Structure determination of A2NaAl3F12 (A=K, Rb)

i

i

Mat. Res. Bull., Vol. 25, pp. 831-839, 1990. Printed in the USA. 0025-5408/90 $3.00 + .00 Copyright (c) 1990 Pergamon Press plc.

STRUCTURE DETERMINATION OF A2NaAI3F12 (A=K, Rb)

A. LE BAIL, Y. GAO, J.L. FOURQUET and C. JACOBONI Laboratoire des Fluorures - U.R.A. CNRS 449 - Facult6 des Sciences Universit6 du Maine - 72017 LE MANS Cedex - FRANCE

(Received January 8, 1990; Communicated by A.W. Sleight)

ABSTRACT: The crystal structures of the isostructural compounds Rb2NaA13F12 and K2NaA13F12 are solved by X-ray diffraction. The model was first established for the Rubidium compound in spite of systematic twinning, it was then confirmed by a Rietveld refinement of powder data and finally by refinement of data of untwinned crystal of K2NaA13F12. The symmetry is monoclinic: P21/m, Z=2, a=12.046(6)/~, b=6.984(4)/~, c=7.093(4)/~ and ~=125.04(4)~ for Rb2NaA13F12 (R=0.038 and Rw=0.037) and a=l 1.882(7)A, b=6.983(4)/~, c=6.942(4)/~ and [3=125.59(3) ° for K2NaA13F12 (R=0.025 and Rw=0.027). The network, built up from (A1F4-)n H.T.B.-like layers, presents in fact a monoclinic distortion of the Cs2NaAI3F12 structural type. MATERIALS INDEX: rubidium, potassium, sodium, aluminum, fluorides

Introduction The A2Na(AlxF3x+I)3 family (A = Cs,~_ b, K) is characterized by Hexagonal Tungsten Bronze (H.T.B.) layers linked with NaF6 - octahedra. Cs2NaAI3F12 [1] is the t'u'st member (x=l) of this family, built up from single H.T.B. like (A1F4-)n layers (S.G.: R-3m); this compound also clearly illustrates the structural correlation between H.T.B. and RbNiCrF6-type pyrochlore structures which was first theoretically pointed out by B. DARRIET [3]. The structure of the second member (x=2) of this family was recently determined for Rb2~aA16F21 [3]; in this case, tilted double H.T.B.-like (AI2F7")n layers are linked by NaF6 - octahedra (S.G.: C2). ~-A1F3 [4] is the last term of the family (x---~o), with tridimensional network built up from H.T.B.-like (A1F4-)n layers connected together. 831

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The aim of this paper is to present the isotypic structures of Rb2NaAI3FI2 and K2NaAI3F12 which were found to crystallize in a different space group than Cs2NaAI3F12 ; Rb2NaAI3F12 structure was first solved in spite of systematic twinning then K2NaA13F12 structure was determined on an untwinned crystal.

Exuerimental Pro~¢¢ure Rb2NaA13F12 crystals were obtained by the previously described HF hydrothermal method [5]. The stoichiometric composition (2RbF+NaF+3A1F3) in 5M aqueous HF is heated to 200°C for 20 hours inside a Teflon bomb, then slowly cooled to room temperature. The colorless crystals have a [111] truncated rhomboedral shape; the chemical analysis confirms the composition. These crystals can also be obtained by the chloride flux method yet used to prepare Cs2NaAI3FI2 [1] and by solid state reaction. K2NaA13F12 was impossible to prepare by solid state reaction, crystals were prepared by HF hydrothermal method from (KF+NaF+AIF3) starting mixture (3days, 600"C). X-ray data collections were performed on a Siemens AED2 four-circle diffractometer. The crystal structures were solved using the SHELX76 program [6]; atomic scattering factors and anomalous dispersion corrections were taken from "International Tables for X-Ray Crystallography" [7].

