Vibrational spectroscopy of glasses

Journal of Non-Crystalline Solids 106 (1988) 347 358 North-Holland, Amsterdam

347

Section 10. Spectroscopy

VIBRATIONAL SPECTROSCOPYOF GLASSES Rui M. Almeida Centro de FTsica Molecular and Departamento de Engenharia de Materiais, I n s t i t u t o Superior T~cnico, Av. Rovisco Pais, I000 Lisboa, Portugal Vibrational spectroscopy is one of the most powerful techniques f o r studying the structure of non- c r y s t a l l i n e materials. I t is p a r t i c u l a r l y useful f o r probing v i b r a t i o n a l motions of non-bridging atoms or ions or those of weakly coupled bridging species. Among the d i f f e r e n t v i b r a t i o n a l methods a v a i l a b l e , i n f r a r e d absorption and Raman scattering w i l l be considered in d e t a i l , along with the s p e c i f i c types of s t r u c t u r a l information which can be extracted in each case, e i t h e r d i r e c t l y or through comparison between spectral data and model c a l c u l a t i o n s . Several types of inorganic glasses are examined, i n c l u d i n g oxide, chalcogenide and halide systems, f o r which t e n t a t i v e selection rules are presented. The problem of e x t r a c t i n g the v i b r a t i o n a l density of states from spectroscopic data is also addressed, together with the effects of d i f f e r e n t Raman data reduction procedures on the so-called "Boson" peak exhibited by most inorganic glasses. approximate analogues of the previous methods

I . INTRODUCTION Vibrational spectroscopy is a powerful tech-

--the "lattice"

(delocalized) model3'4 and the

nique f o r studying the structure of glass, which

"fundamental s t r u c t u r a l u n i t " model 5'6, respec-

has been entensively u t i l i z e d durig the l a s t 20

t i v e l y - - s u f f e r from some serious shortcomings.

years.

Although i t does not usually provide di-

rect s t r u c t u r a l information, i t can be a very

Perhaps the most elaborate method developped so far has been the large c l u s t e r model calcu-

useful tool for probing terminal or weakly cou-

l a t i o n of Bell and Dean7, which was applied to

pled bridging atoms in terms of short range or-

v-SiO 2, v-GeO2 and v-BeF28.

der.

Moreover, v i b r a t i o n a l spectra may be com-

In t h i s approxima-

t i o n , several s t a t i c ball and spoke models of

pared with c a l c u l a t i o n s based on models to

the glass structure (containing a few hundred

y i e l d more d i r e c t short range o r , t o some e x t e n t ,

atoms) were hand b u i l t in agreement with short

intermediate range s t r u c t u r a l data.

range s t r u c t u r a l data from X-ray and neutron

Among the d i f f e r e n t experimental v i b r a t i o n a l

diffraction.

The atomic coordinates were then

methods available (namely i n f r a r e d , Raman, i n -

measured and the v i b r a t i o n a l spectra were com-

e l a s t i c neutron s c a t t e r i n g , B r i l l o u i n and elec-

puted from a harmonic force f i e l d with central

tron energy l o s s ) , i n e l a s t i c neutron scattering,

and non-central force constants.

i n f r a r e d absorption or r e f l e c t i o n and p a r t i c u -

ment was obtained with experimental r e s u l t s ,

l a r l y Raman s c a t t e r i n g (excluding the non-

p a r t i c u l a r l y f o r i n e l a s t i c neutron s c a t t e r i n g ,

-linear effects)will

for which the coupling c o e f f i c i e n t s have only a

tail,

be considered in more de-

along with the s p e c i f i c types of s t r u c -

t u r a l information which can be extracted each case.

in

For c r y s t a l l i n e s o l i d s , both the

Good agree-

weak frequency dependence, whereas the IR and Raman spectra are more d i f f i c u l t

to compute,

since the corresponding matrix elements may

correct f a c t o r group method I and the s i m p l i f i e d

e x h i b i t a strong v a r i a t i o n with frequency.

site-group approach 2 may be employed to assign

important conclusion of the work of Bell and

the experimental IR and Raman spectra.

However,

in the case of n o n - c r y s t a l l i n e materials, the 0022 3 0 9 3 / 8 8 / $ 0 3 . 5 0 ';' Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

An

Dean was t h a t , f o r the tetrahedral AX2 network glasses considered, the spatial l o c a l i z a t i o n of

R.M. A lmeida / Vibrational s?ectroscopv of glasses

348

the normal modes varied s u b s t a n t i a l l y through-

molecular to band-like.

out the frequency spectra 8.

bridging angle e determined to a large extent

The tendency was

The value of the

for modes to be extended at low frequencies and

how s o l i d state e f f e c t s modified the character-

l o c a l i z e d at high frequencies, with more intense

i s t i c s of the isolated tetrahedral modes, p a r t i -

l o c a l i z a t i o n f o r large A/X atomic mass r a t i o s or in the case of non-bridging anionic species

c u l a r l y above a c r i t i c a l value 0 . In t h i s c framework, very simple expressions were obtain-

