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Cation vibrations in inorganic oxide glasses
Solid State Communications, Vol. 11, pp.755—758, 1972. Pergamon Press.
Printed in Great Britain
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES G.J. Exarhos and W.M. Risen, Jr. Department of Chemistry, Brown University, Providence, Rhode Island, 02912, U.S.A.
(Received 9 June 1972 by J. Tauc)
The vibrational frequencies of alkali metal cations in their equilibrium positions in borate, phosphate, germanate, silicate and vanadate alkali oxide glasses have been observed as cation mass dependent bands in the far-i.r. spectra of these vitreous systems.
THE PHYSICAL properties of alkali-mixed oxide rigid glasses depend strongly on alkali cation motion. Current theories of conductivity, diffusion, dielectric relaxation and orientational polarization in such vitreous systems generally are based on an ion-migration, of defect-migration mechanism in which the probability of a particle transition from one equilibrium position to another, separated from the first by a barrier of height H, 1’2 is given by =
vBexp (—H/kT),
We now report cation-vibrational frequencies for alkali oxide metavanadate, — metagermanate, — metasilicate, — metaborate, and — tetraborate glasses. These glasses are of greater theoretical and material-applications interest than the metaphosphates, and are ones for which mote extensive physical measurements have been reported. These results, then, will permit calculations of properties, dependent on i-’ using the measured cation-vibrational frequency4, spectrum.
(1)
Glass samples of stoichiometric compositions were prepared by two methods. Alkali metal carbonate was mixed with a stoichiometric amount of glass-forming oxide, in a Pt or porcelain crucible, and heated in an electric furnace at ca. 1400°C for 4—5 hr. The resulting melts were quenched between two stainless steel blocks to yield clear, calorless products with the compositions: M 2 0.V2 0~,~ Q.P~05~M2 0.Si02, M2 0~B303, M20.2B203 , and M20.Ge02. Direct melting and dehydration of the reagent-grade compounds NaH2PO4, Na2SiO2 .91-130,glasses and Na2B4O7 •10H20 yielded, upon quenching, that were
where u is the oscillation frequency of the particle within an equilibrium position and B is a constant. This leads to the frequency VA , for oscillation of the alkali metal cation, being essential for evaluation of the physical properties involving such processes. Detailed expressions involving VA have been given for conductance, diffusion coefficient, orientation polarization, contribution to the dielectric constant by orientation polarization and dielectric relaxation time 2 and subsequent for oxide glasses by Charles workers.
spectroscopically identical to analogous glasses formed by the first method.
Prior to our recent report of the observation in the far-i.r. of cation-motion vibrations in the rather special oxide-polymetaphosphate glasses,3 it was possible only to estimate their frequencies, with estimates in the range 2 x 10~ to 1 x 1013 Hz commonly being made.
Far infrared spectra were measured on mechanically ground samples dispersed in a poiyethylene matrix using both a Digilab FTS—14 interferometer (10—500 cm~) and a Beckman IR— 11,12 absorption spectrometer (33—800cm~). 755
756
Vol. 11, No. 5
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES
Cs~Rb~K~
I I
tOO
LtI
1Na~
M~0Vz0 5
200
(crw’)
M20Si02~ 400 500
FIG. 1. Correlation of far-i.r. alkali cation vibra-
tional frequencies in inorganic oxide glasses.
That sample preparation did not lead to devitrification was confirmed both by comparing these spectra with those of intentionally devitrified samples, and by the fact that the spectra of thin glass films, where they could be prepared, were identical to those of ground samples in matrices. Spectra of at least two alkali metal forms of each glass-forming system were investigated. The far-i.r. spectra of each set of glasses
M2 O~A3, O~,witha common glass-former A3,011, are very similar except for one outstanding feature which varies with 1430, i.e. M~.This feature is a broad, intense absorption band whose frequency is strongly cation-mass dependent. Since the frequency of thisto band varies as 2, it is assigned VA, the oscillaroughly (rn~)~ tion frequency of the alkali cation about its ‘equilibrium position’, required by equation (1) and derivative transport equations. The bands assigned to VA have been measured for nineteen vitreous systems, and the results are correlated in Fig. 1. It is clear that VA for a given alkali ion varies with the nature of the glass-former A 3,O~.This should be expected since the local environment of M~changes significantly through the range of glasses studied. Despite such changes, however, the variation in V4 for a given 14~ is only large for lithium,
Rb~
__
Nc*
M20 P205
__
FIG. 2. Far-i.r. absorption spectra of alkali metaphosphate and alkali tetraborate glasses.
