Rare-earth elements (REEs) are indispensable in various applications ranging from catalysis to batteries and they are commonly found from phosphate minerals. Xenon is an excellent exogenous NMR probe for materials because it is inert and its 129Xe chemical shift is very sensitive to its local physical or chemical environment.
Microporous and Mesoporous Materials 344 (2022) 112209 Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso 129 Xe NMR analysis of pore structures and adsorption phenomena in rare-earth element phosphates Roya Khalili a, Anu M Kantola a, Sanna Komulainen a, Anne Selent a, Marcin Selent a, b, Juha Vaara a, Anna-Carin Larsson c, Perttu Lantto a, **, Ville-Veikko Telkki a, * a b c NMR Research Unit, University of Oulu, P.O.Box 3000, FIN-90014, Finland Centre for Material Analysis, University of Oulu, P.O.Box 3000, FIN-90014, Finland Chemistry of Interfaces, Luleå University of Technology, SE-97187 Luleå, Sweden A R T I C L E I N F O A B S T R A C T Keywords: Rare-earth element phosphate 129 Xe NMR spectroscopy DFT calculations Rare-earth elements (REEs) are indispensable in various applications ranging from catalysis to batteries and they are commonly found from phosphate minerals Xenon is an excellent exogenous NMR probe for materials because it is inert and its 129Xe chemical shift is very sensitive to its local physical or chemical environment Here, we exploit, for the first time, 129Xe NMR for the characterization of porous structures and adsorption properties of REE phosphates (REEPO4) We study four different REEPO4 samples (REE = La, Lu, Sm and Yb), including both light (La and Sm) and heavy (Lu and Yb) as well as diamagnetic (La and Lu) and paramagnetic (Sm and Yb) REEs 129Xe resonances are very sensitive to the porous structures and moisture content of the REEPO4 samples In the samples treated at a lower temperature (80 ◦ C), free water hinders the access of hy drophobic xenon into small mesopores, but the treatment at a higher temperature (200 ◦ C) removes the free water and allows xenon to explore the mesopores Based on a standard two-site exchange model analysis of the variable-temperature 129Xe chemical shifts, as well as its proposed, novel modification for paramagnetic mate rials, the average mesopore sizes were determined The size was the largest (79 nm) for the La sample with mixed monazite (70%) and rhabdophane (30%) phases and the smallest (6 nm) for the Yb sample with pure xenotime phase The mesopore sizes of the Lu and Yb samples (12 and nm) differed by a factor of two regardless of their similar xenotime phase The 129Xe NMR analysis revealed that the heats of adsorption of the samples are similar, varying between 8.7 and 10.1 kJ/mol For diamagnetic samples, computational modelling confirmed the order of magnitude of the chemical shifts of Xe adsorbed on surfaces and therefore the validity of the two-site exchange model analysis Overall, 129Xe NMR provides exceptionally versatile information about the pore structures and adsorption properties of REEPO4 materials, which may be very useful for developing the extraction processes and applications of REEs Introduction Rare-Earth Elements (REEs), comprising lanthanoids, yttrium and scandium, are broadly used in many important applications ranging from catalysis and magnets to electric motors, and their global need is rapidly increasing [1] Lanthanoids have 4f sublevel in their valence shell with unoccupied orbitals and unpaired electrons This special electron configuration is the reason for their useful electric, magnetic, and optical properties Typically, REEs exist as trivalent cations (REE3+), they show similar physicochemical properties, and they are found in the same ores [2,3] Phosphate compounds (REEPO4 materials) are one of the prevalent hosts of REE3+ ions in minerals [2,4] Depending on the REE3+ ion size, mechanochemistry, method and conditions (such as temperature and pH) of synthesis [2,4–11], they form phosphates in monoclinic mona zite, monoclinic rhabdophane, monoclinic churchite and tetragonal xenotime phases [5,11–13] Rhabdophane and churchite are hydrated structures containing varied amounts of structural water, whereas monazite and xenotime are anhydrous phases, where residual water can only be found on the surfaces of the grains The different synthetic * Corresponding author ** Corresponding author E-mail addresses: perttu.lantto@oulu.fi (P Lantto), ville-veikko.telkki@oulu.fi (V.