	0.3519 (5)	23 (1)	1.0
H11	0.277 (1)	0.290 (6)	0.031 (3)	47	0.985 (4)
H12	0.351 (2)	0.137 (5)	0.016 (3)	47	0.985 (4)
H13	0.357 (2)	0.439 (3)	0.055 (3)	47	0.985 (4)
H14	0.346 (2)	0.224 (6)	0.161 (1)	47	0.985 (4)
H21	0.223 (1)	0.773 (6)	0.255 (3)	46	0.984 (4)
H22	0.145 (2)	0.660 (5)	0.157 (2)	46	0.984 (4)
H23	0.151 (2)	0.713 (6)	0.310 (2)	46	0.984 (4)
H24	0.148 (2)	0.953 (3)	0.209 (3)	46	0.984 (4)

Table 4
Atomic coordinates, equivalent isotropic displacement parameters and occupation factors for the $[\alpha _{2}]$ -LAS polytype

U_eq is defined as one third of the trace of the orthogonalized U^ij tensor.

Atom	x	y	z	U_eq (10⁻³ Å²)	Occ. factor
S1	0.6481 (1)	0.7331 (1)	0.2009 (1)	6 (1)	1.0
O11	0.6399 (4)	0.4374 (5)	0.2061 (1)	41 (1)	1.0
O12	0.7859 (3)	0.8058 (10)	0.2041 (1)	52 (1)	1.0
O13	0.5709 (3)	0.8568 (6)	0.2324 (1)	27 (1)	1.0
O14	0.5950 (4)	0.7924 (10)	0.1631 (1)	57 (1)	1.0
S2	0.8982 (1)	0.2837 (2)	0.0492 (1)	17 (1)	1.0
O21	0.8934 (3)	0.5828 (6)	0.0441 (1)	32 (1)	1.0
O22	1.0370 (3)	0.2110 (6)	0.0462 (1)	30 (1)	1.0
O23	0.8456 (3)	0.2180 (7)	0.0867 (1)	37 (1)	1.0
O24	0.8213 (3)	0.1630 (6)	0.0180 (1)	28 (1)	1.0
S3	0.3996 (1)	0.2162 (2)	0.0490 (1)	17 (1)	1.0
O31	0.5355 (3)	0.2891 (6)	0.0463 (1)	30 (1)	1.0
O32	0.3211 (3)	0.3371 (6)	0.0174 (1)	27 (1)	1.0
O33	0.3916 (3)	−0.0811 (6)	0.0447 (1)	33 (1)	1.0
O34	0.3434 (3)	0.2813 (7)	0.0875 (1)	32 (1)	1.0
S4	0.1488 (1)	0.8032 (3)	0.2009 (1)	36 (1)	1.0
O41	0.1414 (3)	1.1054 (7)	0.2046 (1)	31 (1)	1.0
O42	0.2864 (2)	0.7278 (5)	0.2036 (1)	21 (1)	1.0
O43	0.0927 (3)	0.7312 (6)	0.1630 (1)	27 (1)	1.0
O44	0.0714 (3)	0.6850 (7)	0.2325 (1)	29 (1)	1.0
N1	0.4006 (3)	0.2369 (6)	0.1662 (1)	42 (1)	0.907 (4)
N2	0.6508 (3)	0.7697 (7)	0.0838 (1)	36 (1)	0.959 (4)
N3	0.1517 (3)	0.7309 (7)	0.0833 (1)	33 (1)	0.978 (4)
N4	0.9005 (4)	0.2744 (9)	0.1667 (1)	38 (1)	1.0
Yb1	0.4006 (3)	0.2369 (6)	0.1662 (1)	42 (1)	0.0311 (15)
Yb2	0.6508 (3)	0.7697 (7)	0.0838 (1)	36 (1)	0.0137 (15)
Yb3	0.1517 (3)	0.7309 (7)	0.0833 (1)	33 (1)	0.0074 (14)
Li1	0.3992 (7)	0.7198 (14)	0.2497 (2)	24 (1)	1.0
Li2	0.1017 (7)	0.3041 (15)	0.2508 (2)	28 (2)	1.0
Li3	0.1488 (7)	0.2123 (13)	0.0001 (2)	22 (1)	1.0
Li4	0.6491 (6)	0.2976 (12)	0.0013 (2)	19 (1)	1.0

In general, we have observed that the α-habit was favored by doping with ions of smaller ionic radii than the ammonium one; this can be explained from the obtained crystal structures. The ammonium sites in both polytypes, $[\alpha _{1}]$ - and $[\alpha _{2}]$ -LAS, lead to an environment with six first neighbors, which is a more typical geometry for heavy rare earth ions like Yb³⁺ and Er³⁺ (Guzmán-Afonso et al., 2011 ; Maczka et al., 2012 ). Moreover, although the ionic radius of Dy³⁺ is closer to the NH₄⁺ ion, this rare earth ion leads to an environment with coordination over seven O atoms; then, the structure of the ferroelectric β-phase must be favored (see Fig. 3). For the $[\alpha _{1}]$ -LAS structure, the ammonium ion is surrounded by ten O atoms; six of them are closer to the ammonium cation (see Fig. 3b). For the ferroelectric β-phase, nine O atoms (Mata-Ramírez, 2002) surround the NH₄⁺ cation; in this case, it is more difficult to distinguish a clear subgroup of first neighbors (see Fig. 3a). This fact can explain why we have not obtained doped α-LAS with dysprosium.

Figure 3
Views of the two environments for the ammonium cation in ferroelectric (a) β-LAS and (b) α₁-LAS. The other environments for the ammonium cation in both polytypes: $[\alpha _{{1}}]$ - and $[\alpha _{{2}}]$ -LAS, are very similar.

The S and Li atoms are at the center of oxygen tetrahedra which share corners in order to form the [LiSO₄]⁻ layers perpendicular to the a axis in $[\alpha _{1}]$ -LAS, and to the c axis in $[\alpha _{2}]$ -LAS. The NH₄⁺ ions are located between the layers. All the H atoms of the NH₄⁺ group form hydrogen bonds with O atoms of the nearest layers. Both α-structures consist of the same stacked layers, with the following lattice parameter relationships: a₂ = -c₁, b₂ = -b₁, c₂ = -2a₁-c₁ and with a translation vector (0 0 −1/2). The two different [LiSO₄]⁻layers for each compound are shown in Fig. 4. For $[\alpha _{1}]$ -LAS, these layers are parallel to the planes (h00) and there are only one sulfate and one lithium ion in the asymmetric unit of each layer (labeled 1–1 and 1–2). Then the O13 and O24 atoms do not belong to the lithium tetrahedra, while two O14 atoms and two O23 atoms are connected to the Li2 and Li1 atoms, respectively, in each layer. This scheme of bonds leads sulfate tetrahedra with bonds from 1.456 (2) to 1.487 (2) Å and lithium tetrahedral coordination from 1.929 (5) to 1.976 (5) Å (see the CIF files in the supporting information). For $[\alpha _{2}]$ -LAS, these layers are parallel to the (00l) planes and there are two sulfate ions and two lithium ions in the asymmetric unit of each plane (labeled 2–1 and 2–2). The O23 and O34 atoms are not connected to the Li3 and Li4 atoms in the 2–1 layer and the O14 and O43 atoms do not belong to the Li1 and Li2 tetrahedra in the 2–2 layer; here there are no symmetry-related atoms in any tetrahedral coordination of the Li atoms. Now, the scheme of the bonds is more distorted, with bonds from 1.434 (3) to 1.527 (3) Å for sulfate tetrahedra and from 1.890 (8) to 2.066 (8) Å for lithium tetrahedral coordination (see the CIF files in the supporting information). For the structure proposed by Komornicka et al. (2014) there are two tetrahedra of sulfur and two of lithium, which are not related by symmetry in a unique layer, and the O atoms are connected similarly to each layer in the $[\alpha _{2}]$ -LAS structure.

Figure 4
Comparison of layers for the polytypes: $[\alpha _{{1}}]$ -LAS (upper), called layers 1–1 (left) and 1–2 (right) and $[\alpha _{{2}}]$ -LAS (bottom), called layers 2–1 (left) and 2–2 (right). There are a number of differences between the non-symmetric layers and between both compounds.

In Fig. 5, both stacking layers are shown, where the ammonium ions connect two consecutive layers. Here, only the N atoms from the ammonium ions are plotted. Note that for $[\alpha _{2}]$ -LAS, the periodicity along the direction [00l] is doubled with respect to the corresponding one for $[\alpha _{1}]$ -LAS. This is due to the translation of c/2 given by symmetry requirements (a glide plane perpendicular to the b axis).

Figure 5
View of the layered structure. For (a) $[\alpha _{{1}}]$ -LAS, the layers 1–1 and 1–2 are at the top and the middle of the unit cell. For (b) $[\alpha _{{2}}]$ -LAS, the layers 2–1 and 2–2 are at the top and just below the unit cell. The other layers are generated by symmetry.

In order to quantitatively compare both polytypes: $[\alpha _{1}]$ - and $[\alpha _{2}]$ -LAS, we have calculated the total distortion between them by using the AMPLIMODES computer program (Orobengoa et al., 2009). The distortion of $[\alpha _{2}]$ -LAS, with respect to $[\alpha _{1}]$ -LAS, can be decomposed into two symmetry modes, given by the irreducible representations GM1+ (at the center of the Brillouin zone) and Y2+ [at the point Δ(1/2, 0, 0) of the Brillouin zone]. The amplitude of the second mode is close to 2 Å longer than the first one (5.226 and 3.338 Å, respectively). This indicates that the crystal structure of $[\alpha _{2}]$ -LAS cannot be well described with the crystal structure of $[\alpha _{1}]$ -LAS. In general, the O-atom displacements are larger than those of the S, Li and N atoms and their contributions to the distortion are more important.

