In-situ observation of homogeneous nucleation and growthTo characterize the intermediate states leading to the formation of aluminum deutroxides, the aqueous reaction of NaOD-aluminate was studied in situ using neutron total scattering and pair distribution function (PDF) analysis. The PDF G(r) data, obtained from Fourier transformation of the collected/normalized scattering structure factor S(q), provides a localized view on the probability of finding pairs of atoms separated by some distance, r. The method is thus well suited to understand nanoscale and disordered phases, and if the data requisite times match the reaction kinetics, time-resolved PDF analysis can provide insight into structural evolution, such as nucleation and growth events. Figure S1 (in Supplementary Information, SI) displays infrared camera images captured during the neutron total scattering experiments over a period of 36 h, starting from a homogenous solution to the formation of precipitates. The images reveal a slow nucleation and growth reaction, where cloudiness appears during the first 16 h, then the precipitates begin to fall to the bottom of the tube during the subsequent 16–36 h. To capture structural signals from transient solution phase species, and reduce coherent diffraction signals from crystalline products, the neutron hot-zone was focused on the solution phase, and not the precipitates at the bottom of the tube (Fig. S1). The measured scattering structure factor S(q), corresponding to these infrared images, is given in Fig. S2a, emphasizing small intensity changes (~1–2%) and the practical sensitivity issues underlying in-situ total scattering experiments for probing nucleation and growth reactions. Other studies that probe such small intensity changes in total scattering can be found in refs. 11,26,27,28.The ΔS(q) datasets were created by subtracting the first 4 h of collected data (as homogeneous solution signals) from each of the following time datasets (Fig. 1a). As seen in Fig. 1a, the ΔS(q) datasets indicate the formation of nanoscale solids over time, with Bragg reflections in the position agreeing with those expected for Al(OD)3 polymorphs, including gibbsite, bayerite, doyleite and/or nordstrandite (in the sequence of decreasing thermodynamic stability29,30). These four polymorphs share the same layer structure, consisting of edge-sharing Al(OD)6 octahedra forming an Al(OD)3 dioctahedral layer. They differ from one another by the intralayer H/D-bonding orientations and the interlayer shift vectors, which together lead to variations in the geometry and strength of interlayer H/D-bonding (see their structures in Fig. S3). The intensity profile for the endpoint of the experiment (black curve in Fig. 1a) shows non-uniform peak broadening features, where the 4.32 Å−1 reflection is noticeably narrower than the observed reflections at q values of ~3.63, ~3.83, ~4.72, and ~5.21 Å−1. The 4.32 Å−1 peak is mainly the 330 reflection of gibbsite, bayerite or nordstrandite, or the 30\(\bar{3}\) reflection of doyleite. Within the space group of gibbsite31, bayerite32 and nordstrandite29, each Al(OD)3 layer lies in the ab-plane and the layer stacking direction is along the c-axis. In the structure of doyleite29, the layer is in the ac-plane and the stacking direction is along the b-axis (Fig. S3). Therefore, based on the layer stacking directions in each of the structures, the sharpness of the 4.32 Å−1 peak is related to the mean crystallite dimension of the layers. Other peaks, including the main reflections near 2–3.4 Å−1, are composed of mixed hkl indices, and thus the extent of broadening varies depending on the Miller index-l (in gibbsite, bayerite and nordstrandite) or -k (in doyleite) components. Commonly, non-uniform peak broadening in powder diffraction data is an indicative of anisotropic crystallite (or domain) size/strain line broadening33. For example, anisotropic crystallite size can result from crystal growth, where specific bonding interactions produce layered or columnar structures. Atomic dislocation-induced strain in comparison is a typical example of anisotropic strain broadening in a crystal34. Here, only the 4.32 Å−1 reflection is noticeably narrower than other reflections, and its Miller index nicely matches to the expected intralayer lattice plane in the four Al(OD)3 polymorphs. Thus, the observed non-uniform peak broadening and dependency on Miller indices for the 4.32 Å−1 reflection suggest the lack of translational order along the stacking direction33,35,36, e.g., random or turbostratic stacking, or finite-sized nanoparticles with anisotropic dimensions37,38,39, e.g., suspended monolayers.Fig. 