Multi-Step Crystallization and Chemical Evolution of Sodium Yttrium Fluoride

13 Two-step crystallization mechanisms based on spinodal decomposition followed by nucle14 ation are commonly observed both in the laboratory and in nature. While this pathway 15 may require chemical reactions, subsequent nucleation and growth are often considered as 16 separate, discrete events from the reaction itself. Recent work has also shown a distinct in17 termediate step involving the formation of an amorphous aggregate. Here we report a novel 18 four-step mechanism in the aqueous synthesis of sodium yttrium fluoride involving 1) the 19 segregation of aqueous ions into a dense liquid phase, 2) the formation of an amorphous ag20 gregate, 3) nucleation of a cubic YF3 phase, and 4) subsequent solid-state diffusion of sodium 21 and fluoride ions to form a final NaYF4 phase. The final step involves a continuous, gradual 22 change of the solid phase’s chemical stoichiometry from YF3 toward NaYF4. Unlike previ23 ously studied nucleation and growth mechanisms, the stoichiometry of the final solid phase 24 evolves throughout the crystallization process rather than being determined at nucleation. 25 This novel four-step mechanism provides a new perspective into the nucleation and growth 26 of many other crystalline materials given the ubiquity of nonstoichiometric compounds in 27

rule, which suggests that systems will not necessarily take the most direct route to their most stable 36 phase, but rather that they tend to go through a series of intermediates that are closer in free energy 37 to the initial state. 9,10 38 One such nonclassical crystallization mechanism is two-step nucleation via a dense liquid 39 phase (DLP), typically formed through spinodal decomposition (SD). 11,12 In this mechanism, the 40 highly supersaturated initial phase spontaneously separates free of a thermodynamic energy bar-41 rier 13 into ion-rich and ion-poor liquid phases, and crystals then nucleate from the ion-rich phase, 42 possibly via an amorphous intermediate. 1 This mechanism has been observed directly via liq-  4 These studies, among others, 18 suggest that the two-step mechanism 50 via a DLP can readily be accessed in a wide range of solution-based systems, because, when taken 51 to sufficiently high supersaturation, nearly all solutions will reach their limit of stability. 19 52 One aspect of these two-step pathways via a DLP that remains largely unexplored is that 53 the stoichiometry of the intermediate phase is variable and ill-defined and must evolve to generate 54 the final stable phase. This is because the compositions of the ion-rich and ion-poor liquids are 55 defined by a phase line that traverses a range of compositions rather than by a set of line com-56 pounds. Therefore, for crystallization to proceed, ions must be rejected from or drawn into the 57 solidifying regions of the ion-rich liquid droplets. This adds a level of complexity to other previ-58 ously investigated nonclassical systems, in which the intermediate phases are all line compounds, 59 which can either be identical for each phase, for example, as in the case of CaCO 3 (ignoring waters 60 of hydration), or they can be distinct and require chemical transformation, as documented for the 61 calcium phosphate system. 20 For the latter, charged calcium triphosphate species undergo aggre-62 gation accompanied by Ca 2+ binding and deprotonation to create the amorphous phase, and then 63 undergo a second step of Ca 2+ binding and deprotonation to create the first crystalline phase. In a 64 DLP-mediated pathway, on the other hand, ions may exchange more dynamically rather than via 65 specific transformations to these discrete line compounds. The added complexity in these two-step 66 pathways is further emphasized when the final compound has a ternary or more complex stoi-67 chiometry, which increases the difficulty of the required ionic reorganization. Given the common 68 occurrence of the formation of DLPs in highly supersaturated solutions and the preponderance of 69 ternary and more complex compounds in natural and synthetic systems, this motivates the further 70 study of the chemical evolution of intermediate phases in these systems.

