J. Phys. Chem. B 1997, 101, 8827-8831
8827
Topochemical Rationalization of the Solid-State Polymerization Reaction of Sodium Chloroacetate: Structure Determination from Powder Diffraction Data by the Monte Carlo Method Laurent Elizabe´ , Benson M. Kariuki, and Kenneth D. M. Harris* School of Chemistry, UniVersity of Birmingham, Edgbaston, Birmingham B15 2TT, U.K.
Maryjane Tremayne Department of Chemistry, UniVersity College London, 20 Gordon Street, London WC1H 0AJ, U.K.
Matthias Epple* Institute of Inorganic and Applied Chemistry, UniVersity of Hamburg, Martin-Luther-King-Platz 6, D-20146 Hamburg, Germany
John Meurig Thomas DaVy Faraday Research Laboratory, The Royal Institution, 21 Albemarle Street, London W1X 4BS, U.K. ReceiVed: April 11, 1997; In Final Form: September 16, 1997X
It has been known for a long time that, at sufficiently high temperature, solid sodium chloroacetate undergoes a polymerization reaction to produce polyglycolide and sodium chloride. However, an understanding of this reaction and its mechanism was not previously possible, as sodium chloroacetate is microcrystalline and structural information could not be determined from conventional single-crystal X-ray diffraction methods. In this paper, we report the structure of sodium chloroacetate; this advance has been possible through the application of new methodology, based on Monte Carlo sampling techniques, that we have developed recently for crystal structure determination from powder diffraction data. The reported structure of sodium chloroacetate provides a direct rationalization, based on topochemical principles, of the polymerization reaction to produce polyglycolide.
Introduction When certain crystalline metal halogenoacetates (typified by sodium chloroacetate) are heated to sufficiently high temperature, the polymer polyglycolide (poly(oxy-1-oxoethylene)) is formed together with the metal halide: nClCH2COONa
nNaCl +
CH2COO
n
Such elimination of metal halides from salts of halogenoacetic acids has been known since 1857 when Hoffmann and subsequently Kekule´ heated potassium chloroacetate to obtain potassium chloride and polyglycolide.1,2 Similar behavior has now been found for many other metal halogenoacetates,3 of which the most widely studied have been sodium chloroacetate and sodium bromoacetate. However, although almost 140 years have elapsed since the discovery of these solid-state reactions, little is known about their thermodynamic, kinetic, and structural aspects. Partly in recognition of this paucity of fundamental knowledge and partly in recognition of the potential applications (see below) of the polyglycolide produced in this reaction, detailed studies of this reaction have been carried out recently using a range of experimental techniques, including thermal analysis,3,4 scanning electron microscopy, in situ IR spectroscopy,5 in situ X-ray powder diffraction,3 in situ X-ray absorption spectroscopy (EXAFS)6,7 and in situ solid-state NMR spectroscopy.8 This work has focused predominantly on sodium chloroacetate and * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, October 15, 1997.
