calculated by standard formulas,I6 but a slight modification to ..... 457 (vs). The calculated data omit all bands whose calculated intensity is less than 0.5% of the ..... Calc four-ring stretching four-ring bending six-ring bending. (cm-9. SJ s6. S7.
448
J. Phys. Chem. 1994, 98, 448-459
Computer Simulation and Interpretation of the Infrared and Raman Spectra of Sodalite Frameworks J. A. Creighton,’,? H. W. Deckman, and J. M. Newsam# Exxon Research and Engineering Company, Clinton Township, Route 22 East, Annandale, New Jersey 08801 Received: July 29, 1993; In Final Form: September 22, 1993’
The 105 zero-wavevector vibrational modes of an infinite sodalite framework with atomic positions corresponding to the sodalites M~JAl6Si6Oz4lClz(M = Li, Na, K)and silica sodalite are calculated by the Wilson GF matrix method. Not all of the modes which are formally infrared or Raman active have significant spectral intensity, and point-charge or bond-polarizability models are used to generate synthetic infrared or Raman spectra in order to identify the modes which give rise to the observed bands. The synthetic spectra reproduce most of the features of the experimental spectra very satisfactorily, and for the aluminosilicate sodalites the wavenumbers of the bands are simulated to within 30 cm-I. The changes in the spectra as the framework angles change along the series M = Li, Na, K are also well reproduced. This enables an extensive analysis of the spectra to be made, including the assignment of the symmetries of the modes, and is the first detailed interpretation of the vibrational spectra of a fairly complex aluminosilicate framework. The vibrational modes involved in the observed infrared and Raman bands are analyzed in terms of the contributions from the characteristic vibrations of the TO4 and four-ring or six-ring structural subunits of the aluminosilicate framework, and each of the modes is shown to involve large contributions from only a few of the symmetry coordinates of the four-ring or six-ring subunits. The analysis has identified new relationships between both the intensities and the frequencies in the spectra and structural features of the aluminosilicate framework, notably between the intensity of an infrared band near 750 cm-1 and the Si-0-A1 angle and between the intensity of a Raman band near 1000 cm-* and the degree of ordering of Si and A1 atoms over the tetrahedral sites of the framework.
Introduction
In addition to its important application to the investigation of molecular adsorption in zeolites, considerable use has also been made of infrared spectroscopy for characterizing the structures of the host zeolite frameworks themselves. The infrared spectra of zeolites depend not only on the framework topology but also on theSi/Al ratioand on the natureof the extraframeworkcations that balance the anioniccharge of the framew0rks.l The spectra can therefore in principle be used as fingerprints for zeolite framework identification and for thedetectionof chemicalchanges that affect the framework structures. In addition, it has been found empirically that certain infrared bands are characteristic of some of the common structural subunitsin zeolite frameworks, such as double four- or six-rings or large pore openings.2 Such qualitative correlations are valuable as preliminary indicators of the presence of these subunits in zeolites prior to full structural characterization by diffraction methods. Within groups of compounds with a common framework structure, quantitative correlations between structural parameters and the frequencies of infrared bands have also been made, and thus, for example, relationships between the frequencies of infrared bands of compounds with the sodalite structure and the magnitude of the unit cell constant, T-O bond length and T-0-T angle have been reported.’ Much less use has been made of Raman spectroscopy for investigating zeolite frameworks. Recently, however, it has become clear that Raman spectra provide information on the magnitude of the T-O-T bridge angles linking the TO4tetrahedra in sodalites4Jand other aluminosilicates,6and it has been proposed that certain Raman bands may be characteristic of particular ring structures in zeolites.’ Permanent address: Chemical Laboratory, University of Kent, Canterbury, CT2 7NH, U.K. Part of this work was carried out at the University of Kent. Present address: Biosym Technologies Inc., 9685 Scranton Road, San Diego, CA 92121-2777. *Abstract published in Aduunce ACS Absrracrs, November 15, 1993.
To develop fully the use of vibrational spectroscopy as a structural tool for zeolite frameworks, there is a pressing need for a detailed understanding of the individual vibrational modes that contribute to the infrared and Raman spectra of the frameworks. Early suggestions of the types of motions which may be involved in the principal infrared bands were made by Flanigen et ai.? who recognized that the vibrations are those of strongly coupled TO4 tetrahedra, with no bands attributable to separate Si04 or A104 vibrations. The vibrationswere envisaged as either internal vibrations of the TO4 tetrahedra, which give rise to infrared bands whose frequenciesare rather independent of the particular framework structure, or external vibrations (librations or translations) of the tetrahedra, whose coupling is more dependent on the local geometry of the framework (particularly the T-0-T angle), and whose infrared bands are thus at frequencies which are more sensitive to the presence of particular structural subunits. It was recognized that this is a simplified picture, however, pending theoretical studies of the vibrational modes of individual framework structures.’ The large number of atoms in the unit cells of zeolites has until recently limited such calculationsto studies of the normal modes of individual subunits of the zeolite frameworks. Normal-mode calculations directed at investigating the vibrations of isolated double four-ring and double six-ring units were carried out by B l a ~ k w e l lwho , ~ ~ ~identified modes which have frequencies and descriptions broadly in line with those given by Flanigen et al.2 most notably the characteristic double-ring modes between 500 and 650 cm-I. A calculation of the vibrations of an isolated five-ring, a structural subunit of the pentasil zeolites, has also been briefly outlined.10 The validity of these calculations on isolated units is somewhat uncertain, however, in view both of the strong coupling of the TO4 vibrations throughout the zeolite frameworks and of the strong dependence of the coupling on the full framework geometry. Few calculations of the vibrations of very large or infinite zeolite framework models have yet been reported. The normal modes of an infinite pseudolattice containing double four-rings have been investigated by No et al.11
0022-3654f 94/2098-0448%04.50/0 0 1994 American Chemical Society
Spectra of Sodalite Frameworks Demontis et a1.12 used a molecular dynamics method to simulate the infrared spectrum of zeolite A, and the infrared and Raman spectra of infinite silica frameworkswith the sodaliteand faujasite structures were simulated by de Man et al.13 This work and background symmetry theory have been reviewed by van Santen and Vogel.14 Very recently, simulations of the infrared spectra of several silica polymorphs have been carried out by de Man et al.15 with the objective of elucidating the framework vibrational modes. Good agreement between the simulated and experimental infrared and Raman spectra of silica sodalite and of dealuminated faujasite was obtained, and the relative contributions of the vibrations of the Si-oSi and Si04 structural subunits to the various regions of the vibrational spectrum of the faujasite structure were investigated. Although the vibrational spectra of zeolites are in many cases relatively simple because of the high symmetry of the frameworks, the interpretation of the spectra is nevertheless difficult because of the large size of the repeat units and the highly coupled nature of the vibrations, and as a result of this no detailed interpretation of the infrared and Raman spectra of a zeolite framework has yet been given. Furthermore, by no means all of the vibrations which are formally infrared or Raman-active are observed in the experimental spectra. It is thus clear that an essential step in their interpretation is to simulate the infrared and Raman spectra from calculations of the zero-wavevector modes of the infinite frameworks. Zeolite frameworks are in some respects very suitable for such spectral simulations in spite of the size of the repeat units, since rather few parameters are required to define the valence force field and the band intensities, due to the small number of distinct bond types. In this paper we describe the methods which we have used for such calculations and their application to materials with the sodalite structure. Since our objective has been to interpret in detail the infrared and Raman spectra of these frameworks, an important part of the work has been to determine the symmetries of the modes responsible for each observed band and to analyze the modes in terms of contributions from simpler motions of the structural subunits of the framework. This has enabled new relationships between structural features of the frameworks and the frequenciesor intensities of bands in the experimental spectra to be identified. Normal-Mode Calculations and Spectral Simulation Methods Although it has become normal practice to use potential functions based on Coulombic and short-range repulsion terms for simulating many of the properties of zeolites, we are here concerned only with small-amplitudevibrationsclose to the energy minimum, and we have assumed that the vibrational potential energy can be approximated by quadratic terms in the atomic displacements. This permits us to use the highly efficient Wilson GF method16 for calculating the vibrational frequencies and amplitudes of the framework. This harmonic approximation has been used in several other studies of the vibrational properties of aluminosilicate and related f r a m e w ~ r k s , ~ ~ and J ~ Jit~ follows J~ the normal practice for describing the small-amplitude vibrations of covalently bound molecules. Sincewe are not concerned directly with the extraframework cations, these have been ignored in the calculations;this amounts to an energy factoring of the framework vibrations from the vibrations of the cations, which are known to lie in the far-infrared region.18 The adaptation of the GF method to the calculation of the zero-wavevector modes of infinite repeating lattices has been discussed by Shimanouchi et al.19 and by Piseri and Zerbi.