Unmasking the Mechanism of Structural Para- to Ferroelectric Phase

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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Unmasking the Mechanism of Structural Para- to Ferroelectric Phase Transition in (NH4)2SO4 Leszek M. Malec, Marlena Gryl, and Katarzyna M. Stadnicka* Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Krakow, Poland S Supporting Information *

ABSTRACT: New nontoxic and biocompatible ferroelectric materials are a subject undergoing intense study. One of the most promising research branches is focused on H-bonded organic or hybrid ferroelectrics. The engineering of these materials is based on mimicking the phase transition mechanisms of the well-known inorganic ferroelectrics. In our study, a coupled experimental and theoretical methodology was used for a precise investigation of the ferroelectric phase transition mechanism in ammonium sulfate (AS). A series of single-crystal X-ray diffraction measurements were performed in the temperature range between 273 and 163 K. The detailed inspection of the obtained static structural data, in the abovementioned temperature range, allowed us to reveal dynamical effects at the ferroelectric phase transition. Accurate analysis of all geometrical features within the obtained crystal structures was carried out. The results were discussed in the view of previously discovered physical properties. X-ray studies were complemented by the use of quantum theory of atoms in molecules calculations and Hirshfeld surface analysis. Valence shell charge concentration analysis allowed us to find the subtle changes between charge density distribution within SO42− in para- and ferroelectric phases. H-bond interactions, geometrically classified in both AS phases, were all confirmed by the appropriate critical points. The interaction energies were estimated for the structures at 273, 233, 213, 183, and 163 K. Correlation between the geometrical approach and the results of theoretical calculations enabled us to discover the differences in interaction equilibrium between the AS phases. The mechanism of the phase transition originates from the disruption of the vibrational lattice mode between sulfate anions. Our studies resolved the problem, which was under discussion for more than 60 years.

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INTRODUCTION The development of new ferroelectric materials, since their scientific rebirth provided by the discovery of ferroelectric properties of potassium dihydrogen phosphate (KDP) and BaTiO3,1 continues to be an important challenge for chemists and physicists. This is because of their possible application as a new generation of electromechanical and optical devices,2 especially the ferroelectric random access memory (FeRAM) and ferroelectric field-effect transistors (FeFET).3 A new approach to this experimental branch dominated by perovskite type materials was introduced by the discovery of organic4,5 and hybrid organic−inorganic6,7 ferroelectrics with promising magnitudes of spontaneous polarization and dielectric constant. The core of recent material design is based on inventing new strategies of their engineering8−10 complemented by theoretical calculations11−13 which provide information about the source of the spontaneous polarization. The most promising materials are those in which changes in the hydrogen-bond system are crucial for the appearance of ferroelectric properties. The Hbond-based approach was introduced to the organic ferroelectric crystal engineering as a way of mimicking the phase transition mechanism in KDP.8 Results obtained with this method lead to the conclusion that an exact mechanism of the © XXXX American Chemical Society

phase transition in the hydrogen bonded ferroelectrics can be a fundamental step for synthesis of new inorganic−organic or organic ferroelectrics. Moreover, it was shown that the abovementioned ferroelectrics can exhibit properties at least comparable to those of perovskites.5,14 Nowadays, the KDP family of ferroelectrics is still growing.15 Modern, precise experimental and theoretical methods provide answers to the distinct changes in their crystal structures upon the phase transition.16−18 In our work, we are revisiting ammonium sulfate (AS), for which the mechanism of the ferroelectric phase transition, despite many surveys, was not well understood until now. AS undergoes paraelectric (PE) to ferroelectric (FE) phase transition19 (PT), at Tc = 223 K, from centrosymmetric space group Pnam to polar Pna21, losing the center of symmetry and the mirror plane. The asymmetric unit contains one sulfate anion and two symmetrically nonequivalent ammonium cations, as was observed in the neutron diffraction experiment.20 The unit cell in both phases contains four formula units. Atypical dependence of the spontaneous polarization (Ps) Received: December 15, 2017

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DOI: 10.1021/acs.inorgchem.7b03161 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Lattice parameters and unit cell volume thermal evolution. Tc is marked with the black dashed line. The series in brown represent data published by Hoshino et al.23

and coinciding internal distortions in SO42−. As an effect, the softening of asymmetric stretching and bending modes should be observed. However, to date, the softening of the aforementioned modes has not been experimentally proven.28,35 The most recent explanation of the AS phase transition involves the relaxation of motions of the asymmetric unit [NH4+(I)−SO42−−NH4+(II)] between two possible orientations.36−38 The phase transition was suggested to be induced by the reduction of NH4+(I) motions, which through the stabilization of SO42− librations results in the relaxation of NH4+(II) hindered rotations.38 Although the phase transition in AS was established from the variety of theoretical and experimental studies, its dynamics and the nature of the emerging Ps needs further examination. In our studies a new experimental approach was introduced to the examination of ferroelectrics. It has been based on a series of X-ray diffraction measurements complemented by quantum theory of atoms in molecules (QTAIM)39 calculations and the Hirshfeld surface analysis.40 The compilation of exact sampling of AS structures with modern theoretical methods allows us to obtain a very precise image of differences between the interactions present in both crystal phases.