-V Telkki) https://doi.org/10.1016/j.micromeso.2022.112209 Received 29 June 2022; Received in revised form 25 August 2022; Accepted September 2022 Available online 14 September 2022 1387-1811/© 2022 The Authors Published by Elsevier Inc This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) R Khalili et al Microporous and Mesoporous Materials 344 (2022) 112209 procedures also determine the size and shape of the formed grains [14, 15] For the extraction and utilization of REEs, it is important to know the physicochemical properties of REEPO4:s In our previous study [16], we showed that experimental solid-state 31P NMR spectroscopy, combined with 31P NMR calculations by density-functional theory (DFT) provided detailed information about the local structures of rare-earth phosphate minerals We prepared selected rare-earth phosphate (REE = La, Sm, Lu and Yb) samples through the homogenous acidic solution method, which is one of the most common methods for synthesizing REEPO4:s [4, 5] The experimental and computational 31P NMR analysis of the ob tained homogenous, nanocrystalline products allowed the determina tion of the local structures and water molecule coordination on the surfaces of monazite, xenotime and rhabdophane phases An alternative way to study the properties of materials by NMR spectroscopy is to introduce NMR-active probe molecules to them Xenon gas is an excellent probe for materials, as it is an inert noble gas, its 129Xe spin-1/2 isotope has a relatively high natural abundance and sensitivity, as well as chemical shift that is very sensitive to its local physical or chemical environment Furthermore, its NMR sensitivity can be improved by several orders of magnitude by the spin-exchange op tical pumping (SEOP) method [17–19] 129Xe NMR is especially useful for probing micro- and mesoporous structures of porous materials such as zeolites, clathrates, metal-organic frameworks, porous organic cages and their porous liquids, mesoporous (biogenic) silicas, coals, ionic liquids, geopolymers, electrodes, diesel particulate filters, rubber, starch, soils, clays, cements, and shales [20–47] Furthermore, it is broadly exploited also in biosensor, lung imaging and microfluidics applications [48–55] Here, we for the first time exploit 129Xe NMR in the investigation of REEPO4 samples and demonstrate that it provides extraordinarily ver satile information about the porous structures and gas adsorption properties of the materials Experimental analysis is supplemented by computational modelling [29–33,56,57] assisting in microscopic inter pretation of 129Xe NMR data Complementary information of the particle sizes, porous structures and phases is obtained by laser diffraction and Field Emission Scanning Electron Microscopy (FESEM) analysis 400 spectrometer and a 5-mm BBFO probe The spectra were collected with the spin-echo sequence to reduce baseline distortions The lengths of the 90◦ and 180◦ pulses were 8.75 and 17.50 μs, respectively The number of scans was 16 for the diamagnetic La and Lu samples, 64 for the paramagnetic Sm, and 2048 for the paramagnetic Yb Due to the different magnetic nature of the rare-earth elements in REEPO4, the echo time and the relaxation delay varied for each sample and each experi ment lasted 16–48 Relaxation delay and delay τ between the 90◦ and 180◦ pulses were 85 s and μs, respectively, for the La (80) sample, 85 s and 10 μs for the La (200) sample, 180 s and μs for the Lu (80) sample, 210 s and 10 μs for the Lu (200) sample, 15 s and μs for the Sm (80) sample, 30 s and 10 μs for the Sm (200) sample, s and μs for the Yb (80) sample, and s and μs for the Yb (200) sample The experi ments were performed at variable temperatures ranging from 180 to 301 K with the step of about K and with 30 of temperature sta bilization delay between the experiments The samples were cooled with a liquid nitrogen evaporator 129Xe chemical shifts were referenced with respect to a shift of a 2.15 atm 129Xe gas resonance set to ppm 2.3 FESEM and particle size distribution analysis The crystal and particle shapes of the REE phosphate samples were analyzed by a Zeiss Sigma FESEM instrument, which is equipped with scanning electron microscope, energy dispersive x-ray spectroscopy (EDS) analyzer and electron backscatter diffraction (EBSD) camera High-resolution FESEM images were recorded by detecting the emitted secondary electrons (SE) from the electron beam with kV acceleration voltage The particle size distributions of the REEPO4 samples were measured by a multi-wavelength laser diffraction particle size analyzer (Beckmann Coulter LS 13320) with a universal liquid sample handling module Before the analysis, the samples were dissolved in isopropanol Ultra sonic treatment was used over the samples to break the larger aggregates before the measurements In particle-size calculations, the Fraunhofer optical model [58] was used Particle sizes were analyzed in the range of 0.04–2000 μm 2.4 Computational modelling Materials and methods Quantum-mechanical calculations of 129Xe NMR shielding tensors were carried out at DFT level for the Xe atom on several hydrated sur faces of the dense xenotime and monazite phases of diamagnetic LuPO4 and LaPO4, respectively Starting from the bulk structures optimized at DFT level in the earlier study of 31P NMR of these systems [16], we cut surface models for the most common Miller planes, {100} for xenotime [59] and {010} for monazite [60] To see how the Xe chemical shifts depend on different surfaces, also {110} and {101-Y} surface models for xenotime [59] were built Slab models shown in Figs S8–S11 were constructed with the AMS2020 package, in