Phonons in TiO2SiO2 glasses

Journal of Non-Crystalline Solids 40 (1980) 567-575 © North-Holland Publishing Company

PHONONS IN TiO2-SiO2 GLASSES H.R. CHANDRASEKHAR *, MEERA CHANDRASEKHAR t Department o f Physics, University o f Missouri-Columbia, MO 65211, USA and MURLI H. MANGHNANI Hawaii Institute o f Geophysics, University o f Hawaii, Honolulu 96822, USA

We report the infrared and Raman studies of titanium doped vitreous silica glasses for a number of titanium concentrations. The vibrational modes associated with the randomly oriented chains of SiO4 tetrahedra show broadenings and shifts. The LO-TO splitting of some Raman active modes decreases with increasing titanium concentration. This is attributed to the decrease in long-range coulomb fields associated with the chains of SiO4 tetrahedra which are broken by the titanium atoms. The results are discussed in the context of random network models. An increase in the average intertetrahedral angle of the SiO4 network is calculated from the data. This explains the anomalous decrease in the density of TiO2-SiO2 glasses with increasing titanium content. We identify two new modes associated with the distorted titanium tetrahedra. A polarized Raman mode at 1115 cm-1 which is infrared inactive and an unpolarized Raman mode at 945 em-1 which is infrared active are observed.

1. Introduction Vitreous silica glasses containing titanium have received considerable attention due to their many interesting properties. One of them is their anomalously low thermal expansion over a wide temperature range [1]. Several attempts to understand the structural aspects of these glasses have been attempted by ESR [2], Raman [3,4] and infrared [ 5 - 7 ] studies. In most cases the study was limited to a particular type of titanium doped silica (Corning glass No. 7971). We have undertaken a detailed study of TiO2-SiO2 glasses of different Tie2 content by polarized Raman scattering and infrared reflectivity. We have also made control measurements of vitreous silica (Suprasil-W) for comparison. Systematic changes in the frequencies, intensities and widths of spectral features characteristic of vitreous silica glasses are observed as a function of the concentration of Tie2. Several new features both in the infrared and Raman spectra which grow in intensity with increas* Alfred P. Sloan Foundation Fellow, 1979. ~ Also:. University of Missouri Research Reactor, Columbia, Me 65211 USA. 567

568

H.R. Chandrasekhar et al. / Phonons in T i 0 2 - S i O 2 glasses

ing TiO2 are identified. A study of the spectra of a specimen containing 14.7% of TiO2 before and after high temperature annealing is also performed. We discuss these results in the context of existing theoretical models. It is well known that silicon has a tetrahedral coordination in the crystalline as well as the glassy forms of SiO2 [8]. Each oxygen is bonded to two silicon atoms. The X-ray studies [9] of vitreous silica suggest a continuous network of SiO4 tetrahedra with an average separation of 1.62 A between silicon and oxygen atoms. However, the angular orientation of SiO4 tetrahedra is quite disordered. The S i - O Si angles have a distribution from 120°-180 ° with a median around 144 °. In the crystalline forms of TiO2, oxygen and titanium atoms have threefold and sixfold coordinations, respectively [10]. In the composition range of TiO2-SiO2 glasses studied in this paper it can be easily shown that the probability of finding more than one titanium in the immediate vicinity of an oxygen is very small. Hence the TiO2 in silicate glasses should have twofold and fourfold coordinations for oxygen and titanium, respectively. The concentration of oxygen atoms bonded to one titanium and one silicon atom varies linearly with molar composition. New spectral features should arise principally from the TiO4 tetrahedra and T i - O - S i groups [1]. The above arguments are statistical and assume a homogeneously dispersed TiO2 in silicate glass. Effects due to aggregation and formation of microcrystallites would drastically alter this picture. We discuss this aspect separately in connection with the annealing studies. The density of TiO2-SiO2 glasses is lower than that of vitreous silica [1]. This result is anomalous in that titanium is a heavier atom than silicon. This is suggestive of a more open glassy structure which results from an increase in the average SiO-Si angle as a function of doping with TiO2. We present a calculation based on our Raman data which supports this idea.