versus temperature (T) distinguishes AS from the other known H-bonded ferroelectrics. After reaching its maximum (Ps ≈ 0.6 μC/cm2) just below Tc, Ps continuously shrinks and changes its sign at T ≈ 84.5 K.21,22 Sawada et al.22 have also shown that substitution of the ammonium cations with potassium shifts Tc and the maximum of Ps to lower temperatures. Moreover, when the concentration of K+ ions in the structure exceeds 70%, the phase transition vanishes. As was found by Hoshino et al.,23 AS exhibits a ca. 4 kV/cm coercive field which monotonically increases inversely proportional to T, starting from 10 K below the PT. Furthermore, AS exhibits significant alterations in elastic compliance coefficients24 at Tc and the evolution of unit cell volume and lattice parameters as a function of temperature.23 Because most of the aforementioned features do not coincide with those of the well-known proper ferroelectrics, numerous approaches were proposed to clarify the thermodynamics and the mechanism of the PT. From the neutron diffraction experiment it was found that in the FE phase six moderate H-bonds can be observed instead of only the two present in the PE phase.20 However, the reorganization of the H-bond system was excluded as a possible dragging force of the transition,25,26 because of its gradual character being a result of alterations of ion vibrations.27,28 NMR27,29 and ESR30 studies have shown that both symmetrically nonequivalent ammonium ions experience greater distortions from the ideal tetrahedron in FE than in the PE phase. Moreover, the suggested tilt of cations below Tc by 30° about an a axis out of the mirror plane resulted in emergence of coupled oscillator−relaxator31 and ferrielectric32 models. Both of them concern the PT as the ordering of the ammonium ions, which would experience hindered rotations between two potential minima in the PE phase. Another approach considering alterations in the sulfate ion geometry as crucial for the mechanism of the PT arises from IR and Raman spectroscopy studies.26,33 Simultaneous decrease in the frequency of symmetric stretching bands and the tilt of the anion libration axis34 were ascribed to the freezing of librations

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EXPERIMENTAL SECTION

Single-Crystal X-ray Diffraction. The diffraction measurements were carried out for AS crystals obtained by the recrystallization from an aqueous solution by a slow evaporation at ambient conditions. Diffraction data for the structural analysis were collected for the single crystal with an Agilent Technologies SuperNova diffractometer,41 equipped with an Atlas CCD area detector (resolution 10.3756) and a low-temperature Cryo-Jet device, using a mirror monochromated Mo Kα radiation (50 kV, 0.8 mA). The general strategy of the experiment was preserved for all measurements (complete data with the redundant index of 5.0; detector distance, 73.30 mm; scan width, 1.00 degree; integration time, 1.0 s/deg). The multiscan absorption correction was applied.41 A number of consecutive diffraction measurements at different temperatures was carried out in a cooling manner with a T interval equal to 10 K. The entire experiment was performed on one B

DOI: 10.1021/acs.inorgchem.7b03161 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 2. Thermal evolution of sulfate anion S1−O bond lengths (left panel) and valence angles ∠O−S1−O (right panel). Tc is marked with the black dashed line. single-crystal and consisted of 11 independent diffraction measurements. The first five of them were conducted above Tc [from 273(1) to 233(1) K (Table S1)], and another six were conducted below Tc [from 213(1) to 163(1) K (Table S2)]. Before each measurement, the crystal was cooled slightly below the predefined temperature because of the cooling system stabilization lag. The structures solved by SIR9242 from diffraction data at 298 and 148 K43 were taken as initial models for the refinement in PE and FE phases, respectively. Refinement of structural parameters including anisotropic displacement parameters for all non-H atoms was performed with SHELXL Version 2013/1444 (nonlinear full-matrix least-squares methods based on F2 values against all unique reflections). The results of refinement for the PE phase at 273 K were used as a structural model (non-hydrogen atoms only) for 263 K and so on until 233 K to preserve the same reference system. The results of refinement for the FE phase at 163 K were used as a structural model for 173 K and so on until 213 K. All hydrogen atoms were found from Fourier difference maps and were included in the refinement procedure using riding model and assuming isotropic displacement parameters. Molecular graphics have been prepared with Mercury software.45 All programs mentioned above were used under the WinGX package.46 The appropriate CIF-files were deposited with CCDC (1586261−1586271).