S1089-5647(97)01256-X CCC: $14.00
sodium bromoacetate and has demonstrated, inter alia, that the polyglycolide produced directly from the solid-state polymerization reaction has a novel porous micromorphology.4 There is no evidence that the reaction involves any intermediate phases (liquid or solid), and it is therefore probable that the mechanism of the polymerization reaction is governed by the structural properties of the parent metal halogenoacetate. In this paper, we focus on sodium chloroacetate as the prototypical member of the family of reactive solid metal halogenoacetates. In addition to the fundamental scientific interest in the polymerization reaction, there is considerable scope for the use of the polyglycolide product in a variety of materials applications, inspired partly by the fact that this polymer is both nontoxic and easily biodegradable.9-11 From a fundamental standpoint, it is clearly important to understand the course of the solid-state polymerization reaction and to establish the extent to which it can be understood on the basis of the crystal structure of the parent metal halogenoacetate. In this regard, we note that the topochemical principle12 has often been used successfully to rationalize the course of chemical transformations within crystalline solids.13-18 Reactions under topochemical control follow the pathway involving the minimum amount of molecular movement, and, as a consequence, the course of the reaction and the stereochemistry of the reaction product(s) are governed by the relative positions and orientations of the molecules in the reactant crystal. Thus, it is clear that major advances in understanding the mechanism of the polymerization reactions in metal halogenoacetates may stem from knowing the crystal structures of the parent materials. Unfortunately, however, all previous attempts to prepare single crystals © 1997 American Chemical Society
8828 J. Phys. Chem. B, Vol. 101, No. 44, 1997 of sodium chloroacetate appropriate for single-crystal X-ray diffraction experiments have been unsuccessful, prohibiting determination of the structure by conventional approaches (of the metal halogenoacetates that are known to undergo the solidstate polymerization reaction, the crystal structure has been determined only in the case of silver chloroacetate19). Here we focus on structure determination of sodium chloroacetate from powder diffraction data. Unfortunately, there are several intrinsic difficulties associated with solving crystal structures directly from powder diffraction data.20 In a powder diffraction pattern, three-dimensional diffraction data are “compressed” into one dimension, leading to substantial overlap of peaks and ambiguities in determining the intensities of individual diffraction maxima directly from the powder diffractogram. This is a major problem in the application of traditional methods for structure solution, as these methods require the use of the intensities of individual diffraction maxima extracted from the powder diffraction pattern. The problems are particularly severe for low-symmetry structures for which there is generally extensive peak overlap. Recently we have devised and developed a new technique,21-26 based upon a Monte Carlo sampling algorithm, for structure solution from powder diffraction data. This technique adopts a new philosophy of postulating structural models independently of the experimental diffraction data and then assessing the suitability of these structural models on the basis of their agreement with the experimental diffraction data; importantly, this approach avoids implicitly the problem of extracting intensity information directly from the experimental powder diffraction pattern. In this paper, we present the crystal structure of sodium chloroacetate, determined from X-ray powder diffraction data using the new Monte Carlo technique. Knowledge of this structure provides a direct interpretation of the mechanism of the solid-state polymerization reaction to produce polyglycolide. Until recently, the crystal structures of only two metal halogenoacetates with monovalent cations (sodium fluoroacetate27 and ammonium fluoroacetate28) had been determined, but so far the solid-state reactivity of these materials has not been reported. Recently, the crystal structure of silver chloroacetate was determined by conventional single-crystal X-ray diffraction methods;19 it has been suggested that the proximity of silver and chlorine atoms in this structure probably supports the solid-state polymerization reaction. However, it is important to note that the structure of silver chloroacetate differs considerably from the structure of sodium chloroacetate reported in the present paper. Experimental Section Sodium chloroacetate was prepared from sodium hydroxide and chloroacetic acid using methods described previously.3 The product was characterized by 1H NMR, 13C NMR, IR, elemental analysis (C, H), DSC, and X-ray powder diffraction. X-ray powder diffraction data were recorded on the highresolution powder diffractometer at station 2.3 of the Synchrotron Radiation Source, Daresbury Laboratory, with the sample loaded in a capillary (1.0 mm diameter). The data were recorded at λ ) 1.4000 Å with 2θ in the range 6°-76° in steps of 0.01°. The total data collection time was 120 min. The full range of 2θ was used in the structure determination calculations. It is important to note that, in comparing the above synchrotron X-ray powder diffractogram and diffractograms recorded for the same sample on laboratory X-ray powder diffractometers with reflection geometry and transmission geometry (flat sample), the relative peak intensities are significantly different
