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Amorphous Materials: Vibrational Spectroscopy
Amorphous Materials: Vibrational Spectroscopy Amorphous materials do not possess long-range order, so that elucidation of their structure requires a combination of diffraction and spectroscopic techniques, along with computer modeling. Vibrational spectroscopy provides a detailed probe of molecular structure and bonding in amorphous solids and liquids (Wong and Angell 1976). lnfrared spectroscopy and Raman scattering are the most convenient laboratory techniques for studying vibrational excitations. Inelastic neutron and x-ray scattering give additional information on the dynamics of disordered systems (Sette et al. 1998). Molecular dynamics simulations and ab initio calculations give further insights into the nature of vibrations in glasses and liquids, as well as relaxation processes (Brawer 1985).
1. Infrared and Raman Spectroscopy In infrared spectroscopy, a change in electric dipole moment ∆µ(t) associated with a vibrational mode of the sample interacts with the oscillating electric field E(t) of the incident infrared beam, giving rise to an absorption signal. IR studies of amorphous materials are readily carried out using powder transmission, in which ground aliquots of sample are pressed into discs along with IR-transparent support material (nujol, KBr), or by carrying out transmission experiments directly on thin films. Quantitative information on optical constants, including real and imaginary parts of the refractive index (n, k), dielectric constant (εh and εhh), and the absorption coefficient α(), is best obtained from IR reflectivity studies (Efimov 1995). Raman scattering spectroscopy is an inelastic light scattering technique, in which the electric field (Eo) of the incident light oscillates at much higher frequency (*) than the vibrational modes (frequencies i). The incident light causes instantaneous displacements of the electron density relative to the nuclei, causing an induced dipole, µ] ind l α] E:α is the molecular polarizability (Brodsky 1983). For small vibrational displacements qi, µind(t) l E
E
Eo αo cos 2π*tj F
G
G
1 dα q cos 2π(*pi)t 2 F dq H o i H "
(1)
The time-dependent terms result in re-emission of light not only at the Rayleigh-scattered incident frequency *, but also at the Raman-shifted frequencies *ki and *ji. Raman spectroscopy is carried out by passing a laser beam (frequency *) through the sample, and recording the vibrational spectrum of frequency shifts (*pi).
In addition to the usually broad features caused by vibrational excitations, Raman spectra of glasses typically show a temperature-dependent low-frequency maximum that results from the combined Tand -dependence of the Raman scattering. At low frequency, amorphous materials show a near-continuum of vibrational states. The temperature dependence of the Raman scattered intensity gives rise to a multiplying factor which increases exponentially at small wavenumber. The two effects combine to give an apparent maximum in the Raman spectrum, which disappears if the sample is cooled well below room temperature, or if the spectra are ‘‘reduced’’ by multiplying the observed intensities by the Bose factor \[n(, T )j1] (n l 1\exp(h\kT )k1). A distinct ‘‘boson peak’’ feature is also found in inelastic scattering spectra of amorphous polymers and inorganic systems. This feature occurs at low wavenumber (2–15 cm−") and is not removed by any ‘‘reduction’’ procedures. This feature and its temperature dependence is indicative of the mesoscopic disordered structure of the glass. It is thought that excitations associated with the boson peak play a role in defining the properties of the system at the glass transition (Angell 1995) (see Amorphous Materials: Boson Peak). In resonance Raman spectroscopy, the incident laser excitation frequency corresponds nearly with electronic absorption transitions of the sample. The intensity of particular Raman-active modes is greatly enhanced, and the technique provides a powerful probe of local structure and vibrational–electronic coupling in the sample. Resonance Raman spectroscopy is used extensively in studies of semiconducting glasses, for example, GeSe or As S . Hyper-Raman # spectrum # $ spectroscopy, in which the is recorded around twice the laser frequency (at 2*pi), is used to study polar modes in glasses.