*O The Fand G matrices for an infinite lattice are of infinite dimension, but transforming to symmetry coordinates which are totally symmetric with respect to the translational symmetry of the lattice results in factoring of the infinite matrices to give finite F and G matrices concerned only with the zero-wavevector modes. A method for the construction of the
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 449 zero-wavevector F and G matrices has been given by Shimanouchi et al.I9 This involves constructing the diagonal blocks of the infinite F and G matrices concerned with the coordinates within a single unit cell, together with the off-diagonal blocks which contain the interaction terms between the internal coordinates of that cellwith eachof its nearest-neighbor unit cells. It was shown19 that the symmetry transformation which gives the F and G matrices for the zero-wavector modes is equivalent to summing this diagonal block of F or G with each of these off-diagonal blocks. We have used an equivalent procedure to calculate the zerowavevector F and G matrices, in which only the atoms within a single unit cells are considered, with cyclic boundary conditions equating translationally equivalent atoms at opposite faces of the cell. This has the effect that the interaction terms between coordinates in the unit cell and in neighboring cells are replaced by identical terms involving interactions between coordinates on opposite sides of the single cell. The cyclic boundary conditions must be taken into account both in defining the internal coordinates, where only one coordinate must be defined for translationally equivalent internal coordinates at opposite faces of the unit cell and also in compiling the B matrix, where B defines the transformation between the internal coordinate and Cartesian coordinatedisplacements. The elementsof the B matrix, the s vectors,l6 give the Cartesian displacement of each atom for unit displacement in each of the internal coordinates, and each column of B refers to an individual atom. To satisfy the cyclic boundary requirement, the s vectors for translationally equivalent atoms lying on oppositeboundaries of the unit cell are thus placed in the same column of B. The s vectors for the bond-stretching and angle-bending internal coordinates of the unit cell were calculated by standard formulas,I6 but a slight modification to the standard procedurewas required for angle-bendingcoordinates in which the angle is cut by one of the faces of the unit cell. For such a coordinate, only the part of the angle which lies within the unit cell contributes toward the internal coordinate, the rest of the coordinate being made up of the complementary part of the equivalent angle at the opposite side of the unit cell. The unit vectors required in the standard formula16 for the I vector for such a bending coordinate are thus unit vectors parallel to the bonds which define that angle, where these unit vectorsare arrived at by considering bonds which lie at opposite faces of the unit cell. The G matrix for the unit-cell zero-wavevector modes was then obtained from the B matrix by the standard transformation G = BM-%
where M is the diagonal matrix of atomic masses. In the GF method the vibration frequencies vi are obtained from the eigenvalues
of the matrix product CF.I6 It is usual in the internal-coordinate representation to make use of mass-adjusted normal coordinates, with the normalization condition for the corresponding eigenvectors lj:
-l,Fl, = A,
The eigenvectors 1, then give the internal-coordinate amplitudes for unit displacement in the mass-adjusted normal coordinates. For the unit cell of the sodalite framework there are 48 bond stretching and 24 T-O-T and 72 O-T-O angle-bending internal coordinates, and the F and G matrices are thus of dimension 144 X 144. To take advantage of the fact that F and Care symmetric matrices it is advantageous to diagonalize F and G separately,21 and thus in the internal-coordinate representation for the sodalite framework two diagonalizations of 144 X 144 matrices are required, However, since only 108 Cartesian displacement coordinates are required for the 36 frameworkatomsof thesodalite
450 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
unit cell, the 144 internal coordinates contain 36 redundant coordinates, and these together with the 3 zero-wavevector translational modes result in 39 of the eigenvalues being zero. Although some of the calculations were done in internal coordinates, it was therefore found to be more efficient, after evaluating the B and F matrices, to transform to a Cartesian displacement coordinaterepresentation. This has two significant advantages. First, the matriccs in the Cartesian representation are then of dimension 108 X 108. Second, only one matrix diagonalization is required since the Cartesian C matrix is already diagonal, being the diagonal matrix of reciprocal atomic masses. The F matrix was thus first transformed to the Cartesian force constant matrix F, by means of
F, = BFB
(1)
and the vibration frequencies ui were then obtaiaed from the eigenvalues 4r%? of the symmetric matrix2?
The eigenvectors (I& of this matrix were normalized such that the matrix of eigenvectors L, is an orthogonal matrix, and the normalized eigenvectors (&)t then give the Cartesian amplitudes for unit displacement in non-mass-adjusted normal coordinates. Finally, the eigenvectors I, of the internal coordinate representation were obtained from the Cartesian eigenvectors by the transformation
I, = BM-1’2(lc)i Although considerable factoring of the C and F matrices for the sodalite framework could in principle be achieved by transforming to symmetry coordinates, it was found to be more convenient to calculate the eigenvalues of the matrices without the use of symmetry factoring. It was therefore necessary as a separate operation to associateeach of the calculated frequencies ut with a normal-mode symmetry species. This was done by calculating the characters of the symmetry transformations of the normal modes from the eigenvectors 1,. The symmetry operations of the unit-cell factor group permute symmetrically equivalent internal coordinates, and for the nondegenerate normal modes this has the effect that the normal-coordinate displacements are transformed into plus or minus themselves by a given symmetry operation. To determine the character for a particular nondegenerate mode and a given symmetry operation it is sufficient to consider the effect of the operation on just one of the internalcoordinate displacements, since this is enough to show whether the mode as a whole is symmetric or antisymmetric with respect to the operation. Thus for a nondegenerate normal mode i and a symmetry operation which transforms internal coordinate p into internal coordinate r, the character for that operation is equal to
Creighton et al. degenerate mode ( i j ) , which is thus given by the trace of (4)
An analogous procedure using the nine L matrix elements and their symmetry transforms for three of the internal coordinates gives the characters for the triply degenerate modes. It is necessary in this method of calculating the characters for a particular mode that the L matrix elements refer to internal coordinates which are significantly involved in the motion and thus that the inverses involved in (3) and (4) are well defined. For the nondegeneratevibrationsit was a simple matter to choose an internal coordinate such that the L matrix elements were not of small magnitude. In the case of the degenerate modes, the determinant of the matrix requiringinversion in (4) was evaluated for several choices of internal coordinates, and the coordinates for which the determinant was a maximum were chosen as the internal coordinatesp and q. A table of the permutations of the internal coordinates for each of the symmetry operations of the unit-cell factor group was generated by one of the computer programs (see below) and was used to identify the internal coordinates into which the chosen internal coordinates p and q, etc., were transformed by the given symmetry operation. The full set of characters for each normal mode for all of the symmetry operations of the unit-cell factor group finally enabled the symmetry species of the normal modes to be unambiguously identified. The last step of the spectral simulations was to calculate the infrared and Raman band intensities, and from these to generate the infrared and Raman spectra by plotting the sum of Lorentzian bands centered at the wavenumber calculated for each mode, with peak heights proportional to the calculated relative intensities. Following previous authors,lz13J5infrared intensities were calculatedassumingthat thecharges enontheatomsofthe framework remain constant throughout the vibrational motion. This rather simplified model was adopted since it requires the minimum number of input parameters, although it has been noted that a model in which the magnitude of the atomic charges are allowed to oscillate with the vibrational motion enabled a more accurate simulation of the observed infrared band intensities to be made for the related substance quartz.’’ In the fixed charge approximation used here, the dipole change in the x direction for unit displacement in the normal mode i is given by n