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Here we investigate this multi-step crystal growth pathway using a model system based on 72 ternary sodium-yttrium-fluoride (NaYF) materials. This is an ideal system for exploring the role 73 of chemical evolution during crystallization because the stoichiometry of NaYF materials has been 74 shown 21 to vary as a combination of NaF and YF 3 that varies continuously with a final stoichiome-75 try of Na 0.5-x Y 0.5+x F 2+2x , or (0.5-x)NaF • (0.5+x)YF 3 , with 0<x<0.5. When x = 0, the stoichiometry 76 becomes NaYF 4 , which is used frequently as shorthand for this material. Due to the importance of 77 the variable stoichiometry of this system to our paper, we instead use the shorthand NaYF when re-78 ferring to this material. The majority of aqueous syntheses of NaYF use either microemulsion sol-79 vent systems 22 or organic capping ligands 23 for the purpose of controlling both the size and shape 80 of discrete nanocrystals 24 . In this work we synthesized ligand-free NaYF materials to provide a 81 clear understanding of the role of solvated aqueous ion dynamics by eliminating ion chelation and 82 surface passivation by organic species. Our results demonstrate the formation of a novel DLP in the 83 NaYF system through a two-step mechanism, followed by a third step of solid-state diffusion that 84 determines the final stoichiometry of the material. This change in stoichiometry has not previously 85 been studied in systems that proceed by SD. Further investigation of this mechanism could also 86 lead to the development of many functional materials. For example, the fundamental insights into 87 the multi-step nucleation and growth of materials that display nonstoichiometry in nature could 88 lead to advances in the design of materials for a diverse range of applications including photody-89 namic therapy, 25 solid-state laser refrigeration, 26 , optical thermometry 27 , nanoscale lasing 28 , night 90 vision 29 , and electrochemical energy storage 30,31 .

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In order to probe the nucleation and growth of NaYF materials in the absence of organic ligands we 93 first prepared aqueous electrolyte solutions of both NaF and YF 3 , and then combined them at stan-94 dard conditions with relative concentrations stoichiometric to NaYF 4 ( Figure 1A). Immediately 95 upon mixing the starting solutions, we observed the apparent formation of a gel-like material (Fig-96 ure 1B), which can be filtered to a translucent solid ( Figure 1C). This gel remains relatively stable 97 for several hours, after which it begins to collapse into a white powder ( Figure S1). TEM imaging 98 of the gel shows an interconnected, porous structure ( Figure 1D). Scanning TEM (STEM) tomog-99 raphy reveals not only the interconnected three-dimensional morphology ( Figure 1F) but also the 100 open-cell structure that can't be seen in conventional STEM ( Figure 1G). Brunauer-Emmett-Teller 101 (BET) surface area measurements show a surface area of the gel phase on the order of 100 m 2 /g, 102 and powder X-ray diffraction (XRD) data show very broad peaks consistent with α-NaYF or a 103 similar cubic material ( Figure S2). To the best of our knowledge there has been one previous 104 observation of interconnected particle morphology during the aqueous synthesis of NaYF materi-105 als. 32 However, to date there has been neither discussion of the unusual multi-step gel formation 106 mechanism nor detailed microstructural characterization of the recovered gel material reported in 107 the literature.

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While the XRD data were consistent with nanocrystalline α-NaYF ( Figure S2), the peaks 109 were not sufficiently resolved to be able to definitively conclude that the gel is purely α-NaYF. 110 To further complicate the analysis of these data, TEM data suggest that there are some amor-111 phous, poorly crystalline, or otherwise disordered regions ( Figure 2D). Furthermore, we observe 112 beam-induced crystallization in the TEM ( Figure S3), which suggests that the high resolution TEM 113 (HRTEM) is in fact underestimating the distribution of the amorphous and poorly crystalline mate-114 rial. However, under the assumption that any crystals that are induced by the beam in vacuum will 115 have the same composition as their disordered precursor, we can use this beam-induced crystalliza-116 tion to estimate the local composition of the material. Using custom fast Fourier transform (FFT) 117 indexing software ( Figure 2E), we were able to show that most regions of the gel contain an FFT 118 peak between 3.00 and 3.16Å. This was indexed to the (111) plane of a cubic NaF YF 3 structure, 119 with smaller d-spacings corresponding to a more NaF-rich structure (more similar to NaYF 4 , fig-120 ure 2A), and larger d-spacings corresponding to a more NaF-poor structure (more similar to cubic 121 YF 3 , figure 2B). This analysis shows relatively smooth fluctuations between compositional states, 122 showing that the NaF YF 3 ratio is not constant in the recovered gel and that it should be thought 123 of as in a composition between YF 3 and NaYF 4 . The measured d-spacings are shifted from litera-124 ture values for the (111) planes of cubic NaYF 4 and YF 3 due to approximations in measuring the 125 scale bar, but the individual spots are accurate relative to each other, and therefore the trend is not 126 affected. A histogram of the detected d-spacings can be found in Figure S4. It should be noted 127 that the thermodynamically stable orthorhombic structure of YF 3 ( Figure 2C) was not observed in 128 the gel. Considering the crystal structures of these two phases, it is notable that they share a nearly 129 identical lattice of fluoride ions (though each unit cell of the YF 3 contains an extra fluoride ion at 130 the center), but that the corners of the YF 3 unit cell are unoccupied, which results in large channels 131 that run through the entire crystal structure. We propose that these channels readily allow for the 132 diffusion of ions into the lattice, allowing for local variations in stoichiometry. This is consistent 133 with much of the literature regarding cubic NaF-YF 3 structures grown from melt insofar as that the 134 bulk material can be thought of as a solid solution of NaF and YF 3 . 21,33 However, to our knowl-135 edge, this has not been thoroughly characterized on the nanoscale, nor has any mechanism been 136 described for its structural evolution in solution-phase syntheses. 137 We hypothesize that the gel initially forms both amorphous and cubic domains of YF 3 while 138 the excess NaF in solution slowly incorporates into the matrix to form the more stable cubic NaYF 139 phase. We do not observe distinct XRD peaks for YF 3 and NaYF 4 in recovered gel materials due 140 to the effects of nonstoichiometry and Scherrer broadening. To investigate the gradual transition 141 from YF 3 to NaYF, we attempted a cation substitution experiment on the gel using monovalent 142 potassium cations. By removing the gel from its native solution as shown previously, it is possible 143 to suspend temporarily the process of monovalent sodium ion incorporation. After submerging the 144 recovered NaYF gel in a concentrated (1M) KF solution, we observe that the remaining sodium-145 poor regions incorporate KF to form KY 3 F 10 (KYF) ( Figure 3A), which is distinguishable in XRD 146 after the gel is allowed to fully collapse into single crystals ( Figure 3B). While KYF can form in 147 multiple stoichiometries, the KY 3 F 10 stoichiometry forms in this case because it is stable in the 148 cubic crystal phase and has the lowest potassium / yttrium ion ratio. 34 By varying the amount of 149 time spent incubating in the native solution before filtering and transfering to the KF solution (t inc ), 150 we can observe how much sodium has incorporated into the gel in that time and how much YF 3 151 remains, which we can observe after converting to KYF. As t inc increases from 15 minutes to two 152 hours, we observe the proportion of the sodium phase to increase linearly with a corresponding 153 linear decrease in the relative amount of material that incorporates potassium ( Figure 3C). This 154 shows that the incorporation of sodium into the crystal structure occurs as the result of solid-state 155 diffusion into the gel and is thus unambiguously a separate step from the initial formation of the 156 yttrium-rich gel phase.