Letters from one another. Clearly the sample of sodium chloroacetate used in this work can exhibit a high degree of preferred orientation. As vindicated below, the synchrotron X-ray powder diffraction data are the least significantly affected by this tendency for preferred orientation. The Monte Carlo structure solution calculation was carried out using the program OCTOPUS9729 and structure refinement calculations were carried out using the GSAS program package.30 Structure Determination from X-ray Powder Diffraction Data The X-ray powder diffractogram was indexed using the program TREOR,31 giving the following unit cell: a ) 7.12 Å, b ) 5.36 Å, c ) 10.82 Å, β ) 92.44°. Systematic absences allow the space group to be assigned uniquely as P21/a, and density considerations indicate that the asymmetric unit comprises one sodium cation and one chloroacetate anion. As discussed elsewhere,20,22 the efficiency of finding the correct structure solution in the Monte Carlo method depends critically on the optimum definition of the structural fragment and the optimum choice of how to handle it in the calculation. There are two major considerations: (a) the structural fragment should represent a sufficiently large fraction of the scattering matter in the unit cell, such that the correct position of the structural fragment gives rise to a significantly better agreement between the calculated and experimental powder diffractograms than wrong positions; (b) the number of degrees of freedom in the structural fragment should be as low as possible in order to ensure rapid and efficient propagation of the Monte Carlo procedure. In the present case, the initial Monte Carlo calculation considered a rigid structural fragment, comprising all nonhydrogen atoms of the chloroacetate anion; the geometry of this fragment was set according to standard interatomic distances and angles, and a standard conformation with the Cl atom in the plane of the O2C2 unit was assumed (this is the conformation adopted by the chloroacetate anion in the crystal structure of silver chloroacetate19). [If these calculations with fixed conformation of the structural fragment had not led to a correct structure solution, the next stage would have been to consider a more general structural fragment, with the torsion angle around the C-C bond in the chloroacetate anion considered as a degree of freedom.] Similarly, although the sodium cation represents a significant proportion (ca. 25%) of the total scattering matter in the asymmetric unit, it was not included in the initial structural fragment; as the structural relationship between the chloroacetate anion and the sodium cation is not known a priori, inclusion of the sodium cation in the structural fragment would introduce additional degrees of freedom in the Monte Carlo calculation. These issues highlight some of the options available to the user in applying the Monte Carlo technique and optimizing its efficiency for any particular structural problem. In the initial Monte Carlo calculation, the structural fragment was subjected to simultaneous translation and rotation within the unit cell for 40 000 Monte Carlo moves, with 19 rotations per translation. For each Monte Carlo move, the maximum allowed translation was 0.3 Å along each of the x, y, and z axes of an orthogonal reference frame, and the maximum allowed rotation angle was (45° about each of the x, y, and z axes (with the rotation axis passing through the C1 atom). The modified weighted profile R factor (denoted Rmwp)32 was used to quantify the level of agreement between calculated and experimental powder diffractograms. The value of Rmwp for the overwhelming majority of trial structures was between 100% and 90%. The two trial structures (Monte Carlo move numbers 1045 and
Letters
Figure 1. Value of Rmwp for trial structures versus Monte Carlo move number in the second Monte Carlo structure solution calculation for sodium chloroacetate.
21 147) with lowest Rmwp (85.5%) were discriminated adequately on the basis of Rmwp from all other trial structures (Rmwp > 86%), and these two potential structure solutions were considered further. As described below, only the structure solution corresponding to Monte Carlo move number 1045 led to successful structure determination. For the structure solution obtained in Monte Carlo move number 21 147, difficulties were encountered in attempts to locate the sodium cation, and attempts to refine the structure were not satisfactory. In the knowledge of the correct crystal structure reported below, it is evident that the trial structure obtained in Monte Carlo move number 21 147 has a wrong orientation of the chloroacetate anion, with the chlorine atom close to the positions of sodium cations in the correct structure. It is therefore not surprising that this trial structure did not lead to a satisfactory structure refinement. We now consider only the structure solution obtained in Monte Carlo move number 1045. Difference Fourier analysis generated the position of the sodium cation, in the expected region close to the oxygen atoms of chloroacetate anions. However, subsequent Rietveld refinement of this structural model did not generate an acceptably good fit between experimental and calculated powder diffraction data, although the structure was nevertheless considered plausible. To allow the structure to adjust by more than is normal in a Rietveld refinement, a second Monte Carlo calculation was carried out, with the refined structure from the above calculations taken as the starting structure and the parameters controlling the Monte Carlo calculation taken to constrain the structure to remain close to this starting structure. Both the sodium cation and chloroacetate anion were included in the structural fragment and were handled as independent structural units (with 20 rotations per translation for the chloroacetate anion and translation only for the sodium cation). The maximum allowed translations along each of the x, y, and z axes were 0.1 Å, the rotation of the chloroacetate anion was constrained to a maximum of (45° about each of three orthogonal axes passing through the C1 atom, and the parameter S21 was fixed at a low value (S ) 1). This calculation was carried out for 5000 Monte Carlo moves (see Figure 1); the value of Rmwp for trial structures ranged from 100% to 79% and centered around 86% for many structures. Two trial structures (Monte Carlo move numbers 640 and 2440) had Rmwp ) 78.9% and were discriminated clearly on the basis of Rmwp from all the other structures (for which Rmwp was generally above 84%). These two trial structures actually represent essentially the same structure. Rietveld refinement of this structure was then carried out, with standard restraints applied to the bond lengths and bond
J. Phys. Chem. B, Vol. 101, No. 44, 1997 8829
Figure 2. Experimental (+ signs), calculated (solid line), and difference (lower line) X-ray powder diffraction profiles for the Rietveld refinement of sodium chloroacetate. Reflection positions are marked. The calculated powder diffraction profile is for the final refined crystal structure, details of which are given in Table 1.