1: In-situ observation of nucleation and growth events using neutron total scattering.a Difference ΔS(q) curves every 4 h relative to the first 4 h dataset, showing the reaction progression as indicated by increasing peak intensities. The short ticks at the top of the plot indicate the expected neutron Bragg reflections (of the top 25 peak intensities) for the four Al(OD)3 polymorphs. In each phase, the three most intense reflections are highlighted by red short ticks. These Bragg reflections are calculated using crystal structure data of Balan et al.31 for gibbsite, Zigan et al.32 for bayerite, and Demichelis et al.29 for doyleite and nordstrandite. b Averaged difference PDF ΔG(r) datasets (blues and black curves) obtained at four different time intervals. The PDF of the initial solution structure (completed at/within 4 h after the solution was made) is shown by the red curve in the bottom panel. The vertical black and red lines indicate the relationship of PDF peaks between datasets (see texts for details). See also Fig. S2b, c for plots with extended q and r ranges, respectively.The difference PDF ΔG(r) were obtained via Fourier transformation of the ΔS(q) intensities (using qmax of 28 Å−1) into the real-space signal (Fig. 1b). To reduce Fourier truncation ripples, a Lorch modification function was applied to each ΔS(q) to smooth derived ΔG(r) data. To improve signal-to-noise ratio, ΔG(r) datasets in time windows between 4–16, 16–28, and 28–36 h were then averaged, resulting in an 8–12 h interval for three ΔG(r) segments (Fig. 1b). These intermediate ΔG(r) curves show similar features to the signals obtained at the endpoint of the experiment, with overall intensities increasing with reaction time. In the initial solution PDF data (red curve in Fig. 1b), our previous geometric modeling18 indicates that: (i) peak-0 at ~0.97 Å is the intramolecular O-D bonds in D2O, OD- and aluminate ions, (ii) peak-1 at ~1.51 Å is mostly the intramolecular D-D distances of a D2O molecule, and (iii) peak-2 and -4 at ~1.79 and ~2.2–2.5 Å, respectively, correspond mainly to the intramolecular Al-O bonds and Al-D distances in tetrahedrally-coordinated aluminate species. These four peaks, and the aluminate-water and water-water correlations at longer distances, represent the initial solution structure, and are removed by the difference analysis. Therefore, the observed difference PDF ΔG(r) curves (top panel of Fig. 1b) represent the residual signals that contain pair-wise correlations involving primarily nucleating species, and their transformation into crystalline products.To interpret the structure of the growth phase, a single two-dimensional Al(OD)3 layer model was developed and tested to fit the PDF data observed at the endpoint of the experiment (Fig. 2a). This model consists of an isolated Al(OD)3 layer created from the gibbsite structure31, and no interlayer atom-atom correlations within the r-range being modeled (up to 30 Å; details are given in Section 1 of SI). Based on fitting results, peak intensities labeled 0, 3 and 4 (black) for the four sets of ΔG(r) data (Fig. 1b) correspond to the first coordination shell of O-D (~0.97 Å), Al-O (~1.91 Å), and Al-D (~2.3–2.5 Å) distances in an Al(OD)6 octahedron. The relatively broad peaks/oscillations centered at ~2.7, ~5.0 and ~7.5 Å mainly reflect the ordered O-O + O-D distances in the Al(OD)3 dioctahedral layer (e.g., in the dioctahedral layer the hexagonal cavities are patterned ~5 Å apart; see the insert structure in Fig. 2a). Note that peak-3 (Fig. 1b) also contains the intralayer D-bonds (~2–2.3 Å), which lie approximately in the ab-plane and point towards the vacant sites (Fig. 2a; insert structure). Accordingly, the growth reaction can be expressed as simply: 0.54Al(OD)4− + 0.23Al2O(OD)62− + 1.1Na+ + 0.1OD− + 0.23D2O → xAl(OD)3(s) + (1-x)Al(OD)4− + 1.1Na+ + (0.1+x)OD−, where the variable x defines the amount of precipitates (see the experimental section for solution composition). The intensity variations for the peak at ~1.53 Å (black peak-1 in Fig. 1b) do not match the Al(OD)3 layer structural correlations. Considering that neutron PDF is sensitive to changes involving D-bearing species, this peak likely corresponds to D-bonding interactions between the deuteroxide-Od and water-Dw sites (i.e., OD− solvation correlations18), due to the change in solution composition upon precipitation. Alternatively, the ~1.53 Å peak could correspond to inner-sphere sorption of Na+ to the surface O-sites of the Al(OD)3 layer, e.g., to the side of the hexagonal cavities, as predicted by molecular dynamics simulations of the gibbsite-NaOH(aq) interface40. The 4-to-16 