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THEORETICAL SECTION

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RESULTS AND DISCUSSION

(Figure 1) were preserved with respect to the previous backreflection study.23 However, some differences between the ranges of parameter values are mainly caused by the specific investigation methods applied in both cases. The Cu Kα singlecrystal back-reflection technique derives unit cell parameters from only a few high-angle reflections. In contrast, in each of our diffraction studies, more than 3000 reflections where used for such calculations. The measured lattice parameters decrease monotonically with crystal cooling in the PE phase, except the parameter a undergoing a steep jump to higher values at Tc. For the unit cell volume after the systematic contraction until the PT, a sharp increase in value is observed. Below Tc, the rise of V is maintained until 183 K and corresponds to the behavior of the parameter a. At lower temperatures, V follows the behavior of parameters b and c. The observed complicated characters of a and V versus T indicates the appearance of the relaxation process in the AS structure after the PT. Furthermore, possible structure transformations below Tc can also be indicated by the fluctuations in b values in the FE phase (Figure 1). Geometrical Parameters Analysis. The thermal evolution of bond lengths and valence angles for SO42− (Table S3) is plotted in Figure 2. All S1−O bond lengths in both phases are typical of those of other sulfate anions involved in H-bonds (1.473(13) Å).51 In the PE phase, S1−O bond lengths are almost equal to each other with respect to the measurement uncertainties and remain approximately constant within the entire phase. The bonds fit to the range between the shortest 1.464(2) Å (S1−O1) and the longest 1.469(2) Å (S1−O2) distances, just before the PT at 233 K. In the FE phase, only S1−O1 bond length is preserved, whereas S1−O2, S1−O3, and S1−O4 are slightly elongated. The described bond-length changes appear predominantly in the region until 30 K below Tc. The valence angles in the sulfate anion are temperature-independent within the entire PE phase (Figure 2, right panel). Four angles are below and two are above the typical value of the tetrahedron. In the FE phase, ∠O3−S1−O4 (between the oxygen atoms which were related by the mirror plane in the PE phase) noticeably decreases.

The QTAIM39 and fingerprint plot analysis40 was undertaken to determine relative differences in the sulfate ions in two phases: FE at 163 K and PE at 273 K. Ab initio calculations were performed for clusters formed by taking the nearest (5.5 Å radius) environment of central sulfur atom S1 in a sulfate ion. Geometries for wavefunction calculations were taken from the two sets of experimental data representing the FE phase (at 163 K) and the centrosymmetric PE phase (at 273 K). The calculations of wavefunctions were performed with Gaussian0947 at the DFT B3LYP48,49/6-311G** level of theory. The QTAIM analysis was conducted with AIMAll software.50

Single-Crystal Structure Analysis. The obtained lattice parameters and the unit cell volume as a function of temperature (Tables S1 and S2) are shown in Figure 1 in comparison with the results of Hoshino et al.23 In general, the variations of lattice parameters and unit cell volume (V) with T C

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Figure 3. Temperature dependence of O1···O (left panel) and O2···O (right panel) closest intermolecular distances. Tc is marked with the black dashed line.

Simultaneously, related angles ∠O1−S1−O3 and ∠O1−S1− O4 increase by ca. 0.5(1)°. At the same time all valence angles formed with S1−O2 bond remain almost constant. In the FE phase, only little fluctuations in the angle values are observed, mostly appearing until 193 K. The observed changes result in almost equal values for ∠O1−S1−O2 and ∠O1−S1−O4 as well as for ∠O2−S1−O3 and ∠O3−S1−O4 angle pairs at 163 K (Figure 2, right panel). The overall change in the sulfate anion geometry during the PT can be considered as the deformation of the pseudotetrahedron (Cm symmetry, PE phase) toward the trigonal pyramid (FE phase). Such a phenomenon in AS sulfate anions was first suggested from IR and Raman studies, however, it was never measured quantitatively.26,28 Further estimation of the anion distortion was performed by the continuous shape measurements (CShM) with SHAPE software.52,53 For AS sulfate anions in both phases the tetrahedron shape was evidently indicated by the method. Subsequent computations of the distortion allowed the evaluation of the deviation of SO42− toward the trigonal pyramid. The calculated deformation from the tetrahedron shape of sulfate anions in both AS phases does not exceed 1.5%. The distortion has dynamical character and appears suddenly at the closest vicinity of the PT. Subsequent relaxation of atoms is almost immediate as only slight further changes in the anion geometrical parameters are observed until 193 K. The above results indicate the participation of sulfate anions in the mechanism of the AS structural transformation. However, the influence of the internal changes within SO42− ion geometry at the PT should not be overestimated. The temperature dependences of O···O distances between separate SO42− anions were depicted in Figure 3 (see also, Figure S1 and Table S4). The distances were characterized for oxygen atoms within the 5 Å sphere of enclosure for each of the SO42− oxygen atoms. All measurement uncertainties are smaller than the size of the graphical representations of the data series. Within the PE phase, thermal fluctuations of all O···O distances are less than ca. 0.020 Å. The O2 atom has the most compact surroundings, consisting of six oxygen atoms in distances within a 3.70−4.10 Å range in the investigated temperature scope of both phases (Figure 3, right panel). The

