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Temperature dependence of the Raman spectrum of vitreous silica
Solid State Communications, Vol. 7, pp. 1069—1071, 1969. Pergamon Press.
Printed in Great Britain
TEMPERATURE DEPENDENCE OF THE RAMAN SPECTRUM OF VITREOUS SILICA
*
Marvin Hass U.S. Naval Research Laboratory, Washington, D.C. 20390 (Received 5 June 1969 by J.A. Krumhansl)
A large temperature dependence of the Stokes-Raman spectrum of vitreous silica is observed for low frequency shifts, while there is a much smaller temperature dependence for frequency shifts greater than 200 cm ~‘. The data is consistent with an analysis involving first order processes only.
THE STOKES—RAMAN spectrum of vitreous silica has been obtained and shows a large temperature dependence at frequency shifts of 50 cm1 and below. On the other hand, the spectrum at frequency shifts greater than 200 cm’ shows very little change between room
U ~L.J
STOKES
VITREOUS SILICA
z
~ Ir Lr
theory reveals first-order Stokes—Raman temperature andthat cryogenic temperatures. Simple spectra are only slightly temperature dependent at higher frequencies, but can be highly temperature dependent at low frequencies. As a result, low frequency bands can be greatly enhanced in intensity due to a simple temperature factor, while higher frequency bands will remain essentially unchanged between room and cryogenic temperatures. First-order spectra at low frequencies free of temperature-dependent line broadening or other higher order effects are not very common in ordered crystals. However, scattering maxima at low frequency shifts appear in many silicate-type glasses measured at room temperature. It is shown here that such scattering maxima arise in large part due to such a temperature enhancement and probably do not arise from difference bands, which are also highly temperature dependent.
~L~Jl I—
300°
[ FI
2°
00
0
00 200 300 400 FREQUENCY SHIFT (crn)
500
FIG. 1. Raman spectrum of vitreous silica at
various temperatures. The dots represent the low roomtemperature temperaturespectrum spectrumcalculated assuming from first the order processes. The sharp bands at 13 cm~marked by (*) are due to grating ghosts. is shown at room, liquid nitrogen, and liquid helium temperatures. These data were obtained with an argon ion laser source operating at
The results are illustrated in Fig. 1 where the Raman spectrum of vitreous silica (Suprasil) _____________ *
___________________________________
b -J
r~! ANTI-STOKES
488 nm with a power level of about 250 mw. A 90°geometry was used the electric vectors of the incident andwith scattered beams parallel. The scattered radiation was analysed
Work supported by Advanced Research with a Spex Model 1400 double grating
Projects Agency. 1069
1070
RAMAN SPECTRUM OF VITREOUS SILICA
Vol.7, No.15
monochromator. The spectrum at room temperature shows a broad band centered around 50 cm’ which has been observed previously. At low temperatures, this band decreases in intensity by over a factor of four at 50 cm-’, while the spectrum above 300 cm’ shows only a slight temperature dependence.
contains a large broad maximum near 50 cm This result is consistent with the infrared spectrum which does not show any maximum 1 and has been observed to be near 50 cmessentially independent of temperature.3’4 The temperature dependence of the infrared spectrum due to single excitations for a system of coupled harmonic oscillators is given by (1 + n
This temperature dependence of the Stokes— Raman spectrum can be explained in the following way. The first-order Stokes—Raman intensity is proportional to the term 1 + n0, where = 1/[exp(11w0/kT) — 1] to is the the excitation Bose popu-of lation factor corresponding
where (1 + n0) is the probability of absorption of a photon and n0 is the probability of emission. As a result, the single-excitation infrared spectrum is expected to be independent 5 of temperature in the harmonic approximation.
frequency ~o.2 At frequencies of 300 cm-’ and at room temperature or below, the term 1 + no ranges between 1.31 and 1.00 indicating only a slight temperature dependence. On the other hand, for frequencies at 50 cm-’ at room ternperature, the factor 1 + n 0 is 4.68. As a result, first-order Stokes—Raman spectra at frequency shifts of 50 cm -‘ and below can be expected to be several times as intense at room temperatures as at low temperatures.
The good agreement between the observed and calculated Raman intensities assuming first order processes suggests that this interpretation is a probable one. Second order processes would lead to a different temperature dependence
0)
—
varying as (1 + n,)(1 + n2) for sum bands and (1 + n,)n2 for difference bands. While an exact calculation would involve some knowledge of the density-of-states, it can be seen that this would, in general, lead to quite different temperature dependence.