2. Amorphous Tetrahedral Semiconductors Vibrational excitations in a-Si and a-Ge are studied mainly by Raman scattering spectroscopy (Tauc 1975; Brodsky 1983). The structures consist of covalently bonded tetrahedral units, linked into a continuous random network (CRN). The Raman spectra have principal maxima at 460 cm−" (a-Si) and 240 cm−" (aGe), and resemble broadened vibrational density of states g() functions of the crystalline semiconductors. This observation is due to loss of translational symmetry in the disordered semiconductors. The same process results in loss of inversion symmetry, and the vibrations of the amorphous solids are IR-active. Raman spectroscopy is highly sensitive for studying the onset of crystallization in a-Si or Ge, and for studies of disordering (caused by e.g., irradiation damage) of the crystals. Vibrational spectroscopy is useful for characterizing SiHx and GeHx sites in 1
Amorphous Materials: Vibrational Spectroscopy hydrogenated amorphous alloys (see Amorphous Silicon and Germanium). Disordered carbon-based materials have structures based upon sp#-bonded sheets as in crystalline graphite, which has its principal Raman mode at 1575 cm−". With increasing disorder, this band broadens and moves to " 1600 cm−", and a broad band at " 1355 cm−" grows in intensity. The result is interpreted as a gradual loss of crystalline selection rules and more of the crystalline phonon branches appear in the Raman spectrum as the average ‘‘unit cell’’ becomes larger (Lespade et al. 1982). The 1355 cm−" feature lies close to the Raman peak of tetrahedrally coordinate diamond, and some workers assign part of its intensity to sp$-bonded regions. Differences in band width, shape, and relative intensities of " 1600 cm−" and "1355 cm−" features distinguish a-C samples with differing degree and type of disorder. In amorphous III-V semiconductors, features in Raman and IR spectra are interpreted as broadened ‘‘crystalline’’ g() functions within a CRN model, as for a-Si and a-Ge. The a-(III-V) spectra show additional broadening caused by separation of transverse and longitudinal modes in the polar semiconductor. The spectra also give information on local structure. In a-InP, a band near 440 cm−" is assigned to P P linkages, revealing the presence of ‘‘wrong bonds’’ in the amorphous semiconductor. a-SixGe"−x alloys show features near 500 cm−", 250 cm−", and 370 cm−", assigned to Si Si, Ge Ge, and Si Ge bonds. The relative intensities vary systematically with Si:Ge ratio. This example of ‘‘two-mode’’ behavior demonstrates how the CRN ‘‘density of states’’ model for a-Si and a-Ge is extended to a more local ‘‘molecular’’ interpretation, in intermediate compounds. Raman spectra of a-SixC −x samples show " bands at 525 cm−" and 1430 cm−", assigned to Si Si and C C bonds in the sample. In this case, the C C bonding is planar sp#, unlike the tetrahedral sp$ bonding of the a-Si network.
3. Chalcogenide Glasses The second large family of amorphous semiconductors is that of amorphous chalcogenides (X l S, Se, Te), and their binary (GeSx, AsSx), ternary, and more complex (Ge-As-X, etc.) compounds. These have applications as optical materials (Lucas 1999). Liquid S just above its melting point shows a rich Raman spectrum with peaks at 474 cm−", 218 cm−", 151 cm−", and 77 cm−" (Brodsky 1983). The spectrum resembles that of the orthorhombic crystal, with ‘‘isolated’’ S ring units held together by van der Waals forces. The) Raman spectrum of the liquid is thus given a ‘‘molecular’’ interpretation, contrasting with the CRN interpretation of a-Si and a-Ge. As temperature is increased, the S chains begin to open into Sn poly) and the viscosity increases. The meric chain units, 2
Raman spectrum of a-Se is dominated by a band at 235 cm−", with a prominent shoulder at 255 cm−". These features correspond to the Se Se stretching peaks of the trigonal (helical Se_ chains) and monoclinic (Se rings) crystalline forms. The IR spectrum shows pairs) of bands in the 220–260 cm−" and 90–150 cm−" ranges, assigned to Se Se stretching and bending modes within chain and ring units. The glass consists of Sen chain units with some proportion of Se rings. In the ) case of a-Te, the Raman spectrum is dominated by a − " broad band at " 160 cm , with a weaker feature appearing at " 85 cm−". Although the spectrum is usually given a ‘‘density of states’’ interpretation like a-Si, it does not correspond to a broadened g() function for known crystalline forms of Te. Crystalline As S and As Se have planar structures # $ AsX# (X $ l S, Se) units linked containing pyramidal $ by bridging X atoms. The Raman spectrum of a-As S # $ has a strong, polarized band at 360 cm−" due to As S stretching, whereas the IR spectrum is dominated by a band at 310 cm−". The complementarity between IR and Raman spectra indicate that the pyramidal AsX molecular units have high symmetry. The units vibrate$ ‘‘independently’’ because the AsXAs angle is narrow (90–100m). The polarized Raman band is assigned to symmetric ( ) AsS breathing, and the IR band to " ) stretching. $ asymmetric ( Weaker features in the $ 130–150 cm−" range