environment of the O4 atom is more complex and is assembled from eight contacts within the 3.48−4.60 Å range in the PE phase (Figure S1, right panel). During the PT, the most significant changes are observed for O1···O4 distances (ca. 0.419(2) Å). Further crystal cooling induces the additional enlargement of the distance up to 0.557(2) Å at 163 K (Figures 3 and S1). Simultaneously O1···O3 distances change less significantly (ca. 0.197(2) Å). Additional enlargement of O1··· O3 below Tc is subtle (ca. 0.032(2) Å). The above-mentioned geometrical changes influence the O1 environment, which in the PE phase consists of four pairs of symmetrically equivalent oxygen atoms (Figure 3, left panel). In the FE phase only two distances, O1···O1 and O1···O2, remain almost equal, while O1···O3/4 change significantly. The resulting changes observed in the surroundings of O1 and O3 across the PT cause their resemblance in the FE phase (compare left panels of Figures 3 and S1). O2 atom is involved in the smallest number of contacts, within the assumed environment. Additionally, none of these contacts are formed with the symmetrically equivalent oxygen atom from another SO42− ion. The O4 atom surroundings become more compact in the FE phase with the majority of O···O distances within the 3.7−4.2 Å range. Only the O4···O4 distance is significantly elongated to 4.852(2) Å at 163 K. As in the case of the O1 and O3 pair, the O2 and O4 environments are similar (compare right panels of Figures 3 and S1). The changes of O···O geometrical features allow the description of a considerable dynamical effect related to the AS phase transition. It should be emphasized that the relative distances between the sulfate ions in the AS structure are constant, within the entire temperature range. These structural features indicate that during the PT the mutual reorientation of the sulfate ions occurs as an effect of ca. 10° hindered rotation of SO42− about a resultant axis close to the S1−O2 direction (combined rotation about the a and b crystallographic axes). This complicated transformation could be described as the synchronous rotations of the anion about a and b axes emerging as the precession about the S1−O2 direction. The most pronounced effect of the phenomena is the mutual approach of the sulfate anions related by the a-glide plane. As a D

DOI: 10.1021/acs.inorgchem.7b03161 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 4. AS structure in paraelectric (273 K) and ferroelectric (163 K) phases. The atoms are color coded: sulfate, yellow; nitrogen, purple; oxygen, red; hydrogen, white. HBs and WIs are marked as blue lines.

Figure 5. Hydrogen bond length vs T for H-bonds formed by NH4+(I) (left) and NH4+(II) (right) cations. Tc is marked with the vertical black dashed line. Assumed geometrical criterion for H-bond formation is depicted by horizontal black dashed line.

boundary conditions that indicate H-bond existence. Within such classification, all HBs present in the AS structures can be treated as moderate or weak H-bonds (MHB and WHB, respectively).54 HBs which have H···A shorter than ca. 2.15 Å and ∠DHA greater than or equal to 160° were ascribed to the MHB group. H-bonds which do not fit to the former group and have H···A shorter than 2.40 Å and ∠DHA greater than or equal to 130° were classified as WHBs. The additional rating was introduced for such N−H···O interactions that do not fit to either of the above classes. Contacts, which have either H···A slightly longer than 2.40 Å or ∠DHA a little less than 130° were termed very weak H-bonds (VWHBs). Other considered contacts which simultaneously violate both VWHB restrictions to a certain extent (e.g., H···A lower than 2.60 Å and ∠DHA

result, the significant shortening of O3···O1 to ca. 3.282(2) Å at 213 K is enforced (left panels of Figure 3 and S1). With further crystal cooling to 163 K, the O1, O3, and O4 atoms are reoriented because of the relaxation of SO42−. Hydrogen Bond Analysis. The structures of the AS phases contain highly complicated hydrogen bond (HB) systems formed by numerous N−H···O interactions. The distinct HB systems in the PE (273 K) and FE (163 K) phases are illustrated in Figure 4. Thermally induced changes in the geometry of HBs between the PE and FE phases are visualized in Figures 5, S2, and S3 following the appropriate numerical data in Table S5. The geometrical criteria assumed for the HB length and the DHA angle (donor−hydrogen···acceptor angle) define the E

DOI: 10.1021/acs.inorgchem.7b03161 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. Classification of H-Bonds Formed by Each Acceptor (A) in Both Phases PE phase