where the superscriptx in plc)ddenotes that only the components of (&)i concerned with displacements of each of the atoms n in the x direction are taken in eq 5. Equations in (Y& and (‘I& analogous to eq 5 give the dipole changesin they and z directions. The relative intensity of the infrared band due to mode i, averaged over all crystal orientations, was then taken to be
(3) In the case of a doubly degenerate mode ( i j ) , each of the component vibrations i and j involve motion in particular symmetrically equivalent internal coordinates, and the effect of the symmetry operation is to redistribute the motion in each component vibration over those equivalent internal coordinates. Thus for a symmetry operation R which transforms two internal coordinates p and q into coordinates r and s, the effect of R on the amplitudes of p and q in the two vibrations i and j is given by
These four L matrix elements and their symmetry transforms are sufficient to determine the character of R for the doubly
Raman intensities were calculated from a simplified bond polarizability model. In the model due to WolkensteinZ3the total change in polarizability due to a vibrational displacement is the sum of contributions due to changes in the lengths of individual bonds, plus the sum of contributions due to changes in bond orientations. It is found for molecules that thecontribution from changes in bond orientations is usually much smaller than that from changes in bond lengths, and because of insufficient knowledge of the required bond polarizability parameterswe have, for simplicity, assumed that only bond stretching terms of the type (&x,,lar,)Sr, contribute to the total polarizability change, where a, and r, are the polarizability and length of bond r. In neglecting the terms due to changes in bond orientation, we have thus implicitly assumed that the low-frequency Raman bands
Spectra of Sodalite Frameworks owe their intensity to the small admixture of bond stretching into what are largely angle bending modes. In the bond polarizability model each bond of the framework is taken to have a polarizability with principal values ai and al along and perpendicular to the bond axis. With respect to Cartesian axes it is readily shown that for bondr the polarizabilities are
n
+ (“11 - a,>,*consistsof a three-dimensional network of linked sodalite cages. Each sodalite case is composed of silicon and aluminum atoms (T atoms) alternating around the vertices of a truncated cuboctahedron (Figure la) with bridging oxygen atoms between each T atom, and adjacent sodalite cages are linked to each other by sharing common square or hexagonal faces. All the S i 4 bonds in the framework are symmetrically equivalent, as are all the A 1 4 bonds, and the coordination about each T atom by oxygen is close to regular tetrahedral. The primitive unit cell of the framework consists of one such sodalite cage of composition [A@iaOz4]”, and the anionic charge of the frameworkisbalanced by the charges of the nonframework sodium and chloride ions. There are 36 framework atoms in the primitive unit cell, and therefore 108 zero-wavevector framework modes, comprising 105 optical modes with symmetry species 3AI + 5A2 + 8E + 13T1 + 14T2 in the factor group Td,and three acoustic modes.29 The 14T2modes belong to the infrared-active symmetry species, and the 3A1 + 8E + 14T2 modes are Raman active. Essentially the same framework structure is also found in the polymorph of silica, silica sodalite, but whereas in the aluminosilicate sodalites each TO4 tetrahedron (with site symmetry S4)is rotated about its local S4axis through an angle 8 from its most symmetrical orientation, in silica sodalite at room temperature and above 0 is zero, so that the sodalite cage becomes centrosymmetric, space group Imjm ( = 0 h 9 ) . 3 0 This center of symmetry results in the vibrational selection rules being more restrictive for silica sodalite than for the aluminosilicatesodalites. The presence of only one type of T atom in silica sodalite results in a further simplification of its vibrational spectra, since the primitive unit cell is only half the size of the primitive unit cell
452 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
in the aluminosilicate sodalites. The zero-wavevector optical modes of silica sodalite thus have the symmetry species AI, + 2A2, + 3E, 3T1, 3T2, + A2, + E, 4T1, + 3Tzuin the factor group oh,with only four TI, infrared active modes and seven (AI, 3E, 3TzJ Raman-active modes. Because of this greater simplicity of the infrared and Raman spectra of silica sodalite it is of interest toexamine the relationship of the aluminosilicate sodalite frameworks to centrosymmetric structures. The TO4tetrahedra in the aluminosilicate sodalites are rotated about the S4symmetry axis through a tilt angle 0 so that the oxygen atoms of the T404four-rings lie alternately above and below the plane containing the T atoms. For the sodalites M~[Al,jSi6024]C12,where M is Li, Na, K, and tilt angle is respectively33.1 O, 23.1 ",and 8.3",28.31 and the potassium sodalite framework therefore comes close to having the centrosymmetric space group P m h (=Oh3), the space group appropriate to a sodalite framework of alternating Si and A1 atoms with zero tilt angle 8.30 The correlation of the symmetry species of the spectroscopically active framework modes in P43n (factor group Td) with those in PmJn (factor group oh) is 3A1- AI, + Az,, 8E 6E, + 2E,, 14T2 6T2, + 8Tlu, of which only 8T1, are infrared active and 2A1, + 6% + 6T2, are Raman active in P m h It is therefore expected that some of the infrared- or Ramanactive modes of the P43n frameworks, namely, the infrared-active modes which correlate with gerade modes in P m h and the Raman-activevibrationswhich correlate with ungeradevibrations in PmJn, might be of low spectral intensity, particularly for the potassium sodalite. We have already shown elsewhere4 that the mean of the S i 4 and A 1 4 bond stretching force constantsf,, the Si-0-AI bending force constant fp, and the mean of the 043-0 and & A 1 4 bending force constants fa for an aluminosilicate sodalite framework may be very simply calculated from the three AI frequencies of the framework in the simplest valence force-field approximation, in which it is assumed that all the off-diagonal force constants are zero. A single-crystal Raman study by Ariai and Smith32enabled the A1 frequencies of sodium chloride sodalite to be unambiguously identified as 987, 463, and 263 cm-l, and from these frequencies the calculated force constants weref, = J rad-2.4 J rad-2, fa = 6.55 X 522 J m-2,fe = 7.58 X (the value of f, (=f&) is in error by a factor of 100 in ref 4). These force constants provide starting values for the calculations reported here, in which a common set of force constant values was used to calculate the frequencies for the four compounds M8[Al6Si&]Cl2 (M = Li, Na, K) and silica sodalite. The geometricaldata for the aluminosilicates ~ d a l i t e s and ~ ~ Jfor ~ silica sodalitemwere from published structure determinations. To give good agreement between the calculated and experimental values of the non-A1 frequencies while maintaining the fit for the AI modes, it was necessary to introduce the off-diagonal force constants fm f,,, and fad into the F matrix (note that the TO4 force constantsf, andfa calculated using the simple valence force field approximation in ref 4 correspond tofi + 3fm and f, - 2fa, f,d of a general valence force field). The force constants were adjusted so that the frequencies of the bands above 400 cm-1 in the simulated infrared and Raman spectra reproduced the experimental frequencies to within 30 cm-l for the sodium and potassium sodalites and to within 20 cm-1 for the lithium compound. It was found possible to achieve this level of fitting by including onlyfn,fa,, and f,d as off-diagonal force constants. In addition, the force constants were partitioned between Si-0 and A 1 4 bonds so that the same S i 4 force constant values used for the aluminosilicate frameworks also gave the beat fit to the observed frequencies of silica sodalite that was possible for that limited set of off-diagonal force constants. An essential step in this adjustment procedure was to simulate the infrared and Raman spectra as the force constants were adjusted, since it was otherwisenot known which of the calculated
+
+
+
+
-
+
+
-
Creighton et ai.
