Vibrational spectra and normal coordinate analysis of crystalline lithium metasilicate

Transcription

1 Vibrational spectra and normal coordinate analysis of crystalline lithium metasilicate V. DEVARAJAN AND H. F. SHURVELL' Department of Chemistry, Queen's University, Kingston, Ont., Canada K7L3N6 Received January 12, 1977 V. DEVARAJAN and H. F. SHURVELL. Can. J. Chem. 55,2559 (1977). Infrared and Raman spectra of polycrystalline lithium metasilicate have been recorded. A vibrational assignment in terms of the various symmetry species of the unit cell group, CZ", has been made. A normal coordinate analysis of the unit cell vibrations at the centre of the Brillouin zone (k = 0) was carried out to support the assignment and provide descriptions of the vibrational modes. The results are discussed in the light of previous normal coordinate calculations on the isolated metasilicate chain. V. DEVARAJAN et H. F. SHURVELL. Can. J. Chem. 55,2559 (1977). On a enregistre les spectres infrarouges et Raman du metasilicate de lithium en phase polycristalline. Une analyse des coordonnees normales de vibration du cristal, dans I'approximation de k = 0, a permis de relier les bandes observees dans les spectres aux diverses espkces de symetrie du groupe de la maille Blkmentaire, tout en fournissant une description detaillee des modes normaux. Les rksultats des calculs sont comparks a ceux obtenus precedemment pour une chaine metasilicate isolce. Introduction The vibrational spectra of metasilicate (SiO,) chains are of interest since they form the structural unit of many glasses, and studies of these chains give an indication of structural disorders in the glasses. Recently, Brawer and White (1, 2) recorded the Raman spectra of a number of meta and disilicates in both crystalline and glassy states. By comparing the spectra obtained from these two states and carrying out simple force field calculations on isolated silicate chains and sheets, they were able to study the structural disorders in several alkali silicate glasses. Although the conclusions reached by Brawer and White are qualitatively correct, there is a need for a more complete investigation of the vibrational spectra and force fields of crystalline meta and disilicates. We are not aware of any previous detailed study on lithium metasilicate. In the present work, we have recorded the ir and Raman spectra of crystalline lithium metasilicate (Li2Si0,) and have carried out a normal coordinate analysis of the vibrations at the centre of the Brillouin zone (k = 0) in order to support the vibrational assignments, and give qualitative descriptions of the normal modes. Crystal Structure and Vibrations Lithium metasilicate, Li2Si03, belongs to the orthorhombic system with four molecules per 'To whom all correspondence should be addressed. crystallographic unit cell. The space group is C,': (Cmc2,) (3-5). However, the primitive (Bravais) cell contains only two molecules. The structure contains double (SiO,), chains running parallel to the c, axis. The projection of the orthorhombic unit cell along its c, axis is shown in ref. 3. Figure 1 illustrates an (SiO,), chain. There are twelve atoms per primitive unit cell giving rise to thirty-six vibrations including three acoustic modes. The factor group is C,, and the distribution of the thirty-six vibrations into the various symmetry species can be made using the procedures of Adams and Newton (6) and Fateley et al. (7). The result of this analysis is T,":$ = 10Al + 8A2 + 8B1 + 10B2 Further division of the vibrations into internal and external vibrations of the SiO, double chain and the identification of their symmetry species can be made using the method due to Adams and Newton (6). The results are given below: Motion Internal vibrations (chain) Librations (chain) Translations (Li and chain) Species 6A1 + 4A2 + 4B1 + 6B2 1A2 ~ A+ I 3Az 3B1 3B2 Acoustic modes lb1 + 1B2 Total 10Al + 8A2 + 8B1 + 10B2