are due to bending vibrations. A CRN ‘‘density of states’’ interpretation could equally well be applied to a-As S and a-As Se , in that # $ $ the glass spectra resemble broadened g()# functions derived from the crystalline materials. This observation illustrates convergence between the two ‘‘extreme’’ models for interpreting spectra of amorphous materials. When phonon branches show little dispersion, as in c-As S , they correspond to ‘‘localized’’ # $ and they give rise to sharp vibrational excitations, peaks and rich structure in the vibrational spectra of the amorphous material that are readily interpreted in terms of ‘‘molecular’’ structures. When crystal dispersion is large, as is the case in c-Si and c-Ge, a range of frequency-dependent coherence lengths occurs in the corresponding amorphous material, and detailed information on local ‘‘molecular’’ structure is difficult to extract from the vibrational spectra. In binary As-S glasses, Raman and resonance Raman studies reveal the presence of As As (peak at 231 cm−") and S S (490 cm−") linkages, including S ring units at high sulfur content. The glasses contain) As S molecular units, identified by their spectroscopic % % signature peaks at 220 cm−" and 190 cm−". These units undergo light-initiated polymerization upon prolonged exposure to the laser beam. Amorphous GeX (X l S, Se, Te) systems consist # essentially of tetrahedral GeX units linked by two% coordinated X atoms, as in the crystalline materials. aGeS shows a strong, polarized Raman mode at # −", assigned to symmetric stretching ( ) of GeS 342 cm groups in the structure. The corresponding" mode% $
Amorphous Materials: Vibrational Spectroscopy (asymmetric stretching) is found in the IR spectrum at 367 cm−". In GexS −x glasses with x 0.67, the charac" of S rings (470 cm−") is observed teristic Raman mode ) by IR data. At high Ge in the spectra, confirmed concentrations, broadening of the Ge S stretching band and increased intensity in the 300 cm−" region reveals the formation of Ge Ge linkages in partly substituted Ge(Ge,S) tetrahedral units. %
This large class of amorphous materials is significant for geology as well as glass science (McMillan and Wolf 1995). a-SiO consists of a three-dimensional # (3-D) network of corner-shared SiO tetrahedra. The % vibrational spectrum measured by neutron scattering resembles g() of crystalline SiO polymorphs, and is # dominated by broad bands at " 1100 cm−", 800 cm−", and 350 cm−" (Galeener et al. 1983; Fig. 1). The Raman and IR spectra contain similar bands, assigned to Si O stretching and OSiO, SiOSi bending vibrations within the tetrahedral network. Much discussion has been concerned with the cooperative nature (i.e., correlation length) of these excitations. Hyper-Raman experiments indicate that the highest frequency modes are highly localized, but vibrational coherence exists for the lowest frequency excitations, from neutron studies. The Raman spectrum contains sharp peaks at 606 cm−" and 492 cm−" that are not predicted by structural models based on known polymorphs. These features are due to three and four membered siloxane rings present as ‘‘defect’’ species within the glass. Their formation enthalpies are " 42 kJ mol−" and " 15 kJ mol−", and the Raman intensities are a useful indicator of the state of thermal equilibration of the glass. Ring formation has a negative ∆V, so that the three-ring peak intensity increases both with density, and also in glasses prepared from gels or from the vapor phase. The Raman spectrum is dominated by a polarized 430 cm−" band due to symmetric SiOSi bending in intertetrahedral linkages. The frequency is dependent upon the intertetrahedral (SiOSi) angle, and it shows anomalous behavior with temperature caused by anharmonicity below the glass transition and structural relaxation at high temperature. Adding alkali or alkaline earth metal oxide components (MxOy) to SiO causes depolymerization of # the framework and ‘‘nonbridging oxygens’’ (NBOs) appear with increased O:Si ratio. Silicon is a strong Lux–Flood acid, so that all O atoms are usually bound to at least one Si. Exceptions include Pb O Pb linkages occurring in lead silicate glasses and liquids and Al O Al linkages in aluminosilicates (characteristic Raman peaks at " 200 cm−" and " 570 cm−"). Changing polymerization of the silicate framework results in the successive appearance of silicate units with 1, 2, 3, and 4 NBO, labeled Qn (4kn is the number of NBOs present). Characteristic Raman
Arbitrary units (a)
8
4
0
RAMAN 0.3 Counts
4. Silicate and Aluminosilicate Glasses
12
0.2
HH
0.1 HV (b)
0.0
0.8 0.6 R 0.4 0.2 (c)
0.0
0
500 1000 Wavenumber (cm–1)
Figure 1 Comparison of the IR reflectance (c), polarized (HH and HV) Raman (b) and inelastic neutron scattering (a) spectra of SiO glass, redrawn from Galeener et al. (1983). The # sharp ‘‘defect’’ peaks at 500 cm−" and 600 cm−" are clearly visible in the HH Raman spectrum. The strongly IR-active modes above 1000 cm−" are assigned to tetrahedral Si O stretching vibrations: the highly polarized Raman band at 430 cm−" is assigned to symmetric SiOSi linkage bending vibrations.