TABLE I: Force Constants for the sodilite Frameworks vl)si = 446.8 J m-2 (fl)a= 297.9 J m-2 J rad-2 (fa)si= 1.416 X J rad-* (fa)N= 0.944 X fp = 0.000
(fn)si = 59.1 J m-2 (&,)a = 39.4 J m-2
(fm)si = 2.46 x 10-19 J rad-2 ( f - ) ~= 1.64 X W9J rad-2
(/-)'si = 2.46 X J rad-2 (fa.)" = 1.64 X lo-**J rad-2
frequencies corresponded to the relatively few observed bands in the experimental spectra. The adjustments to the force constants were made by hand, since it proved to be impracticable to use an iterative procedure to refine the force constants to a best leastsquares fit of the calculated and observed frequenciesbecause of the size of the matrices involved. The adjustments were done with the help of the values of the differentials aAi/afi contained in the Jacobian matrix JZ,whose elements are given by26
a w f i =b ) t
(8)
The final set of force constants are listed in Table I, where the notation for the force constants is defined by the potential function
in which the cross terms involve only pairs of internal coordinates which share a common T atom. To carry out the infrared and Raman spectral simulations, it was necessary, in addition to the force constant values, to provide values for the charges on the framework atoms and for the S i 4 and A1-0 bond polarizability derivatives. The values of the charges on the atoms were taken to be those assumed by Mabilia et al.,33 viz., Si, 1.l; Al, 1.39; 0,-0.6225. These partial charges ascribe a greater polarity to the A 1 4 than to the 5i-O bond, in agreement with generally accepted electronegativity values. Models which placed a larger positive charge on the silicon atoms than on the aluminum atoms" gave a slightly less satisfactory fit to the relative intensities of the triplet of infrared bands in the region 700-850 cm-I, but in view of the approximations involved in the infrared intensity calculations this observation may not be significant. As far as we are aware, there are no literature data on the S i 4 and A1-0 bond polarizability derivatives. The following relative magnitudes were therefore assigned to these parameters: all! and aLr = 5.0 and 3.0 for S i 4 bonds and 3.0 and 1.8 for A 1 4 bonds, respectively. These values were chosen so as to satisfy the expectation that the polarizability derivatives are larger for S i 4 bonds than for the more polar (less polarizable) A 1 4 bonds, and that (YIJ! > ult for both types of'bond. A comparison of the simulated and experimental infrared and Raman spectra of Li, Na, and K chloride sodalites are shown in Figures 2 and 3, and Tables I1 and I11 gives the wavenumbers and relative intensitiesin thecalculated and experimentalinfrared and Raman spectra. The calculated data in Tables I1 and 111are only for bands having more than 0.5% of the intensity of the most intense band. The full set of calculated wavenumbers for the zero-wavevectormodes of sodium chloride sodalite, together with their symmetry species, are given in Table IV. It is seen that for the aluminosilicate sodalites not only the frequencies but also the simplicity of the spectra are well reproduced in the simulations. Bearing in mind the very simple model for calculating the infrared and Raman intensities, the distribution of intensities in the simulated spectra is also satisfactory and enables the modes responsible for the observed bands to be clearly identified. There are however two obvious points of discrepancy between the simulated and observed spectra. First, the simulations dpnot reproduce the longitudinal optical (LO) modes which appear in
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 453
Spectra of Sodalite Frameworks
TABLE Ik c.lculrted and Experimentrrl Wavenumbers (cum-') and Relative Intensities (in Parentheses) of the Infrared-Active (T2) M o k ef the Sodalites' Li8[Al&O~]C12 calc ObS
974C10) 963(22) 951(48) 765(21) 737(19) 707(20) 469(29)
Nas [A@isO~lCl2 calc obs
964 (vs) 951 (vs) 761 (8) 741 (m) 693 (s) 481 (s) 454 (vs)
354( 1) 298(5)
990(100) 981 (10) 967(60) 750(16) 713( 28) 676(13) 461(39) 368(l) 286(3)
984 (vs) 960 (I) 734 (m) 712 (w) 667 (m) 466 (s) 438 (s) 2846
K8[AlsSkOul ch
Si12024
calc
obs
calc
obs
1010(100) 1002(1) 988(62) 730(3) 691(25) 639(22) 461(45) 413(1)
996 (vs)
1093(100)
1101 (vs)
748( 19)
871 (w) 780 (m)
541(31)
457 (vs)
705 (w) 683 (m) 642 (m) 443 (s) 416 (m)
263(1)
The calculated data omit all bands whose calculated intensity is less than 0.5%of the intensity of the most intense band. Reference 18.
TABLE m. Calculated and Experimental Wavenumbers (cm-1) and Relative Intensities (in Parentheses) of the Raman-Active Modes of the Sodalites' Li~[AbSbOrlCl2 calc obs 1047 (m)b 1027 ( w ) ~ 974( 12) T2 963(6) T2 960( 1) E 958 (m) 951(6) T2 946( 5 3)/A I 930 (s) 765(2) T2 751 (w) 657(1) E 640 (w) 527 (vs) 524( 100)AI 296( 14) AI 285 (m) 299( 1) T2 259 (m)
Nan [A16Sis%ICh calc obs 1059 (m)b 1013 ( w ) ~ 990( 1 1) T2 989(83) AI 986 (s) 986(5) E 981(8) Tz 967(9) T2 964 (m) 750(7) T2 730 (w) 606(2) E 602 (w) 471(100) Ai 461 (vs) 368(1) T2 287( 1) T2 292 (m) 235(29) Ai 262 (m)
Ks[A16Sis0zdCh calc obs 1078 (m)b
Si12024 calc
obs
1030(100) Ai 1029 (s) 1125(23) E 1020(12) E 789(36) T2 lOlO(2) T2 661(4) E 1002(9) T2 1001 (m) 516(100) Ai 449 988(2) Tz 983 (w) 465(6) E 730(12) Tz 701 (w) 399(5) T2 556(3) E 549 (w) 440( 1) E 445 (w) 434(53) A1 413 (vs) 385(2) T2 367 (w) 365(1) E 321 (m) 95(9) AI a The calculated data omit all bands whose calculated intensity is less than 0.5%of the intensity of the most intense band. LO modes not included in the calculated data.
I
I1
I
I 1200
lo00
800
600
100
700
I
I
(b)
I
u
1200
1000
BOP
LOO
a00
200
u.renun*l.r/cn-1
Figure 3. Simulated (a) and experimental (b) Raman spectra of the sodalitcs Ms[Al&Ou]C12 (M = Li, Na, K). 1
1200
1
1
1000
1
1
800
1
1
600
,
1
Wavenumbsr/cVl
Figure 2. Simulated (a) and experimental (b) infrared spectra of the sodalites Ma[AbSi,&]C12 (M = Li, Na, K).
the Raman spectra of the aluminosilicatesodalites above ca. 1000 cm-1. The phenomenon of LO-TO ~plitting3~ is B property of dipolar nonzero-wavevector modes, whereby an additional potential energy term involving the interaction of local dipoles with the macroscopic oscillating field due to the collective effect of all the oscillating dipoles, pushes up the frequency of the component of the mode travelling longitudinal to the dipole axis, while the transverse component is unaffected. The nonzero-wavevector modes of relevance to optical spectroscopy are those with very small wavevectors, and only the transverse optical (TO) modes are active in the infrared spectrum, where they are superimposed on the corresponding zero-wavevector modes. Thus the LO-TO splitting is not apparent in the infrared spectrum. If, as in the aluminosilicatesodalites and other noncentrosymmetriclattices,
the dipolar modes are also Raman active, however, both the LO and TO components are Raman active, and the LO mode may then be observed as a distinct band in the Raman spectrum. The LO-TO splitting is greatest for modes which are strongly dipole active and which are thus the most intense in the infrared spectra. In the case of the sodalites, therefore, the modes with the greatest LO-TOsplittingaretheT2modesnear lOOOcm-*,and thesplitting is manifest by the presence of the LO bands above 1000 cm-l in the Raman spectra, which have no counterparts in the infrared. (Note however that inactivity of the LO component is truestrictly only for perfectly crystalline solids, and in the experimental infrared spectra ip Figure 2 there is broadening of the 1000-cm-I band on the high-frequency side due to weak absorption by the LO component.) The LO-TO splitting of this mode of 70 cm-1 in the sodalites may be compared with comparable splittings of ca. 90 and 120cm-1, respectively,in a-quartz and vitreousq ~ a r t z . 1 ~ The LO-TO splitting of other T2 modes, which are weaker in the infrared spectra, is apparently too small to be observed on the Raman spectra in Figure 3. Because our method of calculation
454
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
TABLE Iv: Calculated Wavenumbers (cm-1) and the Symmetry Species ( r d ) of the Full Set of Zero-Wavevector Framework Modes of Sodium Chloride Sodalitd
a Also shown in parentheses are the symmetry species (Oh)that the sDcctroscoDicallv active AI. E. and TZmodes wouldhave if the To4 tilt ingle B wire z&o, resulting in the space group PmJn.
I 1200
1000
830
600
I 400 wo"en"mter/cm-~
Figure 4. (a) Simulated infrared (IR) and Raman (R) spectra and (b) the experimental infrared spectrum of silica sodalite.
is restricted to the zero-wavevector modes, our simulations do not calculate the LO modes and thus do not reproduce the Raman bands above 1000 cm-1 or the breadth of the bands near 1000 cm-l in the infrared spectra. It is of note that doubt has been expressedI4 about the assignment3*of the highest wavenumber Raman band of the sodalites to an LO component. In exploring the alternative possibility32 that it is an E symmetry fundamental, however, it was found impossible to reproduce this wavenumber with any set of forceconstants where the interaction forceconstants were within reasonable limits, thus supporting its identification to an LO mode. Second, the experimental infrared spectra of all three aluminosilicate sodalites show a strong doublet band near 500 cm-', whereas in the simulated infrared spectra this band is only a singlet. We are at present uncertain of the reason for this discrepancy. Table I1 shows that for sodium chloride sodalite there is a calculated band at 368 cm-I with no band nearby in the experimental infrared spectrum, and this may represent the lower member of the observed doublet at 438 cm-I. Although this calculated band is of much lower intensity than the observed band at 438 cm-I, it is probable that a set of force constant values which brought its wavenumber up to 438 cm-l would also increase its intensity, due to intensity sharing with the upper member of the doublet at 466 cm-I. The most likely explanation of this discrepancy is therefore that it is due to an inadequacy of the approximate force field used here. It is of note however that evidence has been given of a short-time-scale structural distortion of the silica sodalite framework which was not apparent in the structures determined from diffraction measurement^,'^ and an alternative explanation of the observed doublet band is that it is due to asymmetry splitting of the triply degenerate mode calculated to lie at 461 cm-1. The experimental and simulated spectra for silica sodalite appear in Figure 4 and in Tables I1 and 111. Tables I1 and I11 give the wavenumbers and relative intensities of the calculated and experimental infrared and Raman bands, and the full set of calculated wavenumbers and symmetry species for the zerowavevector modes of silica sodalite is given in Table V. The weak band at 871 cm-1 in the experimental infrared spectrum in Figure 4 is almost certainly due to residual entrapped ethylene glycol which was used in the preparation of the silica sodalite36
Creighton et al.