2 CAN. J. CHEM. VOL. 55, 1977 FIG. 1. An (SO3), chain in the Li2Si03 crystal. Excluding the acoustic modes we should be able to observe 9A, + 8A2 + 7B, + 9B, vibrations in the spectra. All modes are Raman active, while the A, species modes are inactive in the infrared. Although longitudinal optical modes are allowed in the Raman spectrum of noncentrosymmetric crystals, it was not possible to identify any of these modes in the present work. Experimental Lithium metasilicate (LizSi03) was obtained in powder form from Alfa Products and used without further purification. The infrared spectra of the compound in Nujol mulls and KBr or CsI pellets were recorded using a Perkin-Elmer model 180 spectrometer. No important differences were observed between these spectra. The infrared spectrum is shown in Fig. 2. Raman spectra were recorded in the polycrystalline form as a powder and as a solid formed from slowly cooling a melt. The Raman instrument consists of a Jarrell-Ash monochromator, a cooled RCA C photomultiplier, and photon counting electronics. The nm line of an argon ion laser was used as the excitation line, at a power of 500 mw. A filter was not used, since plasma lines were not observed in the spectra. Although it was not possible to grow a single crystal of LizSi03, a Wollaston prism was mounted in c,4 FIG. 2. The infrared spectrum of a CsI pellet of Li,SiO,. FIG. 3. Raman spectra of solid Li2Si03 obtained by cooling a melt. Traces A and B were obtained by using parallel and perpendicular orientations, respectively, of a Wollaston prism analyser. Trace C was obtained using a different orientation of the sample with perpendicular orientation of the prism. front of the entrance slit of the monochromator to detect any polarization effects. In fact, some of the weaker bands did show some enhancement for certain orientations of the prism, or the solid sample formed from the melt. These intensity effects can be seen in Fig. 3. However, these partial depolarization measurements did not enable us to identify the A, modes. Table 1 contains a listing of the observed infrared and Raman wavenumbers. The selection of several very weak features for inclusion in Table 1 was based on their consistent appearance in a number of spectra obtained from different samples. Vibrational Assignment Lack of polarization measurements makes it difficult to assign the vibrational frequencies to specific symmetry species of the C,, factor group. However, it is possible to identify the A, species as they are present in the Raman spectra, but absent in the infrared. A possible assignment can be made in terms of group frequencies of the

3 DEVARAJAN AND SHURVELL 2561 TABLE 1. Observed and calculated wavenumbers (cm-'), descriptions of normal modes, and important contributing force constants for lithium metasilicate Observeda Important contributing Symmetry Raman Infrared Calculated Description force constantsb A w 852 w 1080 vs 850 vs Si-0 Si-0 str str 7, vs 604 s Si-0 bend 9, 10, 12, m 520 vs 540 Si-0 str, Si-0-Si bend 8, 11, vw 450 ms 439 Li-0 str 1,2 410 m 410 s Si-0 bend 1, 3, 7, 10, 11, vw 280 sh 290 Li-0 str 1, 3,4, w 214 vw 223 Li-0 str 3, 4, 10, 11, w 196 w Si-0 bend 9, 10, 12, 13, 31, 36 A w.sh Si-0 str m Si-0 bend 11, w Li-0 str, 0-Si-0 bend 2, w 333 Li-0 str 1,3 291 sh Si-0 bend, Li-0 str 1, 2, 6, Li-0 str, 0-Si-0 bend 4, Li-0 str 1, 2,3, Libration 14,lS BI 1034 w 1034 w.sh 1049 Si-0 str, 0-Si-0 bend 6,11, w.sh 580 vw Si-0 bend, Si-0 str 1, 2, 6, 11, w.sh 398 w 398 Li-0 str, 0-Si-0 bend 2, vw 345 w 342 Li-0 str 1,3 297 m 305 s Si-0 bend, Li-0 str 3, 4, 11, w 21 3 Li-0 str 1,2,3, w Li-0 str, 0-Si-0 bend 4,11,12 Bz 983 vs 980 s.sh 985 Si-0 str 7, w 950 vs 939 Si-0 str, 0-Si-0 bend 6, 7, w 735 s 746 Si-0 str 6,8, w.sh Si-0 bend 6,9, 11, w 505 s.sh Si-0 bend, Li-0 str 2, 3, 10, 12, 30, w.sh 398 w 397 Li-0 str 1, 2, vw 248 vw Si-0 bend, Li-0 str 1,3,10, 12, w 230 w 259 Li-0 str, 0-Si-0 bend 4, 10, w Si-0 bend, Li-0 str 3, 4, 7, 8, 9, 11 'v = very, s = strong, m = med~um, w = weak, and sh = shoulder. -'The numbering of force constants is given in Table 2. metasilicate chain and the Li-0 polyhedra. By using the concept of internal coordinates and the symmetry of the chain in the crystal, we can predict the distribution of stretching, bending, and torsional modes into various symmetry species