Microscopic origin of anomalously narrow Raman lines in network glasses

Journal of Non-Crystalline Solids 63 (1984) 347-355 North-Holland, A m s t e r d a m

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M I C R O S C O P I C ORIGIN OF ANOMALOUSLY NARROW RAMAN LINES IN NETWORK GLASSES J.C. PHILLIPS Bell Laboratories, Murray Hill, New Jersey 07974, USA Received 10 June 1983

Molecular models for the mysterious 495 and 606 cm - 1 "defect" lines in the R a m a n spectra of g-SiO 2 are discussed in the context of a general theory and a survey of a wide range of experimental data. including hydroxylation, neutron bombardment, and isotope shifts.

1. Introduction

The vibrational spectra of most non-crystalline solids are composed of broad, featureless peaks which contain relatively little information of structural interest [1]. Solids in which the coordination numbers of each atomic species are nearly always those predicted by valence rules are described as network solids. A network non-crystalline solid is referred to as a network glass when it can be heated through a melting transition (called the glass transition) into a supercooled liquid. An example of a network glass which has only broad peaks in its vibrational spectra as measured by infrared absorption or neutron or Raman scattering [2] is g-As2Se3, which is based on corner-sharing pyramidal building blocks. Narrow vibrational peaks which may contain considerable information of structural interest are found in several tetrahedral glasses such as g-GeSe 2 and g-SiO 2. The origins of the narrow vibrational lines in the spectra of g-GeS 2 and g-GeSe 2 are by now well-understood [3,4]. Many experiments have shown that there exist, in the glass, large layered units whose internal structure and interlayer spacing are very nearly equal to those of the high-temperature crystalline phase. Some of the narrow vibrational lines in the glass correspond to the crystalline lines, which are only slightly broadened by the small diameters (2-4 crystalline unit cell dimensions) of the paracrystalline clusters in the glass. In addition to these "bulk" vibrational lines further lines associated with cluster edges are seen. These lines are associated with broken chemical order at the edges, whereas the chemical order of the crystal is intact in the cluster interiors. Confirmation of the association of broken chemical order with cluster edges has been dramatically and decisively documented by M/Sssbauer studies which demonstrate remarkable parallels between the c o m 0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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J.C. Phillips / Anomalously narrow Raman lines in network glasses

position dependence of the concentration of like-atom bonds and the strength of Raman lines assigned to cluster edges [5-7].

2. "Defect" lines in g-SiO 2 Two narrow lines have been observed in the Raman spectra [8,9] of g-SiO2, at 490 and 606 cm-~, symbolized by D~ and D 2, respectively. (See fig. 1.) A number of attempts have been made to assign these lines to small clusters or rings embedded in a three-dimensional continuous "random" network [10]. It is important to realize at the outset that from a theoretical viewpoint all of these attempts are likely to fail because small units, embedded in a dense medium, can never give rise to narrow vibrational lines. This is a direct consequence of the uncertainty principle. For example, the narrow lines that are observed in g-GeSe 2 can exist in part because the clusters which are fragments of c-GeSe 2 are so large and indeed have diameters equal to about three unit cells [6,11]. For such large dusters one can define bulk pseudo-wave vectors/~ and apply to the bulk vibrational bands of the quasi-periodic cluster the usual crystalline selection rule for Raman scattering, namely/~ = 0. Similarly for the surface or edge of the quasi-periodic cluster one can define a surface pseudo-wave vector k s and demand/~s = 0. When these selection rules break down the entire band becomes Raman active. In the case of g-GeSe 2, detailed calculations [12] have shown, for example, that the entire A 1 band is 30 cm-1 wide, whereas the observed width [4,13] of the A 1 Raman line is about