FE phase

A

HB type

H-bonds

HB type

O1 O1 O1 O1

MHB WHB VWHB WI

N1−H11···O1 − N2−H23···O1; N2−H24···O1 −

MHB WHB VWHB WI

N2−H23···O1 N1−H11···O1 − −

H-bonds

O2 O2 O2 O2

MHB WHB VWHB WI

N2−H21···O2 N1−H13···O2; N1−H14···O2 − N2−H22···O2

MHB WHB VWHB WI

N2−H21···O2; N1−H14···O2 − N2−H22···O2 −

O3 O3 O3 O3

MHB WHB VWHB WI

N2−H23···O3 N1−H14···O3 N2−H22···O3 N1−H12···O3

MHB WHB VWHB WI

N1−H12···O3 N1−H11···O3 − N2−H23···O3; N2−H22···O3

O4 O4 O4 O4

MHB WHB VWHB WI

N2−H24···O4 N1−H13···O4 N2−H22···O4 N1−H12···O4

MHB WHB VWHB WI

N2−H24···O4; N1−H13···O4 − − N2−H22···O4

stabilized by the linear N2−H21···O2 competing with trifurcated HB in the (001) plane. A symmetry change at Tc follows the distortion of both above-mentioned interactions. As a result, only a small relative NH4+(II) cation displacement from the (001) plane is observed below the PT. Changes within the Connectivity of HB Acceptors. The earlier discussed pronounced thermal evolution of SO42− indicates the major role of O-acceptors within the AS hydrogen bond system reorganization. The lack of interaction equivalence is observed between the acceptors (Table 1). The O1 atom in the PE phase is involved in only one N1−H11···O1 MHB and in two symmetrically equivalent VWHB with NH4+(II) cations. O3 atom and its mirror related analogue O4 are involved in one interaction of each class with the dominating N2−H23/24··· O3/4 MHBs, respectively. Finally, the O2 atom is involved in two WHBs and participates in one WI and in the strongest HB in the PE phase (N2−H21···O2). Before the PT in the PE phase, the largest discrepancy is observed between the interactions of O1 and O2 atoms situated in the mirror plane. Across the PT, moderate N2−H21···O2 is maintained and another MHB (N1−H14···O2) is formed. N1−H14···O2 is created because of the geometry change of only one from the symmetrically related WHBs observed before the PT. As a result, in the FE phase, the O2 atom is the acceptor of two MHBs and one WI (Table 1, right side). An acceptor environment similar to that of O2 was found for the O4 atom in the FE phase. The enforcement of N1−H13···O4 to the MHB class results from the vanishing of the bifurcated WHB (N1−H13−O2/O4). Additionally, in the FE phase, the strongest linear N2−H24···O4 is formed. In contrast to the above-mentioned acceptors, for O1 and O3 atoms, the new surroundings, which in both cases consist of one MHB and one WHB, were observed below Tc (Table 1, right panel). In the O1 environment, the angle distortion as well as the H···A elongation move N1−H11···O1 to the WHB class. Simultaneously, the split of bifurcated N2−H23−O1/O3 leads to the creation of N2−H23···O1 MHB in the FE phase. The O3 atom environment is the one most influenced by the PT. The HB system reorganization results in the loss of MHB,

greater than or equal to 110°), were treated as weak interactions (WIs). In the PE phase, each of the symmetrically nonequivalent cations is involved in a significantly different HB subsystem. NH4+(II) cocreates three MHBs (right panels of Figures 5, S2, and S3), while NH4+(I) forms only one MHB interaction (left panel). Therefore, the cation (I), less constrained by HBs, must undergo more pronounced vibrations in the high-temperature phase. At the PT, almost all geometries of 12 HBs and 3 WIs observed within the PE phase are noticeably changed. Cooling the AS crystal across Tc causes a significant distortion of 6 HBs, while 3 new HBs are formed. As a result, in the FE phase only 9 HBs and 3 WIs are observed. In addition, the difference between NH4+(I) and NH4+(II) HB subsystems disappears. Although in the FE phase fewer HBs are observed, they are significantly stronger.54 Therefore, in the low-temperature phase, each of the NH4+ ions forms 3 almost linear MHBs, which in the case of NH4+(I) are complemented with 2 WHBs. Changes within the Connectivity of HB Donors. The unchanged cation positions in conjunction with the relaxation mechanism of numerous HBs allowed the corroboration of the dynamical feature of the PT already pointed out by the NMR time relaxation studies.29 The change of geometrical parameters of all HBs formed by NH4+(I) is a result of its 30° rotation about the a axis across the PT. The rotation axis does not overlap with any of the N1−H bonds. The pronounced changes of H···A lengths (Figure 5, left panel) range from 0.21(2) Å for N1−H11···O1 to 0.51(2) Å for N1−H11···O3. In the latter case, such significant effect is caused by the superposition of NH4+(I) rotation and the postulated earlier SO42− anion precession about the resultant axis. The same phenomenon induces the change about 0.37(2) Å in the H···A length of N1− H12···O3. With further crystal cooling the prominent relaxation could be observed, while a new structure arrangement equilibrates. Although NH4+(II) does not undergo as pronounced a change across the PT as NH4+(I), a similar relaxation is observed (Figure 5, right panel, N2−H23···O1). In the PE phase, the position and the orientation of NH4+(II) is strongly F

DOI: 10.1021/acs.inorgchem.7b03161 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 6. Fingerprint plots for sulfate ions in FE (163 K) and PE (273 K) phases.