of the factor group C,,. It is more difficult to identify the frequencies and symmetry species corresponding to the external modes involving the motion of lithium atoms. However, some characteristic frequencies and force constants of the Li-0 polyhedra are available in the literature (8, 9) and these may be used for assignment purposes. General valence force constants for the SiO, tetrahedra and Li-0 polyhedra were taken from the literature (9, 10) and a preliminary normal coordinate analysis (see next section) was carried out on the unit cell. It was then possible to associate the observed frequencies with the corresponding calculated frequencies. The calculated frequencies were evaluated according to the symmetry species and this enabled us to assign the observed frequencies. Although the above-mentioned process appears crude, it is unlikely to produce any large error in the internal vibration region for the following reasons: (1) Although the force constants were transferred from similar molecules they are unlikely to be changed in any drastic way in the new environment. (2) The change in geometry, which is included in the kinetic energy term, can account for the observed splitting and shifts in

4 2562 CAN. J. CHEM. VOL. 55, 1977 the frequencies. (3) Because there is only one chain per primitive unit cell there are no complications of correlation splitting. The tentative assignments thus made are given in Table 1. Normal Coordinate Analysis The normal coordinate analysis of the crystal vibrations at the centre of the Brillouin zone (k = 0) was carried out following the Wilson FG matrix procedure adapted to crystals by Shimanouchi et al. (11). The internal coordinates used are based on the SiO, chain and the Li-0 polyhedra. The SiO, chain coordinates are shown in Fig. 1. In the Li-0 polyhedra, only Li-0 stretching coordinates were used. The cartesian symmetry coordinates corresponding to the C,, factor group, which help in reducing the dimensions of the secular equation to be solved, were constructed using the usual projection operator techniques (11). The force constants used to set up the potential energy matrix were of the general valence type. As the SiO, chain is made up of SiO, tetrahedra, force constants for the SiO, group were taken from the work of Devarajan and Funck (10). The lithium atom is surrounded by five oxygen atoms. Of these, four lie at distances of approximately 2.0 A from the lithium atom, whereas the fifth is at a distance of 2.6 A. In the work of Jungerman (9), the value of the Li-0 stretching force constant for a distance of 2.0 A is given as 0.3 mdyn kl. For 2.4 A, the value is practically zero. A total of thirty-six force constants were used for the preliminary calculations which were used for the assignment of the observed frequencies. In the next step, the force constants were adjusted on a trial and error basis, allowing for the different Si-0 bond lengths in the chain and the different Li-0 distances. The Jacobian elements avlaf further aided the adjustment procedure by indicating the value and direction (positive or negative) by which the force constants should be changed. After several calculations, the agreement between the observed and calculated frequencies improved to a satisfactory level, without introducing unrealistic values for any force constants. Considering the approximations and uncertainties involved, it was felt that it would not be worthwhile attempting any further refinement of the force constants. Potential energy distributions in terms of force constants were also calculated. All the TABLE 2. General valence force constants for lithium metasilicate Number Description of force constant Vauea fd,(li-0 str, 2.02 A) fdz(li-0 str, 1.96 A) fds(li-0 str, 2.03 A) fd4(li-0 str, 2.11 A) fd5(li-0 str, 2.60 A) fi(si-0 str, 1.62 A) Lt(Si-0 str, 1.55 A) fi,,(si-0 str, 1.65 A) fs(0-si-0 bend) f.