which pre-optimization was done with DFTB module [61] at the GFN1-xTB semi-empirical level [62,63] First, a unit cell slab model of each Miller plane was constructed A two unit-cell thick slab of four phosphate (and REE) layers in the surface normal (c lattice) direction was separated by ca 20 Å vacuum layer To resemble experimental hydrated conditions, one side of the slab was terminated by two water molecules, for which positions were pre-optimized keeping the slab frozen The actual model for 129Xe NMR calculations consisted of × unit cells in the surface directions to prevent interactions be tween periodic images of the Xe atom placed on the hydrated face of the slab The Xe position was then pre-optimized together with the hydrated top layer of the two phosphate (and REE) layers while keeping the bottom layer fixed to the original DFT geometry The pre-optimized structures were used as inputs for periodic DFT calculations of 129Xe NMR shielding tensors with CASTEP code [64] First, the final slab model structures (see Figs S8–S11 and cif files in Supplementary Information) were optimized at DFT level using “fine” 2.1 Samples Four REEPO4 samples (REE = La, Sm, Lu and Yb) were synthesized through the homogenous acidic solution method [5,8] as described in detail in our previous publication [16] To reach out the diverse features of the large REE group, four REEs were selected to represent the size and magnetic properties of this group Diamagnetic La and paramagnetic Sm were selected from light and large REEs, while diamagnetic Lu and paramagnetic Yb represent heavy and small ones Before adding the samples to mm NMR tubes, they were treated in ambient atmosphere either at 80 ◦ C for h or at 200 ◦ C for 1–2 d to study the effect of water evaporation on the accessibility of pores We note that those moderate treatment temperatures are not expected to change the structure of materials, as seen in our previous publication [16] After the tempera ture treatment, about 0.3 g of REEPO4 was inserted in a mm NMR tube, the tube was connected to a vacuum line and 129Xe isotope-enriched (91%) Xe gas was condensed into the sample by using liquid nitrogen Finally, the tube was flame sealed The amount of 129Xe gas added to the samples corresponds to a pressure of atm in an empty tube Hereafter, the REEPO4 samples are referred to based on their metal element and the treating temperature For example, the La phosphate sample treated at low temperature (80 ◦ C) is referred to as La (80) 2.2 129 Xe NMR experiments 129 Xe NMR experiments were carried out with a Bruker Avance III R Khalili et al Microporous and Mesoporous Materials 344 (2022) 112209 quality, PBE functional [65] and Grimme’s D2 dispersion correction [66] by keeping the bottom layer fixed similarly as in the pre-optimization Then, 129Xe NMR shielding tensors were computed with the gauge including projector augmented waves (GIPAW) method at scalar relativistic zeroth-order regular approximation (SR-ZORA) level utilizing on-the-fly-generated (OTFG) ultrasoft pseudopotentials [67,68] with 572 eV cut-off energy Dense Monkhorst-Pack k-point sampling of the Brillouin zone was assured by choosing Δk < 0.03 Å− in each lattice direction The low-density xenon gas used as the experi mental chemical shift reference was approximated with a single 129Xe atom placed at the center of a cubic periodic cell with sides of 20 Å, for which NMR shielding was computed at the same level of the theory as in the REEPO4 slab models Table Mean particle size (μm) of the rare earth phosphate samples La Lu Sm Yb 8.7 7.3 3.6 4.9 shown in Fig S3 The particle size varies between 3.6 and 8.7 μm, being largest for the La sample and smallest for the Sm sample The particle sizes measured by laser diffraction reflect the sizes of overall crystal aggregates (c.f., FESEM images in Figs S1 and S2), not individual crystals, and therefore they are significantly larger than the crystal sizes reported above 3.2 Results and discussion 129 Xe NMR spectral features and signal assignment 129 Xe spectra of xenon in the REEPO4 samples measured at 180, 240 and 295 K are shown in Fig Full temperature series can be found from Figs S4–S7 The 129Xe spectra reflect the diamagnetic (La and Lu) and paramagnetic (Sm and Yb) nature of the samples, as discussed below In the discussion, it is important to understand that diffusion-driven ex change of Xe between different sites significantly affects the chemical shifts and line shapes If the exchange is slow in the NMR time scale, different sites produce separate peaks If the exchange is fast, only a single exchange-averaged peak is observed, and the chemical shift is a population-weighted average of the shifts of the exchanging sites In the intermediate exchange region, broadened signals are observed In the case of two-site exchange, the NMR time scale is τ = 1/(2πΔν), where Δν is the difference of the resonance frequencies of 129Xe in the two sites [69] At 295 K, the La (80) sample shows two 129Xe resonances at around and 40 ppm The ppm signal is expected