The obtained layered structures are consistent with other α-LAS polytypes and LiNH₄SeO₄ (LASe) found in the literature (Pietraszko & Lukaszewicz, 1992; Waśkowska & Allmann, 1982 ; Tomaszewski, 1992a) which were described in the orthorhombic space group Pbn2₁. Very recently, Komornicka et al. (2014) modeled possible structures for LiNH₄SO₄ leading the formation of different polytypes. They combine a different sequence of layers of A and B types, where each layer is composed of stripes (S+/S-) oriented in ferroelectric or antiferroelectric (AF) order. In particular, they determined a crystal structure in the space group Pca2₁ with a = 10.195 (2), b = 4.9967 (10) and c = 17.127 (3) Å, with layers containing AF domains. The A and B stacked layers are symmetrically related. None of our two structures are completely described with the proposed model, as we can see in Figs. 4 and 5. The $[\alpha _{1}]$ -LAS polytype has two different layers in the unit cell (layers 1–1 and 1–2) that are not related by symmetry. However, the domains of AF type, in each layer, are related by symmetry. The unit cell for the $[\alpha _{2}]$ -LAS polytype is formed by four layers related by symmetry in pairs (from the layers 2–1 and 2–2), but the domains of each layer are AF type and are not related by symmetry.

Lima et al. (2003 ) have characterized new crystals of the lithium sulfate family: the caesium lithium sulfate, Cs_1.15Li_2.85(SO₄)₂, and the caesium lithium rubidium sulfate, Cs_0.90Li_2.88Rb_0.22(SO₄)₂. These compounds are described and discussed in the context of the simple and double polymorphism. Authors associated the typical pseudo-hexagonal axes of double sulfates in the β-ferroelectric phase with the orthorhombic (or monoclinic) cells in the α-modification, where one of the axes of the α-modification corresponds, approximately, to that measured in double sulfates of the β-phase, but where the other axis is shorter. They explained this contraction was due to the low occupation of the heavy-ion sites (in this case, Rb and Cs), which was responsible for the new framework. Both, α and β, polymorphs are again compared in Fig. 6. The β-phases are clearly denser than the α-polytypes. The connectivity between structural groups is also different: the β-phases are built connecting all the vertices of the SO₄ and LiO₄ tetrahedra in a three-dimensional structure, while the α-phases are arranged as the layered structure described above. Moreover, we can see the same chains of combined SO₄ and LiO₄ tetrahedra placed parallel to the a and c axis, respectively. Note that the vertices are connected in two different ways: for the ferroelectric β-phase, the two connected chains are related by a glide plane (the plane of the figure) with a translation, which is parallel to the axes of both chains. For the $[\alpha _{2}]$ -phase, the two connected chains are related by a 2₁ screw axis, parallel to the b axis, and followed by a translation of c/2. Therefore, we have found a structural motif that leads to both polymorphs having a common crystallographic axis with the same (or multiple) length. Now we can explain some of the controversies between these two structural types: on one hand, similar space groups, and on the other, a common lattice parameter. As an example, the structure reported in the ICSD database (Belsky et al., 2002 ) for the NH₄LiSeO₄ is misclassified since it has been considered like the β-type (probably because both have the same space group). Furthermore, it would allow the coexistence of phases belonging to the α- and β-phases, due to an intergrowth from the common axis.

Figure 6
View of the structures of (a) the $[\alpha _{{2}}]$ -polytype and (b) the ferroelectric β-phase, showing different typologies. Chains of SO₄ and LiO₄ tetrahedra connected in different ways to form each structural type: α and β. Note that there is an axis with the same length or multiples thereof in both structures.

3.3. Structural stability of α-LAS

A deeper analysis was performed for doped ground crystals of the α-LAS habit with Yb 1.4 mol%, Yb 0.7 mol% and Er 0.6 mol% (nominal concentration), which were measured using XRD in the temperature cycle of 298 $[\rightarrow]$ 548 $[\rightarrow]$ 298 K.

Fig. 7 shows the diffractograms of a complete cycle for doped LAS Er³⁺ 0.6 mol% (nominal concentration) and the profile matching, where the well known ferroelectric β-LAS phase and any α-LAS polytypes are present. The presence of, at least, these two polymorphs can be visualized by the Bragg reflections. It was impossible to distinguish between $[\alpha _{1}]$ - and $[\alpha _{2}]$ -LAS structures. Both phases and other new different α-polytypes can coexist in the powder sample. We used $[\alpha _{1}]$ -LAS cell parameters to perform the refinements of peaks which did not belong to the ferroelectric β-LAS phase. Thus, we cannot strictly say that the $[\alpha _{1}]$ -LAS polytype was found for samples doped with Er³⁺.

Figure 7
Diffractograms of LAS Er 0.6 mol% powder samples measured on heating and cooling. Observed data are shown in black. As an example, at the bottom of the figure, the profile fit is shown by red lines and the difference between the observed and calculated profiles is plotted by blue lines. The green vertical bars represent the Bragg reflections. The upper group of reflections belongs to ferroelectric β-LAS and the lower ones to α-LAS Er 0.6 mol%. Two marked peaks are used for faster identification.

The results of the refinements provided the reliability factors: $[\chi^{{2}}]$ , R_B and R_wp, which varied from 1.5 to 2.4, from 0.7 to 1.8% and from 0.3 to 2.3%, respectively. Thermal dependence of the lattice parameters between 200 and 548 K are presented in Fig. 8 as well as the concentration of the mixture of α and β polytypes, which was calculated from the intensity of their two characteristic peaks at low angles (around ∼ 10.5 and ∼ 13.5°), given the theoretical intensities. On heating, the α-LAS Er 0.6 mol% polytype coexists (∼ 38%) with the ferroelectric β-LAS until 448 K (see Figs. 7 and 8). Above this temperature, the first characteristic peak disappears. This result was also found by Komornicka et al. (2014). Note that at 460 K the ferroelectric β-phase undergoes a transition to the paraelectric one. Then, at 484 K (from DSC) or 498 K (from XRD), from our data, the phase β-LAS must be paraelectric. In Fig. 8, the thermal dependence of the lattice parameters confirms, definitively, the α-LAS to paraelectric β-LAS phase transition. Moreover, the XRD cooling cycle, just like the previous DSC, reveals the irreversibility of the process; as it was expected.

Figure 8
Thermal dependence of the lattice parameters a, b, c, β angle, volume and concentration percent of α-LAS Yb 1.4 mol%. Data collected by single-crystal XRD, between 200 and 298 K, are indicated with empty symbols. Data collected by XRD in polycrystalline samples, between 298 and 548 K, are indicated with full symbols for α-phases and with half-full symbols for β-phases. The vertical dashed line indicates the ferro-paraelectric phase transition.

We did not perform low-temperature XRD measurements in polycrystalline samples because ytterbium(III) in doped samples can be reduced to ytterbium(II), during the cooling process, by using an Anton Paar TTK camera under vacuum. We observed changes in the diffractogram at lower temperatures but we did not investigate it. Therefore, diffraction data were measured for single crystals (doped LAS–Er 1.2 mol% and LAS–Yb 1.4 mol%, nominal values) with the α-habit, at different temperatures: 200, 240, 250, 260, 273 and 295 K. Reciprocal space images showed the existence of weak and diffuse reflections along c*, as described by Komornicka et al. (2014). Thus, diffraction data were not suitable to solve its crystal structure. However, we were interested in determining the thermal dependence of the lattice parameters. We refined the lattice parameters of $[\alpha _{1}]$ -LAS as an average structure of the α-modification. In the low-temperature range, the structure remains unchanged, i.e. we did not observe any phase transition, in particular at 250 K, as suggested in the literature (Połomska et al., 1994; Mel'nikova et al., 2003) nor at 283 K, where the ferroelastic–ferroelectric transition occurs. However, we observed a very slight anomaly in the thermal dependence of the a and c lattice parameters and the β angle, between 240 and 260 K (see Fig. 8, for the sample α-LAS Yb 1.4 mol%). The observed anomaly could be due to the coexistence of the α- and β-polymorphs, even for single crystals as it was shown for polycrystalline samples. As we have shown in the previous section, an intergrowth between different α- and β-polymorphs belonging to both phases is quite possible.

3.4. Comparative dielectric analysis of pure and doped LAS

In this section, we have performed a detailed study of the dielectric properties for doped and pure LAS single crystals with α-habit for the first time, in order to complete and confirm the results obtained by XRD and thermal analysis, at the same range of temperatures. A single crystal with β-habit was used as a reference material.

Below room temperature, the β-LAS crystal shows an abrupt change in $[\varepsilon _{r}^{\prime}]$ and $[\varepsilon _{r}^{\prime\prime}]$ , which takes place close to 290 K, with a pre-transition around 250 K (Figs. 9a and b). Other authors also comment on the existence of a pre-transition, especially Gaffar & El-Fadl (1999 ) and Połomska (2001). It was attributed to the existence of an order–disorder process that extends over a long range of temperatures. This temperature corresponds to the well-known ferroelastic–ferroelectric phase transition. The single crystals with the α-habit (pure α-LAS and α-LAS Yb 1.4 mol%) show a peak in $[\varepsilon _{r}^{\prime}]$ and $[\varepsilon _{r}^{\prime\prime}]$ at 273 K (see Figs. 9c–f). However, unlike Komornicka et al. (2014), we did not consider any phase transtion because the crystal structure remains with the space group P2₁/c and without changes in the crystal habit, in this range of temperatures. Then this anomaly in the dielectric properties can be due to the mentioned residual intergrowth between both polymorphous. Note that the temperature of this jump is close to the ferroelastic–ferroelectric phase transition. We have already observed slight anomalies in the thermal dependence of the lattice parameters and the DSC curves, in this range of temperatures. Moreover, the values of $[\varepsilon _{r}^{\prime}]$ and $[\varepsilon _{r}^{\prime\prime}]$ , associated with this peak for α-LAS Yb 1.4 mol% and pure α-LAS, are much smaller than the corresponding values for β-LAS.

Figure 9
Variation of $[\varepsilon _{r}^{\prime}]$ and $[\varepsilon _{r}^{\prime\prime}]$ with temperature at 5, 10 and 50 kHz, collected between 220 and 300 K, for (a), (b) β-LAS, (c), (d) α-LAS and (e), (f) α-LAS Yb 1.4 mol%.