h ΔG(r) data (light blue curve in Fig. 1b) also suggests a slightly shorter Al-O bonds than expected for Al-O bonds in octahedrally-coordinated configuration, i.e., the peak centered at 1.85 Å is in between the red dashed line (1.79 Å) for Al-O in tetrahedral aluminate species and the black solid line (1.91 Å) for Al-O in octahedral configuration. This intermediate Al-O bond length (between 1.79 and 1.91 Å) may indicate the presence of pentacoordinate species formed early in the reaction.Fig. 2: 2D Al(OD)3 single layer model fit and comparison of the residual with four interlayer correlation models.a The black circles and the red curve show the observed and calculated PDFs, respectively, and the gray curve at the bottom shows the difference (residual) between the two (Rw = 0.35). The observed PDF data is obtained at the end of neutron experiment. The inset structural plot illustrates the top and side views of an Al(OD)3 single layer. O atoms are shown as red spheres, D as white spheres, and Al as blue octahedra. The unit cell is outlined by black box, and intralayer D-bonds are shown as blue dashed lines. The A and B sites for the surface terminal-OD groups are also indicated. b The gray curve is the residual to the single layer model fit, and was repeated four times to facilitate comparison to the calculated interlayer correlations in all four types of Al(OD)3 polymorphs. Rw values, calculated for every 5 Å segments of the residual data, are given at the bottom of the plot. See also Fig. S4 for the simulated neutron PDFs of Al(OD)3 polymorphs. Here, crystal structure data of Balan et al.31 for gibbsite, Zigan et al.32 for bayerite, and Demichelis et al.29 for doyleite and nordstrandite were used.The residual from the fit of the single layer Al(OD)3 model to the data (Fig. 2b) shows features that could correspond to: (i) solute ions and water molecules coordinated around the layer, and (ii) correlations associated with interlayer stacking. For (i), we expect the weak oscillating residual signal, restricted to the short r range (<10 Å), due to disordering of surface-bound water/ion species (see other examples in refs. 40,41,42). For (ii) on the evaluation of interlayer stacking, the residual data is compared with the calculated interlayer correlations (Fig. S4c; details are given in Section 2 of SI) for all four Al(OD)3 polymorphs. As shown in Fig. 2b, on the basis of Rw analysis (in every 5 Å segments of the data), features in the residual curve correspond to the stacking patterns in either gibbsite or bayerite, but not to stacking patterns in nordstrandite and doyleite. Below ~15 Å, the residual curve corresponds to the bayerite stacking correlation, but between ~15–25 Å, the gibbsite stacking correlation model shows a better match to the overall oscillating widths and intensities (Fig. 2b). This indicates that individual Al(OD)3 nanolayers are intermediary particles that stack together by oriented attachment to form gibbsite- or bayerite-like layered heterostructures.Additional in-situ characterization using 27Al MAS NMR was performed on a sodium aluminate solution of the same concentration (separately prepared) to follow the growth of gibbsite/bayerite phases over 2 weeks period. The 27Al nucleus is quadrupolar, with a spin of 5/2, and the chemical shift of the resonance is sensitive to the Al3+ coordination environment. For Al3+, the isotropic chemical shift is 0 to 20 ppm in octahedral coordination, 30 to 50 ppm in pentacoordination, and 60 to 80 ppm in tetrahedral coordination43. As shown in Fig. S6a, only a single Lorentzian line shape corresponding to tetrahedrally-coordinated aluminate species in solution can be observed initially. After ~3 days, signal intensity in the octahedral region starts to show, which displays a quasi-Lorentzian line attributing to the slow spinning rate. Under the performed acquisition conditions (see Section 3 of SI), individual resonances for bayerite-like or gibbsite-like nanolayers remain unresolved, and instead, a single octahedral resonance is observed, representing the combined octahedral coordination in both polymorphs. The relative integrated intensity of the octahedral Al3+ signal increases to about 3.5% in 2 weeks period (Fig. S6b). We note the variation in the induction time between the two in-situ measurements under the same solution concentration. If one considers the stochastic nature of nucleation and the formed nuclei have to grow to appreciable sizes before they can be detected experimentally, studies have shown that variation in the induction times determined from a large number of measurements under well-defined/identical conditions typically