Figure 3. Final refined crystal structure of sodium chloroacetate (hydrogen atoms not shown) viewed along the crystallographic a axis.
angles of the chloroacetate anion. This refinement proceeded successfully, leading to the following agreement factors32 for the final refinement calculation (26 variables distributed over 3507 profile points): Rwp ) 13.6%, Rp ) 10.2%. All isotropic atomic displacement parameters were fixed at Uiso ) 0.025 Å2 in the refinement calculation. All bond lengths and bond angles in the final refined structure are within acceptable limits, consistent with the precision of the data. Refinement of a preferred orientation parameter led to a slight improvement in fit between the experimental and calculated powder diffraction data, although the small residual discrepancies (see Figure 2) suggest that the effects of preferred orientation are not completely eliminated. The calculated X-ray powder diffractogram for the final refined structure and the experimental X-ray powder diffractogram are compared in Figure 2. The final refined structure is shown in Figure 3 and structural parameters are listed in Table 1. Discussion As shown in Figure 3, the crystal structure of sodium chloroacetate comprises rows of chloroacetate anions along the b axis, with the plane of these anions (defined by the O2CCCl fragment) parallel to the bc plane. The sodium cations coordinate to the oxygen atoms of the chloroacetate anions, with six oxygens associated with each sodium cation (Na‚‚‚O distances in the range 2.4-2.7 Å). The structure can be
8830 J. Phys. Chem. B, Vol. 101, No. 44, 1997
Letters
TABLE 1: Atomic Coordinates for the Non-Hydrogen Atoms in the Final Refined Crystal Structure of Sodium Chloroacetate [P21/a; a ) 7.1177(3) Å, b ) 5.3609(3) Å, c ) 10.8127(5) Å, β ) 92.434(4)°] atom
x/a
y/b
z/c
Cl1 Na1 C1 C2 O1 O2
0.7253(11) 0.8735(14) 0.6406(30) 0.6600(30) 0.6264(21) 0.6168(22)
0.4882(20) 0.2440(26) 0.7562(25) 0.7742(24) 0.5497(26) 0.9423(26)
0.6189(6) 0.8993(10) 0.8274(8) 0.6914(8) 0.8734(7) 0.8819(10)
TABLE 2: O‚‚‚C Distances and O‚‚‚C-Cl Angles for Potentially Reactive Pairs of Neighboring Chloroacetate Anions in the Crystal Structure of Sodium Chloroacetatea atoms
label in Figure 4
symmetry relation
d/Å
δ/°
O(2)‚‚‚C(2) O(1)‚‚‚C(2) O(1)‚‚‚C(2) O(2)‚‚‚C(2) O(2)‚‚‚C(2) O(1)‚‚‚C(2)
1 2 3 4 5 6
x + 0.5, 1.5 - y, z x + 0.5, 1.5 - y, z x - 0.5, 1.5 - y, z x - 0.5, 1.5 - y, z x, y + 1, z x, y - 1, z
4.61 4.45 3.90 3.95 4.93 4.61
103 128 101 76 55 168
Figure 4. Specification of O‚‚‚C distances for potentially reactive pairs of neighboring chloroacetate anions in the crystal structure of sodium chloroacetate (see also Table 2): (a) neighboring chloroacetate anions along the a axis; (b) neighboring chloroacetate anions along the b axis.