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12 cm -1, compared to 3 cm -1 in the crystal. The reason the A 1 Raman line is three times narrower than the A1 band is the applicability of the /~ = 0 selection rule. If we assumed that the observed line came from one ring in the entire pseudo-crystalline structure, we would have had a line width of 30 cm instead. Before we discuss specific structural models for the D~ and D 2 lines in g-SiO 2, there are several experimental signatures of these lines that should be mentioned. The most dramatic effect [9] is obtained by exposing the sample to an integrated flux of > 10 keV neutrons of 102°/cm 2. The density increases by 2.5% which is about half of the density difference between the glass and cristobalite, the high-temperature phase of silica [14]. The strength of the D~ line increases somewhat (perhaps by 10-30%) while the strength of the D 2 line increases enormously (by perhaps an order of magnitude), see fig. 1. The strengths of the D~ and D 2 lines are modified by the incorporation of H 2 0 during sample synthesis (chemisorption, not physisorption). Early infrared studies showed [15] that water chemisroption (as OH, not H20 ) in g-SiO 2 is essentially different from that in other glasses. The asymmetric O - H stretching vibration at 2.75/~ is accompanied by an overtone absorption at 1.4/~ providing hydrogen bonding, O - H . . . O , does not occur. Adams and Douglas assume, in accordance with conventional theories of hydrogen bonding, that the formation of hydrogen bonds can be prevented only when the OH units occur in pairs in broken Si-O-Si bridges. They explain these overtone infrared spectra in g-SiO 2 in terms of such isolated pairs. In other glasses, such as sodium silicates, O - H . . . O bonds are formed and the overtone is absent. The respective structural formulae for these two cases are, for g-SiO 2, >~ Si-O-Si ~< + H20 ~ >i Si-OH HO-Si and for sodium silicate, 2( >.>-Si-O-Si ~<) + N a 2 0 + H20 2(Si-O H . . . O - - S i ~ < ) Na+ where the Na + is loosely associated with the region containing the H bond. I should mention here that the Adams-Douglas data and interpretation fit almost perfectly into the structural model which I proposed previously [14] (see below), although their very important work was not known to me previously. I have adhered very closely to their presentation in describing their results. Stolen and Walrafen showed [16] that D 1 and D 2 a r e partially quenched by OH formation, and that the reduction in the scattering strengths of the Raman peaks D~ and 0 2 is linearly proportional to the OH content as measured by infrared absorption. They also showed that the strengths of D 1 and D E increased with fictive temperature Tf as calibrated by ultrasonic attenuation. This observation has been recently confirmed [17]. For these reasons it has become customary to refer to the D 1 and D 2 lines as "defect" lines, although

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the meaning of "defects" is far from clear in the context of a non-crystalline network. Another experiment which provides information on the microscopic origin of the D 1 and D z lines is isotopic substitution. Replacement of 160 by 180 has shown [18] complete isotope shifts (e.g., D~ from 495 cm-1 to 465 cm -1) which implies little or no Si participation in the D~ and D 2 vibrations. This conclusion has been reinforced by direct measurement of the effect of replacement of 28Si by 3°Si on the D~ and D 2 frequencies, which is zero within the limits of experimental resolution [17]. These experiments, which indicate a " p u r e O" isotope shift for D 1 and D 2 lines, require that the molecular structures responsible for these lines contain a high symmetry element. They therefore rule out many molecular defect models which lack such a high symmetry element. In fact, only two models have been proposed which have the requisite symmetry, the planar ring model [17] and the cristobalite cluster surface model [14,19]. We first review the latter and show that it is consistent with all the experimental data. Then we discuss the ring model and show that while it can explain the isotope shift, it is incompatible with all the remaining decisive experimental information.

3. Paracrystalline cluster interfacial model The central justification [20] for construction of a pluralistic cluster model, as distinguished from a monolithic continuous network model, lies in the observation that glasses formed by quenching melts are expected to retain structural memories of their origin in the gigantically viscous ( 7 - 1013 P) supercooled liquid. My review [14] of a wide range of data suggests that in g-SiO 2 the clusters have the internal topology of cristobalite, a cubic structure with density 5% greater than g-SiO 2 and with the Si atoms arranged on a diamond lattice. The dominant surface texture of the cristobalite paracrystallites is (100) planes and the basic surface molecule is (O1/2)2-Si = O*. The clusters are about 60 ,~ in diameter. The D 1 line at 495 cm -1 in g-SiO 2 is assigned in the cluster model to the /~s = 0 surface vibrational mode associated with motion of the O* atoms normal to the (100) surface normal, i.e., parallel to the (100) surface plane. The width of the surface band has been calculated [19] to be 100 cm -1. The full width half maximum of the experimental line is difficult to estimate because it overlaps the much broader "duster interior" band which peaks at 430 cm-1, but I would guess it is 20-30 cm -1. Some of this broadening may be due to density fluctuations. In any case, a line this narrow must arise from units periodically repeated over a distance of order at least 25 ,~. The actual size of this cristobalite cluster [14], as estimated from the superb TEM data of Zarzycki, is 60 A. Thus the cluster (100) planar surface diameters are easily large enough to account for the narrowness of the observed D 1 Raman line. No specific structure was proposed in the review for the D 2 line, but it is