peaks at " 1100 cm−", 1000 cm−", 900 cm−", and 850 cm−" are assigned to symmetric Si O stretching vibrations of Q$, Q#, Q", and Q! species. Coexistence of Qn-species at a given composition in equilibria like 2Q$ l Q%jQ# is studied by Raman and NMR spectroscopy. The reactions are endothermic, with ∆Hm " 15–30 kJ mol−". In IR reflectance, the strong 3
Amorphous Materials: Vibrational Spectroscopy SiO glass band at " 1150 cm−" decreases rapidly in # reflectivity with added ‘‘modifier’’ oxide component, accompanied by the growth in intensity of a band near 1075 cm−". This band shifts to lower frequency as SiO is decreased, and it is joined by a second component at# 1000–900 cm−". These features correspond to asymmetric Si O stretching in structures dominated by Q$ and Q#. Features at 800–900 cm−" in spectra of glass compositions with lower silica contents are due to asymmetric stretching of Q" and Q! species. The vibrational bands of aluminosilicate glasses are broader than for silicates because of a greater distribution in structural environments, and the perturbing effect of Al on silicate vibrations. ‘‘Charge-balanced’’ SiO -MAl O (M l 2M+ or M#+) glasses have structures #based #on% a polymerized network of SiO and AlO . Magnesium-containing glasses % % have very broad spectra, and contain five and six coordinated Al. The spectra between 850 cm−" and 1250 cm−" contain unresolved bands due to (Si,Al) O stretching vibrations of the tetrahedral framework: components are assigned to ‘‘Q% (n Al)’’ species, in which SiO tetrahedra share up to four linkages with Al atoms.% At high SiO content, Raman spectra # Al-rich domains occurs, indicate that clustering of consistent with positive deviations from ideality found in heats of mixing in M#+-bearing systems. IR and Raman bands in the 400–600 cm−" region are assigned to TOT or OTO (T l Si, Al) bending. Pure aluminates are highly ‘‘fragile’’ (nonArrhenian) liquids that are marginal glass formers (Angell 1995). CaO–(Ga,Al) O bulk glasses and fibers # $ are useful IR-transmitting materials. The three dimensional network of corner-linked AlO tetrahedra in a% CaAl O is analogous to SiO , ‘‘stuffed’’ with Ca#+ # % Raman spectrum contains # ions. The a strong polarized − " band at 580 cm due to AlOAl bending. The band is sharper than its counterpart in SiO because the range # (average AlOAl in intertetrahedral angles is smaller angle " 135m). For CaO:Al O 1, Raman and IR # $ spectra indicate depolymerization of the tetrahedral network analogous to binary silicates. In glasses with CaO:Al O 1, AlO and AlO species appear, and $ &of vibrational ' extreme# broadening spectra occurs. Similar broadening is found in Raman and IR spectra of SiO –Al O glasses. Here, the Raman signature of # regions # $ SiO -rich is superimposed on a background # due to the featureless vibrational ‘‘density of states’’ of an alumina-rich matrix, consistent with the observation of unmixing in the system.
5. Carbonate and Nitrate Glasses Carbonate glasses are studied because of their importance for understanding carbonatite magmas in mantle geochemistry. IR and Raman spectroscopy show that the glasses are based upon the CO#− anion, $ and that different types of carbonate environment 4
exist within the glass (Genge et al. 1995). Similar IR and Raman studies show that nitrate glasses (e.g., KNO –Ca(NO ) ) contain NO#− anions. The Raman$ # stretching ( $) vibration is particuactive$ symmetric " planar units. IR and larly characteristic of the trigonal Raman spectroscopy can detect small concentrations ( 50 ppm) of these species dissolved in glass.