Structure Determination Rb2NaAI3F12 Lane Rb2NaA13F12 photograph studies revealed that most of the crystals are twinned as clearly shown by the splitting of some reflections. An apparently unaffected, but very small crystal, was selected for structural determination. The conditions of the diffraction experiment are summarized in TABLE I. The lattice parameters - a = 12.046(6)A, b = 6.984(4)A, c = 17.484(9)A and g = 90.58(3) - could be consistent with a possible distortion of the hexagonal cell of Cs2NaA13F12 [1] a H = 7.026(3)A, _--> ._.> CH = 18.244A (S.G. R-3m, Z = 3) following the relations: a -- 2a-~ + b-~, b->=b-~, c -- ~ . The condition limiting possible reflections (OkG, k = 2n) leads to the space groups P21/m or P21. The first part of the crystal structure determination was performed in the space group P21/m by the heavy atom method. A model deriving from Cs2NaA13F12 was confirmed, but the refinement of all atomic parameters (isotropic temperature factors) led to R = 0.15; it was not possible to significantly improve by anyway the refinement quality. As almost undetectable twinning was recently established for 13-A1F3 [4] and Rb2NaA16F21 [2] due to the rotation of 120" around the pseudo-hexagonal c axis of the H.T.B. layers, this possibility was examined but without success. Logically, the minimal monoclinic distortion of the Cs2NaA13F12 structure would be achieved in the more direct non-isomorphic subgroup of R-3m : C2/m, following the relation: , and + ned from the registered cell from the relations: a-->m= a-->, ~

+

This m a y be obtai-

=/~->and c--->m= 1/3(--a-->+c~.

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TABLE I Cell parameters, conditions of data collection (20°C-Graphite monochromated MoKa radiation, Scan mode o)-20) and treatment

Formula Space Group

Rb2NaAI3F12 P21/m Cell of data collection

Lattice constants: a(A)

12.046(6) 6.984(4) c(A) 17.484(9) 90.58(3) Crystal size (ram) 0.06x0.08x0.03 Scan range (0min-0max)° 2-25 hklmin/hklmax range -14 -1 1/14 8 20 Standard reflections -224/-22-8/-2-2-4 Data examined 3105 Merged data retained (I>36(I)) 890 Ix (cm -1) 102.12 Absorption correction No Transmission factor (min, max) R (from averaging) 0.036 Final cell (Z=2) Lattice constants: a(A) 12.046(6) b(A) 6.984(4) c(A) 7.093(4) ~(°) 125.04(4) Calculated density 3.416 Data used: 429 (h¢3n) Parameters refined 50 Extinction parameter (x 102) 0.224 Weight scheme ." k/(o-2(F)+G.F 2) k / Gxl03 1.4798/0.475 Reliability factors: R 0.038 Rw 0.037

b(A)

KzNaAI3F12 P21/m 6.942(4) 6.983(4) 9.662(5) 90.15(3) 0.068x0.228x0.114 2-40 -12-9-13/12 12 17 32-3/124/4-24 3394 1669 14.9 Gauss method 0.8413, 0.9029 0.038

11.882(7) 6.983(4) 6.942(4) 125.59(3 ) 2.907 1669 98 0.661 1.2521/0.324 0.025 0.027

Surprisingly, a test in this hypothesis leads to R = 0.12 in the C2/m space group and to R = 0.06 in the P21/m one. Of course, it remains to be explained, the large number of excluded reflections (the volume of this monoclinic cell is only one third of the registered one). The solution was obtained from an hypothesis of twinning according to (001) as shown FIG.1. This proposition leads to the illusion of an am, bm, 3Cm cell: by using the matrix transforming the domain I axes into the domain II axes, the reflections with

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1 = 3n regenerate all those which were observed for 1 ~ 3n; some examples are listed TABLE II; the intensity ratio of the associated triplets is almost a constant, the mean giving the volume ratio of the two domains.

TABLE II : Some of the most intense associated triplets in the domains I and II (cell: am, bin, 3Cm) hi k I I I

2 1 I 2 2 2 4 2 2

0 1 1 0 2 2 0 0 2 2 I 0 I 1 2 0

6 3 6 3 3 6 0 9 3 3 9 9 6

II

h ' k ' i'

1196 1288 1067 1143 2000 1490 1041 430 1560 910 724 955 506

2 I 1 2 2 2 ~ 2 2 4 1 1 2 k' l'

0 1 1 0 2 2 0 0 2 2 0 1 0 =

2 5 4 7 I 2 8 5 7 5 7 7 10

In

II/III

283 301 223 273 409 304 248 98 351 170 153 201 135

4.23 4.28 4.78 4.19 4.89 4.90 4.20 4.39 4.44 5.35 4.73 4.75 3.75

1 0 * k! 0 1 //

Actually, when a (202) reflection is collected in the am, bin, 3era cell, it is in fact the a~=~ (-206) of the domain II; systematic overlapping of reflections belonging to the two domains occurs when h = 3n (because 1' = 3n), for instance the (300) of the domain I is superposed with the (-306) of the domain II. In reality, overlapping would have been exact for g = 90* in the registered cell. The fact that the contribution from domain II is FIG. 1 weak (1/5 of domain I) exTwinning hypothesis, a-~and c--~characterize the replains why an R = 0.06 was gistered cell, amt , cin~ and amu , CmH are those of obtain in the am, bin, Cm cell the final cell in the domains I and II respectively. of domain I in spite of the presence of the h = 3n reflections, but the problem was revealed by variance analysis. The procedure chosen was to do the refinement only using the h ~ 3n reflections of the predominant domain I in the am, bin, ¢m cell. An R = 0.047 was obtained with