TABLE V: Calculated Wavenumbem (cm-1) d tbe S ies (0')of the Zero-Wavevector Framework sodrlitd 1125% 789 Tz' 516 AI, (311 T ~ ) (1 100 Tzu) 748 TI, (477 TI') (305 A$ (1096 A Z ~ ) 661 ' E 465 E, 303 TI, (639 Tzu) (420 EU) 12 Tq 1093 TI, (1076 TI,) 541 TI, 399 Ta a Spectroscopically inactive modes are shown in parenthesea.
3Z2SE
and which in the liquid state has a strong doublet band at 880 and 860 cm-l and no other strong bands below lo00 cm-1. The . qualitativefeatures of the spectra are again reproduced sufficiently well to enable the modes responsible for the observed bands to be clearly identified. The agreement between the calculated and experimental frequencies for silica sodalite is less satisfactory than for the aluminosilicate sodalites, however. This may be a limitation of the assumption that the same S i 4 force constants may be used for silica sodalite and for thealuminosilicatesodalites. In the aluminosilicates there is a contribution to the potential energy from interactions of the framework with the cations, and neglecting the cations in the model adopted here results in the force constants of the S i 4 and A 1 4 bonds implicitlycontaining a contribution from these cation-framework interactions. Discussion The magnitudes offs and the other diagonal force constants in Table I are within the range of values derived from force constant8,9,11,12.15,37 or ab inifid3*38.39calculations on other aluminosilicatesor silicon-oxygencompoundsby previous authors, with the exception of the A 1 4 stretching force constant (f,),,,~, which is slightly larger than previously published ~alues.~.~J~J2J3 Of particular interest in Table I is the magnitude of the T-O-T bending force constant fp We previously obtained a value of& close to zero from an analysis of the three AI frequencies of sodium chloride sodalite with the assumption that all off-diagonal force constants were zero: and this force constant has also been found to be unusually small in quartz and other silica polym o r p h ~ . ~ S JIts ~.~ small ~ magnitude is important since it presumably underlies the high degree of conformational flexibility and the wide range of topologies exhibited by framework silicates and al~minosilicates~.~~ Unfortunately, none of the experimentally observed infrared or Raman bands in the 1200-400-cm-~ range are very sensitive to this force constant because of its small size, and its magnitude is therefore more uncertain than that of the other diagonal force constants and fa. To place upper and lower limits onfs, this force constant was increased from zero in increments of 0.1 X lo-**J rad-2 while holding the other force constants fixed at the values in Table I. This identified the Raman band near 460 cm-l and the infrared band near 730 cm-I as the most sensitive to fp Increasing& to 0.3 X J rad-2 gave calculated wavenumbers for these bands that were too high by 45 and 37 cm-I, respectively, and increased by more than 3-fold the sum of the squares of the differences between the observed and calculated wavenumbers compared with its value for fa = 0. This loss of fit to the observed wavenumbers could only partially be compensated by adjusting the other force constants fi and f . Thus although precise significance cannot be given to the zero value of f5 in Table I, we are confident that fs is unusually small and probably less than 0.3 X J rad-2, in agreement with our earlier concl~sion.~ One of the main objectives of this investigation is to identify the types of framework motion that give rise to the individual bands in the infrared and Raman spectra of the sodalites. Because of the complexity of the frameworks, we have chosen to analyze the motions in terms of the contributionsfrom individualstructural subunits, rather than attempting to describe the vibrations of the entire frameworks. The analysis in terms of each structural subunit presents a different point of view of the motions involved
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 455
Spectra of Sodalite Frameworks in the modes of the frameworkas a whole. The framework modes may for example be regarded as the coupled vibrations of the individual TO4tetrahedra, and the relative contributions of Si04 and A104vibrations to each framework mode may be ascertained. Each TO4 stretching mode is coupled either in phase or in antiphase to the correspondingmodes of adjacent tetrahedra, and the phase of this coupling may be ascertained by decomposing each frameworkmode into vibrationsof the S i U A l subunits. Finally the modes may be analyzed in terms of vibrations of larger structural subunits, such as the T404 or T606 rings, in order to gain a less localized picture of the framework vibrations. In isolation, each TO4 tetrahedron (point group Td) has two stretching modes v1 (Al) and v3 (T2) and two bending modes YZ (E)and v4 (T2). Symmetry correlations partially restrict the contributions that these individual TO4modes make to the overall modes of the framework. Thus the correlation of the symmetry species of Td via the TO4site symmetry group S4 to the unit cell group Td shows that only the VI and v2 modes of the individual TO4 tetrahedra can contribute to the Al unit cell modes, while u2,v3, and v4 can contribute to the A2 and T2 unit-cell modes, and all four TO4modes can contribute to the E and T1 unit-cell modes. To quantify the symmetry-allowedcontributions of each TO4 mode to each mode of the framework, we have made use of symmetry coordinates to represent thecharacteristicT04 motions. These may be constructed by standard methods,l6 bearing in mind the symmetry group S4 which each TO4 has in the framework, and for each TO4 are taken to be of the form Sl(A,) = ( b 1 +
b 2
+ b 3 + b4)/2
S,(E) = r(2Aa12- Aa13 - Aa14 - Aa23 - Aa24 + 2Aff3,)/ 2 d 3
+
S,(E) = r(Aa13- Aa14- Aa23 A ( Y ~ ~ ) / ~ S3(T2) = ( b 1 +
b 2-b 3
- b4)/2
(bl - b2 - b3+ b 4 ) / 2 Su(T2) = (bl - b2+ b,- b 4 ) / 2 S3,(TJ
S4(T2) = r(Aff12- Aff34)/d2 S ~ ~ ( T=J r ( ~ c ~ 1 3A C Y ~ ~ ) / ~ ~ S , ( T J = r ( ~ a 1 4where the numbering of bonds and angles is such that the S4 axis bisects the angle a12 between the bonds rl and rz, and where r is the length of a T-O bond. The coefficient r is included in the definitions of the angle-bending symmetry coordinates so that each symmetrycoordinatehas thedimensionof length. Symmetry coordinates of this form for all 12 TO4tetrahedra in the unit cell define a 108 X 108 U matrix16 which gives the transformation between the internal coordinates and the local symmetry coordinates centered on each of the TO4 tetrahedra. The vibratonal amplitudes expressed in these local symmetry coordinates are then given by the columns of the matrix L,where
L, = UL It is common practice to express the contributions of individual coordinates to a particular mode i by their contributions to the vibrational potential energy, given by 1/z(1,j)2J/, where lij is the amplitude of the coordinatej with force constantfi. This has the effect that coordinatesassociatedwithsmall forceconstantsappear to make a small contribution to the mode, even if there is a large amplitude involved. Applied to aluminosilicate frameworks, the T-0-T angle /3 would thus appear to have very little involvement in any of the modes, and furthermore the A104tetrahedra would appear to make a smaller contribution to the overall motion than the Si04 tetrahedra, because of the smaller A I 4 and 041-0 force constants. We have therefore chosen instead to represent
TABLE VI: Contributions (75) of tbe S mmetry Coordinates of the Individual TO4 Tetrahedra to the &lculated Modes Corresponding to Observed Infrared or Raman Bands of Sodium Chloride Sodalite SiO' s2
s 3
0.0 0.0 27.9 44.9 3.7 0.0 11.1 3.4 26.2 0.0 0.1 33.6 0.0 1.1 30.2 0.0 2.8 1.5 0.0 1.5 2.5 0.0 4.7 4.6 1.1 21.0 2.6 0.7 31.9 0.0 0.0 9.8 0.8 1 .o 25.6 0.0
s4
~ 1 0 ~
s1
22.5 0.0 0.0 38.8 25.9 19.4 26.6 0.0 32.0 0.0 19.9 0.0 18.6 0.0 22.9 0.0 12.5 2.0 0.0 2.1 34.0 0.0 0.0 2.2
s2
s 3
4.6 11.5 4.7 0.5 0.0 2.0 0.3 4.7 19.4 29.2 4.0 29.5
12.8 0.0 1.7 15.9 21.4 11.1 10.0 20.3 11.2 0.0 2.1 0.0
14.8 0.0 2.3 7.8 10.3 33.1 38.7 32.3 29.3 0.0 37.4 0.0
TABLE W: Contributions (a) of Symmetrically Coupled
and Asymmetrically Coupled Stretching Motions of Adjacent TO4 Tetrahedra and of OTO and TOT Beading Motions to the Calculated Modes Corresponding to the Observed Infrared or Raman Bands of Sodium Chloride Sodalite! cm-' v,(TOT) v.(TOT) 6(OTO) 6(TOT) si04 ,4104 39.2 41.9 17.4 50.4 32.2 990 (Tz) 1.5
15.2 1.2 48.6 50.3 0.1 83.5 989 (AI) 986 (E) 1.9 56.5 36.3 5.3 66.6 28.1 47.8 35.0 15.2 2.0 60.3 24.2 981 (Tz) 51.1 43.4 5.1 63.3 31.7 967 (Tz) 0.4 2.5 57.8 29.7 10.0 24.2 46.2 750 (Tz) 1.9 59.1 28.1 22.6 49.0 713 (Tz) 10.9 64.6 10.0 32.2 57.3 4.0 676 (Tz) 21.4 606(E) 15.6 1.5 82.2 0.7 37.2 61.9 0.2 61.1 36.1 32.6 31.3 471 (AI) 2.6 0.6 85.2 12.0 44.6 43.5 461 (Tz) 2.2 0.1 55.1 26.6 31.7 41.8 235 (AI) 3.0 a The sum of columns 2-4 gives the total contributions from all TO4 internal motions, and this total is separated into contributions from Si04 and A104 tetrahedra in columns 6-7.