a The atoms considered in each case are the oxygen atoms of the CO2 group and the carbon atom of the CH2Cl group and are defined in Figure 4. The O‚‚‚C distance is denoted d, and the O‚‚‚C-Cl angle is denoted δ. For each O‚‚‚C distance considered, the oxygen atom is taken on a reference molecule and the molecule containing the carbon atom is designated by the symmetry relation shown. As shown in Figure 4, O‚‚‚C distances labeled 1-4 are between pairs of adjacent chloroacetate anions along the a axis, whereas O‚‚‚C distances labeled 5 and 6 are between pairs of adjacent chloroacetate anions along the b axis.
considered to comprise slabs parallel to the ab plane); the thickness (along the c axis) of each slab is defined by two chloroacetate anions and the intervening sodium cations in the central region of the slab. The oxygen atoms point inward toward the sodium cations, and the chlorine atoms point outward, defining the “surface” of the slab. Thus, each slab comprises two adjacent rows of chloroacetate anions running along the b axis. It is important to note that the sodium cations that link pairs of adjacent chloroacetate anions along the b axis lie above and below the planes (defined by the CO2 units) of the oxygen atoms to which they are coordinated. Along the a axis, there are columns of chloroacetate anions, with adjacent anions related by the a glide plane; as shown in Figure 3, essentially the only difference between adjacent molecules along these columns is in terms of the relative orientations of their C-Cl bonds. We now speculate on possible mechanisms for the polymerization reaction, recognizing that to generate polyglycolide from chloroacetate anions, an oxygen atom of one molecule should attack the carbon atom of the CH2Cl group of another molecule, with elimination (formally) of Cl-. Of relevance here are the O‚‚‚C distances between the oxygen atoms of the CO2 group in a given molecule and the carbon atoms of CH2Cl groups in the neighboring molecules, as well as the trajectories of approach of the oxygen atoms toward the C-Cl direction (characterized by the O‚‚‚C-Cl angles). The ideal trajectory for an SN2 reaction is for the oxygen atom to approach the carbon atom parallel to the direction of the C-Cl bond (i.e. O‚‚‚C-Cl angle 180°). The relevant O‚‚‚C distances and O‚‚‚C-Cl angles are summarized in Table 2 and Figure 4. As shown in Figure 4, there are relatively short O‚‚‚C distances both between neighboring chloroacetate anions along the b axis and the a axis of the crystal, and the polymerization reaction is expected to occur in one of these directions. Along the b axis (Figures 4b and 5), the shortest O‚‚‚C distance between neighboring molecules in the rows of chlo-
Figure 5. Section of the crystal structure of sodium chloroacetate with arrows indicating the propagation of the polymerization reaction within rows of chloroacetate anions along the b axis, as discussed in the text. The hydrogen atoms in this plot have been added in positions corresponding to standard geometry.