Fig. 10 shows the temperature dependence of $[\varepsilon _{r}^{\prime}]$ and $[\varepsilon _{r}^{\prime\prime}]$ , at 10 kHz, during two heating–cooling cycles, for the pure α-LAS and α-LAS Yb 1.4 mol% single crystals. In the heating curves of the first cycle, any phase transition is observed until around 500 K, for both samples (Figs. 10a, b and e, f). It confirms that the α-phase is stable in the temperature range 298–500 K; also, it has been observed using DSC (Fig. 2) and XRD on polycrystalline samples (Fig. 5). The dielectric anomaly observed around 500 K indicates the beginning of the α $[\rightarrow]$ β phase transformation. We did not increase the temperature above 550 K because the decomposition of LAS is expected around this temperature. It is then possible the α $[\rightarrow]$ β phase transition was incomplete. In the heating curves of the second cycle (Figs. 10c, d and g, h), a similar behavior to that performed by the β-LAS crystal (reference sample, in Figs. 10i, j) can be seen, although it is much smoother. This dielectric behavior corresponds to the new β-phases transformed from pure α-LAS and α-LAS Yb 1.4 mol% ones, respectively. It is important to note that the reorder process occurs, in the first cooling (cycle 1), until 382 K, where a possible new phase transition is observed. Solans et al. (1999) found for the β-LAS a transformation, from the crystal structure at 318 K to the structure at 383 K, which consists of a rotation by 41° of the sulfate ions around an S—O bond. This may be the reason for the decrease of almost two orders of magnitude in the electrical conductivity between both temperatures. Thus, this result cannot be explained by a mixture of different components (α- and β-phases) as Tomaszewski (2000) suggests; at this stage, α-LAS polymorphs are precluded. At the end of the thermal experiment, all the samples: pure α-LAS and doped α-LAS with Er 0.6 mol%, Yb 0.7 mol% and Yb 1.4 mol% showed similar behavior and they were twinned crystals with the β-habit.

Figure 10
Variation of $[\varepsilon _{r}^{\prime}]$ and $[\varepsilon _{r}^{\prime\prime}]$ with temperature at 10 kHz, during two heating–cooling cycles (295 $[\rightarrow]$ 550 $[\rightarrow]$ 298 K) for (a), (b), (c), (d) α-LAS, (e), (f), (g), (h) α-LAS Yb 1.4 mol% and (i), (j) β-LAS crystals.

In Fig. 11 we show the frequency dependence of σ′ at different temperatures, on heating (cycle 1) for both α- and β-habits. These curves have been adjusted to equation (1). It is important to note that the experimental values of σ′ for the α-LAS polymorphs are very low between 200 and 496 K. Thus, only a few curves could be fitted to obtain the temperature dependence of $[\sigma _{\rm dc}]$ , $[\nu _{\rm p}]$ and s using equation (1). Above 500 K the increasing conductivity allowed us to fit all these parameters.

Figure 11
Frequency dependence of σ′ at several temperatures, corresponding to the first heating cycles (298 $[\rightarrow]$ 550 K) for α-LAS Yb 1.4 mol% (top) and β-LAS (bottom) single crystals. The solid lines are the conductivity fits given by equation (1)

The s parameter, from equation (1), is very sensitive to different physical processes that may occur in the material, such as phase transitions or decomposition. In particular, we obtained values of the s parameter distributed around 0.5 for pure α-LAS and around 0.8 for α-LAS Yb 1.4 mol%, which were decreasing below 550 K (Figs. 12a and b). Apparently, a phase transition occurs in both compounds, becoming the paraelectric phase of the β-polymorphs. On cooling, the samples presented a completely disordered state (s = 0) between approximately 500 and 400 K, then a reordering process started in the crystal until room temperature was reached (Figs. 12a and b). Initially, there are no substantial differences between pure and doped compounds with an α-habit. By contrast, in the case of β-LAS, the s parameter varied between 0.7 and 0.8, from 200 to 250 K (Fig. 12c). However, a significant disorder between 250 and 290 K is observed (s = 0), at the interval of temperatures where the ferroelastic–ferroelectric phase transition occurs. This range includes the pre-transition showed in the curve of the complex permittivity (Figs. 9a and b). During the existence of the ferroelectric phase, the process became ordered (s = 1) around 340 K. At higher temperatures s is close to 1 until the next phase transition. At the ferroelectric–paraelectric transition, a significant disorder (s = 0.6) is observed; after that, the s parameter took values around 0.8. On cooling, during the paraelectric–ferroelectric transition the values of s remained around 0.9 (Fig. 12c). When the crystal returned to the ferroelectric phase, s became 1 again.

Figure 12
Temperature dependence of the s parameter, measured between 190 and 550 K in cycle 1 (on heating by red stars and on cooling by blue squares) for pure (a) α-LAS, (b) α-LAS Yb 1.4 mol% and (c) β-LAS single crystals. Vertical lines indicate the temperature for the ferroelastic–ferroelectric (black line) and ferroelectric–paraelectric (olive line) phase transitions, approximately.

4. Conclusions

The synthesis of LAS doped with Er³⁺ and Yb³⁺ had led us to obtain single crystals of the α-modification at temperatures between 298 and 313 K, instead of the more favorable and denser ferroelectric β-phase. When the ionic radius of the rare earth decreases, the substitution of the ammonium ion favors the more open layered structure. In particular, when Yb³⁺ is partially substituted, two new crystal structures: $[\alpha _{{1}}]$ - and $[\alpha _{{2}}]$ -LAS, have been determined by X-ray diffraction of single crystals. Both structures belong to the space group P2₁/c and a displacive distortion has been calculated between them. Our two new structures show there are symmetry relations among layers and domains belonging to each layer, which are not completely described in the model proposed by Komornicka et al. (2014).

Moreover, we perform a comparative study between the $[\alpha _{{1}}]$ , $[\alpha _{{2}}]$ polytypes of the α-type and the paraelectric and ferroelectric phases of the β-type. Although there are no symmetry operations relating them, we found a common structural motif that results in one of the lattice parameters having the same magnitude or a multiple thereof in both phases. The slight anomaly in the thermal dependence of the lattice parameters and the dielectric permittivity between 220 and 260 K in single crystals can be related with an intergrowth from the common axis between both phases.

The thermal dependence of diffractograms for polycrystalline samples and dielectric permittivity for single crystals, including an analysis of the order–disorder parameter s, reveals that the α-polytypes undergo an irreversible and reconstructive phase transition around 500 K to the paraelectric β-phase. Doped samples of α-polytypes remain stable between 200 and about 500 K.

Therefore, in this work, we have succeeded in clarifying most of the controversy on the stability of the α-polytypes. We have given information that helps explain the nature of the α-polytypes (with two new structures) and the key for explaining the reconstructive α $[\rightarrow]$ β phase transition (through the common structural motif between both structural modifications). The enriched diversity of LiO₄ and SO₄ tetrahedra-based phases, built by chains, layers or three-dimensional connections, can serve for studies of the macroscopic symmetry lowering or/and changes in the [LiSO₄]⁻ framework dimensionality and their current applications, for instance, ferroic phases, nonlinear and transport properties (Hlinka et al., 2016; Mishra et al., 2013 ).

Supporting information

CCDC references: 1519626; 1530426

Crystal structure: contains datablocks alpha1_LAS, alpha2_LAS. DOI: https://doi.org/10.1107/S2052520616019028/yb5013sup1.cif

Structure factors: contains datablock alpha1_LAS. DOI: https://doi.org/10.1107/S2052520616019028/yb5013alpha1_LASsup2.fcf

Structure factors: contains datablock alpha2_LAS. DOI: https://doi.org/10.1107/S2052520616019028/yb5013alpha2_LASsup4.fcf

Structure factors: contains datablock . DOI: https://doi.org/10.1107/S2052520616019028/yb5013alpha1_LASsup3.hkl

Structure factors: contains datablock . DOI: https://doi.org/10.1107/S2052520616019028/yb5013alpha2_LASsup5.hkl

Computing details top

For both compounds, program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2014). Molecular graphics: Diamond 4.0 for alpha1_LAS.

(alpha1_LAS) top

Crystal data top

O₄SYb_0.005·0.984(H₄N)·Li	F(000) = 497
M_r = 121.54	D_x = 1.836 Mg m⁻³
Monoclinic, P2₁/c	Mo Kα radiation, λ = 0.71073 Å
a = 17.856 (8) Å	Cell parameters from 25 reflections
b = 5.008 (3) Å	θ = 9–21°
c = 10.264 (13) Å	µ = 0.73 mm⁻¹
β = 106.46 (5)°	T = 293 K
V = 880.2 (13) Å³	Prism, colourless
Z = 8	0.18 × 0.14 × 0.09 mm

Data collection top

ENRAF-NONIUS CAD4 diffractometer	θ_max = 30.0°, θ_min = 2.4°
ω/2Θ–scan	h = −25→0
4811 measured reflections	k = −7→7
2549 independent reflections	l = −13→14
2020 reflections with I > 2σ(I)	3 standard reflections every 120 min
R_int = 0.131	intensity decay: none

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.054	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.143	Only H-atom coordinates refined
S = 1.17	w = 1/[σ²(F_o²) + (0.0484P)² + 0.6832P] where P = (F_o² + 2F_c²)/3
2549 reflections	(Δ/σ)_max < 0.001
153 parameters	Δρ_max = 1.05 e Å⁻³
74 restraints	Δρ_min = −0.68 e Å⁻³