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isolropic thermal parameters (429 reflections, 44 refined parameters); the limited data collection, consequence of the very little crystal size, did not allow the full refinement of all anisotropic thermal parameters, so Uij were only refined for Rb, leading to the final reliability factors R = 0.038, Rw = 0.037 (50 refined parameters); TABLE III lists the positional and thermal parameters. All this indicates that this work needs to be supported by a powder diffraction study, in order to establish more accurate cell parameters and to give a final proof. A Rietveld refinement [8] was performed on an X-ray powder diffractogram recorded from 10 to 120°(20) by steps of 0.04 ° on a Siemens D501 diffractometer (Cu K~ wavelength, graphite back monochromated - DACO/MP system); this includes 795 possible reflections. The positional x,y,z, parameters obtained from the single crystal study were used and kept fixed, other parameters being refined (profile, cell and thermal parameters). This leads to the conventional Rietveld reliability factors RI = 0.056, R p = 0 . 0 8 4 , RwP = 0.095, RE = 0.025 (background substracted). The observed and calculated patterns are shown Fig.2. When refining also the atomic coordinates, only small deviations occurs leading to RI = 0.046, Rp = 0.075, RWP = 0.085; however, the weak deviation from a pseudo-hexagonal symmetry causes also severe overlapping problems on the powder diffraction pattern and the single crystal results are believed to be more accurate. K2NaAI3F12 The structure was investigated before chemical analysis. A different cell choice prevented recognition of the analogy with Rb2NaA13F12. The conditions of the diffraction experiment are summarized in TABLE I. The structure was solved using direct methods of SHELX76 program and refined to R = 0.025 (Rw = 0.027) with anisotropic thermal motion or to R = 0.056 with isotropic thermal motion. Then, the cell was transformed to be analogous with that of Rb2NaA13F12; results are given for this final orientation in TABLE III providing an ultimate confirmation of Rb2NaA13F12 structure.

20.0

30.0

40.0

50.0

50.0

70,0

50.0

90.0

100.0

110.0

20 °

FIG. 2 Comparison of observed ( ..... ) and calculated ( ) intensifies of Rb2NaA13F12. The difference pattern appears below at the same scale.

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TABLE III Atomic coordinates (~104) for A2NaAI3FI2, A= Rb, K (italics)with isotropic,4thermal parameter B(/~ ) (* Equivalent B) and anisotropic Uij parameters (xl0). Atom

Site

Rbl K1 Rb2 K2 Na Na All All A12 At2 A13 At3 F1 F1

2e 2e 2e 2d 2c 2e 2e

F2 F2 F3 F3 F4 F4 F5 F5 F6 F6

2e

F7

F7

F8 F8 Atom Rbl K1 Rb2 K2 Na All AI2 AI3 F1 F2 F3 F4 F5 F6 F7 F8

x

882777(7, ) 8 9 3 . ,1) 3618(2) 3581(1) 2450.(5) 2407(1) 1/2 1/2 0 0 2716(3) 2811(1) 5108(8 4984i~

y

1/4 1/4 3/4 3/4 1/4 1/4 1/2 1/2 0 0 1/4 1/4 1/4 1/4 1/4 1/4 3/4 3/4

z

8768(3) 9071 (1) 8805(3) 8923(1) 264(9~ 312t,./ 1//2 .,_ 1/2 1/2 5605(6) 58911) 4,3_3313 418~3~

1.85(13) * 1.78(3) * 1.69(12) * 1.98(3) * 0.87(10)1.05(5) * 069(7',7~. b~56teO * 060(/~ 0155v.,/ * 038(~ 0160v.,/ * 1.03(14) * 0.89(7) 8577(14) 1.32(14) , 8985(2) 1.30(7) 5623(13) 1.00(14) 5843(3) 0.89(7) * 7320(14) 1.13(14) 7174(2) 1.24(7) * 7849(97849i~ 1.13(10) ,_,, 1.08(5) 6068~8~, 093(9 5831(8,_, 1:05i9~) • 2097(9 1108~1~z 2112i~ 114(9 4081i~ 092(9 4499(9 1:09i95)) .

