Topological Analysis of Void Space in Phosphate Frameworks

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A Topological Analysis of Void Space in Phosphate Frameworks: Assessing Storage Properties for the Environmentally Important Guest Molecules and Ions: CO2, H2O, UO2, PuO2, U, Pu, Sr2+, Cs+, CH4, and H2 Alisha J Cramer, and Jacqueline Manina Cole ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.6b00316 • Publication Date (Web): 27 Jun 2016 Downloaded from http://pubs.acs.org on June 27, 2016

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ACS Sustainable Chemistry & Engineering

A Topological Analysis of Void Space in Phosphate Frameworks: Assessing Storage Properties for the Environmentally Important Guest Molecules and Ions: CO2, H2O, UO2, PuO2, U, Pu, Sr2+, Cs+, CH4, and H2 Alisha J. Cramer,a Jacqueline M. Cole,a,b,c,d* a

Cavendish Laboratory, Department of Physics, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE. UK.

b

ISIS Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0QX. UK

c

Department of Chemical Engineering and Biotechnology, University of Cambridge, Charles Babbage Road, Cambridge, CB3 0FS. UK.

d

Argonne National Laboratory, 9700 S Cass Avenue, Argonne, IL 60439. USA. *

Keywords:

Author for correspondence, E-mail: [email protected]

host-guest structure, phosphate, water sanitation, energy fuel storage, CO2

emissions, nuclear waste storage

1 ACS Paragon Plus Environment


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Abstract The entrapment of environmentally important materials to enable containment of polluting wastes from industry or energy production, storage of alternative fuels, or water sanitation, is of vital and immediate importance. Many of these materials are small molecules or ions that can be encapsulated via their adsorption into framework structures to create a host-guest complex. This is an ever-growing field of study and, as such, the search for more suitable porous materials for environmental applications is fundamental to progress. However, many industrial areas that require the use of adsorbents are fraught with practical challenges such as high temperatures, rapid gas expansion, radioactivity, or repetitive gas cycling, that the host material must withstand. Inorganic phosphates have a proven history of rigid structures, thermal stability, and are suspected to possess good resistance to radiation over geologic time scales. Furthermore, various experimental studies have established their ability to adsorb small molecules, such as water. In light of this, all known crystal structures of phosphate frameworks with meta- (P3O9) or ultra- (P5O14) stoichiometries are combined in a datamining survey together with all theoretically possible structures of Ln aPbOc (where a, b, c are any integer, and Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, or Tm) that are statistically likely to form. Topological patterns within these framework structures are used to assess their suitability for hosting a variety of small guest molecules or ions that are important for environmental applications: CO2, H2O, UO2, PuO2, U, Pu, Sr2+, Cs+, CH4 and H2. A range of viable phosphate-based host-guest complexes are identified from this datamining and pattern-based structural analysis. Therein, distinct topological preferences for hosting such guests are found, and metaphosphate stoichiometries are generally preferred over ultraphosphate configurations.


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Introduction Porous materials have a long-standing history of interest for guest inclusion, and have now covered the spectrum of host materials from purely organic covalent organic frameworks (COFs), to the organic-inorganic hybrid metal-organic frameworks (MOFs), to purely inorganic frameworks such as zeolites. In light of recent environmental concerns, much of the focus for guest incorporation within porous materials has centered on the storage of possible alternative fuels such as CH4 and H2,1-6 pollution-control reservoirs for CO2,7-9 storage of dangerous waste products like volatile organic compounds10-12 and radioactive waste,13-16 or water adsorption for sanitation measures.17-19 Initial assessment of the suitability of potential new materials for such encapsulation applications can reasonably focus on the analysis of void space within their crystalline solidstate frameworks. To this end, data mining structure databases is proving to be a useful tool in the search for potential candidates for a given application. We previously performed such a study on possible guest incorporation within tungstate structures, 20 the rigid and thermally resistant nature of this host being particularly well suited to guests that need to be encapsulated under extreme conditions; for example, in the environment of spent nuclear reactor waste. In that case, we were able to demonstrate the analysis of void space within 3dimensional tungstate-based framework structures via Voronoi-Dirichlet partitioning, coupled with topological net descriptors as a means of comparison, utilizing the crystallographic topological program package TOPOS. 21 We herein propose a similar investigation, whereby phosphate framework structures are the subject host. In common with tungstates, metal-based phosphate materials are well known for their rigid nature and thermal resilience; these attributes are particularly marked in rareearth phosphate structures.22-24 Their ability to absorb small molecules, such as water, is