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.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2sigma(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
S1	0.40189 (3)	0.78809 (13)	0.35009 (6)	0.01614 (17)
O11	0.40752 (12)	0.7062 (5)	0.4897 (2)	0.0276 (5)
O12	0.41093 (12)	1.0821 (4)	0.3465 (2)	0.0309 (5)
O13	0.32607 (11)	0.7155 (5)	0.2583 (2)	0.0364 (6)
O14	0.46492 (11)	0.6618 (4)	0.3038 (2)	0.0240 (4)
S2	0.09813 (3)	0.28838 (12)	0.44726 (6)	0.01509 (16)
O21	0.09248 (11)	0.2049 (5)	0.58194 (19)	0.0265 (4)
O22	0.08937 (11)	0.5822 (4)	0.4341 (2)	0.0285 (5)
O23	0.03490 (10)	0.1605 (4)	0.33889 (18)	0.0220 (4)
O24	0.17400 (11)	0.2124 (5)	0.4303 (2)	0.0339 (5)
Yb1	0.33292 (13)	0.2738 (5)	0.0677 (3)	0.0311 (11)	0.0051 (12)
N1	0.33292 (13)	0.2738 (5)	0.0677 (3)	0.0311 (11)	0.985 (4)
H11	0.2772 (6)	0.290 (6)	0.031 (3)	0.047*	0.985 (4)
H12	0.3512 (16)	0.137 (5)	0.016 (3)	0.047*	0.985 (4)
H13	0.3573 (15)	0.439 (4)	0.055 (3)	0.047*	0.985 (4)
H14	0.3461 (17)	0.224 (6)	0.1612 (13)	0.047*	0.985 (4)
Yb2	0.16725 (13)	0.7751 (5)	0.2335 (3)	0.0306 (10)	0.0054 (12)
N2	0.16725 (13)	0.7751 (5)	0.2335 (3)	0.0306 (10)	0.984 (4)
H21	0.2230 (6)	0.773 (6)	0.255 (3)	0.046*	0.984 (4)
H22	0.1446 (16)	0.660 (5)	0.157 (2)	0.046*	0.984 (4)
H23	0.1509 (17)	0.713 (6)	0.310 (2)	0.046*	0.984 (4)
H24	0.1476 (16)	0.953 (3)	0.209 (3)	0.046*	0.984 (4)
Li1	0.0011 (2)	0.2967 (10)	0.1505 (5)	0.0202 (8)
Li2	0.5016 (2)	0.2965 (10)	0.3519 (5)	0.0226 (9)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
S1	0.0186 (3)	0.0195 (3)	0.0119 (3)	0.0004 (2)	0.00700 (19)	0.0006 (2)
O11	0.0352 (9)	0.0369 (12)	0.0142 (8)	0.0014 (8)	0.0125 (7)	0.0070 (10)
O12	0.0404 (10)	0.0197 (9)	0.0394 (13)	0.0025 (8)	0.0223 (9)	0.0033 (10)
O13	0.0224 (8)	0.0535 (15)	0.0296 (11)	−0.0027 (9)	0.0015 (7)	−0.0163 (12)
O14	0.0313 (8)	0.0232 (10)	0.0235 (9)	0.0072 (7)	0.0178 (7)	0.0024 (9)
S2	0.0180 (3)	0.0167 (3)	0.0109 (3)	−0.00004 (19)	0.00455 (18)	0.0003 (2)
O21	0.0346 (9)	0.0341 (11)	0.0116 (8)	−0.0002 (8)	0.0076 (7)	0.0051 (9)
O22	0.0368 (10)	0.0144 (9)	0.0292 (11)	−0.0016 (7)	0.0009 (8)	0.0019 (9)
O23	0.0282 (8)	0.0196 (9)	0.0152 (8)	−0.0050 (7)	0.0012 (6)	−0.0003 (8)
O24	0.0214 (8)	0.0491 (14)	0.0339 (12)	0.0053 (8)	0.0122 (8)	−0.0118 (11)
Yb1	0.0309 (14)	0.0371 (16)	0.0259 (15)	0.0004 (9)	0.0087 (8)	0.0005 (11)
N1	0.0309 (14)	0.0371 (16)	0.0259 (15)	0.0004 (9)	0.0087 (8)	0.0005 (11)
Yb2	0.0344 (14)	0.0325 (15)	0.0266 (15)	−0.0006 (9)	0.0113 (9)	−0.0024 (11)
N2	0.0344 (14)	0.0325 (15)	0.0266 (15)	−0.0006 (9)	0.0113 (9)	−0.0024 (11)
Li1	0.0261 (18)	0.021 (2)	0.0142 (19)	0.0014 (16)	0.0060 (15)	−0.0006 (19)
Li2	0.0269 (19)	0.023 (2)	0.020 (2)	0.0022 (17)	0.0094 (16)	0.004 (2)

Geometric parameters (Å, º) top

S1—O13	1.459 (2)	Yb1—Li2	3.551 (6)
S1—O11	1.466 (3)	Yb1—Li2^xi	3.707 (5)
S1—O14	1.482 (2)	Yb1—Li2ⁱ	3.858 (5)
S1—O12	1.483 (2)	Yb1—H11	0.962 (9)
S1—Li2	3.035 (5)	Yb1—H12	0.976 (9)
S1—Li2ⁱ	3.049 (5)	Yb1—H13	0.963 (9)
O11—Li2ⁱⁱ	1.945 (5)	Yb1—H14	0.954 (9)
O11—Yb1ⁱⁱⁱ	2.966 (4)	Yb2—O24^iv	2.958 (4)
O12—Li2^iv	1.930 (5)	Yb2—O21^ix	2.967 (4)
O12—Yb1^iv	2.965 (5)	Yb2—O22^x	3.077 (5)
O12—Yb1^v	3.067 (4)	Yb2—Li1^vii	3.534 (5)
O13—Yb2	2.791 (3)	Yb2—Li1	3.720 (5)
O13—Yb1	2.978 (4)	Yb2—Li1^iv	3.863 (5)
O14—Li2	1.958 (5)	Yb2—H21	0.957 (9)
O14—Li2ⁱ	1.976 (6)	Yb2—H22	0.968 (9)
S2—O24	1.464 (2)	Yb2—H23	0.963 (9)
S2—O21	1.475 (3)	Yb2—H24	0.966 (9)
S2—O22	1.482 (2)	Li1—O22^vi	1.929 (5)
S2—O23	1.487 (2)	Li1—O23^vii	1.945 (5)
S2—Li1^vi	3.033 (5)	Li1—O21^ix	1.952 (5)
S2—Li1	3.048 (6)	Li1—S2^vii	3.033 (5)
O21—Li1ⁱⁱⁱ	1.952 (5)	Li1—Li1^vi	3.238 (6)
O21—Yb2ⁱⁱⁱ	2.967 (4)	Li1—Li1^vii	3.238 (6)
O22—Li1^vii	1.929 (5)	Li1—Yb2^vi	3.534 (5)
O22—Yb2	2.955 (4)	Li1—Yb2^viii	3.863 (5)
O22—Yb2^v	3.077 (5)	Li2—O12^viii	1.930 (5)
O23—Li1^vi	1.945 (5)	Li2—O11ⁱⁱ	1.945 (5)
O23—Li1	1.976 (5)	Li2—O14^xi	1.976 (6)
O24—Yb1ⁱⁱⁱ	2.789 (3)	Li2—S1^xi	3.049 (5)
O24—Yb2^viii	2.958 (4)	Li2—Li2ⁱ	3.253 (7)
Yb1—O24^ix	2.789 (3)	Li2—Li2^xi	3.253 (7)
Yb1—O12^viii	2.965 (5)	Li2—Yb1ⁱ	3.707 (5)
Yb1—O11^ix	2.966 (4)	Li2—Yb1^xi	3.858 (5)
Yb1—O12^x	3.067 (4)

