Zr4+ solution structures from pair distribution function analysis

The structures of metal ions in solution constitute essential information for obtaining chemical insight spanning from catalytic reaction mechanisms to formation of functional nanomaterials. Here, we explore Zr4+ solution structures using X-ray pair distribution function (PDF) analysis across pH (0–14), concentrations (0.1–1.5 M), solvents (water, methanol, ethanol, acetonitrile) and metal sources (ZrCl4, ZrOCl2·8H2O, ZrO(NO3)2·xH2O). In water, [Zr4(OH)8(OH2)16]8+-tetramers are predominant, while non-aqueous solvents contain monomeric complexes. The PDF analysis also reveals second sphere coordination of chloride counter ions to the aqueous tetramers. The results are reproducible across data measured at three different beamlines at the PETRA-III and MAX IV synchrotron light sources.


Introduction
Metal ion solution species are fundamental chemical objects since they are the initial precursors in chemical processes and their explicit nature impacts both solvent reaction chemistry and mechanisms of nanocrystal nucleation. 1 The formation of nanocrystals in solvent-based reactions is widespread in natural science, but the current chemical understanding of crystallization is poor, and recent in situ studies of solution synthesis processes have revealed signicant shortcomings in classical nucleation theory. [2][3][4] Classically, crystallization should occur through assembly/disassembly of monomeric species until a nucleus of a critical size is formed, but this view neglects the presence of stable metal ion clusters prior to nucleation. [5][6][7] In situ pair distribution function (PDF) studies have shown the importance of stable solution species as structure-directing building units in solvothermal synthesis. 4,8,9 Here, we explore the rich solution chemistry of Zr 4+ ions using PDF analysis across different pH, different metal ion concentrations, different solvents and different metal precursors (and thereby counterions) to provide a basis for understanding the multitude of chemical processes that involve these species. We establish the reliability of the PDF technique by analyzing data measured with different energies at three different beamlines at the PETRA-III (P21.1 and P02.1) and the MAX IV (DanMAX) synchrotron light sources.
ZrO 2 -based nanoparticles are commonly synthesized in hydrothermal or solvothermal processes, and they are important in technological applications such as high-temperature ceramics 10 and catalysis as a pure compound, 11 or in Ce x Zr 1−x -O 2 as three-way catalysts 12 and in yttria-stabilized ZrO 2 for fuel cell membranes. 13 Zirconium solution species are also precursors for archetypical metal-organic framework materials such as UiO-66. 14 As a hard Lewis-acid, Zr 4+ is highly prone to hydrolysis even in strongly acidic solutions, and thus it readily forms polymetal oxo-clusters. 15 In aqueous solutions Zr 4+ presumably exists as square hydroxo-bridged tetramers, [Zr 4 (OH) 8 16 ] 8+ , as suggested by Muha and Vaughan in 1960 using low Q-resolution X-ray total scattering (TS) data, 16 which were compared with a theoretical pattern calculated from the crystal structure of ZrOCl 2 $8H 2 O. 17 The Zr 4+ solution tetramer has been conrmed using EXAFS, 18,19 NMR, 20 SAXS, 21 highresolution PDF 22 and computational methods. 23 Furthermore, as the chemistry of Hf 4+ is quite similar to Zr 4+ due to similar electron conguration and charge density owing to the lanthanide contraction of the f-block, it is not surprising that Hf 4+ ions also exist as a [Hf 4 (OH) 8 16 ] 8+ -tetramer in aqueous Hf 4+ solutions. 16,24 The addition of bidentate ligands to aqueous zirconium solutions tend to change the coordination of the Zr 4+ species, 22,25-27 thereby rendering speciation control possible, if the underlying assembly mechanisms are better understood. modelling ( Fig. S1 and S7-S11 and Tables S1-S15) including repetitions of data. PDFs of HCl solutions (Fig. S2). PDFs of concentration variation including sample images (Fig. S3-S6 Solvothermal syntheses with non-aqueous solvents allow tailoring of nanoparticles with narrow size distribution and limited agglomeration, 28,29 and solvent effects have provided polymorph control in the synthesis of ZrO 2 . 30 In organic chemistry, inorganic Zr 4+ salts are used as promotors and catalysts in non-aqueous reaction media. 31 Potential understanding of these reactions requires information about the solution speciation, but the literature on Zr 4+ in non-aqueous solvents is limited to a few structures in alcohols. 32,33 Here we report the rst comprehensive study of Zr 4+ solution chemistry by examining structures of ZrCl 4 in various solvents (water, methanol, ethanol, acetonitrile), at pH ranging from 0 to 14, in concentrations ranging from 0.1 M to 1.5 M, and we also compare with other zirconium precursor salts (ZrOCl 2 $8H 2 O, ZrO(NO 3 ) 2 ·xH 2 O).