where VA is significantly higher in Li2 O.SiO2 than in the other five vitreous systems studied. This effect is caused by strong coupling of the Li~ motion with that of the metasilicate network internal vibrational modes. General features of the alkali cation vibrational bands are illustrated by the 10—400 cm~ spectra of the tetraborate and metaphosphate glasses 11202B2O3 and 112 O.P2 0. (~!~ = Cs, Rb~,K~,Na), shown in Fig. 2. The bands are very broad, with the band-widths at half maximum being on the order of VA . The band widths are difficult to assess accurately, but an estimate for each is given in Table 1. There are several mechanisms by which the cation vibrations can give rise to broad i.r. bands. First, if there is not only one ‘equilibrium position’ for the cation but several such sites, differing in the value of (~LJ/aQ2 ) — the harmonic force field element evaluated along the normal coordinate at the equilibrium position — and separated by low energy barriers, then the spectrum will consist of several cation vibrational bands in the same frequency range. If the potential at each site is anharmonic, these iridividual bands will be broadened and the observed spectral band will be the envelope of the bands due to the individual cation-site vibrations.
Vol. 11, No. 5
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES
757
Table 1. Alkali cation vibrational bands in oxide glasses Glass composition
VA
Li
20•V205 Na20.V305 Li20.P2O5 Na20.P2O5 K30.P2 05 Rb20.P2 O~ Cs20.P2 O~ Li20.B303 Na2O.B203 Cs20.B203 Li20.2B203 Na20.2B203 K20.2B2O3 Cs2O.2B2O3 Li2 O.Ge02 K20.Ge02 Cs20.Ge02 Li2 O.Si02 Na2 0.Si02 *
Estimates of
(i~)cm~
L\VA
385 195 400 212 147 114 102 405 220 108 410 220 175 103 405 165 112 485 230 AV1,2
/2
(±5)cm~ *
210 (350) 169 109 81 72 *
280 120 *
250 140 83 *
170 100 *
270
not made due to overlap of
VA
band with
internal anion modes. The shape of such an envelope is determined by the populations and absorptivities for each cation site oscillator. This model is consistent with our results, This overall view supported the 4’5 is on also borate glasses.by They work of Bray, et energies at. found activation for Cs* diffusion in cesium borate glasses from Cs 133 NMR to be in the 0.12 — 0.07 eV range, which is an order of magnitude smaller than that observed for d.c. conductivity, and concluded that the cation motion involved is the jumping of ions among sites in a restricted local region in the glasses. These activities energies are only a few times the vibrational quanta measured in this study. Further support is found in our preliminary observation that the maximum in the ‘VA’ band shifts with x when the composition of (Na 2O)3,.P2 05 is varied from x = 0.25—1.50, a stoichiometric variation that necessarily varies the fraction of each type of site available to the cations.
The anharmonicity of the potential energy portion of the vibrational (Q.M.) Haniiltonian has its classical analog in damping forces on the motion of the cation, which shorten the vibrational relaxation time and consequently increase the band width. In this analogy, it isdifferent easier to distinguish damping which couples normal (VA) modes (cation—cation dynamical coupling), from a damping force on the cation vibration force due to the oxide polyanionic system. The latter is present in general, and its importance increases as 1’A approaches resonance with the polyanion’s vibrational modes. Dynamic cation—cation coupling would not only be a damping mechanism leading to vibrational line shape and breadth changes, but would also be significant in any processes involving cooperative cation motion in glasses. It has recently been suggested, for example, that such coupling leads to some ‘mixed alkali’ effects~ Experiments to determine how the VA band varies with ion-fraction in mixed alkali glasses are
758
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES
underway, and are designed to examine the possibility of dynamic cation—cation coupling, Their results will be reported later.
Vol. 11, No. 5
Acknowledgements — We are grateful for the support of this work by the U.S. Office of Naval Research, and Advanced Research Projects Agency, and forthe experimental assistance by Messrs. A. Miguel and C. Chalek.
REFERENCES 1.
FROLICH H., Theory of Dielectrics, 2nd edn., Clarendon Press, Oxford, England (1958).
2.
CHARLES R.J., J. app1. Phys. 32, 1115 (1961).
3.
EXARHOS G.J. and RISEN W.M., Jr., Chem. Phys. Lett. 10, 484 (1971).
4.
RHEE C. and BRAY P.J., Phys. Chem. Glasses 12, 156 (1971).
5.
BISHOP S.G. and BRAY P.J., J. Chem. Phys. 48, 1709 (1968).
6.
HENDRICKSON J. and BRAY P.J., Phys. Chem. Glasses 13, 2 (1972).
Die Schwingungsfrequenzeri der Alkalikationen in ihren Gleichgewichtslagen in Borat, Phosphat, Germanat, Silicat, und Vanadat Alkalioxydgl~sernwurden als katiorienmassenabh~ngige Bander in den fernen Infrarotspektren dieser Systerne beobachtet.