O13—S1—O11	110.81 (15)	O22^x—Yb2—Li1^iv	61.38 (10)
O13—S1—O14	109.66 (14)	Li1^vii—Yb2—Li1^iv	51.69 (10)
O11—S1—O14	110.26 (13)	Li1—Yb2—Li1^iv	82.64 (10)
O13—S1—O12	108.61 (14)	O13—Yb2—H21	9.4 (18)
O11—S1—O12	108.90 (14)	O22—Yb2—H21	120.3 (18)
O14—S1—O12	108.54 (13)	O24^iv—Yb2—H21	90.8 (18)
O13—S1—Li2	103.71 (14)	O21^ix—Yb2—H21	113.3 (18)
O11—S1—Li2	83.67 (14)	O22^x—Yb2—H21	112.0 (18)
O14—S1—Li2	32.67 (13)	Li1^vii—Yb2—H21	148.6 (18)
O12—S1—Li2	137.54 (13)	Li1—Yb2—H21	139.2 (18)
O13—S1—Li2ⁱ	99.45 (15)	Li1^iv—Yb2—H21	137.8 (18)
O11—S1—Li2ⁱ	140.63 (13)	O13—Yb2—H22	100.9 (18)
O14—S1—Li2ⁱ	32.93 (12)	O22—Yb2—H22	101.6 (19)
O12—S1—Li2ⁱ	83.28 (13)	O24^iv—Yb2—H22	157.5 (18)
Li2—S1—Li2ⁱ	64.64 (12)	O21^ix—Yb2—H22	21.2 (19)
S1—O11—Li2ⁱⁱ	128.97 (19)	O22^x—Yb2—H22	50.2 (19)
S1—O11—Yb1ⁱⁱⁱ	125.36 (13)	Li1^vii—Yb2—H22	95.3 (18)
Li2ⁱⁱ—O11—Yb1ⁱⁱⁱ	95.78 (17)	Li1—Yb2—H22	46.2 (18)
S1—O12—Li2^iv	130.39 (19)	Li1^iv—Yb2—H22	96.1 (18)
S1—O12—Yb1^iv	108.70 (13)	H21—Yb2—H22	110.3 (15)
Li2^iv—O12—Yb1^iv	90.47 (17)	O13—Yb2—H23	115.2 (18)
S1—O12—Yb1^v	98.04 (12)	O22—Yb2—H23	10.0 (18)
Li2^iv—O12—Yb1^v	113.64 (19)	O24^iv—Yb2—H23	69.4 (19)
Yb1^iv—O12—Yb1^v	116.77 (11)	O21^ix—Yb2—H23	88.2 (19)
S1—O13—Yb2	139.91 (15)	O22^x—Yb2—H23	137.1 (18)
S1—O13—Yb1	113.95 (13)	Li1^vii—Yb2—H23	41.6 (18)
Yb2—O13—Yb1	104.44 (10)	Li1—Yb2—H23	64.6 (18)
S1—O14—Li2	123.22 (19)	Li1^iv—Yb2—H23	90.4 (18)
S1—O14—Li2ⁱ	123.01 (19)	H21—Yb2—H23	110.4 (15)
Li2—O14—Li2ⁱ	111.50 (19)	H22—Yb2—H23	108.4 (15)
O24—S2—O21	110.42 (14)	O13—Yb2—H24	114.0 (17)
O24—S2—O22	108.95 (14)	O22—Yb2—H24	106.0 (18)
O21—S2—O22	109.47 (14)	O24^iv—Yb2—H24	55.6 (18)
O24—S2—O23	109.34 (14)	O21^ix—Yb2—H24	122.4 (18)
O21—S2—O23	109.88 (14)	O22^x—Yb2—H24	59.8 (18)
O22—S2—O23	108.75 (12)	Li1^vii—Yb2—H24	77.2 (18)
O24—S2—Li1^vi	102.87 (14)	Li1—Yb2—H24	109.1 (17)
O21—S2—Li1^vi	83.77 (14)	Li1^iv—Yb2—H24	28.1 (17)
O22—S2—Li1^vi	137.68 (12)	H21—Yb2—H24	110.2 (15)
O23—S2—Li1^vi	32.26 (12)	H22—Yb2—H24	107.5 (14)
O24—S2—Li1	99.68 (14)	H23—Yb2—H24	109.9 (15)
O21—S2—Li1	140.35 (13)	O22^vi—Li1—O23^vii	107.4 (2)
O22—S2—Li1	83.12 (12)	O22^vi—Li1—O21^ix	120.9 (3)
O23—S2—Li1	33.07 (12)	O23^vii—Li1—O21^ix	110.3 (2)
Li1^vi—S2—Li1	64.34 (11)	O22^vi—Li1—O23	103.5 (2)
S2—O21—Li1ⁱⁱⁱ	128.71 (17)	O23^vii—Li1—O23	106.4 (2)
S2—O21—Yb2ⁱⁱⁱ	125.53 (13)	O21^ix—Li1—O23	107.2 (2)
Li1ⁱⁱⁱ—O21—Yb2ⁱⁱⁱ	96.06 (17)	O22^vi—Li1—S2^vii	88.12 (16)
S2—O22—Li1^vii	130.33 (18)	O23^vii—Li1—S2^vii	24.07 (8)
S2—O22—Yb2	109.24 (13)	O21^ix—Li1—S2^vii	110.7 (2)
Li1^vii—O22—Yb2	90.18 (17)	O23—Li1—S2^vii	126.3 (2)
S2—O22—Yb2^v	97.69 (11)	O22^vi—Li1—S2	127.5 (2)
Li1^vii—O22—Yb2^v	113.85 (18)	O23^vii—Li1—S2	93.46 (17)
Yb2—O22—Yb2^v	116.82 (11)	O21^ix—Li1—S2	93.64 (17)
S2—O23—Li1^vi	123.67 (17)	O23—Li1—S2	24.23 (9)
S2—O23—Li1	122.70 (19)	S2^vii—Li1—S2	117.07 (15)
Li1^vi—O23—Li1	111.31 (18)	O22^vi—Li1—Li1^vi	72.28 (16)
S2—O24—Yb1ⁱⁱⁱ	140.94 (15)	O23^vii—Li1—Li1^vi	128.8 (3)
S2—O24—Yb2^viii	114.43 (13)	O21^ix—Li1—Li1^vi	112.6 (2)
Yb1ⁱⁱⁱ—O24—Yb2^viii	101.68 (10)	O23—Li1—Li1^vi	34.03 (16)
O24^ix—Yb1—O12^viii	128.95 (12)	S2^vii—Li1—Li1^vi	136.6 (2)
O24^ix—Yb1—O11^ix	110.73 (11)	S2—Li1—Li1^vi	57.61 (16)
O12^viii—Yb1—O11^ix	82.76 (10)	O22^vi—Li1—Li1^vii	123.8 (3)
O24^ix—Yb1—O13	95.07 (11)	O23^vii—Li1—Li1^vii	34.65 (7)
O12^viii—Yb1—O13	72.67 (11)	O21^ix—Li1—Li1^vii	113.0 (2)
O11^ix—Yb1—O13	152.18 (10)	O23—Li1—Li1^vii	72.8 (2)
O24^ix—Yb1—O12^x	103.30 (12)	S2^vii—Li1—Li1^vii	58.05 (10)
O12^viii—Yb1—O12^x	127.07 (12)	S2—Li1—Li1^vii	59.03 (16)
O11^ix—Yb1—O12^x	70.00 (9)	Li1^vi—Li1—Li1^vii	101.3 (3)
O13—Yb1—O12^x	115.03 (12)	O22^vi—Li1—Yb2^vi	56.74 (15)
O24^ix—Yb1—Li2	156.80 (13)	O23^vii—Li1—Yb2^vi	71.59 (15)
O12^viii—Yb1—Li2	32.93 (10)	O21^ix—Li1—Yb2^vi	177.6 (2)
O11^ix—Yb1—Li2	84.64 (11)	O23—Li1—Yb2^vi	73.35 (16)
O13—Yb1—Li2	67.66 (11)	S2^vii—Li1—Yb2^vi	70.35 (10)
O12^x—Yb1—Li2	98.22 (13)	S2—Li1—Yb2^vi	87.72 (14)
O24^ix—Yb1—Li2^xi	139.57 (13)	Li1^vi—Li1—Yb2^vi	66.48 (17)
O12^viii—Yb1—Li2^xi	56.60 (10)	Li1^vii—Li1—Yb2^vi	69.41 (17)
O11^ix—Yb1—Li2^xi	31.46 (9)	O22^vi—Li1—Yb2	166.7 (2)
O13—Yb1—Li2^xi	120.74 (12)	O23^vii—Li1—Yb2	68.81 (14)
O12^x—Yb1—Li2^xi	79.39 (11)	O21^ix—Li1—Yb2	52.48 (13)
Li2—Yb1—Li2^xi	53.19 (11)	O23—Li1—Yb2	89.73 (16)
O24^ix—Yb1—Li2ⁱ	134.36 (13)	S2^vii—Li1—Yb2	84.61 (13)
O12^viii—Yb1—Li2ⁱ	83.77 (11)	S2—Li1—Yb2	65.74 (10)
O11^ix—Yb1—Li2ⁱ	103.43 (11)	Li1^vi—Li1—Yb2	120.3 (2)
O13—Yb1—Li2ⁱ	61.78 (10)	Li1^vii—Li1—Yb2	60.57 (12)
O12^x—Yb1—Li2ⁱ	61.16 (11)	Yb2^vi—Li1—Yb2	129.94 (15)
Li2—Yb1—Li2ⁱ	51.88 (10)	O22^vi—Li1—Yb2^viii	102.44 (19)
Li2^xi—Yb1—Li2ⁱ	82.88 (10)	O23^vii—Li1—Yb2^viii	150.02 (19)
O24^ix—Yb1—H11	7.4 (18)	O21^ix—Li1—Yb2^viii	53.72 (13)
O12^viii—Yb1—H11	124.0 (17)	O23—Li1—Yb2^viii	63.13 (14)
O11^ix—Yb1—H11	117.0 (18)	S2^vii—Li1—Yb2^viii	164.14 (16)
O13—Yb1—H11	88.1 (18)	S2—Li1—Yb2^viii	65.58 (9)
O12^x—Yb1—H11	108.8 (17)	Li1^vi—Li1—Yb2^viii	58.90 (12)
Li2—Yb1—H11	149.7 (18)	Li1^vii—Li1—Yb2^viii	122.0 (2)
Li2^xi—Yb1—H11	144.2 (18)	Yb2^vi—Li1—Yb2^viii	125.35 (15)
Li2ⁱ—Yb1—H11	132.1 (18)	Yb2—Li1—Yb2^viii	82.64 (10)
O24^ix—Yb1—H12	101.1 (17)	O12^viii—Li2—O11ⁱⁱ	120.9 (3)
O12^viii—Yb1—H12	99.1 (18)	O12^viii—Li2—O14	107.1 (2)
O11^ix—Yb1—H12	16.4 (18)	O11ⁱⁱ—Li2—O14	111.0 (3)
O13—Yb1—H12	163.5 (17)	O12^viii—Li2—O14^xi	103.3 (2)
O12^x—Yb1—H12	58.1 (19)	O11ⁱⁱ—Li2—O14^xi	107.5 (2)
Li2—Yb1—H12	97.6 (17)	O14—Li2—O14^xi	105.7 (2)
Li2^xi—Yb1—H12	45.7 (18)	O12^viii—Li2—S1	88.02 (17)
Li2ⁱ—Yb1—H12	103.8 (18)	O11ⁱⁱ—Li2—S1	111.1 (2)
H11—Yb1—H12	108.1 (14)	O14—Li2—S1	24.11 (9)
O24^ix—Yb1—H13	110.1 (17)	O14^xi—Li2—S1	125.7 (2)
O12^viii—Yb1—H13	107.7 (18)	O12^viii—Li2—S1^xi	127.2 (2)
O11^ix—Yb1—H13	114.0 (18)	O11ⁱⁱ—Li2—S1^xi	94.00 (19)
O13—Yb1—H13	63.5 (18)	O14—Li2—S1^xi	93.13 (19)
O12^x—Yb1—H13	51.6 (18)	O14^xi—Li2—S1^xi	24.06 (9)
Li2—Yb1—H13	76.9 (18)	S1—Li2—S1^xi	116.79 (16)
Li2^xi—Yb1—H13	102.9 (17)	O12^viii—Li2—Li2ⁱ	123.2 (3)
Li2ⁱ—Yb1—H13	25.4 (17)	O11ⁱⁱ—Li2—Li2ⁱ	113.7 (2)
H11—Yb1—H13	109.2 (15)	O14—Li2—Li2ⁱ	34.43 (7)
H12—Yb1—H13	107.2 (14)	O14^xi—Li2—Li2ⁱ	72.4 (2)
O24^ix—Yb1—H14	116.2 (18)	S1—Li2—Li2ⁱ	57.88 (9)
O12^viii—Yb1—H14	14.1 (18)	S1^xi—Li2—Li2ⁱ	58.92 (17)
O11^ix—Yb1—H14	93.3 (19)	O12^viii—Li2—Li2^xi	72.04 (16)
O13—Yb1—H14	65.1 (19)	O11ⁱⁱ—Li2—Li2^xi	113.0 (2)
O12^x—Yb1—H14	140.5 (18)	O14—Li2—Li2^xi	127.8 (3)
Li2—Yb1—H14	43.3 (18)	O14^xi—Li2—Li2^xi	34.07 (17)
Li2^xi—Yb1—H14	69.7 (18)	S1—Li2—Li2^xi	135.8 (2)
Li2ⁱ—Yb1—H14	90.4 (18)	S1^xi—Li2—Li2^xi	57.48 (17)
H11—Yb1—H14	110.7 (15)	Li2ⁱ—Li2—Li2^xi	100.7 (3)
H12—Yb1—H14	109.7 (15)	O12^viii—Li2—Yb1	56.60 (14)
H13—Yb1—H14	111.8 (15)	O11ⁱⁱ—Li2—Yb1	177.4 (2)
O13—Yb2—O22	124.64 (12)	O14—Li2—Yb1	71.20 (14)
O13—Yb2—O24^iv	99.98 (10)	O14^xi—Li2—Yb1	72.88 (17)
O22—Yb2—O24^iv	72.69 (10)	S1—Li2—Yb1	70.22 (10)
O13—Yb2—O21^ix	104.82 (11)	S1^xi—Li2—Yb1	87.27 (15)
O22—Yb2—O21^ix	82.52 (10)	Li2ⁱ—Li2—Yb1	68.93 (17)
O24^iv—Yb2—O21^ix	152.00 (11)	Li2^xi—Li2—Yb1	65.86 (17)
O13—Yb2—O22^x	106.02 (11)	O12^viii—Li2—Yb1ⁱ	166.9 (2)
O22—Yb2—O22^x	127.10 (12)	O11ⁱⁱ—Li2—Yb1ⁱ	52.76 (14)
O24^iv—Yb2—O22^x	115.42 (12)	O14—Li2—Yb1ⁱ	69.04 (15)
O21^ix—Yb2—O22^x	69.85 (9)	O14^xi—Li2—Yb1ⁱ	89.74 (17)
O13—Yb2—Li1^vii	155.77 (13)	S1—Li2—Yb1ⁱ	84.70 (13)
O22—Yb2—Li1^vii	33.09 (9)	S1^xi—Li2—Yb1ⁱ	65.90 (11)
O24^iv—Yb2—Li1^vii	67.76 (10)	Li2ⁱ—Li2—Yb1ⁱ	60.94 (13)
O21^ix—Yb2—Li1^vii	84.38 (11)	Li2^xi—Li2—Yb1ⁱ	120.5 (2)
O22^x—Yb2—Li1^vii	98.18 (12)	Yb1—Li2—Yb1ⁱ	129.83 (15)
O13—Yb2—Li1	132.54 (13)	O12^viii—Li2—Yb1^xi	102.3 (2)
O22—Yb2—Li1	56.40 (10)	O11ⁱⁱ—Li2—Yb1^xi	53.79 (14)
O24^iv—Yb2—Li1	120.57 (11)	O14—Li2—Yb1^xi	150.3 (2)
O21^ix—Yb2—Li1	31.46 (9)	O14^xi—Li2—Yb1^xi	63.41 (15)
O22^x—Yb2—Li1	79.36 (10)	S1—Li2—Yb1^xi	164.60 (16)
Li1^vii—Yb2—Li1	52.95 (10)	S1^xi—Li2—Yb1^xi	65.78 (10)
O13—Yb2—Li1^iv	142.16 (13)	Li2ⁱ—Li2—Yb1^xi	122.2 (2)
O22—Yb2—Li1^iv	83.74 (10)	Li2^xi—Li2—Yb1^xi	59.19 (12)
O24^iv—Yb2—Li1^iv	61.97 (10)	Yb1—Li2—Yb1^xi	125.02 (16)
O21^ix—Yb2—Li1^iv	103.22 (11)	Yb1ⁱ—Li2—Yb1^xi	82.88 (10)