2. Experiments and data

analysis

High quality TiO2-SiO2 glasses with a TiO2 content of 1.3, 4.6, 6, 7.4, 9.4 and 14.7 wt.% were produced by flame hydrolysis [1]. Some specimens with 14.7% TiO2 were subject to a high temperature annealing. The normal incidence reflectivity spectra were measured on a Perkin-Elmer (Model 180) grating spectrophotometer in the 200-4000 cm -1 region. The Raman spectra were recorded using a Spex double monochromator equipped with photon counting electronics. The 5145 A. radiation of an argon laser was used to excite the spectrum. The spectra denoted by (HH) and (HV) were recorded with the polarizations of the incident and scattered radiation parallel and perpendicular to one another, respectively. The reflectivity spectra were analysed by a Kramers-Kronig (KK) analysis to obtain the phase angle of the complex reflectivity. The optical constants were calculated from Fresnel's formula. The peaks in the Im(d) spectra and the energy loss function -Im(~ -1) are due to the transverse and longitudinal optic frequency response,

569

H.R. Chandrasekhar et aL / Phonons in TiO 2-SiO 2 glasses

respectively. These spectra are useful in that they allow a comparison with the corresponding Raman spectra. In a disordered solid the first order Raman and infrared spectra can be related to a common set of vibrational densities of states. A comparison of the reduced Raman spectra and the conductivity response yields information about the relative strengths of the coupling coefficients that enter in the Raman and infrared processes [11,12]. The infrared reflectivity spectra were also fitted using a coupled oscillator model. Accurate values for the frequencies and dampings of the transverse optic (TO) and longitudinal optic (LO) modes could be obtained by this procedure. It should be remarked that the results of the KK analysis are very sensitive to the absolute value of reflectivity and require accurate data at both the high and low frequency limits. The values of reflectivity in the higher frequency limit of our data were very low which might result in errors in the KK analysis of the high frequency part of the spectra. The results of the oscillator fits, on the other hand, are less sensitive to such errors.

3. Discussion Before we discuss the new features in the spectra of TiO2-Si02 glasses we would like to briefly review the spectra of Suprasil-W (S-W). In fig. 1 is shown the (HH) and (I-IV) Raman spectra and the Im(~) and I m ( - ~ -1) spectra of S-W. We have fol-

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FREQUENCY (cm -1) Fig. 1. The (HH) and (HV) Raman spectra of Suprasil-W at room temperature. The Im(~) spectrum (solid curve) and the Im(-~ -1) spectrum (broken curve) calculated from the reflectivity data are also shown.

570

H.R. Chandrasekhar et al.

/ Phonons in

TiO 2 - S i O 2 glasses

lowed the notation of Galeener [13] in the assignment of the peaks of S-W. The symbols (E), (AI) and (F2) indicate the symmetry species of the motions involved in an isolated molecule of the SiO4 tetrahedron. These features appear in the vicinity of the corresponding modes of gaseous SiF4 and were hence used for comparison [14]. It should be noted that the (A1) mode in fig. 3, displayed later, is unpolarized whereas it should appear only in (HH) and be infrared inactive in order to be the breathing mode of non-interacting tetrahedral molecules. The discrepancy suggests the importance of interactions between successive units. The polarized R peak in the Raman spectrum involves the motions of oxygen atoms [15]. The D peak which increases in intensity with neutron irradiation is assigned to be due to a defect in the SiO4 network [16]. The peaks marked LO in the Raman spectra are the longitudinal optic modes associated with the corresponding transverse optic (TO) modes. This was shown by their correspondence with the peaks in the infrared spectra of transverse and longitudinal responses [14]. The low frequency B mode is associated with the vibrational density of states and thermal population effects. Figures 2 and 3 show the (HH) and (HV) Raman spectra, respectively, of S-W and TiO2-SiO2 glasses. The (HH) spectra contain two sharp lines at 945 cm -1 and 1115 cm -1 which grow in intensity with increasing TiO2. The 945 cm -1 line is present in the (HV) spectrum as well whereas the 1115 cm -1 line does not appear. The 945 cm -1 line is infrared active and appears in the Im(O and I m ( - ~ -1) spectra shown in figs. 4 and 5. The 1115 cm -1 line is infrared inactive. From symmetry arguments the 945 cm -~ and 1115 cm -1 lines can be assigned to the rigid cage

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H.R. Chandrasekhar et al. / Phonons in Ti02-SiO 2 glasses

