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Microporous Titanium Silicates Predicted by GRINSP Armel Le Bail

Global Optimisation Techniques Applied to the Prediction of Structures « Gordon Conference style » Workshop, 5-7 July 2006, University College London. Microporous Titanium Silicates Predicted by GRINSP Armel Le Bail

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Microporous Titanium Silicates Predicted by GRINSP Armel Le Bail

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  1. Global Optimisation Techniques Applied to the Prediction of Structures« Gordon Conference style » Workshop, 5-7 July 2006, University College London Microporous Titanium SilicatesPredicted by GRINSP Armel Le Bail Université du Maine, Laboratoire des oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, 72085 Le Mans Cedex 9, France. Email : alb@cristal.orgWeb : http://cristal.org/

  2. CONTENT • I- IntroductionII- GRINSP algorithm and resultsIII- Results for titanosilicates Prediction conditions Models with real counterparts Highest quality (?) models Models with the largest porosityIV- Opened doors, limitations, problemsV- Conclusions

  3. I- INTRODUCTION Personnal views about crystal structure prediction : “Exact” description before synthesis or discovery in nature. These “exact” descriptions should be used for the calculation of powder patterns included in a database for automatic identification of real compounds not yet characterized crystallographycally.

  4. If we had a really powerful materials theory… It would allow complete prediction. These predictions would be made available in huge databases(currently the case for > 1.000.000 zeolites). We would have predicted the physical properties as well. We would try to synthesize the most interesting compounds. This is pure fiction up to now...But clearly is THE XXIth century challenge. Trying to make a very tiny step on that long way : GRINSP

  5. II- GRINSP algorithm Geometrically Restrained INorganic Structure Prediction Applies the knowledge about the geometrical characteristics of a particular group of inorganic crystal structures (N-connected 3D networks with N = 3, 4, 5, 6, for one or two N values). Explores that limited and special space (exclusive corner-sharing polyhedra) by a Monte Carlo approach. The cost function is very basic, depending on weighted differences between ideal and calculated interatomic distances for first neighbours M-X, X-X and M-M for binary MaXb or ternary MaM'bXc compounds. J. Appl. Cryst. 38, 2005, 389-395. J. Solid State Chem., 2006, in the press

  6. Observed and predicted cell parameters comparison Predicted by GRINSP (Å) Observed or idealized (Å) Dense SiO2 a b c R a b c  (%) Quartz 4.965 4.965 5.375 0.0009 4.912 4.912 5.404 0.9Tridymite 5.073 5.073 8.400 0.0045 5.052 5.052 8.270  0.8Cristobalite 5.024 5.024 6.796 0.0018 4.969 4.969 6.926 1.4 Zeolites ABW 9.872 5.229 8.733 0.0056 9.9 5.3 8.8 0.8EAB 13.158 13.158 15.034 0.0037 13.2 13.2 15.00.3EDI 6.919 6.919 6.407 0.0047 6.926 6.926 6.4100.1GIS 9.772 9.772 10.174 0.0027 9.8 9.8 10.20.3GME 13.609 13.609 9.931 0.0031 13.7 13.7 9.9 0.6Aluminum fluorides-AlF3 10.216 10.216 7.241 0.0159 10.184 10.184 7.174  0.5Na4Ca4Al7F33 10.876 10.876 10.876 0.0122 10.781 10.781 10.7810.9AlF3-pyrochl. 9.668 9.668 9.668 0.0047 9.749 9.749 9.749 0.8 TitanosilicatesBatisite 10.633 14.005 7.730 0.0076 10.4 13.85 8.1 2.6Pabstite 6.724 6.724 9.783 0.0052 6.7037 6.7037 9.824 0.9Penkvilskite 8.890 8.426 7.469 0.0076 8.956 8.727 7.387 1.3

  7. More details about the GRINSP algorithm Two steps : Step 1 -Generation of raw models Haphazard (by Monte Carlo) is used todetermine the cell dimensions; select Wyckoff positions; place M/M’ atoms. The cell is progessively filled up to the respect of geometrical restraints and constraints fixed by the user (exact coordination, but large tolerance on distances), if possible. The number of M/M' atoms placed is not predetermined. Atoms do not move. It is recommended to survey all the 230 space groups.

  8. Step 2 - Optimization The X atoms are placed at the (M/M')-(M/M') midpoints (corner-sharing). Interatomic distances and cell parameters are optimized (by Monte Carlo) : it is verified that regular polyhedra (M/M’)Xn can really be built starting from the raw initial models with M/M’ atoms only. Cost function : R =  [(R1+R2+R3)/ (R01+R02+R03)], where Rn and R0n for n = 1, 2, 3 are defined by : Rn =  [wn(d0n-dn)]2, R0n =  [wnd0n]2, Where the d0n are the ideal distances M-X (n=1), X-X (n=2) and M-M (n=3), the dn being the observed distances in the model. Weighting is applied through the wn . No powder data.