roacetate anions is 4.61 Å, and the relative positioning of adjacent molecules is such that the oxygen atom can approach the carbon atom close to the ideal trajectory parallel to the direction of the C-Cl bond (O‚‚‚C-Cl angle 168°). As all pairs of adjacent molecules along the row have exactly the same geometric relationship, a polymerization reaction is expected. Next, we consider the possibility for polymerization to occur within the columns of chloroacetate anions along the a axis (Figure 4a). In this direction, the relevant O‚‚‚C distances between neighboring molecules along the a axis are in the range 3.90-4.61 Å and are slightly shorter than the O‚‚‚C distance between neighboring molecules along the b axis. However, the O‚‚‚C-Cl angles for neighboring molecules are substantially less than 180°, and a significantly larger amount of molecular reorientation would therefore be required to bring pairs of neighboring molecules along the a axis into a plausible relative orientation for reaction. In summary, while the evidence available does not allow polymerization along the a axis to be ruled out, we believe that polymerization along the b axis should be substantially more facile and will represent the major mechanism for the polymerization reaction in this material. Thus, the polymerization
Letters reaction to produce polyglycolide in crystalline sodium chloroacetate can be rationalized directly from knowledge of the crystal structure and can therefore be considered as a topochemical solid-state reaction. Clearly the thermal activation of the reaction is related to the requirement for a small degree of reorientation of pairs of adjacent molecules relative to each other. For the chloroacetate anions, the largest amplitude libration in the crystal is likely to occur about an axis perpendicular to the molecular plane, which corresponds to the molecular reorientation required to bring oxygen and carbon atoms of adjacent molecules together in order to react along the b axis. It is likely that the reaction is enhanced by cooperative reorientations of adjacent molecules in this way. To explore the reorientational motions of the chloroacetate anions in crystalline sodium chloroacetate, we are currently embarking upon solid state 2H NMR studies of the materials containing the deuterated anions ClCD2CO2-. Although knowledge of the crystal structure of sodium chloroacetate provides a direct rationalization of the polymerization reaction to produce polyglycolide, the mechanism for the production of crystalline sodium chloride cannot be deduced directly, although significant diffusion of the chloride anions (generated, at least formally, as a consequence of the polymerization reaction) and the sodium cations within the crystal is implicated. Clearly, destruction of the crystal structure, which is an inevitable consequence of the polymerization reaction, will create voids through which diffusion of the chloride and sodium ions may be facilitated. Nevertheless, the question of whether free chloride anions exist in the crystal during the reaction, or whether the removal of chlorine atoms from the chloroacetate anions and the generation of sodium chloride particles occur in a concerted fashion, remains unanswered at the present time. It is interesting to note that the crystal structure of sodium chloroacetate reported here differs substantially from the crystal structure of silver chloroacetate reported recently.19 Thus, while both sodium chloroacetate and silver chloroacetate undergo thermally induced polymerization reactions to produce polyglycolide and the alkali chloride, the proposed mechanisms for the polymerization reactions in these solids differ significantly. In principle, different mechanisms of solid-state polymerization may be expected to produce samples of polyglycolide with different physical properties. In this regard, it is interesting to note recent results35 that suggest that the polyglycolide samples produced from sodium chloroacetate and silver chloroacetate are substantially similar with regard to their porosity (after washing out the alkali halide). However, no information on the mechanical properties or the degree of polymerization is yet available for these materials. Equally, it is interesting to contemplate the degree of similarity between the crystal structures of sodium chloroacetate and sodium bromoacetate; in this regard, crystal structure determination of sodium bromoacetate is currently in progress, again using powder diffraction data, and the structural properties of this material will be reported in due course. The crystal structure of sodium chloroacetate reported in this paper was determined from powder diffraction data using the new Monte Carlo technique that we have developed recently, further demonstrating the scope and potential of this method for crystal structure determination. The continued development and application of this method (as well as other approaches for crystal structure determination from powder diffraction data) will lead in due course to the unraveling of other long-standing solid-state problems, such as rationalization of the solid-state polymerization reaction discussed here.