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mode ( F 2 ) and a totally symmetric mode (A1) of isolated TiO4 titanium tetrahedra [17]. There are two difficulties with this interpretation. We have observed only two out of four modes of the TiO4 tetrahedra. The remaining two modes are expected to appear in the low frequency part of the spectrum and are perhaps buried under the (F2) peak of S-W. Secondly the rigid cage mode of TiO4 is lower in frequency than the (A1) mode. Such an occurrence has not been observed in isolated molecules. The interaction of neighbouring SiO4 network might result in such a frequency shift. The overall scattered intensity in both the (HH) and (HV) spectra of figs. 2 and 3 increases with TiO2 concentration. The sharp peak at 495 cm -1 and the D peak at 610 cm -1 get buried under the broadened R peak. Sharp Raman modes of crystalline quartz appear in the spectra of the sample containing 14.7% TiO2. We would like to comment that the (Ax) and (F2) bands of S-W at 800 and 1065 cm -~ show systematic changes with increasing TiO2 as seen in fig. 3. The 800 cm -1 mode displays a shoulder at high frequency for S-W. With increasing TiO2, this shoulder corresponding to LO moves closer to the (A1) mode suggesting a decrease in the L O - T O splitting. A similar decrease in the L O - T O splitting can also be seen for the 1065-1196 cm -1 (F2) mode. The 1065 cm -1 mode actually shifts to higher frequencies whereas the 1196 cm -1 mode shifts down. A qualitative understanding of the changes in the average bond angle 0 and bond stretching angle c~ in the molecular units of SiO4 or TiO4 can be understood by following the model by Sen and Thorpe [18], hereafter referred to as ST. ST consider

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corner sharing AX 4 tetrahedra with the same 0 at the corner o f every tetrahedron and vanishing band bending force constant/3. For high frequency modes this simple model yields impressive agreement with experimental data [ 13]. When 0 = 90 °, the tetrahedral units are uncoupled and the frequencies are same as those of isolated molecules. As 0 increases above 90 °, the F2 mode splits into three features: two unit delta functions and a band of unit area between them. It has been argued [13] that the two observed high frequency modes in S-W are due to such split-off F 2 modes. Using the ST model the values of 0 and o~have been evaluated for S-W and the results are shown in table 1. Also shown in the table are the Values of a and 0 for TiO2-SiO2 glasses. It should be noted that the value of 0 calculated is somewhat smaller than the 140 ° computed by Bell and Dean [19]. We observe a 20 cm -l decrease in the 1065 cm -1 mode for 7.4% TiO2 which yields an increase of ~3 ° in 0. An increase in the average value of 0 represents an opening of the structure which implies a decrease in density. Though titanium is much heavier than silicon, the decrease in density of TiO2-SiO2 glasses compared with S-W can be ascribed to increase in 0.

H.R. Chandrasekhar et al. / Phonons in T i 0 2 - S i O 2 glasses

573

Table 1 Sample

% TiO 2

High frequency modes (cm -1 )

a (N m -1 )

O (deg.)

S-W 1 2 3 4 ULE 6 7a

0 1.3 2.8 4.6 6.0 7.4 9.4 14.7

800 800 800 800 800 803 805 805

478 478 481 48l 490 494 501 501

119 119 120 120 121 121 122 122

1065 1065 1070 1070 1085 1090 1100 1100

It is tempting to estimate 0 and tx for TiO4 tetrahedra in a similar manner using the high frequency modes at 945 cm -1 and 1115 cm -1. F r o m ST theory we get 0 = 104 ° and ot = 702 (N m - l ) . We draw attention to the 1 2 0 0 - 1 0 6 5 cm -1 Raman modes in fig. 3. With increasing TiO2 these modes get broader and the 1200 cm -1 mode becomes asymmetric and shifts to lower frequencies. The decrease in L O - T O splitting would imply a reduction of long range Coulomb fields. Despite their orientational disorder the silicate glasses contain uniterrupted chains o f SiO2 which in turn are broken by the addition o f TiO2. We interpret the decrease in L O - T O splitting o f the 1 2 0 0 - 1 0 6 5 cm -1 Raman modes as being due to this reason. The modes in the infrared spectra in figs. 4 and 5 also exhibit shifts and broadenings consistent with the increased disorder due to TiO2. The 460 cm -1 mode in the Im(d) spectra and the 508 cm -~ mode in the I m ( - d -1) spectra clearly shift to lower frequencies. (See table 2). A similar trend, though not as clear, is observed for the other modes as well. The effect o f high temperature annealing on a sample containing 14.7% TiO2 is shown in figs. 6 and 7. In fig. 6 is a comparison o f the transverse optic response o f