Results and discussion
Aqueous solution structures of ZrCl 4 The PDF of ZrCl 4 in water (1 M) conrms that the dominant solution species is the [Zr 4 (OH) 8 (OH 2 ) 16 ] 8+ -tetramer ( Fig. 1). Here, ts of different tetramer models all based on the initial tetramer structure taken from the single crystal structure of ZrOCl 2 $8H 2 O 34 are shown. Due to the low X-ray scattering power of hydrogen, these atoms were neglected in the ts, and the OH − /H 2 O ratio within the tetramer was assumed to be the same as in the crystalline state. Fig. 1a shows the t of this initial, single crystalline model to the experimental PDF (T1), i.e. where no atomic positions are rened. This simple model provides a decent description of all the main features of the PDF and clearly settles that the primary motif found in 1 M aqueous solutions of ZrCl 4 is indeed the tetramer, as expected. In fact, the tetramer motif is observed across Zr concentrations of 0.1-1.5 M, which cover the range commonly used in solution-based synthesis (Fig. S2 †). Thus, the tetramer is the initial precursor for many common aqueous synthesis pathways.
While the initial tetramer (T1) accounts for the main features of the experimental PDF, the crystalline model is too rigid to describe the PDF data of the solution species in full. This is unsurprising, as the tetramers are prone to both static and temporal disorder in the dynamic environment of the solvent state. Assuming the average composition of [Zr 4 (OH) 8 (OH 2 ) 16 ] 8+ and retaining the topology of the tetramer using box restraints of 0.1 A (T2) and 0.5 A (T3), the atomic positions can be rened to "relax" the initial model to the PDF data with an improved agreement factor (R w ) from 0.411 (T1) to 0.317 (T2) and 0.277 (T3). Note that these renements, while they result in a better mathematical description of the PDF, are overdetermined and as such not statistically different from the initial model (T1). However, as the atomic movements are greatly limited by box restraints, the tetramer topology is unchanged and the models can therefore to some extent give insight into undescribed features of the PDF.
Evidently, both initial (T1) and relaxed (T2 and T3) models do not account for the PDF features around ∼4.5 A and ∼6.5 A (blue and gray region, Fig. 1a) as well as at 3.17 A. In the ZrOCl 2 $8H 2 O crystal structure, chloride ions coordinate to the tetramer with distances at ∼4.5 A and ∼6.5 A (Fig. 1c-e), 33 indicating a possible similar favorable attraction in solution. Model T4, T5 and T6 include chloride ion coordination with initial positions taken from the same single crystal model for the sake of modelling remanent features in the PDF. When included in the model the different chloride ions only move between 0.2 and 1.0 A away from the initial crystal positions, and the most relaxed model (T6, 0.5 A box restraint) achieves an R w value of 0.199 (Fig. 1b). However, for this model, the oxygen atoms attain unphysical positions when attempting to t the peak at 3.17 A. The rigid box restraint of 0.1 A (T5) appears to be the best compromise between describing the PDF and having a physically credible model.
The peak at 3.17 A is consistent with the Cl-O distances for the hydration shell of chloride ions (3.1-3.34 A). [35][36][37] Fig. S5 † shows that hydrated chloride ions give sharp PDF correlations at ∼3.2 A. This effect is included in the nal model (T8) by adding a simulation of isolated, hydrated chloride ions by a simple Cl-O distance to the T5-model improving R w from 0.232 (T5) to 0.204 (T8). In the T7 model, the chloride ions from the T5/T8 models have been removed to highlight their effect on the PDF. The chloride ion positions match distances exactly in the regions where models T1-T3 lack intensity. While again being a result from an overdetermined renement, the physical soundness of the nal model is further evaluated through histograms of all interatomic correlations, which are compared with values for the initial single crystal model ( Fig. 1c-h). Most correlations agree well with the crystalline state, but with slightly larger spread as expected for a dynamic solution environment.
Reported low Q-resolution TS 16 and SAXS 21 experiments also indicated chloride ion coordination to the solution tetramer. Hu et al. hypothesized some contribution to the PDF from chlorides in their study of ZrOCl 2 solutions, but without explicit modelling of the PDF. 22 Effect of pH on the aqueous solution structure of ZrCl 4 Base addition to the zirconium-based precursor solutions is used in synthesis of CeO 2 -ZrO 2 solid solutions, 38-40 YSZ, 41,42 or to control polymorphism of ZrO 2 . 43,44 Low pH conditions (pH < 3) should give the thermodynamically stable monoclinic polymorph of ZrO 2 , whereas high pH (pH > 9) should favor the formation of the metastable tetragonal phase. In the synthesis of the multicomponent systems, CeO 2 -ZrO 2 and YSZ, the precipitation of the metal ions at high pH is utilized to ensure homogenous mixing of the cations before subsequent calcination treatment.
Since the as-prepared aqueous ZrCl 4 solution is highly acidic (pH 0), the full pH range of 0-14 can be achieved by dissolving ZrCl 4 in alkaline NaOH solutions. The alkalinity has limited inuence on the macroscopic appearance of the precursor solution, which is translucent until pH 12, where it becomes a white gel. At pH 9, some turbidity is present possibly indicating minor precipitation (Fig. S6 †).
PDFs at different pH are shown in Fig. 2 24 ] 8+octamer. 21 These observations are not reproduced here, since this would give PDF peaks corresponding to body-diagonal Zr-Zr distances in the cubed octamer, and a change in relative intensity between the nearest neighbor Zr-O and Zr-Zr peaks with the latter increasing.
The only observed changes in the PDFs at pH 2 and pH 9 compared with pH 0 are marked with lines in Fig. 2. The peak corresponding to nearest-neighbor Zr-Zr correlation (red line) is slightly broadened, making it overlap with the Cl-O peak at ∼3.2 A. The broader Zr-Zr peak could indicate a slight distortion of the tetramers, but some partial conversion of the tetramer to another species is equally possible. The slightly turbid pH 9 solution could indicate small amounts of precipitated zirconium species, thus explaining the broader Zr-Zr peak in both the pH 2 and 9 solutions.
Notably, the peak at ∼6.5 A (yellow line) originating from the chloride coordination to the tetramer as argued in the previous section disappears at higher pH. The lack of direct chloride coordination is a result of deprotonation in the tetramer upon addition of NaOH: Deprotonation lowers the charge on the tetramer making direct chloride coordination less electrostatically favorable.
At pH 12 and above, the tetramers break down, and sharp correlations only remain up to 4.3 A (blue region, Fig. 2). The peaks at 2.13 and 3.45 A are from Zr-O and nearest neighbor Zr-Zr interactions, respectively, although slightly shorter than in the tetramer. The relative intensity of the Zr-Zr peak (compared to the Zr-O peak) has increased indicating a more condensed local coordination environment in the precipitated gel. The highly broadened peaks at 5.0, 6.6 and 9.6 A presumably originate from disordered Zr-Zr correlations between the rigid structural units in the amorphous gel (gray region, Fig. 2).
In situ TS experiments revealed an amorphous intermediate in the solvothermal formation mechanism of ZrO 2 , 27 YSZ 2 and HfO 2 . 45 The PDF of the amorphous intermediate observed by Dippel et al. 27 is strikingly similar to the PDFs at pH 12 and 14 (Fig. 2). Thus, high-pressure, high-temperature water mimics alkaline reaction chemistry illustrating the versatility of solvothermal reactions.