  9. Comments Minimizing distance differences is a very basic approach. The cost function would be better defined by applying the bond valence rules or by making energy calculations (in projet for the next GRINSP version) both would be more time consuming, especially for energy calculations. Intuitively, is it clear that this simple approach will give good results only for regular polyhedra.

  10. More details on step 2 Atoms move that time, no jump is allowed which would break coordinations. The cell parameters established at step 1 can change considerably during the optimization (up to 30%). The original space group of which the Wychoff positions were used to place the M/M' atoms at step 1 may not be convenient after placing the X atoms and optimization, this is why the final model is proposed in the P1 space group (coordinates placed into a CIF). The final choice of the symmetry has to be done by applying a checking software like PLATON (A.L. Spek).

  11. Running GRINSP : 1- The user has first to build a file according to his/her desires Example : TiO6/VO5 - all space groups ! Title line 55 55 ! Space groups range (you may test the range 1 230) 2 0 2 192 ! Npol, connectivity, min & max number of M/M’ atoms 6 5 ! Polyhedra coordinations Ti O ! Elements for the first polyhedra V O ! Elements for the second polyhedra 3. 30. 3. 30. 3. 30. ! Min & max a, b, c 5. 35. ! Min & max framework density 20000 300000 0.02 0.12 ! Ncells, MCmax, Rmax, Rmax to optimize 5000 1 ! Number of MC steps/atom at optimization, code for cell 1 ! Code for output files Note : that calculation would need 1 day with a single processor running at 3GHz.

  12. 2 – Verify that the atom pairs are defined : See into the file distgrinsp.txt distributed with the package : V O 5 3.050 4.050 3.550 1.526 2.126 1.826 2.282 2.882 2.582 4.20 7.00 Ti O 6 3.300 4.300 3.800 1.650 2.250 1.950 2.458 3.057 2.758 4.45 6.95 Distances minimum, maximum and ideals for pairs V-V, V-O et O-O in fivefold coordination, plus a range for second V-V neighbours (square pyramids favoured). The same for Ti-Ti, Ti-O et O-O in octahedral coordination TiO6. Trigonal prisms may well be produced, but with larger R values.

  13. 3- Start GRINSP

  14. 4- Wait…(hours, days, weeks, months…) and see the summary at the end of the output file with extension .imp :

  15. 5 – See the results (here by applying Diamond to a CIF) :

  16. GRINSP is « Open Source », GNU Public Licence Downloadable from the Internet at : http://www.cristal.org/grinsp/

  17. Predictions produced by GRINSP Binary compounds Formulations M2X3, MX2, M2X5 et MX3 were examined. Zeolites MX2 More than 1000 zeolites (not 1.000.000) are proposed with R < 0.01 and cell parameters < 16 Å, placed into the PCOD database :http://www.crystallography.net/pcod/ GRINSP recognizes a zeotype by comparing the coordination sequences (CS) of a model with a previously established list of CS and with the CS of the models already proposed during the current calculation).

  18. Hypothetical zeolite PCOD1010026SG : P432, a = 14.623 Å, FD = 11.51

  19. Example of CIF produced by GRINSP and inserted into the PCOD The coordination sequence is added at the end as a comment …..

  20. Does GRINSP can also predict > 1.000.000 zeolites ? Yes if Rmax was fixed at 0.03 instead of 0.01, if the cell parameters limit (16Å) was enlarged, and if all models describing a same zeotype in various cells and space groups were saved. Is it useful ? In a specialized database, yes, in a general database, no.

  21. Other GRINSP predictions : > 3000 B2O3 polymorphs Hypothetical B2O3 - PCOD1062004.Triangles BO3 sharing corners.

  22. > 500 V2O5 polymorphs square-based pyramids

  23. > 30 AlF3 polymorphs Corner-sharing octahedra.

  24. Do these AlF3 polymorphs can really exist ? Ab initio energy calculations by WIEN2K « Full Potential (Linearized) Augmented Plane Wave code » A. Le Bail & F. Calvayrac, J. Solid State Chem. In press

  25. Ternary compounds MaM’bXc in 3D networks of polyhedra connected by corners Either M/M’ with same coordination but different ionic radii or with different coordinations These ternary compounds are not always electrically neutral.