(introduced by using free-end boundary condi-

ed f o r the positions of the main peaks in the

tions).

v i b r a t i o n a l density of states (VDOS), as

I t was concluded that n e i t h e r a purely

a

molecular approach, nor that based on the use

functlon of e and the central force constant.

of crystal l a t t i c e dynamics may be able to give

Another more a n a l y t i c a l approach is the

accurate information on the v i b r a t i o n a l modes

" c l u s t e r - B e t h e - l a t t i c e " method 12.

throughout the wholefrequency spectrum of a

phonon spectrum of a Bethe l a t t i c e may be calcu-

glassy material.

lated 13 and a number of such l a t t i c e s can

to be used 8.

Extended atomic models have

Vibrational spectra can also be

Here, the be

used to conveniently terminate a small piece of

calculated from computer generated models using,

glass network.

f o r example, molecular dynamics simulation tech-

was obtained for several n o n - c r y s t a l l i n e mater i a l s such as a-Si and others 12.

niques.

Reasonable agreement has been obtained

in some cases 9.

Although such numerical tech-

Good agreement with experiment

In conclusion, there is no single theory f o r

niques provide a s a t i s f a c t o r y s o l u t i o n to the

accurately p r e d i c t i n g the f i r s t

v i b r a t i o n a l problem in glass networks, l i t t l e

al spectra of n o n - c r y s t a l l i n e solids (the same

physical i n s i g h t is furnished simultaneously. Certain s i m p l i f i e d models may f i n d s u i t a b l e a p p l i c a t i o n in special cases.

For example,

when the anionic bridging angles are close

order v i b r a t i o n -

being true f o r second or higher order spectra) and one has to resort to certain types of models in order to gain approximate understanding

to

of the

experimentally observed spectra.

In

7/2, the coupling between s t r u c t u r a l units is

t h i s paper, f o l l o w i n g a b r i e f discussion of the

weak and a "molecular" model such as

IR and Raman experimental methods a v a i l a b l e ,

that

developped by Lucovsky and Martin I0 may be used

some representative results w i l l be reviewed

with some success.

f o r oxide, chalcogenide and halide glasses and

This model was applied to

the o p t i c modes of chalcogenide glasses of the

comparisons w i l l be made with model calculations

type As2X3 (X = S, Se, Te) and the v i b r a t i o n a l

whenever possible.

modes were assumed to be the sum of the i n t e m a l

w i l l be given for the IR and Raman responses,

Tentative selection rules

modes of the fundamental s t r u c t u r a l u n i t (a

in a form which is generally applicable to a l l

AsX3 pyramid) plus those of the bent bridging

of the above glass types.

u n i t As-X-As (C2v), treated independently. More r e c e n t l y , Sen and Thorpe I I developped a

e x t r a c t i n g the VDOS from experimental data,name-

model f o r the v i b r a t i o n a l density of states of

F i n a l l y , the nature of the so-called "Boson"

tetrahedral AX2 glasses such as SiO2 in the high

peak in the Raman spectra of most inorganic

frequency region, based on a random network of

glasses w i l l be discussed.

The problem of

l y from Raman spectra, w i l l also be addressed.

AX4 tetrahedra with nearest neighbor central forces.

This model predicted t h a t , as the

A-X-A angle increased from 7/2 to ~,the character of the v i b r a t i o n a l modes changed from purely

2. EXPERIMENTALMETHODS The two standard techniques of optical vibrao t i o n a l characterization involveinfrared(absorp-

R.M. d Imeida / Vibrational spectroscopy of ,~[asse.~

349

tion or r e f l e c t i o n ) and Raman spectroscopies.

spectrophotometer or a single beam Fourier

First order IR absorption spectra may be obtained for thin glass films whose thickness is

transform spectrometer (FTIR).

Normal Raman spectra are usually taken in

ca. within one order of magnitude of the wave-

the 90o scattering configuration, for trans-

length of the infrared l i g h t used. Such spectra

parent samples, or in the approximately 180o

are proportional to the absorption c o e f f i c i e n t

backscattering configuration, for strongly

a = (4~/k)k, where k is the dimensionless ab-

absorbing or opaque samples.

sorption index (the imaginary part of the com-

spectrometer consists of a Ar ion laser, oper-

plex r e f r a c t i v e index).