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already evident from

various experimental studies;

for

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example, ultraphosphate

stoichiometries, RP5O14, are well known for their hygroscopic tendencies. 25,26 In contrast, metaphosphate structures, RP3O9, are generally stable to water;27 yet, both ultra- and metaphosphates present as framework structures which contain sizeable cages.

It therefore

seemed instructive to analyze the suitability of void space in all known meta- and ultraphosphate crystal structures for potential guest inclusion. Accordingly, all published meta- and ultraphosphate crystal structures were mined from the Inorganic Crystal Structure Database (ICSD). These structures were complemented by a series of computationally-derived structures which, together, formed the total data set of possible host structures for assessing the viability of small molecule or ion guest inclusion. The computationally-derived structures were determined from a structure prediction approach of all structures containing Ln 3+ (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, or Tm), P5+ and O2- ions, which are statistically likely to form based on ionic substitution considerations of known related structures.28

The restriction to rare-earth phosphate

structures was made for computationally-generated structures since the rigid and thermal stability of these metal-based phosphates is most relevant to an ultimate guest-host application, and a cap on the otherwise unmanageably large number of hypothetical structures was needed.

The phosphate stoichiometry was not restricted during this

computational process since a particular strength of the approach used is its ability to predict structural networks that one might not intuit. Therefore, allowing for this degree of freedom was judged to be important for providing the best possible diversity of void space in cages of host frameworks based on rare-earth phosphates. The topological nets and void volumes of all the so-formed crystal structure databank are herein determined.

Void volumes that manifest as cage structures are compared with

volumes of a selective range of guest molecules or ions (CO2, H2O, UO2, PuO2, U, Pu, Cs+, 4 ACS Paragon Plus Environment

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Sr2+, CH4, and H2) in order to assess the potential of phosphate-based structures as host frameworks for host-guest media for environmental applications.

As with our previous

study,20 the UO2 and PuO2 oxides, and U, Pu, Sr2+ and Ce+ ions are explored as potential guests for the purposes of nuclear waste storage applications.

Given climate change

considerations, CO2 trapping is also evaluated for the purposes of offsetting carbon emissions, while inclusion of CH4 and H2 molecules is considered for alternative energy storage applications. Finally, H2O is investigated for possible water treatment purposes. The overarching workflow associated with this topologically-generated data-mining study that pair-wise matches host-guest volumes is illustrated in Figure 1.



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Data sourcing Experimental Database (ICSD)

Predicted Structures

Produce graph-theory generated structural net

No

Is a cage present?

Topological analysis

Yes No Cage and guest size match?

Calculate void volume for cages in each structure

Yes

Guest to host matching

CO2

H2O

Greenhouse gas capture

Figure 1.

UO2

STOP

PuO2

Water retrieval

U

Sr2+

Pu

Nuclear waste storage

Cs+

Potential applications

CH4

H2

Alternative energy/fuel storage

The overarching workflow for suiting host-guest pairs in phosphate-based

structures with porous cages for guest inclusion.