3608(818), 3788~z) 564(8) 582(1) 8209(8 8215i82)) 6393(5) 6510(19 3849(5) 3946(1)

319(8~ 405~,-/ 648(8 626i~

4f

9308(5)

9490(1)

9633(9

4f

8371(5) 8260(1)

5612(8 5608i82 )

UI 1

U22

U33

U23

227(9 229i~ 138(8 201i~ 127(3) 89(2) 85(2) 96(2) 136(5) 92(4) 145(5) 90(4) 115(3) 199(4) 104(3) 205(4)

1497t~ 159_(7

2e 2e 4f 4f

257(9 222i~ 193(8) 155(2) 144(4) 78(2) 73(2) 75(2) 156(5) 125(5) 115(5) 137(5) 120(3) 154(3) 187(4) 95(3)

254i93)) 253(9 261(9 359193) 137(4) 54(3) 58(3) 79(3) 62(5) 270(6) 55(5) 235(6) 127(4) 111(4) 125(4) 120(4)

3/4 3/4

9565i~

B(.~ 2)

U13

U12

53(2) 48(2)

-4(2) -2(2)

66(~62) 82(3) 3(2) 1(2) 62(2) 94(4) 59(4) 62(4) 60(4) -7(3) 22(3) -21(3) -29(3)

40(3) -5(3) 141(3) 43(3) 88(3) -16(3) 90(3) 9(3)

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Structure Descrintion And Discussion TABLE IV gives the main characteristic interatomic distances; FIG.3 and FIG.4 present the [010] and [103] projections of K2NaAI~..12 structure; the network is built up with H.T.B. like (A1F4")n layers linked with NaF6 " octahedra. It is the same arrangement yet described for Cs2NaA13F12 [1] (S.G.: R-3m) but the lower size of Rb + or K-+ cations induces a large distortion of the whole structure.

TABLE IV Main interatomic distances (A) and standard deviation (in parenthesis) for Rb2NaAI3F12 and K2NaA13F12 (italics).

Na

-F4 -F2 -F7 -F5 AI2 -F7 -F8 -F3

Na Octahedron 2.27(2) 2.257(3) 2.30(2) 2.302(3) 2x2.332(5) 2.361(1) 2x2.339(5) 2.343(1) 2.318 2.328 AI20ctahedron 2xl.741(7) 1.751(2) 2xl.832(7) 1.824(2) 2xl.833(9) 1.843(2)

1.802 1.806 Rbl (K1) Polyhedron Rbl -F7 2x2.890(7) 2.734(2) -F4 3.012(7) 2.824(2) -F5 2x3.024(7) 2.886(2) -F7 2x3.037(8) 2.834(2) -F8 2x3.505(7) 3.757(2) -F3 3.59(1) 3.232(3) -F4 2x3.596(2) 3.653(2) -F3 3.61(1) 3.773(3) -F1 3.712(7) 3.875(2) -F6 2x3.714(5) 3.873(2)

All

-F5 -F1 -F6

All Octahedron 2xl.748(5) 1.755(1) 2xl.833(2) 1.831(1) 2xl.847(7) 1.841(2)

1.810 1.809 AI30ctahedron AI3 -F4 1.701(9) 1.730(2) -F2 1.731(9) 1.749(2) -F6 2xl.819(9) 1.831(2) -F8 2xl.831(9) 1.842(2) 1.788 1.804 Rb2 (K2) Polyhedron Rb2 -F2 2.736(8) 2.568(2) -F5 2x2.827(7) 2.730(2) -F3 3.015(8) 2.898(2) -F8 2x3.084(5) 2.921(2) -F6 2x3.168(7) 3.144(2) -F1 3.35(1) 3.444(3) -F6 2x3.483(4) 3.247(2) -F2 2x3.496(1) 3.499(1) -F7 2x3.775(7) 3.870(2)



For all the known compounds of the A2Na(AlxF3x+I)3 family, the A1F63 octahedra behave as rigid structure components. The mean AI-F distance is never out of the range 1.797-1.809 A if one excepts the case of Rb2NaA13F12 for which the precision is low due to systematic twinning and small size of studied crystals. Th~ shorter A1-F distances are always observed fOrs_fluorines which do not bond two A1F6 - octahedra (1.730-1.755 A, they belong to NaF6 - octahedra). The extreme F-A1-F angles are 85.0* for fluorine in cis-position and 175.0 ° for those in trans-position in the