In practice, the labo-

ratory preparation of thin glass f i l m s , e.g. by blowing, is d i f f i c u l t

in most cases and many

A typical Raman

ating in the blue (488.0 nm) or green (514.5 nm), a double monochromator equiped with ruled or holographic d i f f r a c t i o n gratings, a photo-

researchers u t i l i z e a l t e r n a t i v e mulling techni-

m u l t i p l i e r detector (or optical multichannel

ques, where a small quantity of fine glass powder is dispersed in a transparent matrix such

analyzer) and photon-counting electronics. Polarized Raman spectra may be taken by pass-

as KBr or polyethylene ( f o r the middle and far

ing the scattered l i g h t through a polarization

IR, r e s p e c t i v e l y ) .

analyzer and a polarization scrambler and

These procedures may have

certain undesirable consequences, such as dis-

collecting l i g h t which is polarized p a r a l l e l to

persion at short wavelengths (Christiansen

the e l e c t r i c vector of the incident l a s e r -

e f f e c t ) , loss of spectral band shape and inten-

- p o l a r i z e d or p a r a l l e l spectrum, designated

s i t y information, residual water from mulling

e.g. by HH, for " h o r i z o n t a l / h o r i z o n t a l " -- and

agent (in KBr p e l l e t s ) and d i f f i c u l t y

also collecting l i g h t which is polarized perpen-

tion of weak absorption bands.

in detec-

dicularly

On the other

hand, the two fundamental optical constants

n

to the same e l e c t r i c vector -- depo-

larized or perpendioular spectrum, designated

(real r e f r a c t i v e index) and k may be obtained

by HV.

The r a t i o of the HV/HH i n t e n s i t i e s is

simultaneously through Kramers-Kronig analysis 14

called depolarization ratio (DR) and i t pro-

of IR r e f l e c t i v i t y data taken at near-normal

vides information about the symmetry of the v i -

incidence (e.g. 20o off-normal), over a s u f f i -

brational modes. Certain Raman measurements

c i e n t l y large frequency range.

may be plagued by intense fluorescence emission

The real ( e l )

and imaginary part (e2) of the complex dielec-

which may be reduced or elliminated by further

t r i c constant may then be computed and peaks in

purifying the material (in cases where i t is of

C2

and ~2/(c12+ ~22) have been associated with

an e x t r i n s i c nature), by switching to a laser

the presence of transverse optical and longitu-

line of longer wavelengtn or, sometimes,

dinal optical s p l i t modes, respectively, in the 15 IR spectra of v-SiO 2, v-GeO2 and v-BeF 2 Such r e f l e c t i o n spectra may e a s i l y be recorded

photobleaching under laser i r r a d i a t i o n .

- l i n e a r techniques l i k e Coherent Anti-Stokes

for any polished bulk glass surface, although

they are not available in most Raman laborato-

some uncertainty may remain, associated with

ries.

taking "near-normal" incidence as normal

also with the truncation error arising from

form Raman spectrometers, operating with excitation in the near IR 16, may completely e l i m i -

measurement of r e f l e c t i v i t y over a f i n i t e f r e -

nate t h i s problem.

quency range.

both FTIR and Raman spectrnmeters may be used

and

The infrared instrumentation nor-

mally used consists of a double-beam grating

by Non-

Raman Spectroscopy are also e f f e c t i v e , but The recent development

of Fourier trans-

With microscope accessories,

as microprobes for analyzing very small volumes

350

R.M. A Imeida / Vibrational spectroscopy of glasses

within a given sample.

~ LR j. AMASN PECTR~

3. VIBRATIONAL SPECTROSCOPYRESULTS

(a)

3.1. Oxide glasses A great deal of IR and Raman data has been accumulated for oxide glasses in both bulk and thin film form, p a r t i c u l a r l y during the last 30 17 years. The work of Wong and Angell constitutes an excellent survey up to 1976, which also includes chalcogenide and halide glasses. Vitreous s i l i c a w i l l be taken as an example of a typical oxide glass. Figure 1 shows the polarized Raman, infrared r e f l e c t i o n and v-SiO 2, together with the theoretical VDOS calculated by Bell and Dean with fixed surface ox~ gens, from reference 15. A comparison of the

I I I--

I III III I II -INFRARED i _REFLECTIVITY

I

0oio;

i n e l a s t i c neutron scattering spectra of bulk

I I I I P.,P'FI--I •,.-

~

o ~1

Z

I

I II l

~b) I

i tl~

500 lOOO 1500 ' ' I I , I I I I I I I I_

spectra of figures l - ( a ) and l - ( b ) shows a certain degree of mutual exclusion which suggests the existence of some kind of selection rules operating for this glass, a point which w i l l be discussed in more detail in Section 3.4. Figure l - ( c ) shows a best approximation to the experimental phonon spectrum (VDOS), as calculated from i n e l a s t i c neutron scattering data 15. The VDOS of AXe network glasses was calculated by Sen and Thorpe 11 using central forces only and

I-

LARGE CLUSTER THEORY

/d)

this model (ST) was l a t e r applied by Galeener 18 to the vibrational spectra of vitreous s i l i c a . In the framework of the ST model, the dominant -I highly polarized Raman band near 435 cm