thecontributions byjust the squareof theamplitudes. The relative contribution of a set of TO4symmetry coordinates (for example the six Si04symmetric stretching symmetry coordinates of the type SI)to a particular framework mode is thus the sum of the squares of the relevant elements of I.I. The contributions of the Si04and A104symmetry coordinates to the modes observed in the infrared and Raman spectra of sodium chloride sodalite are given in Table VI, in which the contributions from the degenerate symmetry coordinates are the sum over all of the degenerate components. A similar procedure usinga U matrix which transforms thebond stretchingcoordinates into the T-0-T local symmetry coordinates
S, = (bsio + b A o ) d 2
sa = (bsio - bAlo)/42 enables the bond stretching contributions to be separated into contributions from symmetricallycoupled and antisymmetrically coupled TO4tetrahedra. These contributions are listed in Table VII, together with the contributions from 0-T-O and T-0-T angle bending. The total contribution made by Si04tetrahedra to each mode and the total A104 contribution were obtained by summing over the Si04 or A104 coordinates SI,Sz,S1,and S4 from Table VI, and these are also given in Table VII. Tables VI and VI1 show that, as has already been recognized,lS there are no framework vibrations which, even approximately, can be regarded as only Si04 or only A104 modes. There is, however, a small preponderanceofSi04 contributionsto the modes above 900 cm-1, and of A104 contributions to the modes in the region 60&800 cm-1, due to the fact that the Si04 tetrahedra
456 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
Creighton et al.
TABLE VIIk Contributions (76) of the T404 Ring-Stretching Symmetry Coordinates to tbe Calculated Modes Corresponding to Observed Infrared or Raman Bands of Sodium Chloride Sodahte Calc
four-ring stretching S7 SS Sg
(cm-9
SJ
s6
990(T2) 989 (Ai) 986 (E) 981 (Tz) 967 (Tz) 750 (Tz) 713 (Tz) 676(T2) 606(E) 471 (AI) 461 (Tz) 235 (AI)
0.0 0.1 1.9 0.0 0.0 0.0 0.0 0.0 15.6 2.6 0.0 3.0
0.0 83.5 56.5 0.0 0.0 0.0 0.0 0.0 1.5 0.2 0.0 0.1
0.0 0.0 0.0 46.8 1.1 2.1 0.2 0.8 0.0 0.0 0.0 0.0
0.1 0.0 0.0 1.8 0.0 9.3 0.9 0.0 0.0 0.0 0.2 0.0
39.2 0.0 0.0 1.0 50.0 0.4 1.7 3.2 0.0 0.0 0.6 0.0
four-ring bending SIO 1.4 0.0 0.0 0.2 0.4 0.7 10.0 21.4 0.0 0.0 2.0 0.0
SII 0.0 0.7 10.9 0.0 0.0 0.0 0.0 0.0 32.2 41.4 0.0 37.3
have larger force constants than the A104 tetrahedra. There is also no sharp division of the modes appearing in the infrared spectra into internal and externalvibrationsof the TO4tetrahedra, as some previous authors have suggested.' Nevertheless there are just a few of the modes which are almost entirely internal TO4 vibrations, as shown by the small contributions made to them by T-0-T bending (see Table VI). The only such modes which are experimentally observed are in the Raman spectra (Nag[A16Si6024]C12:calcd 989 and 606 cm-l); the other modes of this sodalite which are essentially of internal TO4 character (calcd 971, 651, 241, 128 cm-1) are weak or forbidden in the infrared and Raman spectra. Table VI1 shows that all of the vibrations above 900 cm-l are very largely motions of adjacent TO4tetrahedra which are coupled in anti-phase through the T-0-T bridge, and in which the motion of the 0 atom is therefore approximately parallel to the direction linking the two T atoms. The corresponding in-phase coupled stretching vibrations of adjacent TO4 tetrahedra, in which the motion of the 0 atom of each T-0-T bridge is approximately perpendicular to the direction linking the two T atoms, lie in the lower frequency range 600-800 cm-1 on account of the larger amount of T-0-T and 0-T-0 angle bending which inevitably accompanies T-0-T symmetric bridge stretching due to the constraints of the framework geometry. These conclusions are in agreement with those of previous a u t h o r ~ . ~It ~isJclear ~ from Table VI1 that in fact the vibrationaldisplacements in this middlefrequency range involve greater contributions from angle bending than from bond stretching. This is slightly different from the picture given by the potential energy contributions listed in Table IX, which show that over 50% of the vibrational potential energy is contributed by bond-stretching potential energy terms for framework modes above 600 cm-' and over 90% for modes above 900 cm-1. To obtain a less localized picture of the framework vibrations, we have also investigated their representation as the coupled vibrations of the Si2A1204or Si3A1306rings (four-rings and sixrings). Each unit cell contains six four-rings, three of which make up the square faces of the cubooctahedral sodalite cage, and the other three receive a quarter share from each of the 12 edges of the cuboctahedron which link the square faces. The four-rings are linked into linear chains, a portion of one of which is shown in Figure la, and indeed the sodalite framework may be regarded as being entirely a rectangular lattice of such intersecting linear chains. Each T-O bond is shared by a fourring and two six-rings, and all the T-O bonds and T-O-T angles and one-third of the 0-T-O angles are accounted for by the four-rings. The remaining angles are the 0-T-O angles of the six-rings. For simplicity we take the Si and A1 to be equivalent tetrahedral atoms, so that the four-rings have point symmetry Du, with vibrations of the following symmetry species: stretching, AI + BI + AZ + B2 + 2E; 0-T-O bending, AI + B1 + E; T-O-T bending, A1 + B2 + E. The correlation of the symmetry species
SIZ 0.0 9.5 20.3 0.0 0.0 0.0 0.0 0.0 9.8 0.0 0.0 0.0
SI3 14.4
0.0 0.0 0.6 31.9 0.1 4.6 15.8 0.0 0.0 39.7 0.0
SI4
SIJ
0.0 1.2 5.2 0.0 0.0 0.0 0.0 0.0 0.7 36.1 0.0 41.7
8.7 0.0 0.0 4.0 1.8 11.3 25.7 0.0 0.0 0.0 3.8 0.0
SI6
SI7
8.6 0.0 0.0 11.6 3.1 18.3 3.2 10.6 0.0 0.0 8.2 0.0
0.0 0.4 0.0 5.8 0.6 50.5 1.6 0.2 0.0 19.6 1.0 17.1
six-ring bending SIS SI^ Sa 1.4 4.6 0.0 9.6 5.0 0.5 0.3 0.2 0.0 0.0 0.0 0.0
11.0 0.0 1.5 8.0 3.8 6.1 1.8 31.4 0.1 0.0 14.0 0.0
15.1 0.0 3.7 10.7 2.4 0.6 50.0 16.5 40.2 0.0 30.3 0.0 '
of D M with those of the unit cell group Td (via Dz, the point symmetry appropriate to a Si2A1204 ring) show that only the Al and BI modes of the T404 rings can contribute to the AI, A2, and E modes of the framework, while only the A2, B2, and E ring modes can contribute to the TI and T2 framework modes. For an isolated T606 six-ring (point group 0 3 6 ) the symmetry species of the 0-T-O bending vibrations are AI, + AI, EI E,,,and the correlation of the symmetry species of D3d and Td shows that only the A,,, AI,, and the E,, E, bending modes can contribute respectively to the AI and E modes of the framework, while all four species of six-ring bending modes can contribute to the T2 framework modes. The following were chosen as the localsymmetry coordinates:
+ +
T404 rings
(D2&
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 451
Spectra of Sodalite Frameworks
TABLE Ix: Potential Energy Contributions (%) of the Diagonal Force Constants to the Calculated Modes Correspondin to Observed Infrared or Raman Bands of sodium a o i d e w i i t e cm-1 (fLI (falsi Cfrk 68.6 62.3 68.4 69.7 62.5 9.6 16.4 18.7 18.6 9.5 7.7 13.3
21.0 35.9 25.9 21.9 29.6 48.4 43.2 54.9 43.7 18.7 13.5 20.3
1.9 0.7 1.1 8.3 2.6 42.0 38.2 21.9 22.5 29.8 50.1 21.6
1.1 4.5 0.1 5.3 0.0 2.2 4.5 15.2 42.0 28.8 38.8
lbl
la1
b d le1
IC1
Id)
b If)
Figure 5. Approximaterepresentationsof the four-ring motions involved in the vibrations of sodium chloride sodalite at (calcd): (a) 989, (b) 471, (c) 235, (d) 990, 967, (e) 461 cm-l. (f) The B2 ( D u ) four-ring motion partially involved in the 750 cm-1 mode. The smaller circles reprent oxygen atoms, and e and Q denote motion in and out of the plane of the Paper.