to arise from free-like Xe in large, micrometer-size pores in between the particles (particle size 8.7 3.1 FESEM and particle size distribution analysis Fig shows FESEM images and previous results [16] of the powder x-ray diffraction (PXRD) phase analysis of the REEPO4 samples FESEM images with different magnification are shown in Figs S1 and S2 Ac cording to the PXRD analysis [16], La (both 80 and 200) is a mixture of monazite (70%) and rhabdophane (30%) phases The phase of Sm (80 and 200) is rhabdophane, while the phase of both Lu (80 and 200) and Yb (80 and 200) is xenotime The FESEM images show a cylindrical shape for the La and Sm nanocrystals while the Lu and Yb nanocrystals are spherical The crystal dimensions vary from tens to hundreds of nanometers, and the crystals are aggregated together, forming larger particles The La sample with a mixed monazite and rhabdophane phase shows smaller crystals with average length and width of 120 and 25 nm in comparison to the pure rhabdophane Sm sample crystals with average length and width of 250 and 30 nm The average diameters of the spherical nanocrystals in the Lu and Yb samples are 90 and 80 nm, respectively The mean particle sizes of the REEPO4 samples measured by laser diffraction are reported in Table and the particle size distributions are Fig 129Xe NMR spectra of xenon in the REEPO4 samples measured at 180, 240 and 295 K Number 80 in parentheses refers to samples treated at 80 ◦ C and 200 refers to samples treated at 200 ◦ C Note the extended chemical shift scale for the paramagnetic Yb samples (spectra on the right) Fig FESEM images of the rare-earth phosphate samples as well as their phase structures determined by PXRD [16] The La and Lu samples are diamagnetic, while the Sm and Yb samples are paramagnetic R Khalili et al Microporous and Mesoporous Materials 344 (2022) 112209 μm, see Table 1), because its chemical shift is close to that of the free Xe the particles is observed at higher temperatures However, some meso pore sites are still accessible, and their signal becomes observable at lower temperatures due to increased adsorption and decreased exchange rate At the lowest temperature (180 K), the chemical shifts of the mesopore signals of the Lu (80) and Lu (200) samples are almost equal, supporting the interpretation about their similar origin The second, broad, lower chemical shift signal of the Lu (80) sample may arise from partially water-filled mesopores, leading to faster exchange between the mesopore and free Xe sites The spectra of the paramagnetic Sm (80) sample (with Sm3+ ions in the f configuration and the spin, orbital and total angular momentum quantum numbers S = 5/2, L = and J = 5/2, respectively) include a single, broad peak, whose chemical shift increases from about 35 to 205 ppm when the temperature decreases from 295 to 180 K Again, the peak is interpreted to arise predominantly from Xe in mesopores in between the cylindrical nanocrystals of the Sm sample (see Fig 1) The broadness of the signal may partially reflect the paramagnetic nature of the Sm sample On the other hand, the asymmetric broadening of the peak to wards lower chemical shift values at higher temperatures may be a consequence of intermediate exchange between the mesopore and free Xe sites As for the Lu sample, the sites are not well resolved in the spectrum due to the relatively small particle size (3.6 μm, see Table 1) Spectral features of the Sm (200) sample are similar to Sm (80), but the chemical shifts are 10–15 ppm higher As for the other samples, we interpret that the increased chemical shift is a consequence of the increased accessibility of mesopores due to water evaporation The total water content of the Sm (80) sample (0.91 mol per mole of SmPO4) is higher than that of La (80) but lower than that for Lu (80), and the weight of the Sm sample decreases about 4% when the sample is heated from 80 to 200 ◦ C [16] Both the 129Xe chemical shifts and line widths of the Yb samples (Yb3+ in the 4f13 configuration with S = 1/2, L = and J = 7/2) are significantly larger than those of the other REEPO4 samples due to strong paramagnetic interactions The fact that the shift is even larger in Yb samples than in the other present paramagnetic systems involving Sm, is expected based on the five times larger magnitude of the magnetic √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ moment of Yb3+, μ = gJ J(J + 1)μB ≈ 4.54μB (with gJ the Land´e gfactor of the ion and μB the Bohr magneton) than that of Sm3+, μ ≈ 0.85μB Such differences are reflected, besides the observable chemical shifts, also in the relative sizes of the “blind spheres” around the lanthanide ions, in which rapid paramagnetic relaxation renders the NMR resonances altogether unobservable [70] At 295 K, the chemical shift is about 160 ppm, and the line width is about 150 ppm We note that, as described in our previous publication, also the 31P resonance of the Yb sample was much broader than that of the other paramagnetic Sm sample (see Fig in Ref [16]) At 180 K, the 129Xe