0

500 1000 WAVENUMBER|CM -1}

I 1500

(DR - O, corresponding to a completely symmetric vibration) involves a symmetric stretching (SS) motion of all the bridging oxygens along the bisectors of the Si-O-Si intertetrahedral angles o, about fixed silicon atoms. The square of the angular frequency ~SS is given as the following function of ~ the (bridging) stretching force constant k 2 an the oxygen mass mo: 2 WSS -

k2 mo (I + cos 0)

(1)

FIGURE 1 Vibrational spectra of v-Si02: (a) polarized Raman spectra; (b) infrared r e f l e c t i o n spectrum) at near-normal incidence; (c) experimental one-phonon i n e l a s t i c neutron scattering, a f t e r subtraction of two-phonon estimate; (d) theoretical VDOS calculated with fixed surface oxygens. (Adapted from reference 15). Except for low frequencies, there is a reasonable s i m i l a r i t y between the Raman spectra and

R.M. A Imeida / Vibrational spectroscopy of glasses

the experimental VDOS of f i g u r e l - ( c ) .

3 51

with f i x e d surface oxygen atoms, by Bell

The

Dean8.

dominant Raman band is found near the high f r e -

and

Despite the absence of long range

quency edge of the strongest band of the VDOS.

Coulomb forces in the model, which would

The r e l a t i v e l y weak and p a r t i a l l y polarized

account f n r the TO-LO s p l i t t i n g s , the agreement

Raman band near 800 cm- I

between figures l - ( d ) and l - ( c ) ,

m

also weakly IR-active

in terms

of

may be a t t r i b u t e d to SS v i b r a t i o n s of the

the position and r e l a t i v e i n t e n s i t y of the VDOS

bridging oxygens with a s i g n i f i c a n t amount of

bands, appears quite good.

Si cation motion 18, perhaps including some weak

less good f o r v-GeO2 and i t was not good f o r

transverse o p t i c a l - l o n g i t u d i n a l o p t i c a l (TO-LO) splitting.

The highest frequency IR-active mode

The agreement

was

v-BeF215

For modified s i l i c a t e or other oxide glasses, major changes appear in the Raman spectra,

peaking near II00 cm- I , which corresponds to very weak depolarized Raman bands near 1050 cm-I

related to the occurence of strong polarized

and 1200 cm- I , was assigned to antisymmetric

high frequency or intermediate frequency peaks

stretching (AS) of the bridging oxygens along a

due to v i b r a t i o n s of non-bridging (terminal)

l i n e p a r a l l e l to Si - Si, with a substantial

oxygens 19.

Some of these features also appear

amount of s i l i c o n motion, and the two Raman com-

in the calculated VDOS of Bell and Dean8 when

ponents may correspond to a s p l i t TO-LO pair 18.

surface oxygens are l e f t free to vibrate.

I t should be pointed out that the above argu-

3.2. Chalcogenide Glasses

ments concerning the occurrence of TO-LO

The i n f r a r e d and Raman spectra of vitreous

s p l i t t i n g s in s i l i c a glass, which were extended

chalcogenides such as GeS2 or As2S3, as opposed

to v-GeO2 and v-BeF 2, were put forward on the

to those of oxide glasses, tend to show sharp,

basis of a comparison of reduced infrared

molecular-like spectral features and a more

(Kramers-Kronig) and reduced Raman responses

15

.

pronounced mutual exclusion between IR and

Since such reduction procedures are not u n i v e r -

Raman bands.

s a l l y accepted, t h i s topic w i l l De discussed in

of the lower halide glasses, is explained, in II the framework of the ST model , by the fact

more d e t a i l in Section 3.5.

In the ST model,

This behavior, also found in some

the pure AS mode (without cation motion) would

that the bridging angles in these glasses

have the f o l l o w i n g angular frequency:

usually smaller than in oxides, often close to

2 wAS -

k2 mo (I - cos e)

(2)

are

I00 ° . As an example of a t y p i c a l chalcogenide glass, f i g u r e 2 shows the polarized Raman spectra of

For v-SiO 2, the AS frequency calculated using

v-Geo 3So 7' taken from reference 20, an amor-

the X-ray d i f f r a c t i o n estimate of 0 992 cm- I ) does not coincide with any (Was

phous a l l o y with a composition very close to

substantial IR or Raman a c t i v i t y and i t f a l l s

t h i s glass can be understood in terms of the

near the low frequency edge of the highest f r e -

idealized s t r u c t u r a l model for v-GeS2

quency s p l i t band in the experimental VDOS.

the GeS2 compound. The v i b r a t i o n a l spectra of

Both the IR and Raman 800 cm"I and I050/1200cm -I

(Ge0.33S0.67), which contains t e t r a h e d r a l l y coordinated Ge atoms and twofold coordinated

bands closely correspond to features in the

bridging S atoms, with an average bridging

density of states.

angle 0 near I00 °.