J. Phys. Chem. B, Vol. 101, No. 44, 1997 8831 Acknowledgment. We are grateful to the University of Birmingham (studentship to L.E.), Ciba Geigy plc (postdoctoral fellowship to B.M.K.), and the Nuffield Foundation for financial support. EPSRC and Daresbury Laboratory are thanked for the provision of beam time for synchrotron X-ray powder diffraction experiments. M.E. thanks the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for financial support. References and Notes (1) Hoffmann, R. Liebigs Ann. Chem. 1857, 102, 1. (2) Kekule´, A. Liebigs Ann. Chem. 1858, 105, 288. (3) Epple, M.; Kirschnick, H. Chem. Ber. 1996, 129, 1123. (4) Epple, M.; Tro¨ger, L. J. Chem. Soc., Dalton Trans. 1996, 11. (5) Epple, M.; Kirschnick, H.; Thomas, J. M. J. Therm. Anal. 1996, 47, 331. (6) Epple, M.; Sazama, U.; Reller, A.; Hilbrandt, N.; Martin, M.; Tro¨ger, L. Chem. Commun. 1996, 1755. (7) Epple, M.; Kirschnick, H.; Greaves, G. N.; Sankar, G.; Thomas, J. M. J. Chem. Soc., Faraday Trans. 1996, 92, 5035. (8) Aliev, A. E.; Harris, K. D. M.; Epple, M.; Thomas, J. M. Manuscript in preparation. (9) Ylinen, P. J. Mater. Sci., Mater. Med. 1994, 5, 522. (10) Ashammakhi, N.; Makela, E. A.; Vihtonen, K.; Rokkanen, P.; Kuisma, H.; To¨rma¨la¨, P. Biomaterials 1995, 16, 135. (11) Hofmann, G. O. Arch. Orthop. Trauma Surgery 1995, 114, 123. (12) Kohlschutter, V.; Tuscher, J. L. Z. Anorg. Allg. Chem. 1920, 111, 193. (13) Cohen, M. D.; Schmidt, G. M. J. J. Chem. Soc. 1964, 1996. (14) Schmidt, G. M. J. Pure Appl. Chem. 1971, 27, 647. (15) Thomas, J. M. Philos. Trans. R. Soc. London 1974, 277, 251. (16) Cohen, M. D. Angew. Chem. Int. Ed. Engl. 1975, 14, 386. (17) Thomas, J. M. Pure Appl. Chem. 1979, 51, 1065. (18) Ramamurthy, V.; Venkatesan, K. Chem. ReV. 1987, 87, 433. (19) Epple, M.; Kirschnick, H. Chem. Ber. 1997, 130, 291. (20) Harris, K. D. M.; Tremayne, M. Chem. Mater. 1996, 8, 2554. (21) Harris, K. D. M.; Tremayne, M.; Lightfoot, P.; Bruce, P. G. J. Am. Chem. Soc. 1994, 116, 3543. (22) Kariuki, B. M.; Zin, D. M. S.; Tremayne, M.; Harris, K. D. M. Chem. Mater. 1996, 8, 565. (23) Tremayne, M.; Kariuki, B. M.; Harris, K. D. M. J. Appl. Crystallogr. 1996, 29, 211. (24) Tremayne, M.; Kariuki, B. M.; Harris, K. D. M. J. Mater. Chem. 1996, 6, 1601. (25) Tremayne, M.; Kariuki, B. M.; Harris, K. D. M. Angew. Chem. Int. Ed. Engl. 1997, 36, 770. (26) Tremayne, M.; Kariuki, B. M.; Harris, K. D. M.; Shankland, K.; Knight, K. S. J. Appl. Crystallogr. in press. (27) Vedavathi, B. M.; Vuayan, K. Acta Crystallogr., Sect. B 1977, 33, 946. (28) Wei, K. T.; Ward, D. L. Acta Crystallogr., Sect. B 1976, 32, 2768. (29) Tremayne, M.; Kariuki, B. M.; Harris, K. D. M. OCTOPUS97 (Monte Carlo Technique for Powder Structure Solution), 1997. (30) Larson, A. C.; Von Dreele, R. B. Los Alamos Lab. Report No. LA-UR-86-748; Los Alamos National Laboratory: Los Alamos, NM, 1987. (31) Werner, P.-E.; Eriksson, L.; Westdahl, M. J. Appl. Crystallogr. 1985, 18, 360. (32) The general expression for the agreement factors used in this work is
(
∑ w [y (obs) - y (calc)]
R ) 100 ×
i
i
i
i
∑ w [y (obs)]
2
i
i
i
)
2
1/2
where yi(obs) is the intensity of the ith point in the experimental powder diffraction profile, yi(calc) is the intensity of the ith point in the calculated powder diffraction profile and wi is a weighting factor for the ith point. The profile R factor (Rp) employs unit weights for all data points,30,33 the weighted profile R factor (Rwp) employs the standard weighting scheme,30,33 used for Rietveld refinement, and the modified weighted profile R factor (Rmwp) employs a weighting scheme optimized34 for use in Monte Carlo structure solution from powder diffraction data. (33) Young, R. A., Ed.; The RietVeld Method; IUCr/OUP: Oxford, 1993. (34) Elizabe´, L.; Kariuki, B. M.; Tremayne, M.; Harris, K. D. M. Manuscript in preparation. (35) Epple, M.; Herzberg, O. J. Mater. Chem. 1997, 7, 1037.