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plain from its very large growth following intense neutron bombardment that it should be associated with a rearrangement of the cluster surfaces. Because the neutron bombardment also compacts the material substantially, eliminating half of the interfacial volume, it is natural to assume that the thermal spikes associated with energy deposition by the > 10 keV neutrons have actually fused the clusters over about half of the interfacial area. Thus one expects that the D 2 line is a ring mode associated with intercluster cross-linking. Such a ring could contain, in contrast to the six-membered rings characteristic of the bulk, four Si atoms. This would, as Galeener has shown [10], increase its frequency. I hesitate to estimate the increase, however, because the compaction alters (probably increases) frequencies from those of the free molecular radicals used by Galeener. The general trend towards higher frequencies, both from reduction of ring size and from compaction, is evident. We now turn to the isotope data [17,18], which quite remarkably show that both the D 1 and D 2 lines are associated with nearly pure ( > 95%) O motion. This is qualitatively very easily explained in the (100) cristobalite surface model which is illustrated in fig. 2. It is easy to see that when the surface O I i

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as we see by comparing fig. 3 with fig. 2. Moreover, the OH units are formed in pairs, as described by Adams and Douglas [15]. The reduction (perhaps by as much as a factor of 3) in the D 1 and D 2 strengths by the chemisorption of H20 points " t o a picture of frozen-in defects which, in the melt, have been filled in part by OH groups" [16]. This is a perfect description of fig. 3. I assume that the reaction =O* + H20 ~ 2(-OH) does not go to completion because some of the interfaces are too snug to accommodate the additional molecular volume.

4. Planar ring model Galeener has recently proposed [10,17] a small (3 and 4 Si atoms) planar rings model to explain the D E and D 1 lines in g-SiO 2. Because the rings are small he can explain why the frequencies of D 2 and D 1 are above these of the broad band which peaks at 430 cm- 1. And because the rings are planar he can explain the "pure O" isotope effect as an " O only" coplanar radial ring breathing mode. The tings are suppose to be present only in - 1% concentration because the rings in common crystalline forms of SiO 2 (quartz, cristobalite, tridimyte) are six-membered. These ring statistics are similar to those of the continuous random network model of Bell and Dean [21]. The weakness of the planar ring model is that corner-sharing tetrahedra, in contrast to B(O1/2) 3 groups (such as boroxyl), do not readily adapt themselves to a planar or layer morphology. As we have indicated in the preceding section, the narrow D1 and D 2 line widths require periodically repeated units covering at least about four unit cells. This is easy to do with 3-2 coordinated boroxyl groups, but with 4-2 coordinated silica groups it is not possible to do this in a planar geometry. On the other hand, the isolated planar tings postulated by Galeener will generate lines 100 cm-1 wide when embedded in silica CRN. This is a disastrous topological failing of the planar ring model. Another failing of the planar ring model is that it does not provide sites for OH units which are specific to the planar rings. Of course, one could simply assume that the OH units selectively attack the planar rings because they are compressed (relative to the normal six-membered rings), but this assumption is not really consistent with the CRN philosophy. Even if this assumption is made, one would have to go further and assume that the OH groups attack the tings in pairs (and not as O H . . . O units, as in sodium silicate). By now the efficacy of the planar ring concept as a panacea for unresolved problems appears questionable indeed. Still another ineffectual aspect of the planar ring model is its implications for neutron bombardment. The gigantic growth of the D 2 line would require that a large number of three-membered rings be generated by thermal spikes. If anything, one would expect the thermal spikes to reduce the small-ring population. By contrast, the cluster-fusing model predicts a reasonable density change (about half the "free volume" difference between g-SiO2 and cristobalite).

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Galeener has suggested that the cristobalite surface model [14,19] cannot yield a pure isotope effect for the D 1 and D z lines. This is because he embeds the basic (O1/2)2-Si = O* building block in a Bethe lattice, instead of repeating it periodically, corresponding to a cristobalite (100) plane. This loses the planar symmetry, which according to fig. 2 is the factor responsible for the pure isotope effect.

5. Conclusions The cristobalite paracrystallite model naturally explains all the principal features of the D 1 = 4 9 5 cm -1 and D 2 = 606 cm -1 lines in the Raman spectrum of g-SiO 2. These are, in order of importance, (1) The lines are at least four times narrower than expected for small, non-periodic molecular clusters. (2) The scattering strengths of these lines are greatly reduced by chemisorption of H 2 0 as 2 OH units. (3) The scattering strength of the D 2 line is enhanced by an order of magnitude by intense neutron bombardment. (4) Both lines involve almost pure O (no Si) motion. Other models, based on small molecular clusters, such as planar rings, may explain one of these four points [e.g., planar rings explain (4)], but they cannot explain all four features. N o small cluster model explains (1), which is the sine qua non of this subject. I am grateful to J.R. Banavar for discussions of unpublished results, and to F. Galeener for preprints of ref. 17.