chemical shift of Yb (80) is very high, about 340 ppm The 129Xe shift of Yb (200) is about 80–100 ppm larger than that of Yb (80) due to the increased accessibility of mesopores in between the spherical nanocrystals (see Fig 1) because of water evaporation The water content of Yb (80) is the highest (1.58 mol per mole of Yb) among the REEPO4 samples studied here, and the weight of Yb decreases slightly over 2% when the sample is heated from 80 to 200 ◦ C [16] Due to the relatively small particle size (4.9 μm), the free Xe site is not resolved in the spectra gas (0 ppm) The 40-ppm signal is interpreted to arise from Xe adsorbed into nanometer-size (~1–100 nm, mostly in the mesoporous region) pores, because the shift is typical for Xe in mesoporous materials [71], and there are lots of nanometer-size porous structures visible in between the cylindrical nanocrystals in the FESEM images (see Fig 1) The chemical shift of the mesopore signal increases with decreasing tem perature and reaches the value of about 170 ppm at 180 K Simulta neously, the intensity of the free Xe signal decreases with decreasing temperature, most probably due to increased adsorption of Xe into mesopores The spectra of the La (200) sample are very similar to those of La (80), indicating that water evaporation at the higher temperature does not significantly change the porous structures and surface in teractions probed by Xe According to the thermogravimetric analysis (TGA) reported in our previous publication (Fig and Table in Ref [16]), the total water content of the La (80) sample is relatively low (0.69 mol per mole of La), and the weight of the sample decreased by less than 2% when the preparation temperature was increased from 80 to 200 ◦ C, which may explain the similarity of the La (80) and La (200) spectra We note that a part of the evaporated water may be included in the rhabdophane structure, and that water is not expected to block mesopores At 295 K, the 129Xe spectrum of the Lu (80) sample includes a single peak around 10 ppm The chemical shift of the peak increases with decreasing temperature, and it is about 170 ppm at 180 K At the lower temperatures, below 240 K, another, narrower signal appears at a higher chemical shift, which reaches the value of about 210 ppm at 180 K In contrast, the Lu (200) sample only shows a single, broad 129Xe resonance at all temperatures, with the chemical shift increasing from about 90 to 215 ppm when temperature decreases from 295 to 180 K We interpret that this signal arises predominantly from the mesopores residing in between the spherical nanocrystals of Lu (see Fig 1) However, most likely the signal is significantly broadened because of relatively fast exchange between the mesopore-adsorbed and the free Xe sites at higher temperatures Contrary to the La sample, those sites not produce well-resolved peaks to the spectrum because the exchange between the sites is faster due to smaller particle size of Lu (La: 8.7 μm; Lu: 7.3 μm; see Table 1) According to the TGA analysis, the total water content of the Lu (80) sample is relatively high (1.14 mol per mole of Lu), and the weight of the sample decreases by 2% when the preparation temperature was increased from 80 to 200 ◦ C [16] We interpret that water hinders the access of the hydrophobic Xe to the mesopores in Lu (80) samples, and therefore only a signal characteristic to the free Xe site in between Table Parameters resulting from the fits of Eq (1) with the experimentally observed 129 Xe chemical shifts of xenon in the mesopores of the REEPO4 samples (δs = chemical shift of129Xe adsorbed on the surface of the pore; D = mean pore diameter; Q = effective heat of adsorption) As explained in the text, the pa rameters of the samples treated at the higher temperature (200 ◦ C) are expected to better represent the real physical properties of the REEPO4 samples The re sults of fits of the modified Terskikh equation (Eq (2)) for the paramagnetic Sm (200) and Yb (200) samples are reported in Table REE δS (ppm) D/ɳRK0 D (nm)b Q (kJ/mol) La (80) La (200) Lu1 (80)a Lu2 (80)a Lu (200) Sm (80) Sm (200) Yb (80) Yb (200) 268 ± 265 ± 340 ± 360 ± 241 ± 480 ± 413 ± 550 ± 483 ± 6300 ± 200 6770 ± 80 400000 ± 100000 11000 ± 3000 1020 ± 120 12300 ± 500 5000 ± 200 537 ± 15 550 ± 40 73 ± 78.8 ± 0.9 4300 ± 1200 120 ± 30 11.8 ± 1.4 143 ± 58 ± 6.3 ± 0.2 6.4 ± 0.4 9.83 ± 0.11 10.13 ± 0.04 15.3 ± 0.7 10.3 ± 0.7 9.2 ± 0.3 9.7 ± 0.3 9.02 ± 0.14 6.1 ± 0.3 8.3 ± 0.2 40 40 40 15 30 3.3 Analysis of adsorption 129 Xe chemical shifts: mesopore sizes and heats of The 129Xe chemical shifts of xenon adsorbed in mesopores of the REEPO4 samples are plotted in Fig As described by Terskikh et al [71], the chemical shift of Xe in mesoporous materials can be approxi mated to be a population-weighted average of the shifts in the free and adsorbed Xe sites, leading to the following dependence between the shift and physical properties of the sample: a Lu (80) had two mesopore signals in its spectrum, Lu1 refers to the lower chemical shift signal and Lu2 refers to the