Aqueous solution structures of other zirconium salts
The tetramer persists for ZrOCl 2 $8H 2 O and ZrO(NO 3 ) 2 ·xH 2 O dissolved in water, and the main PDF features resemble the 1 M ZrCl 4 solution (Fig. 3a). Since the tetramer already exists in the crystal structure of ZrOCl 2 $8H 2 O, it is not surprising that it is also observed in aqueous ZrOCl 2 solution. However, the chloride coordination peak at ∼6.5 A is almost absent for the ZrOCl 2 solution (insets, Fig. 3a). This indicates that chloride ions coordinate less to the tetramer in the ZrOCl 2 solution compared with the ZrCl 4 solution. The chloride ion feature is subtle, but it is reproducible across measurements on different solutions, at different beamlines (P02.1, P21.1 and DanMAX) and at different synchrotron facilities (PETRA-III and MAX IV), clearly suggesting that it is not a data artifact (Fig. S7 †).
The   solution. 17,22,46 The coordination of chloride ions to the tetramer in aqueous ZrOCl 2 solutions can be controlled by adjusting the R-ratio using HCl (Fig. 3b). At increased chloride ion concentration, the 6.5 A peak increases in relative intensity, whereas the reference experiment of aqueous HCl solutions do not show sharp correlations in this region (Fig. S5 †). Thus, the peak at 6.5 A must originate from direct coordination of the chloride ions to the tetramer as also seen in the tting of ZrCl 4 PDFs.
For ZrO(NO 3 ) 2 in water, the tetramer accounts for the majority of the PDF peaks, but distinct features are seen above 10 A, i.e. exceeding distances in the tetramer. Zr 4+ exists as innite chains of edge-sharing polyhedra in the crystal structure of ZrO(NO 3 ) 2 ·xH 2 O, 47 and the longer-range correlations may be untransformed chains in the solution. However, the primary structural motif is still the tetramer and as expected there is no 6.5 A chloride coordination peak in the ZrO(NO 3 ) 2 solution. Due to the low X-ray scattering power of nitrogen and oxygen, it is not possible to determine if nitrate ions coordinate to the tetramer in a manner similar to the chloride ions in the ZrCl 4 solution.
The structural similarity between the different precursor salts in water could indicate that the precursor salt plays a minor role for the synthesis outcome. However, the effect of the anion species during particle formation cannot be neglected, and future in situ X-ray scattering studies advantageously could investigate this aspect.