Quantitative methods for classification of chemical bonding were employed to get a deeper insight into the crystal structure. This was done in the framework of the QTAIM method. Positive values of the Laplacian, ∇2ρ(r), combined with relatively high values of electron density, ρ(r), indicated highly polar covalent bond character of all S−O bonds (Table S6). Additionally, it is known that from QTAIM calculations we can obtain the values of local kinetic G(r) and the potential V(r) energy densities using a local form of the virial theorem.39,55,56 The local kinetic energy density depends upon the values of the Laplacian and electron density at the critical point. Both vales of the local energy density, their sum E(r) and their relationship with ∇2ρ(r) and ρ(r), give an estimate of the nature of chemical bonding. Initial assessment based solely on energetic criteria pointed toward an intermediate between closed and shared shell character of S−O interactions [|V(r)|/G(r) > 1 and E(r) < 0, E(r)/ρ(r) < 0, where E(r) = V(r) + G(r)]. This is due to a substantial charge transfer between atomic basins of sulfur and oxygen atoms. It has been shown that atypical topological properties are in fact common for polar covalent bonds in different systems.57 Because of the specific nature of covalentpolar bonds, a further analysis of electron density was required; thus, a detailed analysis of ∇2ρ(r) was performed. The 2D contour maps of ∇2ρ(r) in the O−S−O plane (Figure 7a) show a shift of electron density from atomic basins of sulfur toward oxygen atoms. This is evidenced by substantial depletion of the valence shell charge concentration (VSCC) zone of S1. Closer inspection of VSCCs was possible through the calculations of ∇2ρ(r) critical points (Figure 7b). This approach enables analysis of valence shells within atoms and thus provides a physical support for the VSEPR model.58 Charge concentrations (CCs) can be identified as regions with nucleophilic character, whereas charge depletions (CDs) are sites with an electrophilic nature. From the topological point of view, CCs are (3, +3) Laplacian critical points, whereas CDs are represented by (3, −3) ∇2ρ(r) critical points. In Figure 7b, CCs are divided into bonded maxima (BM) localized on the bonds and nonbonded (NBM) ones closely related to lone electron pair distribution. As expected, the charge transfer

WHB, and VWHB formed by the O3 acceptor before the transition. Instead of them, the new N1−H12···O3 MHB and N1−H11···O3 WHB appear in the FE phase (compare O3 sections in Table 1). The above-mentioned changes in the acceptors’ connectivity lead to the conclusion that at the PT a new balance between O2 and O4 as well as O1 and O3 acceptor pairs is formed within the SO42− anion. The reorganization of the HB system at the phase transition can be connected with the significantly different ability of acceptors to form the distinct H-bonding scheme above and below Tc. QTAIM and Fingerprint Plot Analysis. Hirshfeld surfaces and fingerprint plots were generated using experimental data sets collected at 273, 263, 253, 243, 233, 213, 203, 193, 183, 173, and 163 K, thus showing the evolution of a PE to a FE system (Figure S4). For comparison, two data sets at 163 and 273 K were selected. The overall shape and color distribution of fingerprint plots (Figure 6) indicate distinct accepting properties of oxygen atoms in both PE and FE phases. However, the overall percentage of O···H interactions is almost identical in both structures (98.7% in FE and 98.8% in PE). This is in agreement with the geometrical analysis showing strengthening of some interactions and weakening of others during the PT. The accumulation of slightly shorter and thus stronger contacts can be seen for the low-temperature phase (FE). This is reflected in the larger concentration of points on the 163 K fingerprint in the low region of di and de marked in red. Where di marks a distance from the surface to the nearest atom interior to the surface, whereas de indicates a distance from the surface to the nearest atom exterior to the surface. For the 273 K fingerprint, the largest concentration of points is more equally distributed along the lower and higher values of di and de (red parts of the plot). Also, there is a lower concentration of dispersed points in the top of the drawing, proving a more equal distribution of HB strengths in this structure (PE phase). The presence of a dispersed set of points with very high values of de and di can be attributed to the O···O interactions. Those weak contacts have a contribution of ca. 1% to a Hirshfeld surface of the sulfate ion. G