results an exponential distribution function44,45. Thus, ruling out concentration errors, variation in the induction times observed here may result from differences between neutron and NMR experiment conditions, such as temperature and solution volume used. Another possibility for such variation could originate from multiple nucleation and growth processes, i.e., not a single nucleation/growth mechanism. That is during the initial stage of precipitation, the individual Al(OD)3 layers could be formed by monomer-by-monomer addition to a candidate nucleus (classical nucleation), or they could grow from an amorphous phase that facilitates the coordination change of tetrahedral Al3+ to octahedral Al3+ (nonclassical nucleation). Ex-situ characterization of precipitates is performed to differentiate between these two potential pathways.Ex-situ characterization of precipitatesPrecipitates were retrieved, via vacuum filtration, from sodium aluminate solutions after the neutron experiment at three different time points: 6 days, 45 days, and 3 months. Based on a combination of XRD characterization and 27Al MAS NMR spectroscopy, a clear signature of an amorphous phase was identified. The presence of an amorphous phase is expected, given the chemical complexity and high chemical potential of the starting solution. Quantitative phase analysis (Table 1) using the Rietveld method on XRD data showed that the precipitate is comprised of gibbsite and bayerite (consistent with in-situ neutron PDF analysis), and an amorphous phase (see XRD patterns in Figs. S7a, b and S8). The amount of gibbsite, bayerite and amorphous phase remained approximately constant across the time series. Raman spectra of the three precipitates also show band positions in the OD stretching vibration region corresponding to a mixture of gibbsite/bayerite (Fig. S9).Table 1 Results of XRD phase identification and Rietveld quantification (e.s.d. values in parentheses)The coordination state of Al3+ in the amorphous phase was determined using solid-state27Al MAS NMR. The 27Al MAS NMR spectra (Fig. 3) indicate that Al3+ is present in tetrahedral, penta and octahedral coordinations over the course of the experiment. This is to our knowledge the first time that a pentacoordinated Al3+ signal has been resolved during nucleation and growth of gibbsite/bayerite from a supersaturated alkaline aluminate solution. Previously, pentacoordinated species have only been reported in amorphous aluminum hydroxides precipitated at near neutral pH, or in alumina produced from the calcination of aluminum hydroxide46,47,48 and aluminum oxyhydroxide49.Fig. 3: Ex-situ characterization of precipitates at three time points.Single pulse, direct excitation 27Al MAS NMR spectra for precipitates collected/filtered after 6 days, 45 days, and 3 months. Vertical magnifications of select regions (8× in tetrahedra and 128× in pentacoordinate) are offset.The precipitates retrieved via vacuum filtration were then washed with either deuterated water (D2O) or deuterated ethanol (ETOD) at room temperature. ETOD was used to prevent dissolution of high soluble compounds, such as amorphous phases, during the washing step. The 27Al MAS NMR spectrum of the precipitate washed with D2O has only an octahedral resonance (Fig. 4) corresponding to gibbsite and/or bayerite, which is expected as these phases are poorly soluble in water (solubilities of 10−8.1 and 10−7.9 m50,51, respectively, in pure water at 25 °C). The 27Al MAS NMR spectrum for the precipitate washed with ETOD had both octahedral and tetrahedral resonances, suggesting that ETOD preserved the amorphous phase, which then partially crystallized into tetrahedral MSA, according to the XRD results (Table 1 and Fig. S7c). The pentacoordinated species was not observed in precipitates washed with either D2O or ETOD. The wt% proportion of the phases was dependent on the washing process (Table 1), and different amounts of gibbsite and bayerite resulted in a subtle increase in the shoulder of the octahedral resonance near 5 ppm (Fig. 4).Fig. 4: Effects of washing procedures on phase alternations.Single pulse, direct excitation 27Al MAS NMR spectroscopy of precipitates after 3 months that were washed with D2O, filtered only, or washed with ETOD. Vertical magnifications of select regions are offset. The filtered only sample is reproduced from Fig. 3 for comparison.To better resolve 27Al resonances, 27Al triple quantum MAS NMR (3QMAS NMR) spectroscopy was performed (Fig. 5). 