S20/= r(Act,
+ Aa3 - Aas - A a , ) / 2
The numbering of the TO bonds, the 0-T-O angles a and the T-0-T angles fi in these definitions are as shown in Figure 1b. Table VI11 gives the total contributions of these symmetry coordinates to the modes observed in the infrared and Raman spectra of sodium chloride sodalite, summed over all of the fourrings and six-rings. An important conclusion revealed by these data is that for each vibration the motion involves large contributions from only a few of the symmetry coordinates. It is therefore possible to give a fairly simple approximate description of the vibrations in terms of the four-ring or six-ring symmetry coordinates. It should be stressed however that although fourring symmetry coordinates are more convenient for describing most of the framework modes, this should not be taken to imply that the vibrations are predominantly four-ring modes rather than six-ring modes, since each T-O bond is common to one four-ring and two six-rings,and it is therefore fundamental to the sodalite structure that no separation into vibrations of the fourrings and the six-rings can be made. The simplest framework vibrations are the AI modes since here all the Si04tetrahedra vibrate in phase with equal amplitudes and are either in phase or in anti-phase with all the A104 tetrahedra. In addition, in the A1 modes but not in other modes, there is no movement of the Si or A1 atomse4 Inspection of the L matrix shows that in the highest wavenumber AI mode (calcd 989cm-1) themotionis almost entirelya vibrationin thesymmetric stretching symmetry coordinate SIof the Si04tetrahedra in antiphase with S1 of the A104 tetrahedra. Viewed as a four-ring motion, this mode is thus (see Table VIII) mainly BI (OM) fourring stretching represented by S6,and involving oxygen atom motion tangential to the four-ring (Figure 5a). Thecorresponding mode (471 em-I) in which the symmetric stretching of all the Si04and A104 tetrahedra are in phase involves motion of the 0 atoms in directions approximately radial to the four-ring (Figure 5b) and thus receives its main contribution from the four-ring symmetric bending coordinates SII and S I 4 (Table VIII). In the third AI mode (235 em-I) the 0 atoms move in directions orthogonal to their displacements in the other two AI modes, and this mode may thus be regarded as approximately an out-of-
plane four-ring motion of the 0 atoms (Figure 5c), involving again mostly SIIand s14. Symmetry correlations between Td and DM show that not only the AI framework modes but also the E modes may be traced back to the Al and Bt modes of the four-rings. In the AI framework modes at 986 and 471 em-' all the four-ring displacements represented by Figure 5a or 5b are in phase as already noted. In the corresponding E vibrations at 986 and 606 em-' these A1 or BI displacements are in anti-phase in four-rings lying on orthogonal faces of the cuboctahedron. This anti-phase relationship between the four-ringsresults in the large contribution from the u-symmetry six-ring displacement S20 (see Table VIII), since the six-rings are bounded by these four-rings. Of greater interest than the framework E modes are the T2 vibrations, since they are responsible for all of the bands in the infrared spectra. All of the observed infrared bands are associated with strongly dipolar vibrations of the framework structural subunits, andTableVIII shows that the four- or six-ring symmetry coordinates mainly involved in the infrared bands are the Bz or E (DM)symmetry coordinates of the four-rings or the ,!E (D3d) coordinates of the six-rings. The most intense modes in the infrared spectrum, namely, the doublet (calcd 990, 967 em-1) and the mode at 461 em-', respectively, involve mainly the fourring asymmetric stretching coordinates S9 and the bending coordinate S13 of E (DM)symmetry, and Figure 5d.e are approximate representations of the motions involved in these symmetry coordinates. The weaker triplet ofbands in theinfrared spectrum (calcd 750,713, and 676 em-') involve relatively small contributions from the four-ring symmetry coordinates, and are predominantly six-ring bending modes. A point of considerable interest in the vibrational spectra of sodalites and indeed of other aluminosilicate frameworks is the marked discrepancy between the number of modes which are infrared or Raman active by symmetry and the number of bands which are observed in the experimental spectra. The computed spectra show that this is principally due to two factors, first, the overlapping of bands in the 900-1 000-em-I region where several asymmetric T-O-T stretching modes are concentrated into a narrow region, and second the low intensity of some of the bands below -500 em-'. There are 14 modes ( 14T2)that are infrared active and 25 (3Al + 8E + 14T2) that are Raman active. Comparison of Tables I1 and IV shows that for sodium chloride sodalite five of the 14Tz modes (all below -500 em-!) are calculated to have less than 0.5% of the infrared intensity of the strongest band, and indeed none of these appear in the experimental infrared spectrum. Eight of the remaining nine modes do appear as distinct bands in the infrared spectrum, the ninth mode (calcd 98 1 em-I) being overlapped by nearby more intense bands. Of the 25 Raman-active modes, 14 (6E + 8T2) are calculated to have less than 0.5% of the Raman intensity of the strongest band, and 11 of these modes (5E + 6T2) are below
458 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
-500 cm-1. Table I11 shows that of the remaining 11 modes which are calculated to have intensities greater than 0.5%of that of the strongest band, seven are observed as distinct bands in the Raman spectrum, three (calcd 990,986,98 1 cm-I) are overlapped by the intense AI band at 986 cm-1, and one fairly weak mode (calcd 368 cm-1) is apparently too weak to be observed. Also of interest is the correlation between the infrared and Raman spectra of the aluminosilicate sodalites and the much simpler spectra of silica sodalite. The aluminosilicate sodalite structure may be transformed so that of silica sodalite first by reducing the tilt angle B to zero, giving the space group P m h , and then by setting the Si and A1 atoms to be equivalent, giving space group Zmjm. Both of these steps markedly simplify the spectra: In P 4 m h there is a center of symmetry, and thus more restrictive selection rules than in Pa34 while setting Si A1 halves the volume of the primitive cell so that only half of the modes of the cubic unit cell are of zero wavevector. Considering only the spectroscopically active modes, Table IV shows the correlation of these modes in sodium chloride sodalite with the symmetry species of Pmjn. The six active modes above 900 cm-1 become AI, + 2E, + Tzs 2T1, in P m h , of which only two (E, + TI,) become zero wavevector in Imjm, and these correspond to the single infrared-active and single Raman-active mode of silica sodalite in this region. Of the three T2 modes of sodium chloride sodalite near 700 cm-l (T2, 2T1, in P m h ) , two (T2, + TI,) remain zero wavevector in Imjm, giving one infraredactive and one Raman-active mode of silica sodalite in the 700800-cm-1 region. The intense infrared band of sodium chloride sodalite near 460 cm-1 and the intense Raman band also near 460 cm-1 have obvious counterparts in the infrared and Raman spectra of silica sodalite at 457 and 449 cm-1. Also of interest is a comparison of the spectra of sodium and potassium chloride sodalites, since the structure of the potassium compound is quite close to P m h because of the small tilt angle 8. Referring to Table IV, we expect the modes correlating with gerade symmetry species of PmJn to become weaker in the infrared spectrum and