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Figure 7. (a) 2D Laplacian maps in planes of O1−S1−O2 bonds. Blue lines, charge depletion; red lines, charge accumulation. (b) Bonded (BM) and nonbonded (NBM) maxima for S1−O interactions in sulfate ions. Blue maxima are the ones found near oxygen VSCC, and brown ones are located close to a sulfur atom on a S1−O bond path; green spheres represent bond critical points. The values of the Laplacian of electron density are given for each of the maxima. Two distinct temperatures indicate the geometries of ions taken for the calculations.

ions in K2SO4 also indicated a possible contribution of resonant forms to the bonding in SO42−. The QTAIM method has also proven to be vital for the examination of other interactions in AS structures. The existence of the interactions found from a geometrical search (MHBs, WHBs, VWHBs, and WIs; Table 1) was confirmed by the presence of bond paths and bond critical points of electron density. For the sake of clarity, the results for all structures are presented in Tables S7 and S8. The values of the Laplacian of electron density and the analysis of energetic criteria based on local potential and kinetic energy densities indicated pure closed-shell character of all hydrogen bonds classified as moderate by geometrical criteria. This was confirmed by the values of |V(r)|/G(r), which fall in the range between 0 and 1, and by the values of ∇2ρ(r), which are greater than zero. Other interactions, such as hydrogen bonds with long H···A distances and O···O and N···O contacts are purely electrostatic in nature. Hydrogen bond strengths were assessed from the topological analysis of electron densities.60 The sum of H-bond energies in which the particular acceptor or donor is involved was derived for both phases and is depicted in Figure 8 (see also Table S9). In line with the analysis of geometrical parameters, in the PE phase, the biggest difference occurs between O2 and O1 (≈4.3

between sulfur and oxygen atoms is evident for both 163 and 273 K data. The difference between those two phases is the amount of transferred charge and its location. In particular, oxygen O2 in the 163 K data set seems to be distinct. For that atom electron density is more spherical on the side facing the sulfur atomic basin. This is reflected by one missing BM on the S1−O2 bond. Electron density is transferred from the sulfur atom to O2 atom NBMs. This is consistent with an increased electron density on the O2 atom NBMs with respect to the remaining oxygen atoms (Figure 7b). It is worth mentioning that the S1−O2 bond in the 163 K model is the longest of all S−O bonds in both structures (Table S3). The presence of three NBMs and one BM for oxygen atoms is closely associated with their sp3 hybridization and polar character of the S−O bonds. Similar characteristics were observed in the sulfate ion in K2SO4.59 QTAIM net atomic charges increase when moving from FE to PE, both for sulfur atom (from 3.85 to 3.95) as well as for the sulfate ion itself (from −1.80 to −1.83). The ellipticity for all S−O bonds is very small, indicating a cylindrical symmetry. It is worth noting that a hypervalent description of the sulfate ion was ruled out by Schmøkel et al.59 Their study on sulfate H

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Figure 8. Temperature dependence of the sum of H-bond energies in which the particular acceptor or donor is involved. Tc is marked with the vertical black dashed line.

sulfate ions (Films S1−S3) and enforces the reorganization of HBs. As a result, the NH4+(I) cation is rotated by ca. 30° about the crystallographic a axis while NH4+(II) is displaced from the (001) plane. Six H-bonds observed in the PE phase are broken, and three new HBs are formed. Within the new arrangement, each of the ammonium cations has almost identical HB subsystem. Simultaneously, O···O distances between the different sulfate ions significantly change. Finally, the interaction balance between strongly H-bonded O2 and O4 as well as weakly H-bonded O1 and O3 acceptors within the sulfate anions is achieved. As a result, in the low-temperature phase, the polar structure of AS is formed. In the FE phase, the mutual orientation of ions is stabilized by the newly formed MHBs. The new HB network in the studied system influences the internal geometry of the anion, causing its small distortion. Along with the crystal cooling, almost all H-bonds become more linear and shorter as a result of the structure relaxation. This process is also observed in further changes of O···O distances, especially those between O1, O3, and O4 atoms. Source of Spontaneous Polarization. AS has been classified as an improper24 or pseudoproper ferroelectric,31 in which Ps was not considered as an order parameter.61 The origin of Ps was suggested to be a result of the ordering of two cation sublattices within the ferrielectric model.32 The second approach connected Ps with the mutual displacements of distorted ions in the AS structure.28,37,38 However, no signs of the disorder were found in our X-ray study as well as in the preceding neutron diffraction experiment.20 Moreover, the observed changes between the relative positions of cations and anions at the PT were found to be small (Figure S5 and Table S10). In addition, the indicated relative displacement of the ions equilibrates in the structure. Therefore, at the PT, the elongation of distance between one ion pair results in the decrease of distance between another pair. However, the nonequivalent distribution of HBs of different strength within both observed AS phases confirms the substantial distortion of NH4+(I) and NH4+(II). This finding is in line with NMR27,29 and neutron20 diffraction studies. In the FE phase, a larger number of moderate H-bonds cause more pronounced deformations of cations (both of site symmetry 1). As the polar structure of AS is formed along the PT, the multipoles