3QMAS NMR spectroscopy reduces the second order quadrupolar broadening in MAS NMR spectra of quadrupolar nuclei by correlating multiple quantum coherences with their conversion into single quantum coherence52. This NMR acquisition results in two-dimensional spectra, where unique resonances that are often superimposed in one-dimensional spectra can be better resolved. However, the technique has low sensitivity compared to single pulse spectra (Figs. 3 and 4), so the less abundant pentacoordinated species is below the limit of detection in the 3QMAS NMR data. The 27Al 3QMAS NMR spectra of the solids washed with ETOD exhibit at least two tetrahedral environments (Fig. 5e). The first resonance, at an F1 dimension of 69.7 and an F2 dimension of 78.3 ppm, exhibits a well-defined quadrupolar line shape and similar to the resonance for protonated MSA22, in agreement with the XRD data. The second tetrahedral resonance is broad and shows no discernable quadrupolar line shape features, which can be attributed to tetrahedral aluminum in an amorphous phase. Only the second tetrahedral resonance corresponding to the amorphous phase is present in the spectrum for the filtered-only sample (Fig. 5c), and there are no tetrahedral resonances in the D2O washed sample (Fig. 5a). In the octahedral region, the 27Al 3QMAS NMR spectra shows three peaks (Figs. 5b, d, f). These can be assigned to the two Al sites in gibbsite and the two Al sites in bayerite, with partial overlap resulting in three peaks43. While the differences in wt. % of gibbsite and bayerite observed in XRD may be attributed to some changes in the octahedral region of the 3QMAS NMR spectra between the filtered and samples washed with ETOD or D2O, these could also potentially mask subtle contributions of octahedrally-coordinated amorphous species.Fig. 5: Verification of multiple Al3+ coordination states in precipitates.27Al 3QMAS NMR spectroscopy of samples washed with D2O, filtered only, or washed with ETOD, respectively, at a field strength of 14.1 T. The tetrahedral region is shown in (a), (c), and (e). The octahedral region is shown in (b), (d), and (f).The ex-situ NMR results indicate that transformation of Al3+ coordination from tetrahedral in solution to octahedral in aluminum deuteroxide may proceed either through, or in the presence of, an amorphous phase. This amorphous phase found in the current studied solutions is distinguished from other amorphous phases produced from neutralizing aqueous, acidic solutions of aluminum nitrate53. The amorphous phase is very sensitive to washing procedures, which may induce crystallization into gibbsite, bayerite, or monosodium aluminate hydrate (MSA). SEM images (Fig. S10), showing the morphology of aggregated solids, support XRD (Table 1) and NMR (Figs. 3–5) data. Washing with D2O precipitates show platelet aggregates resembling typical gibbsite morphology53,54, while precipitates washed with ETOD form smoother, more globular aggregates resembling an amorphous phase (Fig. S10). Note that there might have some potential impacts on products morphology with D54, the exact isotope effects of D for H on the morphology and rates of precipitation are however beyond the scope of this work.Multiple nucleation and growth processesCombining both in-situ and ex-situ observations, Fig. 6 illustrates the proposed multiple reaction pathways for gibbsite/bayerite nucleation and growth from alkaline sodium aluminate solutions. The starting supersaturated solution contains a distribution of aluminate species featuring tetrahedral Al3+ coordination, i.e., monomers, dimers, and possibly larger oligomers, all of which can play a role in nucleation and growth. In route 1, the formation of Al(OD)3 monolayers may start by monomer-by-monomer addition to form octahedrally-coordinated Al3+ nuclei, followed by the development of these nuclei into individual nanolayers visible to the naked eye (Fig. 6). This process is a classical nucleation and growth pathway in which the Al3+ coordination changed from tetrahedral in small aluminate species to octahedral in nanoplatelets is endergonic. The pentacoordinate Al3+ species found with solid state NMR spectroscopy, potentially bridges Al3+ coordination changes from tetrahedral solution species to octahedral Al3+ nuclei and/or is present at the edge of the nuclei. However, its presence is poorly abundant and not clearly resolvable via both the in-situ neutron total scattering and NMR approaches. At this stage of the reaction, the development of Al(OD)3 monolayers, instead of direct growth of gibbsite/bayerite nanocrystals, are preferred likely due to the effects of: (i) the bond-valence sum requirements55 between OD− and octahedrally-coordinated Al3+ (i.e., 0.5 bond valences for each OD− group in bridging two octahedrally coordinate Al3+, forming a neutral