  26. Borosilicates PCOD2050102, Si5B2O13, R = 0.0055. SiO4tetrahedraandBO3triangles > 3000 models

  27. Aluminoborates Example : [AlB4O9]-2, cubic, SG : Pn-3, a = 15.31 Å, R = 0.0051: AlO6octahedra andBO3triangles > 2000 models

  28. Fluoroaluminates Known Na4Ca4Al7F33 : PCOD1000015 - [Ca4Al7F33]4-. Two-sizesoctahedra AlF6and CaF6

  29. Unknown : PCOD1010005 - [Ca3Al4F21]3-

  30. Satellite programs distributed with the GRINSP package GRINS : allows to build quickly isostructural compounds by substitution of elements from previous models. - FeF3, CrF3, GaF3, etc, from AlF3 - gallophosphates, zirconosicilates, or sulfates, etc, from titanosilicates. CUTCIFP, CIF2CON, CONNECT, FRAMDENS programs for - cutting multiple CIFs into series of single CIFs, - extraction of coordination sequences from CIFs, - analysis of series of CIFs, recognition of identical/ different models and sorting them according to R, - extraction of framework densities, sorting.

  31. III – Results for titanosilicates TiO6octahedra andSiO4 tetrahedra > 1000 models

  32. Prediction conditions : Si4+ and Ti4+ Si O 42.570 3.570 3.070 1.310 1.910 1.610 2.229 3.029 2.629 4.40 6.00 Ti O 63.300 4.300 3.8001.650 2.250 1.9502.458 3.058 2.7584.45 6.95 Cell parameters : max 16 Å 230 space groups, one day calculation per space group, processor Intel Pentium IV 2.8 GHz

  33. More than 70% of the predicted titanosilicates have the general formula [TiSinO(3+2n)]2- Numbers of compounds in ICSD version 1-4-1, 2005-2 (89369 entries) potentially fitting structurally with the [TiSinO(3+2n)]2- series of GRINSP predictions, addingeither C, C2 or CD cations for electrical neutrality. n +C +C2 +CD Total GRINSP ABX5 1 300 495 464 35 1294 93AB2X7 2 215 308 236 11 770 179AB3X9 3 119 60 199 5 383 174AB4X11 4 30 1 40 1 72 205AB5X13 5 9 1 1 0 11 36AB6X15 6 27 1 13 1 42 158Total 2581 845 Not all these ICSD structures are built up from corner sharing octahedra and tetrahedra.

  34. Models with real counterparts

  35. Example in PCOD Model PCOD2200207 (Si3TiO9)2- :a = 7.22 Å; b = 9.97 Å; c =12.93 Å, SG P212121 Known as K2TiSi3O9.H2O (isostructural to mineral umbite):a = 7.1362 Å; b = 9.9084 Å; c =12.9414 Å, SG P212121(Eur. J. Solid State Inorg. Chem. 34, 1997, 381-390) Not too bad if one considers that K et H2O are not taken into account in the model prediction...

  36. PCOD2200042 [TiSi2O7]2-identified as corresponding toNenadkevichite  NaTiSi2O72H2O

  37. The CS(Coordination Sequence)is not sufficient for a perfectidentification… Narsarsukite :Na2TiSi4O11 Both have same CS, but the model is a subcell with subtle differences. # PCOD2200033# 2# 2 8# 6 18 34 54 86 126 166 214 # 4 12 28 52 82 118 164 216 PCOD2200033 :[TiSi4O11]2-

  38. A few other identified models PCOD entry Mineral name/formula 2200093 Vlasovite3200122 VP2O7-I3200543 VP2O7-II2200170 Gittinsite2200178 KTiPO52200040 ZrP2O72200030 Armstrongite2200032 Bazirite2200095 Komkovite/Hilairite3200659 Zekzerite etc, etc (overview not completed…)

  39. Highest quality (?) models

  40. Models with the largest porosity

  41. Porosity examined with PLATON (option SOLV or VOID) Küppers, Liebau & Spek, J. Appl. Cryst. 39 (2006) 338-346. Calculation with PLATON commands : SET VDWR O 1.35 Si 0.5 Ti 0.6 CALC VOID PROBE 1.25 (and 1.50) GRID 0.12 LIST The titanosilicate model with largest channels attains 70% porosity, FD = 10.6 (Framework Density : number of cations for 1000 Å3) This is close to the best zeolites.

  42. PCOD3200086 : P = 70.2%, FD = 10.6, DP = 3 (dimensionality of the pore/channels system) Ring apertures9 x 9 x 9 [Si6TiO15]2- , cubic, SG = P4132, a = 13.83 Å

  43. PCOD3200867, P = 61.7%, FD = 12.0, DP = 3 [Si2TiO7]2- , orthorhombic, SG = Imma Ring apertures10 x 8 x 8

  44. PCOD3200081, P = 61.8%, FD = 13.0, DP = 3 [Si6TiO15]2- , cubic, SG = Pn-3 Ring apertures12 x 12 x 12+10+6

  45. PCOD3200026, P = 59.6%, FD = 13.0, DP = 3 [Si4TiO11]2- , tetragonal, SG = P42/mcm Ring apertures12 x 10 x 10

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