Symmetry codes: (i) −x+1, y+1/2, −z+1/2; (ii) −x+1, −y+1, −z+1; (iii) x, −y+1/2, z+1/2; (iv) x, y+1, z; (v) x, −y+3/2, z+1/2; (vi) −x, y−1/2, −z+1/2; (vii) −x, y+1/2, −z+1/2; (viii) x, y−1, z; (ix) x, −y+1/2, z−1/2; (x) x, −y+3/2, z−1/2; (xi) −x+1, y−1/2, −z+1/2.

(alpha2_LAS) top

Crystal data top

O₄SYb_0.013·0.961(H₄N)·Li	F(000) = 1000.0
M_r = 122.51	D_x = 1.831 Mg m⁻³
Monoclinic, P2₁/c	Mo Kα radiation, λ = 0.71073 Å
a = 10.177 (15) Å	Cell parameters from 25 reflections
b = 5.106 (4) Å	θ = 9–19°
c = 34.234 (16) Å	µ = 0.89 mm⁻¹
β = 90.2 (1)°	T = 293 K
V = 1779 (3) Å³	Prism, colourless
Z = 16	0.17 × 0.11 × 0.09 mm

Data collection top

ENRAF-Nonius CAD4 diffractometer	θ_max = 30.0°, θ_min = 2.0°
ω/2Θ–scan	h = −14→14
9573 measured reflections	k = −7→7
5071 independent reflections	l = −48→0
3231 reflections with I > 2σ(I)	3 standard reflections every 120 min
R_int = 0.068

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.060	Hydrogen site location: notdet
wR(F²) = 0.163	H-atom parameters not defined
S = 1.20	w = 1/[σ²(F_o²) + (0.0263P)² + 6.4506P] where P = (F_o² + 2F_c²)/3
5071 reflections	(Δ/σ)_max < 0.001
256 parameters	Δρ_max = 1.89 e Å⁻³
0 restraints	Δρ_min = −1.04 e Å⁻³

Special details top

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
S1	0.64805 (7)	0.73307 (14)	0.20089 (2)	0.00608 (14)
O11	0.6399 (4)	0.4374 (5)	0.20610 (11)	0.0406 (9)
O12	0.7859 (3)	0.8058 (10)	0.20413 (11)	0.0521 (12)
O13	0.5709 (3)	0.8568 (6)	0.23235 (9)	0.0274 (7)
O14	0.5950 (4)	0.7924 (10)	0.16305 (10)	0.0566 (13)
S2	0.89820 (8)	0.28368 (18)	0.04920 (3)	0.01657 (19)
O21	0.8934 (3)	0.5828 (6)	0.04414 (10)	0.0324 (8)
O22	1.0370 (3)	0.2110 (6)	0.04620 (9)	0.0298 (7)
O23	0.8456 (3)	0.2180 (7)	0.08669 (9)	0.0368 (8)
O24	0.8213 (3)	0.1630 (6)	0.01798 (9)	0.0280 (7)
S3	0.39959 (8)	0.21622 (18)	0.04902 (3)	0.01718 (19)
O31	0.5355 (3)	0.2891 (6)	0.04630 (10)	0.0304 (7)
O32	0.3211 (3)	0.3371 (6)	0.01735 (9)	0.0273 (7)
O33	0.3916 (3)	−0.0811 (6)	0.04468 (10)	0.0330 (8)
O34	0.3434 (3)	0.2813 (7)	0.08748 (9)	0.0324 (7)
S4	0.14878 (11)	0.8032 (3)	0.20093 (4)	0.0364 (3)
O41	0.1414 (3)	1.1054 (7)	0.20461 (9)	0.0314 (7)
O42	0.2864 (2)	0.7278 (5)	0.20357 (8)	0.0211 (5)
O43	0.0927 (3)	0.7312 (6)	0.16299 (9)	0.0272 (6)
O44	0.0714 (3)	0.6850 (7)	0.23248 (9)	0.0292 (7)
N1	0.4006 (3)	0.2369 (6)	0.16624 (10)	0.0417 (11)	0.907 (4)
N2	0.6508 (3)	0.7697 (7)	0.08377 (10)	0.0364 (13)	0.959 (4)
N3	0.1517 (3)	0.7309 (7)	0.08326 (11)	0.0331 (14)	0.978 (4)
N4	0.9005 (4)	0.2744 (9)	0.16666 (12)	0.0381 (10)
Yb1	0.4006 (3)	0.2369 (6)	0.16624 (10)	0.0417 (11)	0.0311 (15)
Yb2	0.6508 (3)	0.7697 (7)	0.08377 (10)	0.0364 (13)	0.0137 (15)
Yb3	0.1517 (3)	0.7309 (7)	0.08326 (11)	0.0331 (14)	0.0074 (14)
Li1	0.3992 (7)	0.7198 (14)	0.2497 (2)	0.0237 (14)
Li2	0.1017 (7)	0.3041 (15)	0.2508 (2)	0.0278 (16)
Li3	0.1488 (7)	0.2123 (13)	0.0001 (2)	0.0218 (14)
Li4	0.6491 (6)	0.2976 (12)	0.0013 (2)	0.0190 (13)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
S1	0.0035 (3)	0.0084 (3)	0.0063 (3)	−0.0004 (3)	−0.0014 (2)	−0.0003 (3)
O11	0.065 (2)	0.0118 (13)	0.045 (2)	−0.0014 (14)	0.0142 (18)	−0.0014 (13)
O12	0.0098 (13)	0.114 (4)	0.0322 (19)	−0.0037 (18)	0.0014 (12)	−0.005 (2)
O13	0.0287 (15)	0.0257 (14)	0.0279 (17)	−0.0020 (12)	0.0078 (13)	−0.0013 (12)
O14	0.0377 (19)	0.122 (4)	0.0099 (14)	0.016 (2)	−0.0061 (13)	0.001 (2)
S2	0.0104 (3)	0.0249 (4)	0.0144 (4)	0.0028 (3)	−0.0027 (3)	−0.0003 (3)
O21	0.0384 (18)	0.0255 (14)	0.0332 (19)	0.0041 (13)	−0.0138 (14)	−0.0020 (13)
O22	0.0117 (11)	0.051 (2)	0.0270 (16)	0.0109 (12)	−0.0030 (11)	−0.0023 (14)
O23	0.0348 (17)	0.060 (2)	0.0155 (14)	−0.0126 (16)	0.0031 (12)	−0.0080 (15)
O24	0.0218 (14)	0.0364 (16)	0.0257 (17)	0.0053 (12)	−0.0079 (12)	−0.0079 (13)
S3	0.0114 (3)	0.0266 (5)	0.0135 (4)	0.0016 (3)	−0.0026 (3)	−0.0019 (3)
O31	0.0112 (11)	0.0487 (19)	0.0313 (17)	−0.0048 (12)	−0.0051 (11)	−0.0013 (14)
O32	0.0209 (14)	0.0369 (15)	0.0238 (16)	0.0019 (12)	−0.0116 (12)	0.0060 (13)
O33	0.0323 (17)	0.0259 (15)	0.041 (2)	−0.0004 (12)	−0.0165 (15)	0.0033 (14)
O34	0.0259 (14)	0.0484 (19)	0.0230 (15)	0.0146 (14)	0.0050 (12)	−0.0002 (14)
S4	0.0179 (4)	0.0704 (9)	0.0209 (5)	−0.0018 (5)	0.0000 (4)	−0.0005 (6)
O41	0.0173 (13)	0.057 (2)	0.0205 (15)	0.0063 (14)	0.0055 (11)	0.0008 (15)
O42	0.0074 (10)	0.0309 (14)	0.0249 (14)	0.0036 (10)	−0.0002 (9)	−0.0053 (12)
O43	0.0234 (13)	0.0381 (16)	0.0200 (14)	−0.0162 (13)	−0.0093 (11)	−0.0002 (13)
O44	0.0111 (12)	0.056 (2)	0.0207 (15)	0.0053 (12)	0.0038 (11)	0.0073 (13)
N1	0.0405 (18)	0.0413 (17)	0.0432 (19)	−0.0032 (13)	−0.0030 (12)	−0.0037 (14)
N2	0.034 (2)	0.043 (2)	0.032 (2)	0.0015 (15)	0.0024 (13)	−0.0043 (15)
N3	0.0247 (18)	0.043 (2)	0.032 (2)	−0.0003 (15)	−0.0039 (13)	−0.0048 (16)
N4	0.0216 (16)	0.067 (3)	0.0252 (19)	−0.0026 (19)	−0.0052 (14)	0.002 (2)
Yb1	0.0405 (18)	0.0413 (17)	0.0432 (19)	−0.0032 (13)	−0.0030 (12)	−0.0037 (14)
Yb2	0.034 (2)	0.043 (2)	0.032 (2)	0.0015 (15)	0.0024 (13)	−0.0043 (15)
Yb3	0.0247 (18)	0.043 (2)	0.032 (2)	−0.0003 (15)	−0.0039 (13)	−0.0048 (16)
Li1	0.019 (3)	0.034 (4)	0.018 (3)	−0.001 (3)	0.004 (2)	0.002 (3)
Li2	0.018 (3)	0.040 (4)	0.025 (4)	0.003 (3)	−0.006 (3)	0.000 (3)
Li3	0.024 (3)	0.021 (3)	0.021 (3)	0.002 (2)	−0.002 (3)	−0.006 (3)
Li4	0.011 (3)	0.023 (3)	0.023 (3)	0.000 (2)	−0.002 (2)	−0.006 (2)