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Experimental and Computational Methods Experimentally-derived crystal structure data of phosphate framework structures. Data for all 137 previously-reported crystal structures of meta- and ultra-phosphates of the general formulae MaP3O9 or MaP5O14 (M = any combination of elements) were extracted from the Inorganic Crystal Structure Database (ICSD). 115 of this total, which displayed structural frameworks that bear cages, were taken forward for full data analysis. Search parameter filters within the ICSD restricted structures to those containing either P3O9, or P5O14. Disordered structures, and structures with partial occupancy in one or more of the atomic sites were manually excluded from the results. The remaining list of structures was further refined by manually removing duplicates (structures with the same chemical formula, spacegroup, with differences in unit cell parameters < 0.5 Å or 0.5°); among duplicate structures, those with the lowest R1 factor were kept, or where R1 factors were the same, the most recent structure was kept. Theoretically calculated predictions for phosphate structures. All hypothetically possible crystal structures containing any statistically conceivable combination of Ln (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, or Tm), P, and O ions were generated computationally by using previously described methods.28 The possibility of individual crystal structures existing was based on the statistical probability for a priori known structural motifs in the Inorganic Crystal Structure Database (ICSD) to be transmuted into phosphates via ionic substitution. In turn, the probability of ionic substitution was determined via a reference pair correlation matrix of various ion combinations, where each matrix element, gAB, represents the probability of ionic substitution between a given pair of ions A and B. This probability has been pre-calculated by enumerating the relative number of crystal structure examples in the ICSD, which differ only in the ions A and B. This method accordingly assesses the relative



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ease by which a given ion can fit into the crystallographically equivalent site of another ion. Values for gAB were therefore derived from a pre-trained reference library of structural homologues of A and B. While this was not part of the probabilistic calculation, it is hardly surprising that two ions of similar size, chemical properties (e.g. from the same group in the periodic table), and/or identical charge tend to have higher g AB values, since substitution for each proceeds more readily. For example, when A = P5+, the highest gAB value was obtained for B = As5+. Only charge-balanced crystal structures, and those not already in the ICSD, were considered in the theoretical structure prediction results. In total, 1170 hypothetical rare-earth phosphate structures of the general formula Ln aPbOc (a, b, c = any integer) were generated computationally. 491 of these calculated structures were taken forward for full void-space analysis since only these produced cages, which are of course necessary for hosting guest molecules or ions.

Topological Analysis TOPOS methods. The potential for hosting the subject guest molecules and ions for all selected phosphate-based framework structures was assessed using the crystallographic topological analysis program package, TOPOS 4.0 Professional.29

This enabled the

topological classification of each phosphate structure, and the determination and analysis of the void space residing within its framework. This analysis was accomplished by first defining the net of each structure using the ADS module in TOPOS. Such nets were identified using graph theory to calculate a map of the circuits contained therein by viewing all atoms as nodes, and all bonds as edges, thereby


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ascertaining the geometrical patterns in the crystal structure.

These nets were then

categorized as n-nodal in the presence of n different kinds of inequivalent vertices in the net. The net may contain tiles, defined as generalized polyhedra (cages) which have at least two edges incident upon each vertex and two faces incident upon each edge.30,31 These tiles are described according to how many faces a given tile possesses with each face being defined by its m-membered rings. This nodal/tiling topological representation is illustrated in Figure 2, using the example of Nd(P5O14) (ICSD ref. 6216 – [32]). The full classification of a net is based on several conventional descriptors, which may be used to search the TOPOS Topological Database (TTD) for the topological type of the net (for a full explanation and list of these descriptors see 33,34).

Figure 2. An example of a 16/8 net using Nd(P5O14) [ICSD ref. 6216 – [32]]: [44.74] tile, whereby 16/8 denominates the total number of nodes/tiles; [44.74] indicates the presence of 4



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faces consisting of 4-membered rings (e.g. pink plane), 4 faces consisting of 7-membered rings (e.g. yellow plane).