charged Al(OD)3 layer), and (ii) the stabilization of layers by interaction with surrounding water molecules, Na+, and/or OD−, which together act as steric forces preventing direct D-bonding between layers40. With time, the crystalline Al(OD)3 monolayer intermediates ultimately assemble into gibbsite/bayerite structures by particle attachment and alignment processes.Fig. 6: Schematic of multiple nucleation and growth processes.Gibbsite/bayerite formation from alkaline sodium aluminate solutions. The final faceted crystals are illustrative representations of final bulk crystal states. The exact crystal morphologies (SEM images in Fig. S10) are more complicated than the illustrations presented here.The amorphous precipitates observed via ex-situ characterization suggest the presence of an alternative nonclassical pathway to gibbsite/bayerite crystallization (Fig. 6, route 2), via aggregation of Na+-aluminate oligomeric precursors. This amorphous compound consists mainly tetrahedral Al3+ bridged together by μ2-oxygene (i.e., similar to both the Al2O(OH)62− dimer and the MSA phase), and with some minor pentacoordinated Al3+. Association of pentacoordinate Al3+ species with the amorphous surface or as a part of oligomeric network formers would potentially provide a lower energy pathway enhancing Al3+ coordination transformation (from tetrahedra to octahedra) and growth of the Al(OD)3 monolayers. Once the monolayers are formed, the subsequent layer assemblages can be expected, i.e., the processes likely similar to the fabrication of multilayer assemblies based on D/H bonding using the existing surfaces/seedings56.Alternatively, the two nucleation pathways leading to the formation of Al(OD)3 monolayers, could be independent events. That is, the amorphous phases may not contribute substantially to the Al(OD)3 layer nucleation and growth. The fact that we are able to observe amorphous materials from the precipitates after several months of dispersion in the solution suggests that the oligomeric precursors for the nucleation of amorphous intermediates may impede Al(OD)3 layer formation via consuming active aluminate monomers/dimers species to form complex Na+-aluminate-D2O networks. This creates a dynamically arrested state for part of aluminate species within the amorphous network, where aluminate species may become active again upon dissolution of amorphous precipitates. Particularly, if the free energy barriers to form gibbsite/bayerite from amorphous phase are too high to overcome, this would entail that the amorphous phase would eventually transfer only to the MSA salt (due to structure similarity) given a long reaction time or upon partial dehydration (Fig. 6; green dashed line).The precipitation of Al(OD)3 polymorphs (gibbsite vs. bayerite) from supersaturated alkaline aluminate solutions must also be addressed. In the past, using solubility data to reflect metastable equilibria50,51,57, the tendency for bayerite formation (with respective to gibbsite) is generally understood as a result of metastable precipitate from supersaturated solutions. However, many of the thermodynamic properties of Al(OD/H)3 polymorphs are controlled by modes of stacking of the Al(OD/H)3 layers29,30. Thus, layer-by-layer assembly of Al(OD)3 monolayers must play a significant role in polymorphism and phase selection. In the Al(OD)3 monolayers, the surface -OD groups are in hexagonal close packing arrangements, and therefore the -OD groups are positioned differently on each side of the surfaces, termed A vs. B sites (Fig. 2a; top insert). In the processes of layer attachment, the likelihood of A-site termination seeing another A-site termination (A-A, or equivalently B-B) is the same as A-site termination seeing B-site termination (A-B or B-A). Hence, from a statistical point of view, the A-B stacking sequences (in bayerite, doyleite and nordstrandite) have the same occurrence probability as the A-A stacking sequences (in gibbsite). The lack of doyleite and nordstrandite phases indicates that the controlling reactions at the interfaces between two monolayers are complicated, involving not only the dynamics of water and ions in the interfacial region, but also the orientational movements of the terminal -OD groups, and their D-bond cross-linkage strength upon attachment. Our findings on gibbsite/bayerite-like layered heterostructures may provide insights into the development of mechanistic descriptions for layer assembly processes. A few of theoretical works dedicated to connect molecular-scale details and energy barriers for layer-layer interactions in aluminum (oxy)hydroxide systems can be found in refs. 58,59,60,61,62,63.