(o-si-0 bend) fp(o-si-0 bend) fbt(o-si-0 bend) f,(si-0-si bend) f,,(si-0 torsion) f,,(o-si torsion) Ll A,, - - 'Stretching and stretch-stretch interaction constants are in mdyn/a; bending and bend-bend interaction constants are in mdyn-a; stretchbend interaction constants are in mdyn. above-mentioned calculations were carried out using the modified versions of computer programs AXSMZ and LSMX of Shimanouchi (12). The final set of force constants and their values are given in Table 2. The observed frequencies, calculated frequencies with descriptions of the normal modes and important contributing force constants are given in Table 1. Discussion In a recent paper, Brawer (1) calculated the frequencies and intensities in the Raman spectrum of the metasilicate chain in some alkali metasilicate glasses and crystals. He used a central Si-0 stretching force constant k = 5.0 mdyn A-' and a non-central Si-0 force

5 DEVARAJAN P ind SHURVELL 2563 constant of 0.17k. The Si-0-Si bending force constant was neglected. Bilton et al. (13) used fs,-o = 4.0 mdyna-l, fo-si-o = 0.3 mdynaw1, and fsi -O-si = 0.03 mdyn in a simplified calculation on the silicate chains in the pyroxene minerals enstatite and augite. Another normal coordinate calculation on silicate chains was carried out by Etchepare (14) using force constants taken from the earlier work of Siebert (15). It is difficult to compare the results of the present complete unit cell calculation with the previous calculations on isolated chain models. However, it appears that our results do not agree at all well with this earlier work. There may be several reasons for this. The vibrational frequencies and assignments on which the previous workers based their calculatioi~s may not have been reliable. The simple force fields used are probably inadequate and the isolated metasilicate chain model may not be applicable to lithium metasilicate. It can be seen in Table 1 that the frequencies assigned to Si-0 stretching modes have contributions from bending force constants. This is expected in view of the chain structure. The Li-0 stretching modes all lie below 500 cm-i and couple with chain bending modes. Conclusions A fairly complete assignment of the unit cell vibrations of crystalline lithium metasilicate has been made. The observed coincidences between Raman and infrared wavenumbers for the normal modes is in agreement with the reported C,, factor group. Although the results of the normal coordinate calculations reported here do not agree with previous calculations on isolated metasilicate chains, it is felt that the present results are more reliable, since they correlate well with experimentally observed frequencies and are based on a complete unit cell model. The simple short range general valence force field used in this work appears to be adequate. However, the inclusion of additional long range forces would no doubt further improve the calculation. It is hoped that the more complete force field reported here for the metasilicate chain structure might be useful for further studies of glasses containing this structural unit. Acknowledgement This work was supported by a grant from the National Research Council of Canada. 1. S. BRAWER. Phys. Rev. B11,3173 (1975). 2. S. BRAWER~~~W. B. WHITE. J. Chem.Phys.63,2421 (1975). 3. R. W. G. WYCKOFF. Crystal structures. Vol. 4. Interscience, New York p G. DONNAY and J. D. H. DONNAY. Am. Mineral. J. 38, 163 (1953). 5. H. J. SEEMANN. Acta Crystallogr. 9,251 (1956). 6. D. M. ADAMS and D. C. NEWTON. Tables for factor group and point group analysis. Beckman, U.K W. G. FATELEY, F. R. DOLLISH, N. T. MCDEVITT, and F. F. BENTLEY. Infrared and Raman selection rules for molecular and lattice vibrations: the correlation method. Wiley-Interscience, New York S. MESHITSUKA, H. TAKAHASHI, and K. HIGASI. Bull. Chem. Soc. Jpn. 44,3255 (1971). 9. A. JUNGERMANN. Doctoral Thesis, University of Freiburg, Germany V. DEVARAJAN and E. FUNCK. J. Chem. Phys. 62, 3406 (1975). 11. T. SHIMANOUCHI, M. TSUBOI, and T. MIYAZAWA. J. Chem. Phys. 35, 1597 (1961). 12. T. SHIMANOUCHI. Computer programmes for normal coordinate analysis of polyatomic molecules. University of Tokyo, Tokyo M. S. BILTON, T. R. GILSON, and M. WEBSTER. Spectrochim. Acta, %A, 2113 (1972). 14. J. ETCHEPARE. Spectrochim. Acta, %A, 2147 (1970). 15. H. SIEBERT. Z. Anorg. Allgem. Chem. 275,225 (1954).