stronger in the Raman spectrum of the potassium compound and vice versa for modes correlating with ungerude species, and the calculated intensities in Tables I1 and I11 shows several examples of this, e.g., the T2 mode near 730 cm-1 or the E mode near 1000 cm-1. The main purpose of investigating the motions responsible for the observed infrared and Raman bands is to look for new relationshipswhich may exist between the frequenciesor intensities of the bands and details of the structure of the sodalite framework. We have noted four such relationships from this study. First, the two most intense bands in the Raman spectra, respectively near 1000and 500cm-1, become increasingly far apart along the series of sodalites Ms[A16Si6024]C12(M = Li, Na, K) as may be seen from Figure 3. This is due to the increase in the T-O-T angle along this series and arises from the fact that these A1 modes of the framework are respectively the asymmetric and symmetric motions of the T-O-T linkages between the tetrahedra. As the T-0-T angle increases from 125.6O to 138.3' to 155.4' along this series, the higher AI mode is thus increasingly T-O-T stretching in character, whereas the lower AI mode increasingly involves T-O-T bending. A quantitative relationship between the frequencies of the A1 modes and the T-0-T angle may be given, as we have discussed in detail elsewhere: and this correlation enables the T-O-T angle in sodalites to be estimated from the frequencies of these prominent bands in the Raman spectra. Second, Table VI11 shows that the symmetry coordinates Sa, Sls,andS16Ofthefour-ringsaremainly responsible for the infrared activity of the 750-cm-1 mode, since the six-ring symmetry coordinates SI, and Si9 which are also involved in this mode are infrared-inactive. Ss and Sls (B2 in D u ) also become infrared inactive (symmetry species B g ( D a ) )if the four-ring is planar, as may be seen from the four-ring B2 motion represented in Figure
+
+
Creighton et al. 0.00
-
a c
0.40
m
E 0
-
0.36
0
>
g 0.24
I
2 0.12 0.00
170
160
150
140
130
120
T-0-T angle (degrees) Figure 6. Variation of intensity of the infrared band near 750cm-1versus T-0-T angle for the sodalites M8[A&Si&&.& (M = Li,Na, K)and silica sodalite.
5f, and a strong dependenceof the infrared intensity of this mode on the degree of nonplanarity of the four-rings is therefore expected. This is indeed seen to be the case in both the experimental and calculated infrared spectra (see Figures 2 and 4). These show that the intensity of the band near 750 cm-l decreases along the series Ms[A16Si60z4]C12(M = Li, Na, K)as the TO4tilt angle 6 decreases from 3 3 O to 23O to 8O and becomes zero for silica sodalite in which the four-rings are planar. A systematic variation of the intensity of this band with unit-cell constant for a series of sodalites has been noted previously without explanation by Henderson and Taylor.3 The tilt angle B is related to the T-O-T angle by
3 cos 6 = 2 sin2 o - d b s e if it is assumed that the sodalite frameworks consist of regular tetrahedral TO4subunits, and Figure 6 shows a plot of the relative intensity of this band (the peak absorbance relative to that of the intense absorption near lo00 cm-1) against T-O-T angle. It is seen that there is an almost linear variation in the relative intensity of this band with T-O-T angle over the range 125-155O. Although giving a more approximateresult than the value obtained from the frequencies of the AI Raman bands: a rough estimate of the T-O-T angle in sodalites may therefore also be made from infrared intensity data by interpolation in Figure 6. Third, although the infrared spectra of the three sodalites Ms[Al&i6024]Clz (M = Li, Na, K) all contain an intense double near 1000cm-1, the corresponding band in the infrared spectrum of silica sodalite is a singlet. As noted above, in the case of sodium chloride sodalite both components of this doublet receive their main contribution from the four-ring asymmetric stretching symmetry coordinate S 9 (represented by Figure 5d), and examination of the L matrixshows that in the upper component S9 has a large amplitude only in chains of four-rings linked through shared AI atoms, whereas in the lower component the Sg motion is only in four-ring chains linked through Si atoms. The splitting in the intense doublet infrared band is thus a consequence of the presence of the two types of T atoms in the aluminosilicate sodalites. To verify this, model calculations were carried out for the sodium chloride sodalite framework which showed that the separation between the two componentsof the doublet converged to only 3.2 cm-1 as the difference between the masses and force constants of the S i 4 and A 1 4 bonds were reduced to zero, whereas there was relatively little change in the separation of the components of the triplet band near 700 cm-l. Fourth, the prominent AI band in the Raman spectra of the aluminosilicate sodalites near lo00 cm-1 is due to the symmetric stretching of the S O 4 tetrahedra in anti-phase with the tetrahedra and owes its intensity to the fact that the polarizability changes associated with the two types of tetrahedra arenot equal.
Spectra of Sodalite Frameworks The corresponding vibration in silica sodalite has zero Raman intensity (see Figure 4), since the polarizability change in one Si04 tetrahedron cancels that of its neighbor which is vibrating in anti-phase. This absenceof a strong Si04symmetric stretching band near 1000 cm-1 is indeed a feature of the Raman spectra of all the structural forms of silica, and an explanation similar to that above has already been given to account for the weakness of the 1082-cm-I Raman band of quartz by Kleinman and Spitzer.17 The essential feature of this mode to be noted here is that alternate TO4 tetrahedra vibrate in anti-phase, and in the aluminosilicate sodalites it is because of the ordering of Si and A1 atoms onto alternate tetrahedral sites in compliance with Loewenstein’srule that this mode becomes one in which the Si04 are in anti-phase with the A104 tetrahedra. This raises the interesting possibility that the Raman intensity of this mode may be used to investigate Si/Al atom ordering in sodalites with Si/ A1 > 1.O, in which Loewenstein’srule no longer requires that the A1 atoms occupy alternate sites. The use of the intensity of this band to investigate A1 atom distributions in sodalites and its extension to other aluminosilicate framework structures will be the subject of a future paper.
References and Notes (1) Flanigen, E. M. In Zeolite ChemistryandCata1ysis;ACSMonograph Series 171; Rabo, J. A., Ed.;American Chemical Society: Washington, D.C., 1976; pp 80-117. (2) Flanigen, E. M.; Hassan, K.; Szymanski, H. A. Ado. Chem. Ser. 1971,101,201. (3) Henderson, C. M. B.; Taylor, D. Spectrochim. Acta 1977,33A, 283. (4) Creighton, J. A.; Deckman, H. W.; Newsam, J. M. J. Phys. Chem. 1991, 95, 2099. ( 5 ) Buckley, R. G.; Deckman, H. W.; Newsam, J. M.; McHenry, J. A.; Persans, P.; Witzke, H. In MicrostructureandPropertiesof Catalysts;Treacy, M. J., Thomas,J. M., White, J., Eds.;MRS Symposium Proceedings Series; Materials Research Society: Pittsburgh, 1988; Vol. 111, p 141. Dutta, P. K.; Shieh, D. C.; Puri, M. Zeolites 1988, 8, 306. (6) Deckman, H. W.; Creighton, J. A.; Buckley. R. G.; Newsam, J. M. In Synthesis, Characterization, and Novel Applications of Molecular Sieve Materials; Bedard, R. L., Bein, T., Davis, M. E., Garcts, J., Maroni, V. A., Stucky, G. D., Eds.; M.R.S. Symposium Proceedings Series; Materials Research Society: Pittsburgh, 1991; Vol. 233, p 295. (7) Dutta, P. K.; Puri, M. J. Phys. Chem. 1987, 91, 4329. (8) Blackwell, C. S.J . Phys. Chem. 1979, 83, 3251.
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