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To further understand the nature of the gel, we used solid-state nuclear magnetic resonance 158 spectroscopy (SSNMR) to characterize the gel product compared to its eventual fully crystallized 159 α-NaYF product ( Figure 4A) as well as orthorhombic YF 3 ( Figure 4B). We used orthorhombic YF 3 160 rather than the previously discussed cubic phase because the cubic phase is a metastable product 161 that seems to only form in reactions similar to that reported here, and which literature suggests 162 is nearly impossible to isolate without considerable incorporation of the countercation from the 163 fluoride precursor. 35,36 As shown in 19 F spin-echo magic angle spinning (MAS) NMR ( Figure 4C) 164 the gel exhibits a broad resonance centered at -61 ppm with a peak width of 30 ppm. As reported 165 by Bessada, et al., 37 the 19 F chemical shift is highly sensitive to its coordination environment in 166 molten fluoride mixtures, displaying a nonlinear and monotonous increase from -225 ppm to -28 167 ppm by increasing the concentration of YF 3 from 0 to 100% in the NaF-YF 3 mixture. Compared 168 to orthorhombic YF 3 , which shows a relatively sharper peak at -58 ppm with a width of 12 ppm, 169 and α-NaYF, which has a similarly broad resonance at -77 ppm with a width of 28 ppm, these 170 data are again consistent with a gel that consists of some regions that are more similar to YF 3 and 171 others that are closer to NaYF 4 . Because the broadness of the NaYF 19 F spectrum can be attributed 172 to a large distribution of isotropic chemical shifts due to the random arrangement of Na + and Y 3+ 173 around F -, 38,39 we show T 2 -filtered 19 F spectra in Figure 4D, which reduce signals from faster- we would expect to observe YF 3 are not consistent with the major peak of orthorhombic YF 3 at 58 178 ppm, due to the variation in the coordination geometries of bridging fluoride ions between the cubic 179 and orthorhombic polymorphs of YF 3 as well as amorphous regions. This emphasizes that the YF 3 180 product in the gel is not the orthorhombic phase but rather cubic and amorphous YF 3 . Furthermore, 181 Figure 4E shows that the 19 F spin-lattice relaxation time constant T 1 drops significantly from 19 182 s for α-NaYF and 9.2 s for orthorhombic YF 3 to 3.2 s for the gel, which indicates that the major 183 fluoride species are more mobile and less ordered in the gel phase. This is consistent with our 184 observation that there are significant amorphous, poorly crystalline, and disordered regions in the 185 gel and also emphasizes the propensity for this material to undergo solid-state diffusion, as we 186 have observed. Single-pulse 23 Na NMR spectra of the gel and the α-NaYF samples, respectively 187 ( Figure S6), both contain major resonances centered at -18 ppm and -9.5 ppm, which were assigned 188 respectively to Na + sites in the bulk nanoparticles, and to Na + sites at the surface or near defects, 189 as originally reported by de Queiroz, et al. 39 The fraction of the -9.5 ppm peak changes from 35% 190 in α-NaYF to 75% in the gel sample, suggesting that the gel has over twice as many surface or 191 defective Na + sites as compared to the final crystalline product. ena. This intricacy illustrates the most intriguing aspect of this ternary NaYF system, namely, that 223 its formation cannot be viewed purely as a two-step nucleation and growth mechanism. Rather, the 224 gradual solid-state diffusion must be thought of as a fundamental part of the overall growth path-225 way. Future work will combine molecular dynamics simulations with our classical modeling in 226 order to create a more comprehensive model that considers additional electrostatic contributions.