Void space analysis was then accomplished via a two-step process: the determination of all cages found within each structure, prior to calculating the void space volume within each cage using Voronoi-Dirichlet polyhedra (VDP). Thus, a comparison basis for the cavity volumes in each structure was established in the first step. Cages can be found from the net topology, and were determined using the ADS module in TOPOS. For three-dimensional periodic framework structures, the circuits formed by the atoms and bonds can be combined to form generalized polyhedra that are topologically equivalent to spheres. For an in-depth discussion of cages and tiling, see 30,35. The second step of void-space analysis comprises the calculation of a Voroni-Dirichlet partition of the crystal space for each cage, using the Dirichlet module in TOPOS to construct VDP for all independent framework atoms. From this partition, the location and size of voids were obtained by placing a node at the intersection of four or more VDP vertices. Subsequently, the Voroni-Dirichlet partition was reconstructed taking the void nodes into account, which resulted in a map of the void space of the structure. In order to analyze the cavity size within individual cages, the cages were isolated and void nodes were generated from the atoms forming the cage. Subsequently, VDP were generated for these void nodes, from which their volumes were calculated.

Guest volume determination. The intrinsic volumes of the guest molecules or ions were estimated in three different ways. For individual atoms and ions (U, Pu, Cs+, Sr2+), radii of 1.75 Å, 1.75 Å, 2.60 Å, and 2.00 Å, respectively, were obtained from the Slater radii 36


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database in TOPOS.

Subsequently, these radii were employed to calculate spherical

volumes. The volumes of the UO2 and PuO2 oxides were extracted from their previously reported experimentally-determined crystal structures, as sourced from the ICSD. Owing to the three dimensional frameworks formed by UO2 and PuO2 crystal structures, volume determination of discrete molecules is unfeasible. Hence, the volumes of a single U or Pu atom, and the eight valence-bonded O atoms for each were determined for chosen samples of UO237 and PuO2,38 respectively. Volumes for small guest molecules, such as CO2, CH4, H2O, and H2 were established based on previously published kinetic diameters (3.3 Å, 3.8 Å, 2.6 Å and 2.89 Å, respectively), from which spherical volumes were calculated. As the kinetic diameter represents only the smallest dimension of a given molecule, the calculated spherical volumes are necessarily the smallest possible volume for that molecule, and there is no consideration of the shape of the molecule in this calculation. This is acceptable as long as an upper bound of guest volumes within a cage can be set to provide the necessary latitude to allow for the molecule size to be greater in its other dimensions. The resulting volumes for all guest molecules and ions were rounded up to the nearest whole integer, in order to establish the lowest bound of the desired cage size. An upper bound was set 4 Å3 above this lower bound, which should allow the guest some spatial flexibility, without allowing more than one guest within a single cage.

Results and discussion Guest/host comparisons for environmental applications. A total of 1307 phosphate-based extended frameworks were evaluated for their prospects as host materials for the environmentally important guest molecules, atoms, or ions: CO 2, H2O, UO2, PuO2, U, Pu, 11 ACS Paragon Plus Environment


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Sr2+, Cs+, CH4, and H2.

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1170 were hypothetical crystal structures generated from

computational predictions, while the other 137 were sourced from previously reported crystallographic data from diffraction experiments. Of these, 115 previously reported crystal structures, and 491 hypothetical structures produced tilings; the ten largest cages in these 606 tilings were subsequently identified and their corresponding void volumes calculated (see Supporting Information). Possible guest-host matches were then assessed by comparing these void space volumes of the framework structures against the size of each subject guest molecule or ion. CO2 capture. In the interests of offsetting carbon emissions, encapsulation of CO 2 was chosen for evaluation in the context of environmental waste associated with climate change. The optimal cavity size for CO2 incorporation was determined using a kinetic diameter of 3.3 Å,39 presenting a target volume of 19 – 23 Å3. 22 previously reported experimentallyderived crystallographic structures were identified as forming 31 cages with appropriate void space volumes (see Figure 3). Of these, 14 structures had one suitable cage volume per structure; the remaining 8 structures contained two or more suitable cages (hereafter designated as ‘multiple cages’) per structure. The subsequent breakdown of all suitable cages by type found that in one specific framework structure (ICSD ref. 78373 – [40]), the cage suited for hosting a guest was found to be the largest (primary, 1°) cage, whereas in two of these structures it was the secondary (2°) cage, and in 19 structures the cages of interest was tertiary (3°) or higher (3°+). Among the calculated host compounds, a total of 60 framework structures were found to contain 65 suitable cages (2 x 1°; 18 x 2°; 45 x 3°+; 4 x multiple cages). Figure 3 summarizes these statistics, while representative example structures from the most common experimentally verified (7-nodal) nets that demonstrate capacity to host CO2 are displayed in Figure 4.