Figure l - ( d ) shows the r e s u l t of the theor e t i c a l c a l c u l a t i o n of the VDOS for v-SiO 2,

Here, given the weak i n t e r -

molecular coupling e f f e c t s , the "molecular" model of Lucovsky and Martin I0 would, in p r i n -

3 52

R.M. A lmeida / Vibrational .spectroscol~v of glasses

-I 485 cm could not d e f i n i t e l y be accounted for in terms of the Ge-S-Ge "water" molecule, or as due to S-S v i b r a t i o n s of the S-rich a l l o y , but were i d e n t i f i e d as i n t r i n s i c modes of the 3-D network 20. ,

t I DR

,,"",,

', .HH

In conclusion, the dominant features

in the o p t i c a l v i b r a t i o n a l spectra of v-Geo.3So. 7 can be explained in terms of a mo-

0.5

l e c u l a r model based on the GeS4 tetrahedral

0.4

!

s t r u c t u r a l u n i t , although the effects of i n t e r molecular coupling are c l e a r l y present.

03

~. tl

The

i n t e n s i t y of such e f f e t s is expected to increase

0.2

with the dimensionality of the vitreous network,

0.1

cular model of Lucovsky and Martin I0 is more

in agreement with the observation that the molesuitable for v-As2S 3, which may be described as

0

200

400

600

a 2-D random network, than f o r the 3-D network of v-GeS2 . 3.3. Halide glasses

R A M A N S H I F T (CM -1)

One of the possible c l a s s i f i c a t i o n s of h~lide glasses consists of two groups: the more i o n i c FIGURE 2 Polarized Raman spectra of Geo.3So. 7 glass. (Adapted from r e f . 20).

f l u o r i d e s and the more covalent lower halides ( c h l o r i d e s , bromides and iodides).

Typical

f l u o r i d e glasses are BeF2 and tnose based on c i p l e , be applicable.

The overall v i b r a t i o n a l

spectrum would then consist of the modes of the

ZrF 4 or HfF 4, whereas zinc bromo-iodides t y p i c a l covalent halide glasses.

are

In terms of

isolated GeS4 tetrahedral molecule and those of

s t r u c t u r e , BeF2

the bridging Ge-S-Ge " w a t e r " - l i k e molecule.

which was examined in d e t a i l in Section 3 . 1 . .

In

is quite s i m i l a r to v-SiO 2,

f a c t , the dominant, h i g h l y polarized Raman peak

Therefore, I w i l l s t a r t by considering

at 342 cm-I may be associated with the t o t a l l y

example of fluorohafnate glasses, which are

symmetric breathing ( s t r e t c h i n g ) mode v I

i s o s t r u c t u r a l with the f l u o r o z i r c o n a t e s .

of

the tetrahedral molecule, although i t appears

the

Figure 3 shows the IR absorption and

to be s l i g h t l y IR-active due to the effects of

polarized Raman spectra of lead dihafnate glass

the weak intermolecular coupling.

2HfF4.PbF2o The two spectra are found to be mutually e x c l u s i v e , except f o r the strong 490 -I cm infrared band, which appeared to be weakly

The IR

spectrum, on the other hand, appeared to be dominated by the antisymmetric s t r e t c h i n g mode v~ of the tetrahedron 20 near 367-405 cm- I . However, i t was very d i f f i c u l t

to separate the

Raman active.

A comparison with the spectra of

lead dizirconate glass 21 showed that the do-

other two expected Raman-active bending modes

minant Raman band, at 575 cm"I in both glasses,

of the tetrahedron from the Raman scattering

did not involve Hf(Zr) cation motions.

continuum below 300 cm- I , which is a shortcoming

occurence of a s i n g l e , sharp (FWHM = 63 c m ' l ) ,

of the molecular model.

completely polarized (DR - 0 . I ) Raman l i n e

F i n a l l y , the features

observed in the Raman spectrum at 200, 435 and

The

-I i n v o l v i n g no Hf cation motion, near 580 cm - -

R.M. A lmeida / Vibrational spectroscopy of %lasses

I

I

I

I

I

I

•

3 53

Hf

f'~,_

r-

8 io 460mW

(b)

) 8

5OO

FREQUENCY

[CM -~1 FIGURE 4 Chain-like structural model of 2HfF4.PbF2 glass.

FIGURE 3 Vibrational spectra of 2HfF4.PbF 2 glass: (a) IR transmission; (b) polarized Raman spectra. --the same frequency of s i m i l a r dominant Raman bands in octahedrally coordinated Li2ZrF 6

and

Cs2ZrF6 crystals 2 2 - is in best agreement with highly symmetrical

F atom environments about

Hf, predominantly 6-fold coordinated. (Hf has the same chemistry as Zr).