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This multi-step crystal growth mechanism is not only interesting in its own right, but it also 228 opens the door for further applications of NaYF and similar materials that take advantage of its 229 high surface area. For example, NaYF-gel materials could be useful for future energy storage ap-  We have shown that upon the mixture of NaF and YCl 3 in water, a gel separates from solution 243 which then undergoes crystallization, similar to many other two-or three-step crystallization sys-244 tems. However this system also includes an additional step of solid-state diffusion, where the 245 product initially resembles cubic YF 3 but then undergoes a gradual change of chemical stoichiom-246 etry to form NaYF over the course of several hours. We anticipate that this multi-step mechanism 247 is not specific to NaYF and more research is needed into other chemical systems where aspects of 248 crystal growth is understood best through more complex nucleation and growth pathways.  Ion Replacement in Gel The gel is synthesized as described above and allowed to incubate in its 256 original solution for a period of time, t inc . After t inc has passed, the sample is filtered as described 257 above and rinsed with nanopure water, and the product is resuspended in a solution of 1M KF. This 258 mixture is vortexed until it appears uniform and is allowed to settle overnight. After fully settling, 259 the product is centrifuged and washed with water and ethanol respectively and oven-dried.  The data that support the findings of this study are available from the corresponding author on 310 reasonable request.     Smaller d-spacings correspond to a unit cell closer to NaYF 4 and larger d-spacings correspond to a unit cell closer to YF 3 . For more details on the peak assignments, see the supporting information. Scale bar = 10 nm (F) STEM-EDS spectrum showing the elemental analysis. Note the lack of any significant Cl peak. Cu is residual from the TEM grid. STEM-EDS maps are in Figure S5. Representative XRD at t inc = 60 minutes zoomed in to show 022 peaks (C) Peak height of the 022 peaks corresponding to either KY 3 F 10 or NaYF 4 normalized to the sum of the 022 peak heights for both phases as a function of t inc . The 022 peak was chosen due to its relatively high intensity as well as the relatively low convolution of the two peaks at that 2θ. This plot shows clearly that the longer the gel is allowed to develop in its native solution prior to filtration, the more sodium is retained by the final product, and the less potassium is incorporated. Figure 4: NMR experiments. 19 F solid state NMR comparing the gel with α-NaYF and orthorhombic YF 3 standards at 55C. (A) TEM (left), SAED (bottom inset) and dark field TEM (right) of single-crystalline α-NaYF grown from the gel. The dark field TEM indicates that the whole particle is single crystalline. Top inset shows the α-NaYF crystal structure. Scale bar = 400 nm for the TEM and 5 nm -1 for the SAED. (B) TEM of orthorhombic YF 3 synthesized in a similar, organic-free method. Inset shows orthorhombic YF 3 crystal structure. Scale Bar = 100 nm (C) 19 F spin-echo MAS NMR spectra of the gel, YF 3 , and α-NaYF at a spinning speed of 32 kHz and an interpulse delay of 31.25 µs (one rotor cycle). The asterisks indicate the spinning sidebands. (D) 19 F T 2 -filtered NMR spectra of the gel, YF 3 , and α-NaYF after eight π-pulses with an interpulse delay of 65.2 µs (two rotor cycles). (E) 19 F inverse-recovery normalized signal intensity (markers) vs. interpulse delay of gel, YF 3 , and α-NaYF as well as the fits (lines) for obtaining the spin-lattice relaxation time constant T 1 .