Printed in Great Britain
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES G.J. Exarhos and W.M. Risen, Jr. Department of Chemistry, Brown University, Providence, Rhode Island, 02912, U.S.A.
(Received 9 June 1972 by J. Tauc)
The vibrational frequencies of alkali metal cations in their equilibrium positions in borate, phosphate, germanate, silicate and vanadate alkali oxide glasses have been observed as cation mass dependent bands in the far-i.r. spectra of these vitreous systems.
THE PHYSICAL properties of alkali-mixed oxide rigid glasses depend strongly on alkali cation motion. Current theories of conductivity, diffusion, dielectric relaxation and orientational polarization in such vitreous systems generally are based on an ion-migration, of defect-migration mechanism in which the probability of a particle transition from one equilibrium position to another, separated from the first by a barrier of height H, 1’2 is given by =
vBexp (—H/kT),
We now report cation-vibrational frequencies for alkali oxide metavanadate, — metagermanate, — metasilicate, — metaborate, and — tetraborate glasses. These glasses are of greater theoretical and material-applications interest than the metaphosphates, and are ones for which mote extensive physical measurements have been reported. These results, then, will permit calculations of properties, dependent on i-’ using the measured cation-vibrational frequency4, spectrum.
(1)
Glass samples of stoichiometric compositions were prepared by two methods. Alkali metal carbonate was mixed with a stoichiometric amount of glass-forming oxide, in a Pt or porcelain crucible, and heated in an electric furnace at ca. 1400°C for 4—5 hr. The resulting melts were quenched between two stainless steel blocks to yield clear, calorless products with the compositions: M 2 0.V2 0~,~ Q.P~05~M2 0.Si02, M2 0~B303, M20.2B203 , and M20.Ge02. Direct melting and dehydration of the reagent-grade compounds NaH2PO4, Na2SiO2 .91-130,glasses and Na2B4O7 •10H20 yielded, upon quenching, that were
where u is the oscillation frequency of the particle within an equilibrium position and B is a constant. This leads to the frequency VA , for oscillation of the alkali metal cation, being essential for evaluation of the physical properties involving such processes. Detailed expressions involving VA have been given for conductance, diffusion coefficient, orientation polarization, contribution to the dielectric constant by orientation polarization and dielectric relaxation time 2 and subsequent for oxide glasses by Charles workers.
spectroscopically identical to analogous glasses formed by the first method.
Prior to our recent report of the observation in the far-i.r. of cation-motion vibrations in the rather special oxide-polymetaphosphate glasses,3 it was possible only to estimate their frequencies, with estimates in the range 2 x 10~ to 1 x 1013 Hz commonly being made.
Far infrared spectra were measured on mechanically ground samples dispersed in a poiyethylene matrix using both a Digilab FTS—14 interferometer (10—500 cm~) and a Beckman IR— 11,12 absorption spectrometer (33—800cm~). 755
756
Vol. 11, No. 5
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES
Cs~Rb~K~
I I
tOO
LtI
1Na~
M~0Vz0 5
200
(crw’)
M20Si02~ 400 500
FIG. 1. Correlation of far-i.r. alkali cation vibra-
tional frequencies in inorganic oxide glasses.
That sample preparation did not lead to devitrification was confirmed both by comparing these spectra with those of intentionally devitrified samples, and by the fact that the spectra of thin glass films, where they could be prepared, were identical to those of ground samples in matrices. Spectra of at least two alkali metal forms of each glass-forming system were investigated. The far-i.r. spectra of each set of glasses
M2 O~A3, O~,witha common glass-former A3,011, are very similar except for one outstanding feature which varies with 1430, i.e. M~.This feature is a broad, intense absorption band whose frequency is strongly cation-mass dependent. Since the frequency of thisto band varies as 2, it is assigned VA, the oscillaroughly (rn~)~ tion frequency of the alkali cation about its ‘equilibrium position’, required by equation (1) and derivative transport equations. The bands assigned to VA have been measured for nineteen vitreous systems, and the results are correlated in Fig. 1. It is clear that VA for a given alkali ion varies with the nature of the glass-former A 3,O~.This should be expected since the local environment of M~changes significantly through the range of glasses studied. Despite such changes, however, the variation in V4 for a given 14~ is only large for lithium,
Rb~
__
Nc*
M20 P205
__
FIG. 2. Far-i.r. absorption spectra of alkali metaphosphate and alkali tetraborate glasses.