First-order Stokes—Raman spectra at low temperatures can be calculated using room ternperature data. The results of such calculations for vitreous silica are shown by the dots in Fig. 1. It can be seen that the calculated spectra are in very good agreement with the observed results. Here the room temperature and low temperature data were at high frequencies to correct for anormalized slight change in
The low temperature spectrum given here indicates that the density of low frequency modes is much lower than would be assumed from an inspection of the room temperature data. This has important implications as the occurrence of such low frequency modes would 1be 6,7 consistent A with anomalies in the heat capacity. discussion of the Raman spectra and vibrations
sample position due to contraction of the dewar at low temperatures,
of vitreous silica and other silicate-type glasses will be presented elsewhere.
It can be seen from Fig. 1 that the low ternperature spectrum of fused silica no longer
Acknowledgement
— The author wishes to thank Dr. M. GomezRodriguez for helpful discussions.
REFERENCES
1.
FLUBACHER P., LEADBETTER A.J., MORRISON J.A. and STOICHEFF B.P., Physics Chem. Solids 12, 53 (1959).
2.
LOUDON R., Adv. Phys. 13, 423 (1964).
3.
BAGDADE W. and STOLEN R., Physics Chem. Solids 29, 2001 (1968).
4.
PLENDL J.N., MANSUR L.C., HADNI A., BREHAT F., HENRY P., MORLOT G., NAUDIN F. and STRIMER P., Physics Chem. Solids 28, 1589 (1967). ROSENSTOCK H.B., J. chem. Phys. 27, 1194 (1957).
5.
Vol.7, No.15
RAMAN SPECTRUM OF VITREOUS SILICA
6.
LEADBETTER A.J., Phys. Chem. Glasses 9, 1 (1968).
7.
ANDERSON O.L., Physics Chem. Solids 12, 41(1959).
Für niedere Frequenzsprünge wurde eine starke Temperaturabhãngigkeit des Stokes—Raman-Spektrums von glasigem Siliziumdioxyd beobachtet, wogegen die Temperaturabhängigkeit für Frequenzsprflnge über 200 cm’ viel geringer ist. Dieses ergebnis stimmt mit einer Analyse überein, die nur Prozesse der ersten Ordnung berücksichtigte.
1071
Printed in Great Britain
TEMPERATURE DEPENDENCE OF THE RAMAN SPECTRUM OF VITREOUS SILICA
*
Marvin Hass U.S. Naval Research Laboratory, Washington, D.C. 20390 (Received 5 June 1969 by J.A. Krumhansl)
A large temperature dependence of the Stokes-Raman spectrum of vitreous silica is observed for low frequency shifts, while there is a much smaller temperature dependence for frequency shifts greater than 200 cm ~‘. The data is consistent with an analysis involving first order processes only.
THE STOKES—RAMAN spectrum of vitreous silica has been obtained and shows a large temperature dependence at frequency shifts of 50 cm1 and below. On the other hand, the spectrum at frequency shifts greater than 200 cm’ shows very little change between room
U ~L.J
STOKES
VITREOUS SILICA
z
~ Ir Lr
theory reveals first-order Stokes—Raman temperature andthat cryogenic temperatures. Simple spectra are only slightly temperature dependent at higher frequencies, but can be highly temperature dependent at low frequencies. As a result, low frequency bands can be greatly enhanced in intensity due to a simple temperature factor, while higher frequency bands will remain essentially unchanged between room and cryogenic temperatures. First-order spectra at low frequencies free of temperature-dependent line broadening or other higher order effects are not very common in ordered crystals. However, scattering maxima at low frequency shifts appear in many silicate-type glasses measured at room temperature. It is shown here that such scattering maxima arise in large part due to such a temperature enhancement and probably do not arise from difference bands, which are also highly temperature dependent.