In f a c t , the vibra-

tional spectra of figure 3 can be understood in terms of the low dimensional, chain-like structural model shown in figure 4, which is compati b l e with the 2:1 stoichiometry. This model, where each Hf atom is surrounded by two bridging (Fb) and four non-bridging (Fnb) f l u o r i n e atoms, was the f i r s t proposed for heavy metal f l u o r i d e glasses 23.

A few

other

models have been proposed afterwards,

namely

one for fluorozirconate glasses where

Zr atoms

have much more asymmetrical seven and eight- f o l d coordinated f l u o r i n e environments 24, with only two or three non-bridging fluorines

per

polyhedron and with the inclusion of a s i g n i f icant amount of double bridging (edge sharing). Although such a model is in better agreement with existing X-ray d i f f r a c t i o n data 25,

it

contradicts some recent EXAFS results 26 and serious d i f f i c u l t i e s are i n e v i t a b l y found when trying to i n t e r p r e t the known vibrational spectra on i t s basis. Taking the corner-connected, chain-like model of figure 4 as a basis, one has e s s e n t i a l l y two types of vibrational modes:

( I ) those associated with

non-bridging anions and (2) those involving

354

(~[g/asses

R.M. A Imeid~l / Vibrational spectroscopy

bridging

anions.

Thus, the dominant high f r e -

mass ~ replaced by mF28. Figure 5-(a) shows the Raman spectrum of

quency Raman band can be a t t r i b u t e d to the symmetric stretch of Fnb species about f i x e d Hf

t y p i c a l modified zinc halide-based

atoms 27.

50 ZnBr2-50 KI (in mol%).

I t s frequency is simply given by:

2 ~ss(Fnb) -

kl mF

Z 0u i11

constant and mF is the mass of the f l u o r i n e The other major features in the IR and

Raman spectra can be a t t r i b u t e d to the Fbatoms. In order to i n t e r p r e t bridging modes of modified, corner-connected h a l i d e , oxide

chalcogenide glasses, i t is convenient to use in-

cludes a bridging bending (non-central) force the

1.0

wI

(a'~ uP"~ ° ' 8

2 - r~

~ 0.6

'

, I,'°,ii _AI 1

Z

0

:3

Oo .1-

l I 1 I I (a) --

t

["~l

i

DR-a ~9.h

~ :o9/L

;'~

~ 0.2

,N-IN

/"~H H I <

r,/1

I--

p o s s i b i l i t y of network forming (Hf) cation

I I_~ 250m

A

mm

I.M 0,.

Z :3 0u

or

a generalization of the ST model I I , which constant k 3, in addition to k2 and also

I I 3 -53 I

I'--

modified heavy metal halide glasses or other

motion.

glass with

This spectrum, whose

(3)

where k I is the non-bridging stretching force atom.

a

z

0

'Hv-X- - l

100 200 300

o

0

100 200 300

RAMAN SHIFT (CM -1)

The highest frequency IR mode at

490 cm"I is an antisymmetric stretch of Fb along the Hf - Hf d i r e c t i o n , with simultaneous Hf cation motion (C) in the opposite d i r e c t i o n ,

FIGURE 5 Polarized Raman spectra of 50 ZnBr2-50 KI glass: (a) raw data; (b) reduced spectrum.

whose frequency is a function of the bridging appearance was s t r i k i n g l y s i m i l a r to that of

angle 8:

pure v-ZnC1229, was dominated by a completely 2 2k2 - - wAS(C) -

(I - cos O)

(4)

where ~ is the reduced mass of the F and HfF4 particles. -l

235 cm

polarized band at 136 cm- I (DR = 0.06), a f r e quency 92 cm-I lower than in zinc chloride

The lower frequency IR mode at .

glass.

There was also a strong depolarized -I band (DR = 0.6) near 53 cm , with a shoulder near 30 cm- I , which could be due to rocking

is a symmetric stretch of Fb atoms

p a r a l l e l to the bisector of 8, with simultaneous

motions of the anions 30 (Br and I , respectively)

Hf motion in the opposite d i r e c t i o n and a f r e -

and whose strong i n t e n s i t y is probably related

quency given by:

to the very large p o l a r i z a b i l i t i e s of halide anions.

~SS(C)2 = _ _ I [k2(l+cosO ) + 4k3(l-cose)]

(5)

-I The r e l a t i v e l y weak Raman features at 497 cm and near 200 cm-I are believed to correspond to AS(Fb) and SS(Fb), r e s p e c t i v e l y , but without simultaneous Hf cation motion, and with fre quencies given by expressions nearly i d e n t i c a l to equations (4) and (5), but with the reduced

those

The dominant Raman band can be

assigned to a combination of SS(Inb ) at 136cm-I and also to SS(Brb) at 150 cm" I .