where VA is significantly higher in Li2 O.SiO2 than in the other five vitreous systems studied. This effect is caused by strong coupling of the Li~ motion with that of the metasilicate network internal vibrational modes. General features of the alkali cation vibrational bands are illustrated by the 10—400 cm~ spectra of the tetraborate and metaphosphate glasses 11202B2O3 and 112 O.P2 0. (~!~ = Cs, Rb~,K~,Na), shown in Fig. 2. The bands are very broad, with the band-widths at half maximum being on the order of VA . The band widths are difficult to assess accurately, but an estimate for each is given in Table 1. There are several mechanisms by which the cation vibrations can give rise to broad i.r. bands. First, if there is not only one ‘equilibrium position’ for the cation but several such sites, differing in the value of (~LJ/aQ2 ) — the harmonic force field element evaluated along the normal coordinate at the equilibrium position — and separated by low energy barriers, then the spectrum will consist of several cation vibrational bands in the same frequency range. If the potential at each site is anharmonic, these iridividual bands will be broadened and the observed spectral band will be the envelope of the bands due to the individual cation-site vibrations.
Vol. 11, No. 5
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES
757
Table 1. Alkali cation vibrational bands in oxide glasses Glass composition
VA
Li
20•V205 Na20.V305 Li20.P2O5 Na20.P2O5 K30.P2 05 Rb20.P2 O~ Cs20.P2 O~ Li20.B303 Na2O.B203 Cs20.B203 Li20.2B203 Na20.2B203 K20.2B2O3 Cs2O.2B2O3 Li2 O.Ge02 K20.Ge02 Cs20.Ge02 Li2 O.Si02 Na2 0.Si02 *
Estimates of
(i~)cm~
L\VA
385 195 400 212 147 114 102 405 220 108 410 220 175 103 405 165 112 485 230 AV1,2
/2
(±5)cm~ *
210 (350) 169 109 81 72 *
280 120 *
250 140 83 *
170 100 *
270
not made due to overlap of
VA
band with
internal anion modes. The shape of such an envelope is determined by the populations and absorptivities for each cation site oscillator. This model is consistent with our results, This overall view supported the 4’5 is on also borate glasses.by They work of Bray, et energies at. found activation for Cs* diffusion in cesium borate glasses from Cs 133 NMR to be in the 0.12 — 0.07 eV range, which is an order of magnitude smaller than that observed for d.c. conductivity, and concluded that the cation motion involved is the jumping of ions among sites in a restricted local region in the glasses. These activities energies are only a few times the vibrational quanta measured in this study. Further support is found in our preliminary observation that the maximum in the ‘VA’ band shifts with x when the composition of (Na 2O)3,.P2 05 is varied from x = 0.25—1.50, a stoichiometric variation that necessarily varies the fraction of each type of site available to the cations.
The anharmonicity of the potential energy portion of the vibrational (Q.M.) Haniiltonian has its classical analog in damping forces on the motion of the cation, which shorten the vibrational relaxation time and consequently increase the band width. In this analogy, it isdifferent easier to distinguish damping which couples normal (VA) modes (cation—cation dynamical coupling), from a damping force on the cation vibration force due to the oxide polyanionic system. The latter is present in general, and its importance increases as 1’A approaches resonance with the polyanion’s vibrational modes. Dynamic cation—cation coupling would not only be a damping mechanism leading to vibrational line shape and breadth changes, but would also be significant in any processes involving cooperative cation motion in glasses. It has recently been suggested, for example, that such coupling leads to some ‘mixed alkali’ effects~ Experiments to determine how the VA band varies with ion-fraction in mixed alkali glasses are
758
CATION VIBRATIONS IN INORGANIC OXIDE GLASSES
underway, and are designed to examine the possibility of dynamic cation—cation coupling, Their results will be reported later.
Vol. 11, No. 5
Acknowledgements — We are grateful for the support of this work by the U.S. Office of Naval Research, and Advanced Research Projects Agency, and forthe experimental assistance by Messrs. A. Miguel and C. Chalek.
REFERENCES 1.
FROLICH H., Theory of Dielectrics, 2nd edn., Clarendon Press, Oxford, England (1958).
2.
CHARLES R.J., J. app1. Phys. 32, 1115 (1961).
3.
EXARHOS G.J. and RISEN W.M., Jr., Chem. Phys. Lett. 10, 484 (1971).
4.
RHEE C. and BRAY P.J., Phys. Chem. Glasses 12, 156 (1971).
5.
BISHOP S.G. and BRAY P.J., J. Chem. Phys. 48, 1709 (1968).
6.
HENDRICKSON J. and BRAY P.J., Phys. Chem. Glasses 13, 2 (1972).
Die Schwingungsfrequenzeri der Alkalikationen in ihren Gleichgewichtslagen in Borat, Phosphat, Germanat, Silicat, und Vanadat Alkalioxydgl~sernwurden als katiorienmassenabh~ngige Bander in den fernen Infrarotspektren dieser Systerne beobachtet.