Non-aqueous solution structures of ZrCl 4
The coordination chemistry of Zr 4+ in the non-aqueous solvents is different from the aqueous tetramer, but it is noteworthy that the structural correlations observed in methanol, ethanol and acetonitrile are very similar with peaks in three regions only (Fig. 4).
When ZrCl 4 is dissolved in the non-aqueous solvents, Zr 4+ preserves primary coordination to chloride, and since the extent of the PDF signal is limited, Zr 4+ must exist as monomers in these solutions (indeed a dimer would have correlations far exceeding those observed experimentally, Fig. 5).
In Fig. 5, model PDFs of common coordination geometries are superimposed on the experimental PDF of the ZrCl 4 /methanol solution. The bond lengths in the model structures are manually adjusted to match the rst sharp pair correlation observed in the experimental PDF at ∼2.5 A, which agrees well with a Zr-Cl distance. The other peaks originate from ligand-  ligand correlations, which are distinctly different for the various monomeric motifs.
Both the trigonal bipyramidal and octahedral models qualitatively agree with the experimental PDF with peaks in same three regions as the experimental PDF. Yet, both structures do not account for the broad nature of the ∼3.2 A peak. For the other models, the nearest-neighbor ligand-ligand (NN L-L) correlations are either too long (tetrahedral model) or too short (capped trigonal prismatic and square antiprismatic). As stated previously, a model structure extending beyond a monomeric motif e.g. a dimer predicts correlations greatly exceeding those observed experimentally.
Studies on simple coordination complexes of Zr 4+ have found a preference for cis-ZrCl 4 X 2 (X = pinacolone, pyridine, THF) octahedral complexes, [48][49][50] and in the crystalline state of ZrCl 4 , Zr 4+ is coordinated to Cl − in zig-zag chains of edgesharing irregular octahedra. 51 Models based on the irregular octahedra from the crystal structure of ZrCl 4 are tted to the experimental PDF without rening atomic positions in Fig. 6.
In the O1 model, bond lengths and angles are preserved from the crystalline state, however, there is a clear mismatch, since the experimental PDF has a single, sharp Zr-Cl peak at ∼2.5 A, whereas the model has three distinct Zr-Cl distances of 2.655 A, 2.498 A and 2.307 A. In the O2 model, these three distances are manually adjusted to match the rst sharp peak in the PDF while preserving the bond angles from the crystalline state. Adjusting the bond lengths improves R w from 0.860 (O1) to 0.385 (O2) and describes the NN L-L peak better.
If the Zr 4+ monomers are in fact octahedrally coordinated in the ZrCl 4 /methanol, some ligand exchange with the solvent must occur to balance the stoichiometry of four chloride ions per Zr 4+ ion. In the O3 model, two chloride ions are exchanged with oxygen (as a proxy for coordinating methanol molecules) to produce a cis-ZrCl 4 O 2 octahedron. Notably, the Zr-Cl peak in the experimental PDF has a weak shoulder matching a Zr-O distance (yellow and green lines, Fig. 4), and so the Zr-O bond lengths are adjusted to 2.25 A to match this. This model achieves an R w value of 0.271 and provides a good visual description of all the main features in the experimental PDF.
From the above considerations, it is probable that the Zr 4+ monomers are in large part octahedrally coordinated to chloride ions and solvent molecules to balance the stoichiometry. Note that since the experimental PDF is both a temporal and static average of the whole ensemble of structures in the solution, several other structures with different coordination geometries can exist and contribute to the PDF.   S10 †). O1: fixed crystal geometry, i.e. both bond lengths and angles are preserved. O2: fixed bond angles from crystal geometry, but bond lengths manually adjusted to 2.46 A to match the first sharp correlation in the PDF. O3: based on O2, but with two chlorides exchanged with oxygen and bond lengths manually adjusted to 2.25 A. For all fits, an exponentially damped sinusoidal function is included in the models to account for long-period modulation of the intensity in the PDF (see ESI Section 6 †) with parameters obtained from the fit of O3 model. Data collected at P21.1@PETRA-III.