Geometric parameters (Å, º) top

S1—O14	1.434 (3)	S4—O43	1.464 (3)
S1—O12	1.455 (4)	S4—O44	1.469 (3)
S1—O13	1.477 (3)	S4—O41	1.550 (4)
S1—O11	1.522 (3)	S4—Li2^ix	3.043 (9)
S1—Li1	3.040 (8)	O41—Li2ⁱⁱⁱ	1.922 (9)
S1—Li1ⁱ	3.045 (7)	O41—Yb1ⁱⁱⁱ	3.027 (6)
O11—Li1ⁱⁱ	1.920 (8)	O42—Li1	1.950 (8)
O12—Li2ⁱ	1.918 (8)	O44—Li2^ix	1.951 (8)
O13—Li1ⁱ	1.976 (8)	O44—Li2	2.066 (8)
O13—Li1	1.976 (8)	Li1—O11ⁱ	1.920 (8)
O14—Yb1ⁱⁱⁱ	3.013 (6)	Li1—O13ⁱⁱ	1.976 (8)
S2—O23	1.432 (3)	Li1—S1ⁱⁱ	3.045 (7)
S2—O24	1.459 (3)	Li1—Li1ⁱⁱ	3.275 (9)
S2—O22	1.464 (3)	Li1—Li1ⁱ	3.275 (9)
S2—O21	1.538 (3)	Li1—Yb1ⁱ	3.520 (8)
S2—Li4	3.016 (7)	Li1—Yb1ⁱⁱⁱ	3.891 (8)
O21—Li3^iv	1.890 (8)	Li2—O12ⁱⁱ	1.918 (8)
O21—Yb3^v	3.042 (6)	Li2—O41^vii	1.922 (9)
O22—Li3^v	1.948 (8)	Li2—O44^x	1.951 (8)
O22—Yb3^vi	2.996 (5)	Li2—S4^x	3.043 (9)
O23—Yb2^vii	3.030 (5)	Li2—Li2^ix	3.287 (9)
O24—Li4	1.966 (7)	Li2—Li2^x	3.287 (9)
O24—Li3^viii	2.037 (7)	Li3—O21^iv	1.890 (8)
S3—O31	1.436 (3)	Li3—O22^xi	1.948 (8)
S3—O34	1.475 (3)	Li3—O24^viii	2.037 (7)
S3—O32	1.479 (3)	Li3—Li4^iv	3.239 (9)
S3—O33	1.527 (3)	Li3—Li4^viii	3.319 (9)
S3—Li3	3.047 (8)	Li3—Yb2^iv	3.530 (9)
O31—Li4	1.930 (8)	Li3—Yb3^vii	3.760 (8)
O32—Li3	1.954 (8)	Li4—O33^viii	1.966 (7)
O32—Li4^iv	1.995 (7)	Li4—O32^iv	1.995 (7)
O33—Li4^viii	1.966 (7)	Li4—Li3^iv	3.239 (9)
O33—Yb3^vii	2.941 (6)	Li4—Li3^viii	3.319 (9)
O33—Yb2^vii	3.050 (6)	Li4—Yb3^iv	3.542 (9)
S4—O42	1.455 (3)	Li4—Yb2^vii	3.904 (8)