As in the

case of heavy metal f l u o r i d e glasses,

the

generalized ST model can also be applied

to

the Raman and IR spectra of these glasses, in order to make semi-quantitative predictions of average bridging angles and force constants, which may in turn be used to confirm the vi -

R.M. Almeida / Vibrational spectroscopy off, lasses

355

brational mode assignment. Equations similar

trio stretching vibrations on non-bridging

to (1) through (5) can also be used. The main mass values, related to the occurence of mixed

fluorine atoms about fixed network forming cations. Such selection rules should also hold, in principle, for other modified halide,

anion coordination shells and also to the unu-

oxide or chalcogenide glasses.

sually small cation/anion mass ratios,

types of situations are presently known where

d i f f i c u l t y lies in the definition of the Feduced

which

are less than one in the case of iodine.

These

vibrational spectra can be understood in terms

However, two

the second of the above rules clearly does not apply.

First, in the case of heavy metal-

of a chain-like structure of four-fold

-containing modified oxide glasses including

coordinated Zn atoms surrounded, on the average,

major amounts of Tl20, PbO, Bi2O3 or Sb203 in

by two Brb atoms, one Brnb and one Inb species30. This is schematically shown in

combination with GeO2, SiO2 or As2O3, very

figure 6.

peaks have been observed32.

strong intermediate or low frequency Raman These peaks have

been attributed either to bridging anion •

Zn

vibrations (intermediate frequency), or to

0

Br

acoustic and/or heavy metal vibrational modes

i'L

(low frequency).

Secondly, in the case of

fully bridged (normally non-modified) glasses, the dominant Raman feature is associated with

symmetric stretches of bridging anions, about fixed network forming cations, as was shown in Section 3.1.. 3.5. Data reduction The Raman spectra of most inorganic glasses are enhanced at low frequencies, exhibiting a weakly polarized or depolarized band (DR ~0.6) often near 50 cm- l .

The nature of this

low

frequency region (Raman s h i f t below lO0 cm- l ) is s t i l l uncertain. FIGURE 6 Chain-like structure of 50 ZnBr2-50 KI glass.

In addition to i n t r i n s i c

Raman active vibrational modes of low frequency, such as rocking, localized (cage-like) heavy metal or acoustic Raman modes32, the raw

3.4. Selection rules

spectra are enhanced at low frequencies,due to:

In the case of modified heavy metal f l u o r i d e

(1) an increase in the Bose-Einstein thermal

glasses such as the f l u o r o z i r c o n a t e s or the

phonon population n(~) = I / [ e x p ( ~ / k B T ) - I ] ,

fluorohafnates, the f o l l o w i n g t e n t a t i v e

where

empirical selection rules were put forward31:

in the Raman scattered i n t e n s i t y proportional

( I ) the infrared spectrwn is dominated by stretching vibrations of bridging fluorine

to (wL - w) 4,

atoms, accompanied by a small amount of network forming cation motion; (2) the Raman spectrum is dominated by high frequency symme-

scattered r a d i a t i o n wing, due to Rayleigh and,

~

is the Raman s h i f t , where

(2) an increase

wL is the

frequency

of

the laser l i n e and (3) the e l a s t i c a l l y sometimes, Mie or Tyndall scattered light.

stray

I t has been a common b e l i e f that

the

3 56

R.M. A lmeida / Vibrational spectroscopy of glasses

-I "Boson" peak around 50 cm is b a s i c a l l y due to the thermal population increase with decreasing phonon frequency, at room temperature. the "Boson" peak designation.

1.0

I

Hence

I

I

I

I

In order to put

the raw Raman spectra in a form suitable

for

0.8

comparison with the VDOS, two s l i g h t l y d i f f e r e n t data reduction procedures have been proposed. That of Shuker and Gammon33 and another due Galeener and Sen34.

According to the

latter

method, the temperature f a c t o r , which is thermal population of the i n i t i a l

to

the

states,

can

be removed and the data reduced to absolute zero

Z

>. m~
by dividing the raw data by [n(~) + I ] ; the raw data should also be divided by

(~L - ~)~

w.

0.4 r~ <

and m u l t i p l i e d by the harmonic o s c i l l a t o r factor

0.6

I lj'.'.''''.'.'"

While the thermal population

factor alone does not usually imply the disappearance of the low frequency peak in

I'I

0.2

the

reduced spectrum, a combination of the thermal and harmonic o s c i l l a t o r factors does that

in

I1"~"1

most cases (SiO 2, GeO2, BeF2, e t c . ) . Therefore, the "Boson" designation is not e n t i r e l y adequate.

0

Figure 7 shows the appearance of the HH Raman

I

I

I

I

I

500 RAMAN S H W T ( C M -1)

spectra of a glass with 70 ZrF4-30 PbF2 (in mol%) a f t e r d i f f e r e n t types of corrections were applied.