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Compound

Cage Attribute

Na3(AlP3 O9N) Ca(NH4)P3 O9 Mn(P3O9) CaK(P3O9) HgKP3 O9 CuLi(PO3)3 Na2K(P3 O9) CeP3O9(H2O)3 LaP3O9(H2O)3 Na2HP3O9 CsUO2(PO3)3 Y(P5O14) ErP5O14 TmP5 O14 DyP5 O14 Lu(P5O14) NH4Pb(PO3)3 Y(PO3)3 Er(P3 O9) BaAg(P3 O9)(H2O)4 BaNaP3 O9(H2O)3 Cs3(P3 O9)(Te(OH)6(H2 O)) PrPO4 CePO4 La2P4 O13 Pr2P4O13 Nd2 P4O13 Sm2 P4O13 Tb2 P4 O13 Dy2 P4O13 Ho2 P4O13 TbPO4 Gd3PO7 Tb3PO7 Dy3PO7 Ho3PO7 Er3PO7 Tm3PO7 Nd(PO3)3 Er(PO3)3 CePO4

E, 1° E, 2° E, 2° E, 3° E, 4° E, 4° E, 4° E, 4° E, 4° E, 4° E, 5° E, 5°- 6° E, 5°- 6° E, 5°- 6° E, 5°- 6° E, 5°- 6° E, 6°- 7° E, 7°- 8° E, 8°- 10° E, 9° E, 9° E, 9° C, 1° C, 1°- 3° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2° C, 2°

Ref. [ICSD – paper] 78373 – [40] 4275 – [41] 1720 – [42] 281588 – [43] 61239 – [44] 2808 – [45] 2346 – [46] 25386 – [47] 240963 – [48] 37167 – [49] 200684 – [50] 419078 – [51] 23304 – [52] 300029 – [53] 240973 – [54] 241229 – [55] 62158 – [56] 98556 – [57] 20935 – [58] 1124 – [59] 60947 – [60] 63136 – [61]

Compound

Cage Attribute

Er2P4O13 SmPO4 DyPO4 Ho(PO3)3 Gd2P4O13 Sm(PO3)3 Eu(PO3)3 Tb(PO3)3 GdPO4 TbPO4 ErPO4 TmPO4 Tm(PO3)3 La2P4 O13 Ce2P4O13 Pr2P4O13 Nd2P4O13 Dy2P4O13 Tm2P4 O13 HoPO4 Ho2P4O13 La(PO3)3 Ce(PO3)3 Pr(PO3)3 Nd(PO3)3 Gd(PO3)3 Dy(PO3)3 Er(PO3)3 SmPO4 Gd2P4O13 Er2P4O13 La(PO3)3 Ce(PO3)3 Pr(PO3)3 Nd(PO3)3 Gd(PO3)3 Dy(PO3)3 Er(PO3)3 La(PO3)3 Gd(PO3)3 Er(PO3)3

C, 3° C, 3° C, 3° C, 3° C, 3° C, 3°- 4° C, 3°- 4° C, 3°- 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 5° C, 5° C, 5° C, 5° C, 5° C, 5° C, 5° C, 5° C, 5° C, 5° C, 6° C, 6° C, 6° C, 6° C, 6° C, 6° C, 6° C, 7° C, 7° C, 7°

Ref. [ICSD – paper]



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Figure 3. (top) Distribution of cage types (1°, 2°, 3°+) of host structures comprising n-nodal nets that can incorporate CO2, according to their frequency observed in experimental (E) and calculated (C); (bottom) a list of their associated compound identifiers (ICSD number and reference citation).