Relation to materials synthesis
In general, solvothermal synthesis of ZrO 2 nanoparticles results in the thermodynamically stable monoclinic polymorph, when water is used as a solvent (hydrothermal), 43,52-54 whereas alcoholic solvent mixtures results in mixtures of particles with the monoclinic and the (metastable) tetragonal polymorph. 27,55,56 By tuning the water/ethanol ratio, the ratio of monoclinic/ tetragonal phase can be tuned with less monoclinic phase formed in the absence of added water. 55 In borderline nonhydrolytic sol-gel syntheses, the ratio of formed ZrO 2 phase can even be tuned by choosing alcohols of different thermal stability or by lowering the reaction temperature, so the in situ formation of water molecules are reduced. 57 This suggests that the availability of water molecules is crucial in determining the reaction outcome.
The fact that the Zr 4+ is found to exist as hydroxy-bridged tetramers in water regardless of precursor salt and concentration corroborates well with the fact that the monoclinic phase exclusively forms in hydrothermal syntheses. In these solutions, all zirconium species will already be saturated with the required amount of water molecules and connected in larger ("prenucleation") assemblies, and so the monoclinic phase can readily form. In the non-aqueous solvents (disregarding acetonitrile in the current discussion of ZrO 2 synthesis), the Zr 4+ ions maintain their coordination to chloride from the crystal structure in isolated monomers and only partially coordinate to the oxygen source (methanol/ethanol). Inevitably, the nucleation of ZrO 2 nanoparticles from these solutions will involve more chemical steps (solvent decomposition, ligand exchange, monomer assembly), thus possibly creating reaction conditions suitable for forming the tetragonal phase. To investigate the formation mechanism from these non-aqueous ZrCl 4 solutions, in situ X-ray scattering experiments could advantageously be utilized.