O14—S1—O12	112.0 (2)	O13ⁱⁱ—Li1—Yb1ⁱ	71.4 (2)
O14—S1—O13	111.7 (2)	O13—Li1—Yb1ⁱ	74.2 (2)
O12—S1—O13	110.5 (2)	S1—Li1—Yb1ⁱ	88.2 (2)
O14—S1—O11	107.2 (3)	S1ⁱⁱ—Li1—Yb1ⁱ	70.03 (16)
O12—S1—O11	107.3 (3)	Li1ⁱⁱ—Li1—Yb1ⁱ	69.8 (3)
O13—S1—O11	108.0 (2)	Li1ⁱ—Li1—Yb1ⁱ	67.4 (3)
O14—S1—Li1	101.0 (2)	O11ⁱ—Li1—Yb1ⁱⁱⁱ	100.8 (3)
O12—S1—Li1	140.2 (2)	O42—Li1—Yb1ⁱⁱⁱ	52.7 (2)
O13—S1—Li1	33.14 (19)	O13ⁱⁱ—Li1—Yb1ⁱⁱⁱ	149.8 (3)
O11—S1—Li1	82.4 (2)	O13—Li1—Yb1ⁱⁱⁱ	62.2 (2)
O14—S1—Li1ⁱ	105.6 (2)	S1—Li1—Yb1ⁱⁱⁱ	64.90 (15)
O12—S1—Li1ⁱ	84.5 (2)	S1ⁱⁱ—Li1—Yb1ⁱⁱⁱ	164.3 (2)
O13—S1—Li1ⁱ	32.91 (18)	Li1ⁱⁱ—Li1—Yb1ⁱⁱⁱ	122.0 (3)
O11—S1—Li1ⁱ	137.4 (2)	Li1ⁱ—Li1—Yb1ⁱⁱⁱ	58.09 (19)
Li1—S1—Li1ⁱ	65.12 (16)	Yb1ⁱ—Li1—Yb1ⁱⁱⁱ	125.4 (2)
S1—O11—Li1ⁱⁱ	132.7 (3)	O12ⁱⁱ—Li2—O41^vii	122.5 (4)
S1—O12—Li2ⁱ	129.2 (3)	O12ⁱⁱ—Li2—O44^x	107.6 (4)
S1—O13—Li1ⁱ	123.1 (3)	O41^vii—Li2—O44^x	105.6 (4)
S1—O13—Li1	122.7 (3)	O12ⁱⁱ—Li2—O44	109.1 (4)
Li1ⁱ—O13—Li1	112.0 (3)	O41^vii—Li2—O44	106.2 (4)
S1—O14—Yb1ⁱⁱⁱ	111.8 (2)	O44^x—Li2—O44	104.4 (3)
O23—S2—O24	110.9 (2)	O12ⁱⁱ—Li2—S4^x	93.5 (3)
O23—S2—O22	111.5 (2)	O41^vii—Li2—S4^x	128.7 (3)
O24—S2—O22	110.9 (2)	O44^x—Li2—S4^x	23.27 (15)
O23—S2—O21	108.8 (2)	O44—Li2—S4^x	92.4 (3)
O24—S2—O21	108.67 (18)	O12ⁱⁱ—Li2—Li2^ix	112.5 (4)
O22—S2—O21	105.90 (19)	O41^vii—Li2—Li2^ix	122.1 (4)
O23—S2—Li4	100.2 (2)	O44^x—Li2—Li2^ix	71.2 (4)
O24—S2—Li4	33.25 (17)	O44—Li2—Li2^ix	33.96 (10)
O22—S2—Li4	140.99 (19)	S4^x—Li2—Li2^ix	58.8 (3)
O21—S2—Li4	83.62 (17)	O12ⁱⁱ—Li2—Li2^x	113.0 (4)
S2—O21—Li3^iv	130.3 (3)	O41^vii—Li2—Li2^x	73.2 (3)
S2—O21—Yb3^v	99.80 (16)	O44^x—Li2—Li2^x	36.3 (3)
Li3^iv—O21—Yb3^v	114.2 (3)	O44—Li2—Li2^x	129.3 (4)
S2—O22—Li3^v	128.5 (3)	S4^x—Li2—Li2^x	58.6 (3)
S2—O22—Yb3^vi	123.5 (2)	Li2^ix—Li2—Li2^x	101.9 (4)
Li3^v—O22—Yb3^vi	96.8 (2)	O21^iv—Li3—O22^xi	121.3 (4)
S2—O23—Yb2^vii	113.19 (18)	O21^iv—Li3—O32	105.2 (4)
S2—O24—Li4	122.7 (3)	O22^xi—Li3—O32	106.4 (4)
S2—O24—Li3^viii	122.7 (3)	O21^iv—Li3—O24^viii	108.1 (3)
Li4—O24—Li3^viii	112.0 (3)	O22^xi—Li3—O24^viii	109.4 (4)
O31—S3—O34	112.1 (2)	O32—Li3—O24^viii	105.3 (3)
O31—S3—O32	111.2 (2)	O21^iv—Li3—S3	128.6 (3)
O34—S3—O32	110.49 (19)	O22^xi—Li3—S3	92.6 (3)
O31—S3—O33	107.58 (19)	O32—Li3—S3	23.58 (14)
O34—S3—O33	106.9 (2)	O24^viii—Li3—S3	92.7 (2)
O32—S3—O33	108.37 (18)	O21^iv—Li3—Li4^iv	72.7 (3)
O31—S3—Li3	140.5 (2)	O22^xi—Li3—Li4^iv	112.8 (3)
O34—S3—Li3	99.5 (2)	O32—Li3—Li4^iv	35.30 (19)
O32—S3—Li3	31.90 (19)	O24^viii—Li3—Li4^iv	128.8 (3)
O33—S3—Li3	84.04 (17)	S3—Li3—Li4^iv	58.17 (16)
S3—O31—Li4	129.6 (3)	O21^iv—Li3—Li4^viii	124.2 (3)
S3—O32—Li3	124.5 (3)	O22^xi—Li3—Li4^viii	111.9 (3)
S3—O32—Li4^iv	122.8 (3)	O32—Li3—Li4^viii	72.8 (2)
Li3—O32—Li4^iv	110.2 (3)	O24^viii—Li3—Li4^viii	33.33 (19)
S3—O33—Li4^viii	130.4 (3)	S3—Li3—Li4^viii	59.68 (16)
S3—O33—Yb3^vii	108.95 (19)	Li4^iv—Li3—Li4^viii	102.3 (2)
Li4^viii—O33—Yb3^vii	90.2 (2)	O21^iv—Li3—Yb2^iv	57.5 (2)
S3—O33—Yb2^vii	99.22 (15)	O22^xi—Li3—Yb2^iv	178.6 (3)
Li4^viii—O33—Yb2^vii	113.0 (2)	O32—Li3—Yb2^iv	73.5 (3)
Yb3^vii—O33—Yb2^vii	116.06 (16)	O24^viii—Li3—Yb2^iv	71.9 (2)
O42—S4—O43	111.2 (2)	S3—Li3—Yb2^iv	87.8 (2)
O42—S4—O44	111.4 (2)	Li4^iv—Li3—Yb2^iv	66.37 (18)
O43—S4—O44	109.9 (2)	Li4^viii—Li3—Yb2^iv	69.43 (18)
O42—S4—O41	107.78 (18)	O21^iv—Li3—Yb3^vii	165.9 (3)
O43—S4—O41	107.7 (2)	O22^xi—Li3—Yb3^vii	52.3 (2)
O44—S4—O41	108.9 (2)	O32—Li3—Yb3^vii	88.9 (3)
O42—S4—Li2^ix	140.8 (2)	O24^viii—Li3—Yb3^vii	67.3 (2)
O43—S4—Li2^ix	99.1 (2)	S3—Li3—Yb3^vii	65.44 (15)
O44—S4—Li2^ix	31.65 (19)	Li4^iv—Li3—Yb3^vii	120.9 (2)
O41—S4—Li2^ix	85.04 (19)	Li4^viii—Li3—Yb3^vii	59.66 (18)
S4—O41—Li2ⁱⁱⁱ	127.1 (3)	Yb2^iv—Li3—Yb3^vii	129.0 (2)
S4—O41—Yb1ⁱⁱⁱ	98.23 (15)	O31—Li4—O33^viii	120.1 (3)
Li2ⁱⁱⁱ—O41—Yb1ⁱⁱⁱ	115.2 (3)	O31—Li4—O24	107.2 (4)
S4—O42—Li1	128.3 (3)	O33^viii—Li4—O24	102.8 (3)
S4—O44—Li2^ix	125.1 (3)	O31—Li4—O32^iv	111.6 (3)
S4—O44—Li2	122.0 (3)	O33^viii—Li4—O32^iv	107.6 (4)
Li2^ix—O44—Li2	109.8 (3)	O24—Li4—O32^iv	106.5 (3)
O11ⁱ—Li1—O42	120.2 (4)	O31—Li4—S2	94.0 (3)
O11ⁱ—Li1—O13ⁱⁱ	109.3 (4)	O33^viii—Li4—S2	126.6 (3)
O42—Li1—O13ⁱⁱ	111.2 (4)	O24—Li4—S2	24.01 (13)
O11ⁱ—Li1—O13	102.6 (4)	O32^iv—Li4—S2	93.9 (2)
O42—Li1—O13	105.5 (4)	O31—Li4—Li3^iv	114.3 (3)
O13ⁱⁱ—Li1—O13	106.9 (3)	O33^viii—Li4—Li3^iv	123.7 (3)
O11ⁱ—Li1—S1	126.6 (3)	O24—Li4—Li3^iv	73.1 (2)
O42—Li1—S1	92.5 (3)	O32^iv—Li4—Li3^iv	34.47 (19)
O13ⁱⁱ—Li1—S1	93.7 (3)	S2—Li4—Li3^iv	59.59 (16)
O13—Li1—S1	24.12 (14)	O31—Li4—Li3^viii	111.5 (3)
O11ⁱ—Li1—S1ⁱⁱ	90.1 (3)	O33^viii—Li4—Li3^viii	71.1 (2)
O42—Li1—S1ⁱⁱ	111.9 (3)	O24—Li4—Li3^viii	34.71 (18)
O13ⁱⁱ—Li1—S1ⁱⁱ	23.96 (13)	O32^iv—Li4—Li3^viii	129.3 (3)
O13—Li1—S1ⁱⁱ	126.7 (3)	S2—Li4—Li3^viii	57.96 (15)
S1—Li1—S1ⁱⁱ	117.2 (2)	Li3^iv—Li4—Li3^viii	102.3 (2)
O11ⁱ—Li1—Li1ⁱⁱ	125.3 (4)	O31—Li4—Yb3^iv	175.9 (3)
O42—Li1—Li1ⁱⁱ	112.8 (4)	O33^viii—Li4—Yb3^iv	56.1 (2)
O13ⁱⁱ—Li1—Li1ⁱⁱ	34.03 (11)	O24—Li4—Yb3^iv	73.2 (2)
O13—Li1—Li1ⁱⁱ	73.9 (3)	O32^iv—Li4—Yb3^iv	71.9 (2)
S1—Li1—Li1ⁱⁱ	59.8 (2)	S2—Li4—Yb3^iv	87.77 (18)
S1ⁱⁱ—Li1—Li1ⁱⁱ	57.36 (15)	Li3^iv—Li4—Yb3^iv	69.78 (18)
O11ⁱ—Li1—Li1ⁱ	71.1 (2)	Li3^viii—Li4—Yb3^iv	66.38 (18)
O42—Li1—Li1ⁱ	110.8 (3)	O31—Li4—Yb2^vii	53.7 (2)
O13ⁱⁱ—Li1—Li1ⁱ	129.3 (4)	O33^viii—Li4—Yb2^vii	101.0 (3)
O13—Li1—Li1ⁱ	34.0 (2)	O24—Li4—Yb2^vii	63.0 (2)
S1—Li1—Li1ⁱ	57.5 (2)	O32^iv—Li4—Yb2^vii	151.2 (3)
S1ⁱⁱ—Li1—Li1ⁱ	137.1 (4)	S2—Li4—Yb2^vii	65.70 (15)
Li1ⁱⁱ—Li1—Li1ⁱ	102.4 (4)	Li3^iv—Li4—Yb2^vii	122.9 (2)
O11ⁱ—Li1—Yb1ⁱ	57.5 (2)	Li3^viii—Li4—Yb2^vii	57.83 (17)
O42—Li1—Yb1ⁱ	177.3 (3)	Yb3^iv—Li4—Yb2^vii	124.17 (19)

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

Acknowledgements

With this work we want to pay tribute to our teacher, colleague and friend Xavier Solans, who died in the course of this research. We acknowledge the financial support of Ministerio de Economía y Competitividad (MAT2013-43319-P) from Spain and Servicios Generales de Apoyo a la Investigación (SEGAI) from Universidad de La Laguna (Spain). The authors are very grateful to Dr Emilio Matesanz from CAI Difracción de Rayos X de la Universidad Complutense de Madrid (Spain) and Dr Tomasz Breczewski from Departamento de Física Aplicada II de la Universidad del País Vasco (Spain) and Dr Juan Rodríguez-Carvajal from Institut Laue–Langevin (Grenoble, France) for their invaluable help.

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