After the Bose-Einstein correction,

the i n t e n s i t y of the low frequency mode was s u b s t a n t i a l l y reduced, but i t was completely eliminated only when the applied.

~

factor was also

In f a c t , i t can be shown that

isostructural fluorozirconate glasses with low

FIGURE 7 Polarized (HH) Raman spectra of 70 ZrFa-30 PbF2 glass: ( - - ) raw'spectrum; ( - - - ) Bose-einstein corrected, coincides with the raw spectrum beyond 600cm'l;(...)Bose-Einstein and omega to the four corrected, coincides with Bose-Einstein corrected spectrum beyond 500cm-l; ( - . - ) f u l l y reduced 34, coincides with Bose-Einstein corrected spectrum between 500 cm-I and 600 cm-l.

frequency peaks of widely d i f f e r e n t i n t e n s i t i e s y i e l d nearly identical spectra a f t e r the reduction procedure.

In addition, for

full certain

glasses such as the modified zinc halides, the low frequency peak does not vanish a f t e r

full

reduction, as can be seen by comparing figure 5-(b) with 5-(a).

F i n a l l y , i t can also

shown that neither the In(w) + I ] / ~

forms

of the VDOS which can be assumed have a maximum at any frequency.

Therefore, certain

for glasses containing ions of large polarizability

such as Pb2+, Br- and I - , probably have

a major contribution towards the so-called "Boson" peak.

be

factor nor

i t s product with any of the reasonable

active low frequency modes, c l e a r l y i n t e n s i f i e d

Raman

4. CONCLUSIONS Vibrational spectroscopy is one of the most direct techniques for probing the structure of glass.

However, there is no single theory

R. M. A lrneida / Vibrational spectroscopy ~f g&sses

which allows the d i r e c t calculation of glass structure from the spectral data, so that struG ture models must be inferred and b u i l t within the constraints provided by the available spectra.

Vibrational spectroscopy results have glasses.

Tentative analized,

in conjunction with the nature of the frequency "Boson" peak.

8. R.J. Bell and P. Dean, Localization of Phonons in Vitreous S i l i c a and Related Glasses, in: Amorphous MateriaTs, ed. R.W. Douglas and B. E l l i s (Wiley-lnterscience, London, 1972) pp. 443-452.

low

Due to space l i m i t a -

tions, a few important aspects l i k e

the

low

frequency IR c a t i o n - s i t e v i b r a t i o n a l bands35 and the possible occurence of second order v i b r a t i o n a l features in the spectra

of

oxide

and chalcogenide glasses 36 or in the IR spectra of heavy metal halide glasses 37 have not addressed.

been

More extensive modelling of glass

structure, several additional i n e l a s t i c neutron scattering experimental measurements of the VDOS and more sophisticated methods for calcula~ ing the infrared and Raman optical matrix

ele-

ments are welcome in the future.

9. H. Inoue and I. Yasui, J. Non-Crystalline Solids 95 (1987) 217. IO. G. Lucovsky and R.M. Martin, J. Non-Cryst a l l i n e Solids 8-10 (1972) 185. I I . P.N.Sen and M.F. Thorpe, Phys. Rev. BI5 (1977) 4030. 12. J. Joannopoulos, A.I.P. Conference Proceedings 31 (1976) 108. 13. M.F. Thorpe, Phys. Rev. B8 (1973) 5352. 14. T.S. Moss, Optical Properties of Se~conductors (Academic Press, New York, 1959).

ACKNOWLEDGEMENTS I would l i k e to thank the Junta Nacional

de

Investigag~o CientTfica e Tecnol~gica, the Instituto de Engenharia de Sistemas e Computadores, the I n s t i t u t o Nacional de Investigag~o CientTfica and the Fundagao Calouste Gulbenkian,

5. H. Moore and P.W. Mcmillan, J. Soc. Glass Technol. 40 (1969) 66T.

7. R.J. B e l l , N.F. Bird and P. Dean, J. Phys. C 1 (1968) 299.

selection rules were presented and the Raman data reduction process was b r i e f l y

4. E.B. Wilson J r . , J.C. Decius and P.C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955).

6. R.V. Adams and R.W. Douglas, J. Soc. Glass Technol. 43 (1959) 147T.

been analized for some t y p i c a l oxide, chalcogenide and halide

for

15. F.L. Galeener, A.J. Leadbetter and M.W. Stringfellow, Phys. Rev. B27 (1983) 1052. 16. T. Hirschfeld and B. Chase, Appl. Spectrosc. 40 (1986) 133. 17. J. Wong and C.A. Angell, Glass Structure by Spectroscopy (Marcel Dekker, New York,1976).

financial support of the present work.

18. F.L. Galeener, Phys. Rev. BI9 (1979) 4292.

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