Appendix Recently Levi et al. have reported [22] measurement of the phonon spectrum of g-SiO 2 in a novel manner, by tunneling spectroscopy through an evaporated SiO 2 film. Their results do not show the D 1 line, but they do show a very broad and fairly strong D 2 peak. Although the experimental technique was reported for the first time, the structural significance of the observed D 2 peak merits discussions. The first point is that the energy gap of g-SiO 2 is so large (about 10 eV, compared to 4 eV for A1203 [23]) that no current will pass directly through the SiO 2 film, which contains alternate channels of alumina-filled pinholes. These pinholes, in turn, are very small, with a sufficiently large s u r f a c e / v o l u m e ratio that phonon structure from the AI203/SiO 2 interface may show up in the inelastic tunneling spectrum. Low-density SiO2 has been studied as an "anomalous SiO 2 evaporated film" by Hauer and coworkers [23]. They find an rf dielectric constant of order c o - 6 compared to ~0 - 4 in normal SiO 2. Thus

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the low-density SiO 2 is very "floppy," and may have a very large electron-phonon coupling, which would help to explain why the SiO 2 phonons show up in the inelastic tunneling spectrum. Now we turn to the strong D 2 peak. We suppose this is related to the fused A1203-SIO2 interface, and specifically to the same kind of ring interfacial units as produce the 606 c m - 1 line in the Raman spectrum of g-SiO 2. N o w the peak is much broader, which implies that the evaporated and plasma-oxidized film's interfacial rings may be much less periodically extended than those in meltquenched and neutron-bombarded g-SiO 2.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

J. Wong and C.A. Angell, Glass Structure by Spectroscopy (Dekker, New York, 1976). R. Zallen and M. Slade, Phys. Rev. 9B (1974) 1627. N. Kumagai, J. Shirafuji and Y. Inuishi, J. Phys. Soc. Jpn 42 (1977) 1261. P.M. Bridenbaugh, G.P. Espinosa, J.E. Griffiths, J.C. Phillips and J.P. Remeika, Phys. Rev. B20 (1979) 4140. W.J. Bresser, P. Boolchand, P. Suranyi and J.P. de Neufville, Phys. Rev. Lett. 46 (1981) 1689. P. Boolchand, J. Grothaus and J.C. Phillips, Sol. State Commun. 45 (1983) 183. M. Stevens, J. Grothaus, P. Boolchand and J.G. Hernandez, Sol. State Commun. 47 (1983) 199. P. Flubacher, A.J. Leadbetter, J.A. Morrison and B.P. Stoicheff, J. Phys. Chem. Solids 12 (1960) 53. R.H. Stolen, J.T. Krause and C.R. Kurkjian, Disc. Farad. Soc. 50 (1970) 103. F.L Galeener, Sol. State. Commun. 44 (1982) 1037; and refs. therein. P. Boolchand, J. Grothaus, W.J. Bresser and P. Suranyi, Phys. Rev. B25 (1982) 2975. J. Aronovitz, J.R. Banavar, M.A. Marcus and J.C. Phillips, Phys. Rev. B28 (1983) 4454. J.E. Griffiths, J.C. Phillips, G.P. Espinosa, and J.P. Remeika, Phys. Rev. B26 (1982) 3499. J.C. Phillips, Sol. State Phys. 37 (1982) 93. R.V. Adams and R.W. Douglas, J. Soc. Glass Tech. 43 (1959) 147T. R.H. Stolen and G.E. Walrafen, J. Chem. Phys. 64 (1976) 2623. F.L. Galeener and A.E. Giessberger, unpublished; F.L. Galeener, Bull. Am. Phys. Soc. 28 (3) (1983) 398; see also A.G. Revesz and G.E. Walrafen, J. Non-Crystalline Sol. 54, (1983) 323. F.L. Galeener and J.C. Mikkelsen Jr, Phys. Rev. B23 (1981) 5527. J.R. Banavar and J.C. Phillips, Phys. Rev. B28 (1983) 4716. J.C. Phillips, Phys. Today (February, 1982) p. 1. R.J. Bell and P. Dean, Phil. Mag. 25 (1972) 1381. A.F.J. Levi, W.A. Phillips and C.J. Adkins, Sol. State Commun. 45 (1983) 43. W.F. Brinkman, R.C. Dynes and J.M. Rowell, J. Appl. Phys. 41 (1970) 1915. J.J. Hauser, G.A. Pasteur, A. Staudinger, and R.S. Hutton, J. Non-Crystalline Sol. 46 (1981) 59.