Figure 4. Representative example host framework structures from the most common type of n-nodal nets whose cages have suitable void space volumes (black/grey) to accommodate CO2 molecules: 7-nodal (Er(P5O14) [ICSD ref. 23304 – [52]]).

H2O capture. Incorporation of H2O within phosphates utilized the kinetic diameter 2.6 Å for water,62 resulting in an occupancy volume of 9.20 Å3 and a target cage volume of 10 – 14 Å3. 57 cages were found within 34 previously reported structures, with a distribution of suitable cages as 2 x 2°; 55 x 3° +; 13 x multiple cages. Calculated structures revealed 110 suitable cages within 90 structures: 1 x 2°; 109 x 3°+; 14 x multiple cages. These statistics are


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summarized in Figure 5; Figure 6 demonstrates a representative example structure of the most common experimentally verified (11-nodal) nets that exhibit capacity to host H2O.



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Compound

Cage Attribute

Ba(NH4)P3 O9(H2 O) Ba(NH4)P3 O9(H2 O)2 RbSr(P3 O9)H2 O)3 Ce(P3O9) Pr(PO3)3 LaP3O9 Al3(P9O27) BaTl(P3 O9)(H2 O)2 Na2H(PO3)3 Pr(P3 O9)(H2 O)3 Na2K(P3O9) LiFeP3 O9 LiCo(PO3)3 LiMn(PO3)3 Na3P3O9(H2O) CuLi(PO3)3 Ag3(P3O9)(H2O) Ag3(P3O9)(H2O) LiK2 P3O9(H2O) HoP5 O14 HgKP3 O9 Y(P5O14) DyP5 O14 ErP5O14 TmP5 O14 Lu(P5O14) YP5O14 Er(P5 O14) BaNa(P3O9) LiPb(PO3)3 AgBa(PO3)3 BaAg(P3 O9)(H2O)4 NH4Pb(PO3)3 BaNaP3 O9(H2 O)3 CePO4 Gd2P4O13 Pr2P4O13 Ho2P4O13 La2P4 O13 Dy2P4O13 Nd2P4O13 La(PO3)3 EuPO4 NdPO4 TbPO4 DyPO4 HoPO4 SmPO4 GdPO4 ErPO4 TmPO4 CePO4 Tm(PO3)3 Sm(PO3)3 TbPO4 HoPO4 TmPO4 PrPO4 CePO4 Ce(PO3)3 Dy(PO3)3 Er(PO3)3

E, 2° E, 2° E, 3° E, 3° E, 3° E, 3° E, 3° E, 4° E, 4° E, 4° E, 5°- 6° E, 5°- 6° E, 5°- 6° E, 5°- 6° E, 5°- 6° E, 5°- 7° E, 5°- 8° E, 5°- 8° E, 5°- 10° E, 6° E, 6°- 8° E, 7° E, 7° E, 7° E, 7° E, 7° E, 7° E, 7° E, 7°- 9° E, 8°- 9° E, 8°- 9° E, 10° E, 10° E, 10° C, 2° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3° C, 3°- 4° C, 4° C, 4° C, 4°