kcal/mol). When temperature decreases, the overall interaction energies for each acceptor and donor increase (Table S9). At the PT, the HB system reorganization results in the creation of two pairs of equally interacting acceptors: O2, O4 and O1, O3. Furthermore, the difference in the interaction energy between donors N1 and N2 shrinks. The performed calculations thereby corroborate the formation of the new interaction balance in the FE phase. Origin of the Phase Transition. The geometry of interactions observed in a crystal structure is a result of tendency of the system to reach the thermodynamic equilibrium under the specified conditions (T, p, V, etc.). If the parameters are altered, the structure is changed because of the new conditions. In some cases, the symmetry of the structure is broken to achieve this aim, and the nonisomorphous structural phase transition is observed.61 The combination of structural analysis and theoretical calculations allowed us to unmask the origin of such phenomenon in AS. In the PE phase of AS, every symmetrically nonequivalent oxygen atom in SO42− is involved as an acceptor in numerous HBs that vary in their geometry and strength. The biggest difference is observed for the interactions cocreated by O1 and O2. The strength of interactions, in which NH4+(I) and NH4+(II) are involved as donors, differ significantly from each other. Neither of the ions in the AS structure is disordered because of the existence of the complex HB network in the studied system. Along with the crystal cooling until the PT, the decrease of all unit cell geometrical parameters is observed. The decrease of the unit cell volume and thermally induced slowing of the ion vibrations result in the reinforcement of the interactions within the system. Therefore the differences between the interaction network of each symmetrically nonequivalent acceptor increase, resulting in the “internal strain” in the librating anion. The interactions’ reinforcement has growing influence on the disturbance of the SO42− vibrational modes. At Tc, the differences between the interactions of Oacceptors with the ammonium cations cause the disruption of the lattice mode between SO42− anions. As a consequence, the simultaneous precession of each sulfate ion about the resultant axis placed near the S1−O2 bond is observed. Such reorientation breaks the inversion symmetry between the I

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Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

related to distorted cations do not compensate each other as in the PE phase. In such a way, Ps arises with only a small contribution of the mutipoles of slightly distorted SO42−. Further relaxation of the structure influences the geometry and mutual orientation of both ammonium cations. As a result, the Ps value changes with the temperature decrease, as was confirmed experimentally.21,22

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*E-mail: [email protected].

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ORCID

Marlena Gryl: 0000-0003-2267-1588 Katarzyna M. Stadnicka: 0000-0002-3898-5824

CONCLUSIONS From our study it is evident that the order parameter of PT has to be ascribed to the disruption of the vibrational lattice mode between the sulfate anions. The atypical T-dependence of Ps has to be connected with the relaxation of the H-bond system formed in the FE phase. The counteracting impact of certain cations on the spontaneous polarization leads to changing of the sign of Ps at about 84.5 K.21,22 When both features of the phase transition in AS are combined, the following can be inferred: 1. The PT has a pseudoproper character, but in contrast to the approach of Petzelt et al.,31 the order parameter is connected to the SO42− vibrational lattice mode. 2. Ps as a nonzero resultant polarization of both distorted NH4+ cations in the FE phase is a side effect of the Hbond system reorganization to the polar structure induced at the PT. The contribution of mutual displacement of cations and anions at Ps is canceled out. Perspectives. In our study we resolved the problem of phase transition in AS, which remained open for more than 60 years. Combined X-ray structure analysis and quantum crystallography techniques were shown to be beneficial in understanding the complicated nature of ferroelectric phase transitions. The presented approach will be useful for structural analysis of PT in MOFs62−64 and organic ferroelectrics. The obtained precise information about the crystal structure evolution with T change may enable the simulation of AS phase transition using ab initio molecular dynamics methodology, as well as enable the correct interpretation of its recently discovered barocaloric properties.65 In addition, our phenomenological approach should stimulate the development of the correct interpretation of phase transition in pseudo and improper ferroelectrics within the Landau theory.

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AUTHOR INFORMATION

Corresponding Author

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was carried out with the equipment purchased thanks to the financial support of European Regional Development Fund in the framework of Polish Innovation Economy Operational Program (Contract No. POIG.02.01.00 12-023/08). This research was supported in part by PL-Grid Infrastructure.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b03161. Tables of crystal data and structure refinement details, SO42− bond lengths and valence angles, H-bond geometrical parameters, O···O distance numerical data, additional fingerprint plots, and QTAIM numerical results (PDF) Film S1 (AVI) Film S2 (AVI) Film S3 (AVI) Accession Codes

CCDC 1586261−1586271 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The J

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