higher chemical shift signal b D is calculated by assuming that ɳ = (cylindrical pore geometry) and K0 = 3.47⋅10− 13 m mol K1/2 J− R Khalili et al Microporous and Mesoporous Materials 344 (2022) 112209 Here, δO S is the orbital shift and the second term, associated with the constant A, considers the inverse temperature dependence due to hy perfine interaction If zero-field splitting is included (in triplet or higher spin states), A may also be temperature dependent, but here A is assumed constant Consequently, the modified Terskikh model for paramagnetic materials is: δ= δOS + TA D + ηR√̅̅T K exp(Q/RT) (3) The parameters resulting from the fits of Eq (3) with the chemical shifts of the paramagnetic samples Sm (200) and Yb (200) are shown in Table In the fits, parameter δOS was fixed to be equal to the δS of the diamagnetic sample with similar phase reported in Tables and i.e., δS of La (200) for Sm (200) and δS of Lu (200) for Yb (200) The parameter A related to the hyperfine interaction is 70% higher for Yb (200) than Sm (200), reflecting again the stronger paramagnetic interactions in the former sample The theoretical expression for this parameter, based on the Kurland-McGarvey theory of paramagnetic shift [72] involves the hyperfine coupling tensor of the 129Xe nucleus in the two materials The latter, in turn, depends on both the extent of spin delocalization and the detailed dynamics of the Xe guest in the systems, explaining why one cannot expect the size of the relative paramagnetic shifts to directly follow the size of the magnetic moments of the paramagnetic metal centers, quoted above The modified Terskikh model fits result in smaller pore diameters D and slightly different heats of adsorption for Sm (200) and Yb (200) The fact that the changes are larger than the error bars stresses the importance of using the modified model repre senting more accurately the paramagnetic systems The values of D and Q are taken as correct parameter values for the Sm (200) and Yb (200) samples in the discussion below According to the 129Xe chemical shift fits of the REEPO4 samples treated at the higher temperature (200 ◦ C), the mean pore diameters of the La and Sm samples, 79 and 40 nm, are significantly larger than those of the Lu and Yb samples, 12 and nm According to the FESEM images shown in Fig 1, the La and Sm samples have similar cylindrical nano crystals, and the average crystal width is about 25–30 nm Most likely the mesopores probed by Xe are cavities in between the crystals or crystal bundles The Lu and Yb samples contain spherical nanocrystals with a diameter of about 80–90 nm, and the 129Xe NMR analysis implies that the mesopores in between the spherical nanocrystals are smaller than those between the needle-shaped nanocrystals Interestingly, the mesopore sizes of the Lu and Yb samples (12 and nm) differ by the factor of two, regardless of their similar xenotime phase structure Ac cording to the FESEM images, the spherical nanocrystals of Lu are slightly larger than those of Yb, which may explain the different sizes of mesopores in between the nanocrystals Furthermore, the mean particle size of Lu (7.3 μm) is also higher than that of Yb (4.9 μm), see Table The observed differences may be interesting from the point of view of extraction processes and applications of REEs The mean pore sizes, as Fig 129Xe chemical shifts of xenon adsorbed in the mesopores of the REEPO4 samples as a function of temperature Solid and dash lines show the fits of Eq (1) with the experimental data Only the Lu (80) sample spectra feature two pore peaks (see Fig 2) δ= δS D + ηR√̅̅T K exp(Q/RT) (1) Here, δS is the chemical shift of 129Xe adsorbed on the surface of the pore, D is the mean pore diameter, η is the pore geometry factor (e.g., equal to for cylindrical pores), R is the universal gas constant, T is the temperature, K0 is a pre-exponential factor, and Q is the effective heat of adsorption According to the model, the observed increase of chemical shift with decreasing temperature is a consequence of increased relative population of Xe on the surface site due to adsorption The fits of Eq (1) with the 129Xe chemical shifts of xenon adsorbed in the mesopores of the REEPO4 samples are shown in Fig (solid and dash lines) Adjustable parameters in the non-linear least squares regression were δS, D and Q The resulting fitting parameters are listed in Table The values of pore diameter D were calculated by assuming cylindrical pore geometry (ɳ = 4) and a value of pre-exponential factor K0 of 3.47⋅10− 13 m mol K1/2 J− The latter value was estimated based on the general correlation between the chemical shift and pore size in porous silica-based materials using a typical heat of adsorption of 10 kJ/mol [24] According to the fits, the chemical shifts of Xe adsorbed on the sur faces of the diamagnetic La (80) and La (200) samples are equal within the error bars, about 265 ppm For the diamagnetic Lu (200) sample, δS is almost equal to the La samples, about 241 ppm, regardless of their different phase structures (La: monazite 70%, rhabdophane 30%; Lu: xenotime) On the other hand, Lu (80) shows significantly higher δS for both signals, about 350 ppm The higher δS might be a consequence of water on surfaces; on the other hand, it may also be an artefact caused by the assumptions of the chemical shift model for mesoporous materials (Eq (1)), which may not be valid because of the restricted accessibility of the mesopores due to the moisture Therefore, the fitting parameters of the samples treated at the higher temperature (200 ◦ C) are expected to represent more accurately the real physical properties (e.g., pore sizes) of the REEPO4 samples Sm (200) shows significantly higher δS, about 413 ppm, than La (200) and Lu (200) samples, most probably due to its paramagnetic nature The shift of Sm (80) sample is even higher, about 480 ppm The shift of paramagnetic Yb (200), about 483 ppm, is slightly higher than that of the other paramagnetic sample, Sm (200), and the shift of Yb (80) is even higher, 550 ppm In the model described by Eq (1), it is assumed that chemical shift of Xe on the surface is independent of temperature This is not true for materials with paramagnetic ions, where the chemical shifts of the neighboring nuclei are expected to be inversely dependent on temper ature [70,72]: A δS (T) = δOS + T Table Parameters from modified Terskikh model for paramagnetic samples (Eq (3)) δO S = orbital shift; D = mean pore diameter; Q = effective heat of adsorption; A = constant associated with hyperfine interaction REE a δO S (ppm) D/ɳRK0 D (nm) Q (kJ/ mol) A (ppm K) Sm (200) Yb (200) 265 ± 3500 ± 200 500 ± 50 40 ± 8.7 ± 0.2 5.7 ± 0.6 9.6 ± 0.3 22000 ± 3000 36400 ± 500 241 ± a The orbital shift δO S was fixed to the value of δS of the diamagnetic sample with similar phase reported in Tables and i.e., δS of La (200) for Sm (200) and δS of Lu (200) for Yb (200) (2) R Khalili et al Microporous and Mesoporous Materials 344 (2022) 112209 determined by 129Xe NMR, of the Lu and Sm samples treated at the lower temperature (80 ◦ C) appear to be larger than in the corresponding samples treated at the higher temperature, but this is because of the restricted access to the smaller mesopores due to moisture The meso/ nanopore sizes experienced by fluids in the REEPO4 samples are very difficult to interpret from the FESEM images, and therefore 129Xe NMR analysis provides valuable additional information about the porous structures The heats of adsorption (Q) for the samples treated at the higher temperature are quite similar, ranging from 8.7 kJ/mol for Sm (200) to 10.1 kJ/mol for La (200) The values are within the range of heats of adsorption of the silica gels (8–21 kJ/mol) [71] 3.4 Computational modelling of 129 Table Calculated 129Xe chemical shifts (CSs) of xenon on monazite (LaPO4) and xen otime (LuPO4) surfaces The CS values calculated for the most common Miller planes are shown along with the closest distances between Xe and REEPO4 surface atoms Phase Surface CS (ppm)a Xe– REE (Å) Xe–P (Å) Xe–O (Å) Xe– Ow (Å) Xe– Hw (Å) Monazite LaPO4 {010} LuPO4 {100} LuPO4 {110} LuPO4 {101-Y} 381 3.86 4.21 3.41 3.58 3.96 185 4.99 4.48 3.50 3.62 3.01 240 3.84 4.69 3.43 3.62 2.75 243 3.86 4.28 3.47 3.55 3.21 Xenotime Xenotime Xenotime Xe chemical shifts Table reports the calculated 129Xe chemical shifts (CSs) of xenon on the diamagnetic monazite (70% of La sample) and xenotime (Lu sample) surfaces The structures used in the calculations included also surface water (see Section 2.4), because, according to the TGA analysis [16], the sample treatment at 200 ◦ C removes all free water, but surface water evaporates only at higher temperatures In this regard, the computed 129 Xe CSs are comparable with the experimental CSs of Xe on the sur faces of REEPO4 samples (parameter δS in Table 2) In the most common Miller plane for LaPO4 monazite, {010} [60], the calculated CS is about 380 ppm, which is about 115 ppm higher than experimentally observed CS of Xe on La (200) surface (265 ppm) There are at least three conceivable reasons explaining the overestimation: firstly, pure DFT functionals, like the current PBE, are known to lead to a drastic (even on the order of 100 ppm) systematic overestimation of Xe chemical shift in molecular environments [29,56] Secondly, the computed shift corresponds to one local minimum-energy configuration with naturally high chemical shift due to the close vicinity to sur rounding atoms, while in the experiments Xe is diffusing on the surface and probing various other local energy minima, arguably leading to a lower average CS Thirdly, La (200) is not pure monazite, but it includes also 30% of rhabdophane, which is not modelled here Therefore, the order of magnitudes of the experimental and computational CSs are roughly in agreement, which provides support that the two-site ex change model used for the analysis of experimental CSs (Eq (1)) is appropriate for the REEPO4 samples and the experimentally observed, relatively large δS value is realistic The modelled high CS can be un derstood by looking at