Ref. [ICSD – paper] 4277 – [63] 91809 – [64] 90833 – [65] 240880 – [66] 97950 – [67] 202640 – [68] 409479 – [69] 154999 – [70] 23920 – [71] 155271 – [72] 2346 – [46] 20610 – [73] 153515 – [74] 51632 – [75] 18140 – [76] 2808 – [45] 105417 – [77] 56885 – [78] 23936 – [79] 9258 – [80] 61239 – [44] 419078 – [51] 240973 – [54] 23304 – [52] 300029 – [53] 241229 – [55] 260203 – [81] 151957 – [82] 2807 – [83] 1123 – [84] 50672 – [85] 1124 – [59] 62158 – [56] 60947 – [60]

Compound

Cage Attribute

La(PO3)3 Gd(PO3)3 Pr(PO3)3 Ho(PO3)3 Nd(PO3)3 Eu(PO3)3 Tb(PO3)3 Gd2P4O13 Pr2P4O13 Ho2P4O13 La2P4 O13 Dy2P4O13 Ce4P2O11 Er2P4O13 Tm2P4 O13 Nd2P4O13 La4P2 O11 Pr4P2O11 Eu2P4O13 Sm2P4 O13 Tb2P4O13 Nd4P2O11 Er2P4O13 La2P4 O13 Dy2P4O13 Tm2P4 O13 Nd2P4O13 Tb2P4O13 Nd(PO3)3 Ce2P4O13 Eu2P4O13 Sm2P4 O13 Tb2P4O13 Gd2P4O13 Er(PO3)3 PrPO4 Ho(PO3)3 Nd2P4O13 Ce2P4O13 Pr2P4O13 Ho2P4O13 La2P4 O13 Dy2P4O13 Tm2P4 O13 CePO4 Er2P4O13 Er2P4O13 Ce(PO3)3 Dy(PO3)3 Er(PO3)3 La(PO3)3 Pr(PO3)3 Gd(PO3)3 Nd(PO3)3 Ho(PO3)3 Tm(PO3)3 Eu(PO3)3 Sm(PO3)3 Tb(PO3)3 Er2P4O13 Gd2P4O13 Gd2P4O13

C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4° C, 4°- 5° C, 4°- 5° C, 4°- 5° C, 4°- 5° C, 4°- 5° C, 4°- 5° C, 4°- 5° C, 5° C, 5° C, 5° C, 5° C, 5° C, 5°- 6° C, 5°- 6° C, 5°- 9° C, 6° C, 6° C, 6° C, 6° C, 6° C, 6° C, 6° C, 6°- 7° C, 6°- 9° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 7° C, 8°- 10°

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Ref. [ICSD – paper]


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Figure 5. (top) Distribution of cage types (2°, 3°+) of host structures comprising n-nodal nets that can incorporate H2O, according to their frequency observed in previously reported experimental (E) or calculated (C) crystal structures; (bottom) a list of their associated compound identifiers (ICSD number and reference citation).

Figure 6. Representative example host framework structures from the most common type of n-nodal nets whose cages have suitable void space volumes (black/grey) to accommodate H2O molecules: 11-nodal (LiCo(PO3)3 [ICSD ref. 153515 – [74]]).

Nuclear waste storage. Spent nuclear fuel from nuclear facilities is found predominantly in the form of uranium or plutonium oxides. 86

These oxides are often encapsulated by

vitrification within borosilicate glass, however, there is interest in moving to iron phosphate glass which makes their inclusion here appropriate, when considering that crystalline forms provide the structural baseline for their glassy counterparts.87-90 Other efforts involving encapsulation via ion exchange of radioactive waste13,14,91-94 render the evaluation of U and



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Pu ions equally important. An additional focus is found in the high activity fission product radionuclides, 137Cs and 90Sr, which can require separate processing from the rest of the waste stream owing to the high thermal heat that they generate, and their relatively short half-lives (100 Å3 were 56.5% and 55.4% of all 1° cages for experimental and theoretical structures respectively; 21.7% (experimental) and 36.5% (theoretical) of 1° cages were within 50-100 Å3; 21.7% (experimental) and 8.1% (theoretical) of 1° cages were

Topological Analysis of Void Space in Phosphate Frameworks

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