Table 2 Dependence of % TiO2 on the low-frequency IR mode Sample

% TiO2

TO1 (cm -1 )

LOI (era -1 )

S-W 1 3 4 ULE 6 7a

0 1.3 4.6 6 7.4 9.4 14.7

460 459 457 458 454 451 451

508 508 507 506 504 502 501

574

H.R. Chandrasekhar et al. / Phonons in Ti02-Si02 glasses N

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the infrared spectra of S-W, annealed (7b) and unannealed (7a) samples of 14.7% TiO2. It should be recalled that the modes of S-W get broad and shift to somewhat lower frequencies and an additional mode at 945 cm -1 appears in TiO2-SiO2 glasses. In fig. 6 we show that the spectrum of annealed sample is similar to that of a sample containing smaller amounts of TiO2. This implies a loss of TiO2 upo,1 annealing either by the formation of microcrystals or precipitation. The Raman spectrum in fig. 7 exhibits a large number of sharp modes superimposed on the broad spectrum of the glass. By comparison of the frequency positions of the infrared and Raman modes of lower concentration TiO2-SiO2 glasses with those of

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1400

H.R. Chandrasekhar et al. / Phonons in Ti02-SiO 2 glasses

575

sample fig. 7b, we conclude that about half of TiO2 has been lost due to annealing.

Acknowledgements We thank A. Breitschwerdt and G. Fr61ich of the Max-Planck-Institut fiir Festk6rperforschung (MPI), Stuttgart, Federal Republic of Germany for technical assistance. We are grateful for the hospitality of MPI where part of the work was performed. One of us (HRC) is grateful for grants from the Research Corporation and Research Council of the Graduate School of the University of Missouri, Columbia.

References [ 1] P.C. Schultz and H.T. Smyth, in: Third Int. Conf. Physics of Non-Crystalline Solids, eds. R.W. Douglas and B. Ellis (Wiley-Interscience, London, 1970) p. 453. [2] A.W. Amosov, V.K. Zakharov and D.M. Yudin, Sov. Phys. 15 (1973) 167. [3] M.C. Tobin and T. Baak, J. Opt. Soc. Am. 58 (1968) 1459. [4] Y.S. Bobovitch, Opt. Spektrosk. 14 (1963) 647. [51 P. Tarte, Silicates Industrials 28 (1963) 345. [6] M.H. Manghnani, J.R. Farraro and L.J. Bassele, Appl. Spectr. 28 (1974) 256. [7] C.F. Smith, R.A. Condrate and W.E. Votara, Appl. Spectr. 29 (1975) 79. [8] W.H. Zachariasen, J. Am. Chem. Soc. 54 (1932) 3841. [9] R.L. Mozzi and B.E. Warren, J. Appl. Cryst. 2 (1969) 164. [10] See for example F.A. Grant, Rev. Mod. Phys. 31 (1959) 646. [ 11 ] R. Shuker and R.W. Gammon, Phys. Rev. Letters, 25 (1970) 222. [12] F.L. Galeener and P.N. Sen, Phys. Rev. B17 (1978). [13] F.L. Galeener, in Proc. Int. Conf. on Lattice dynamics, ed. M. Balkanskii, Paris, (Sept 1977) p. 345. [14] F.L. Galeener and G. Lucovsky, Structure and Excitation of Amorphous solids (A. I. P., New York, (1976) p. 223. [15] R.J. Bell, P. Dean and D.C. Hibbings-Butler, J. Phys. C: Solid Sr. Phys. 4 (1974) 1214. [16] J.B. Bates, R.W. Hendricks and L.B. Shaffer, J. Chem. Phys. 61 (1974) 4163. [17] G. Herzberg, Infrared and Raman spectra of polyatomic molecules (Van Nostrand, New York, (1945) p. 100 ibid. p. 167. [18] P.N. Sen and R.F. Thorpe, Phys. Rev. B15 (1977) 4030. [19] R.J. Bell and P. Dean, in: Procs. Int. Conf. on Localized Excitations in Solids (Plenum, New York, 1968) p. 124.