the optimized structure in Fig S8: Xe atom has sank close to the second-layer La ion Therefore, it is surrounded by several water molecules coordinated to the first-layer La ions, as well as the phosphate groups in the first layer The most common Miller planes of LuPO4 xenotime (in descending order) are {100}, {110} and {101-Y} [59] Corresponding, calculated 129 Xe chemical shifts are 185, 240 and 242 ppm, and their average value is 222 ppm This is close to the experimental δS value of Lu (200), 241 ppm, which confirms, similarly to the case of La (200), the adequacy of the experimental analysis Considering the above-mentioned systematic error due to the DFT functional it seems, however, that the modelled smaller CS is somewhat underestimated Detailed scrutiny of the three optimized structures reveals that, on xenotime surfaces, Xe is not in contact with the second-layer atoms but lies on top of the first water layer in each of them Hence, there are not so many neighboring atoms that are close enough - as also displayed in distances in Table - to contribute to the increase of CS a Chemical shifts were referenced with respect to the calculated free129Xe atom nuclear shielding of 6007.64 ppm, corresponding to low-density Xe gas chemical shift reference at ppm water, which was present in the samples treated at the lower tempera ture (80 ◦ C), restricted the access of hydrophobic Xe into mesopores 129 Xe NMR analysis of the REEPO4 samples treated at the higher tem perature (200 ◦ C, free water removed) enabled the determination of the average sizes of mesopores explored by Xe gas The size is largest (79 nm) for La, which has predominantly (70%) monazite phase (30% rhabdophane), and smallest (6 nm) for Yb, which has xenotime phase The pore sizes of Lu and Yb (12 and nm) differed by the factor of two regardless of their similar xenotime phase structure Interestingly, the mesopore size experienced by Xe did not always follow the nanocrystal size visible in the FESEM images The heats of adsorption are quite similar for all the REEPO4 samples, ranging from 8.7 kJ/mol for Sm (200) to 10.1 kJ/mol for La (200) Computational modelling showed that the relatively high experimentally observed 129Xe chemical shifts of xenon adsorbed on diamagnetic REEPO4 surfaces (265 ppm for La (200); 241 ppm for Lu (200)) are realistic, providing support for the validity of the analysis of the experimental chemical shifts by the two-site meso pore model The proposed, modified two-site exchange model for paramagnetic materials renders the structural parameter values for the Sm (200) and Yb (200) samples more realistic Overall, this novel analysis technique provides extraordinarily versatile information about the structures of rare-earth element phosphates, which may be very useful for developing their extraction processes and applications CRediT authorship contribution statement Roya Khalili: Writing – original draft, Visualization, Investigation, Data curation Anu M Kantola: Writing – review & editing, Supervi sion, Investigation, Data curation Sanna Komulainen: Writing – re view & editing, Investigation, Data curation Anne Selent: Writing – review & editing, Investigation, Data curation Marcin Selent: Writing – review & editing, Investigation Juha Vaara: Writing – review & edit ing, Conceptualization Anna-Carin Larsson: Writing – review & edit ing, Supervision, Conceptualization Perttu Lantto: Writing – review & editing, Supervision, Investigation, Conceptualization Ville-Veikko Telkki: Writing – review & editing, Supervision, Resources, Funding acquisition, Data curation, Conceptualization Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Conclusions We demonstrated, for the first time, the usefulness of 129Xe NMR in the characterization of porous structures and adsorption properties of rare-earth element phosphates 129Xe spectra of xenon adsorbed on four different REEPO4 samples (REE = La, Lu, Sm and Yb) turned out to be very sensitive to both pore size and water content of the sample Free Data availability Data will be made available on request R Khalili et al Microporous and Mesoporous Materials 344 (2022) 112209 Acknowledgements [28] B Zhou, S Komulainen, J Vaara, V.-V Telkki, Microporous Mesoporous Mater 253 (2017) 49–54, https://doi.org/10.1016/j.micromeso.2017.06.038 [29] M Selent, J Nyman, J Roukala, M Ilczyszyn, R Oilunkaniemi, P.J Bygrave, R Laitinen, J Jokisaari, G.M Day, P Lantto, Chem Eur J 23 (2017) 5258–5269, 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pretation of 129Xe NMR data Complementary information of the particle sizes, porous structures and phases is obtained by laser diffraction and. .. 40 15 30 3.3 Analysis of adsorption 129 Xe chemical shifts: mesopore sizes and heats of The 129Xe chemical shifts of xenon adsorbed in mesopores of the REEPO4 samples are plotted in Fig As described... NMR in the characterization of porous structures and adsorption properties of rare-earth element phosphates 129Xe spectra of xenon adsorbed on four different REEPO4 samples (REE = La, Lu, Sm and