Conclusions
Zr 4+ ions in solution are precursors in many chemical reactions either to produce important zirconia-based nanomaterials or to carry out catalytic chemical transformations in organic chemistry, and the structures of the ions in solution should therefore form core chemistry textbook material.
When dissolving ZrCl 4 in methanol, ethanol and acetonitrile, Zr 4+ exists as monomers primarily preserving the coordination to the chloride ions. An octahedral model provides the best description of the features in the experimental PDF. Based on stoichiometry consideration and features in the PDF some ligand exchange must have occurred. Yet, it cannot be ruled out that multiple other structures coexist.
Zr 4+ exists as [Zr 4 (OH) 8  The subtle features in the PDFs related to the chloride coordination are consistent across repeated measurements at different synchrotron facilities, strongly supporting that modern PDF analysis is a reliable and powerful tool for structural analysis of complex solution systems.
The systematic study of Zr 4+ solution structures across a wide parameter space provides a baseline understanding for synthesis of zirconia-based functional nanomaterials and solution-based zirconium chemistry in general.

Solution preparation
Anhydrous ZrCl 4 (Sigma Aldrich, 99.99%), ZrOCl 2 $8H 2 O (Sigma Aldrich, 99.5%) and ZrO(NO 3 ) 2 ·xH 2 O (Sigma Aldrich, 99%) were used without further purication. The zirconium salts were dissolved in either deionized water, absolute ethanol, methanol or anhydrous acetonitrile to a total metal concentration of 1 M. Since the exact degree of hydration is unknown for ZrO(NO 3 ) 2 ·xH 2 O, only an approximate 1 M concentration was obtained. Upon dissolution, translucent solutions were obtained with no sign of gelation. For all 1 M aqueous solutions, the pH was 0. A series of aqueous ZrCl 4 solutions with concentrations ranging from 0.1-1.5 M was made to study the effect of dilution on the solution structures.
A pH series was made by dissolving ZrCl 4 in diluted aqueous NaOH solutions with concentrations of 1, 2, 3 and 6 M such that pH values of 2, 9, 12 and 14, respectively, were obtained. The total zirconium concentration was maintained at 1 M. For pH 12 and 14, the alkalinity of the solutions resulted in gelation (Fig.  S6 †).
Another series was made by dissolving ZrOCl 2 $8H 2 O in aqueous HCl solutions with concentration of 2, 4 and 6 M while maintaining the total zirconium concentration at 1 M.
All samples were prepared immediately prior to measurement.

Total scattering experiments
Total scattering (TS) experiments were conducted at the P02.1 and P21.1 beamlines at PETRA-III (DESY, Hamburg, Germany) using photon energies of ∼60 keV (l = 0.2072 A) and ∼103 keV (l = 0.1204 A), respectively, as well as at the DanMAX beamline at MAX IV (Lund, Sweden) using photon energy of ∼35 keV (l = 0.3553 A). Both PETRA-III beamlines feature 2D PerkinElmer XRD 1621 area detectors for data acquisition, whereas DanMAX features a Dectris PILATUS3 X CdTe 2 M area detector. At P02.1, the sample-to-detector distance was ∼20 cm allowing for an instrumental Q max of 23 A −1 , whereas the distance was ∼30 cm at P21.1 giving a Q max of 28.8 A −1 and it was ∼9.3 cm at DanMAX giving a Q max of 20.5 A −1 .
The solutions were loaded into 1.45 mm and 1.00 mm Kapton capillary tubes sealed with epoxy at PETRA-III and MAX IV, respectively. Data acquisition was performed at ambient conditions with an acquisition time of 5-10 min per experiment. Background measurements of the solvent loaded into Kapton capillaries were performed to account for air, capillary and solvent scattering.
The procedure for data treatment and details on the renements can be found in the ESI. †

Author contributions
MK designed the project, measured data, carried out data analysis, wrote the initial dra and did review and editing. RSC, IGN, and SS measured data and carried out data analysis, discussion, review and editing. ACD and MRVJ measured data and contributed discussion, review and editing. BBI designed the project, conducted supervision, discussion, resource acquisition, validation, review and editing.

Conflicts of interest
There are no conicts to declare.