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case of Rb2NaAI6F21 [2] which presents the more distorted octahedra in a double H.T.B. layer; the extremes for K2NaA13F12 are respectively 88.3* and 176.~.°. On the contrary, the NaF6 - octahedron is able to reflect the large distortion of K2 the H.T.B. layer produced by the variation in the A + (Cs, ~Rb, K ) size. In Cs2NaAI3F12 , all AI j+ ions lie in the same plane of the H.T.B. layer, the cooperative tilting between o~tahedra leads to an almost ideal NaF6"- octahedron. OK1 The polyhedron occupied by Cs remains very close to that which would be observed in an ideal pyrochlore (FIG.5). Rb2NaA16F21 is the only known example for x=2; the presence of a double FIG. 3 H.T.B. layer consolidates the structure: [010] view of K2NaAI3F12 structure. despite the low symmetry (S.G. : C2) and NaF6 ~- octahedra are shaded

o

~

OI

I° O

O KI O ~'K2 u

-a-

~LI~

u -

o

-bFIG. 4

3 [103] views of K2NaAI3F12 structure. AllF63" , A12F6 - and A~3F63- octahedra are respectively 3-shaded, unshaded and 2-shaded.-a- without NaF6"- octahedra (-b- with ) three different A1 sites, all AI 3+ ions stay practically in the mean planes of the H.T.B. layers; the NaF65- octahedron, in this case, is compressed between the double layers. The Rubidium environment is similar to that of Cs in Cs2NaA13FI2. K2NaAI3F12 is more distorted than Rb2NaAI3F12, this is attested by the fact that A13 deviates by _+0.50/~ from the mean plane defined by All and A12 (only by 0.35/~ it[ Rb2NaA13F12). However, the two phases show similar features: there is now two A" sites. When considering the seven first F neighbours, the K1 (or Rbl) polyhedron is an acceptable monocapped trigonal prism (the next F neighbour beeing 0.35 A away for K and 0.47 /~ for Rb). K2 (or Rb2) cannot easily be defined in any regular polyhedron; FIG.5 shows that F atoms belonging to all of the four shells of the 8b-pyrochlore 18~_ cavity participate to the K2 (Rb2) polyhedron. In these two last phases, the NaF6 ~octahedron is highly distorted.

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Rb in Rb2NaA16F21

Cs in Cs2NaA13F12

Cs in Cs2NaA13F12 projection along [001]

K1 in K2NaA13F12

K2 in K2NaA13F12

The 8b cavity in A1F3 hypothetic pyrochlore

FIG. 5 Perspective representation of the A I- 18F environment

Conclusion

It is very frequent that materials built as part from the H.T.B. layer present difficulties in structure solution due to systematic twinning and/or pseudo-symmetry. The results of this study confirm that it is now possible to accurately determine the crystal structure of such complicated systems; the same method could be apply to numerous oxide systems where both basic H.T.B. network is involved and such twinning problems known.

References 1. G. COURBION, C. JACOBONI and R. DE PAPE, Acta Cryst., B32, 3190 (1976). 2. B. DARRIET, M. RAT, J. GALY and P. HAGENMULLER, Mat. Res. Bull., 6, 1305 (1971). 3. A. LE BAIL, Y. GAO and C. JACOBONI, Eur. J. Solid State Inorg. Chem., 26, 281 (1989). 4. A. LE BAIL, C. JACOBONI, M. LEBLANC, R. DE PAPE, H. DUROY and J.L. FOURQUET, J. of Solid State Chem., 77, 96 (1988). 5. F. PLET, J.L. FOURQUET, G. COURBION, M. LEBLANC and R. DE PAPE, J. of Crystal Growth, 47, 699 (1979). 6. G.M.SHELDRICK, SHELX 76. A program for crystal structure determination. Univ. of Cambridge, England (1976). 7. "International Tables for X-ray Crystallography", Vol.4, Kynoch Press, Birmingham (1968). 8. A. LE BAIL, H. DUROY and J.L. FOURQUET, Mat. Res. Bull., 23, 447 (1988). 9. Y. LALIGANT, A. LE BAIL and G. FEREY, Eur. J. Solid State Inorg. Chem, 26,445 (1989)