~L~Jl I—
300°
[ FI
2°
00
0
00 200 300 400 FREQUENCY SHIFT (crn)
500
FIG. 1. Raman spectrum of vitreous silica at
various temperatures. The dots represent the low roomtemperature temperaturespectrum spectrumcalculated assuming from first the order processes. The sharp bands at 13 cm~marked by (*) are due to grating ghosts. is shown at room, liquid nitrogen, and liquid helium temperatures. These data were obtained with an argon ion laser source operating at
The results are illustrated in Fig. 1 where the Raman spectrum of vitreous silica (Suprasil) _____________ *
___________________________________
b -J
r~! ANTI-STOKES
488 nm with a power level of about 250 mw. A 90°geometry was used the electric vectors of the incident andwith scattered beams parallel. The scattered radiation was analysed
Work supported by Advanced Research with a Spex Model 1400 double grating
Projects Agency. 1069
1070
RAMAN SPECTRUM OF VITREOUS SILICA
Vol.7, No.15
monochromator. The spectrum at room temperature shows a broad band centered around 50 cm’ which has been observed previously. At low temperatures, this band decreases in intensity by over a factor of four at 50 cm-’, while the spectrum above 300 cm’ shows only a slight temperature dependence.
contains a large broad maximum near 50 cm This result is consistent with the infrared spectrum which does not show any maximum 1 and has been observed to be near 50 cmessentially independent of temperature.3’4 The temperature dependence of the infrared spectrum due to single excitations for a system of coupled harmonic oscillators is given by (1 + n
This temperature dependence of the Stokes— Raman spectrum can be explained in the following way. The first-order Stokes—Raman intensity is proportional to the term 1 + n0, where = 1/[exp(11w0/kT) — 1] to is the the excitation Bose popu-of lation factor corresponding
where (1 + n0) is the probability of absorption of a photon and n0 is the probability of emission. As a result, the single-excitation infrared spectrum is expected to be independent 5 of temperature in the harmonic approximation.
frequency ~o.2 At frequencies of 300 cm-’ and at room temperature or below, the term 1 + no ranges between 1.31 and 1.00 indicating only a slight temperature dependence. On the other hand, for frequencies at 50 cm-’ at room ternperature, the factor 1 + n 0 is 4.68. As a result, first-order Stokes—Raman spectra at frequency shifts of 50 cm -‘ and below can be expected to be several times as intense at room temperatures as at low temperatures.
The good agreement between the observed and calculated Raman intensities assuming first order processes suggests that this interpretation is a probable one. Second order processes would lead to a different temperature dependence
0)
—
varying as (1 + n,)(1 + n2) for sum bands and (1 + n,)n2 for difference bands. While an exact calculation would involve some knowledge of the density-of-states, it can be seen that this would, in general, lead to quite different temperature dependence.
First-order Stokes—Raman spectra at low temperatures can be calculated using room ternperature data. The results of such calculations for vitreous silica are shown by the dots in Fig. 1. It can be seen that the calculated spectra are in very good agreement with the observed results. Here the room temperature and low temperature data were at high frequencies to correct for anormalized slight change in
The low temperature spectrum given here indicates that the density of low frequency modes is much lower than would be assumed from an inspection of the room temperature data. This has important implications as the occurrence of such low frequency modes would 1be 6,7 consistent A with anomalies in the heat capacity. discussion of the Raman spectra and vibrations
sample position due to contraction of the dewar at low temperatures,
of vitreous silica and other silicate-type glasses will be presented elsewhere.
It can be seen from Fig. 1 that the low ternperature spectrum of fused silica no longer
Acknowledgement
— The author wishes to thank Dr. M. GomezRodriguez for helpful discussions.
REFERENCES
1.
FLUBACHER P., LEADBETTER A.J., MORRISON J.A. and STOICHEFF B.P., Physics Chem. Solids 12, 53 (1959).
2.
LOUDON R., Adv. Phys. 13, 423 (1964).
3.
BAGDADE W. and STOLEN R., Physics Chem. Solids 29, 2001 (1968).
4.
PLENDL J.N., MANSUR L.C., HADNI A., BREHAT F., HENRY P., MORLOT G., NAUDIN F. and STRIMER P., Physics Chem. Solids 28, 1589 (1967). ROSENSTOCK H.B., J. chem. Phys. 27, 1194 (1957).
5.
Vol.7, No.15
RAMAN SPECTRUM OF VITREOUS SILICA
6.
LEADBETTER A.J., Phys. Chem. Glasses 9, 1 (1968).
7.
ANDERSON O.L., Physics Chem. Solids 12, 41(1959).
Für niedere Frequenzsprünge wurde eine starke Temperaturabhãngigkeit des Stokes—Raman-Spektrums von glasigem Siliziumdioxyd beobachtet, wogegen die Temperaturabhängigkeit für Frequenzsprflnge über 200 cm’ viel geringer ist. Dieses ergebnis stimmt mit einer Analyse überein, die nur Prozesse der ersten Ordnung berücksichtigte.
1071