6. Borate and Phosphate Glasses Glasses based upon B O form a large class of # $ materials (Konijnendijk technologically important 1975, Wong and Angell 1976). The Raman spectrum of a-B O is dominated by a narrow, polarized band at 808 cm#−" $ caused by symmetric breathing of B O # $ ‘‘boroxol’’ rings within the glass structure based upon linked trigonal BO units. The IR spectrum shows a $ cm−", due to B O stretching, strong band at " 1250 and a weaker band at " 700 cm−" due to OBO\BOB bending. As metal–oxide ‘‘modifier’’ component is added to B O , the boroxol ring peak in the Raman $ spectrum is# replaced by a feature at " 770 cm−" and broad B O stretching vibrations at 1400–1500 cm−" become prominent. These changes indicate the appearance of tetrahedral BO groups in the glass. The % earth borosilicate and structures of alkali and alkaline boroaluminate glasses have been investigated using Raman and IR spectroscopy. In borosilicates close to a ‘‘charge balanced’’ join (SiO –M+BO ), the glass # # structures are analogous to aluminosilicates, with tetrahedral B$+ replacing Si%+ in the network. For ternary glasses with high B O contents, the boroxol # in $ the spectra indicating ring peak becomes prominent the presence of BO units. Phosphate glasses$ have applications in biomedicine, in high-power lasers, and in semiconductor packaging. Hygroscopic a-P O has a network structure based on tetrahedral PO , #in &which three oxygens are bridging (POP linkages) %and the fourth is terminal (P O). The Raman spectrum is dominated by a polarized narrow band at 1390 cm−" due to P O stretching, and strong IR and Raman bands in the 650–800 cm−" region characteristic of POP linkages. Bulk glasses and fibers are easily formed from melts around the metaphosphate (-PO#) to pyrophosphate (P O%) compositions. $ # ( of PO tetraMetaphosphates are based upon chains % per hedra, with two bridging oxygens and two NBO tetrahedron (i.e., PO units). The IR and Raman # spectra show peaks at 1100–1200 cm−" and " 700 cm−" due to P O stretching and POP bending, respectively. The width and frequency of each peak is sensitive to the number and type of counter ion present. Lowfrequency (far-IR) peaks are due to characteristic cation modes decoupled from the phosphate glass framework (Exarhos 1983). Vibrational spectroscopy is useful in studies of phase separation and fluorine incorporation in silicophosphate glasses for laser applications. Characteristic P F and Si F stretch-
Amorphous Materials: Vibrational Spectroscopy ing vibrations are observed in the 750–900 cm−" region of the spectra.
associated with increased Zr coordination and degree of polymerization (Aasland et al. 1996). See also: Excitations
Amorphous
Materials:
Vibrational
7. Fluoride Glasses a-BeF has a tetrahedral network structure based # upon tetrahedral BeF units linked by bridging F ions (Galeener et al. 1983;% Brawer 1985). Fluorides based upon fluorozirconate (ZrF ) and fluorohafnate (HfF ) components give rise to a %wide range of binary (ZrF% BaF ), ternary (ZrF –BaF –NaF:ZBN) and complex% % # (ZrF# –BaF –LaF –NaF:ZBLAN) glass forming com% # applications $ positions with as IR-transmitting fibers (Lucas 1999). The liquids are highly fragile (Angell 1995), and vibrational spectroscopy is used to study changes in glass and liquid structure with temperature and composition (Simmons et al. 1991, Aasland et al. 1996). Fluorozirconate glasses and liquids have structures containing Zr polyhedra in six-, seven-, and eight-fold coordination, linked by bridging fluoride ions. The ‘‘doubly-bridged’’ Zr–(F,F)–Zr unit formed by edge sharing between adjacent ZrFn polyhedra is also important. Systematic variations in glass properties with composition are explained by changes in the Zr coordination and the relative numbers of bridging and nonbridging fluorines. The main Raman peak at 570–590 cm−" is assigned to symmetric stretching (s) of terminal Zr F bonds within ZrFn polyhedra. The IR band at 490–520 cm−" is due to asymmetric (as) Zr F stretching, involving bridging and nonbridging fluorines. The Raman bands at 330–490 cm−" are assigned to Zr F stretching within Zr F Zr linkages. The lowest frequency bands (180–200 cm−" in the Raman spectrum, and 250–285 cm−" in the IR spectrum) are assigned to ZrFn bending vibrations, as well as counter-cation vibrations. The stretching frequencies (s and as) in fluorozirconate glasses occur at lower frequency than in corresponding melts, indicating that the average Zr coordination number is greater in the glass. This is achieved by increased formation of Zr F Zr linkages on vitrification. The rapid structural change with temperature is used to rationalize the extreme fragility in these systems. Both s and as frequencies also decrease with increasing F\Zr ratio for glasses and melts. This observation indicates increased average Zr F distance, as shorter, stronger terminal Zr F bonds are replaced by longer Zr F Zr bridges
Bibliography Aasland S, Einarsrud M A, Grande T, McMillan P F 1996 Spectroscopic investigations of fluorozirconate glasses in the ternary systems ZrF –BaF –AF (A l Na, Li). J. Phys. Chem. % # 100, 5457–63 Angell C A 1995 Formation of glasses from liquids and biopolymers. Science 267, 1924–35 Brawer S A 1985 Relaxation in Viscous Liquids and Glasses. American Ceramic Society. Columbus, OH Brodsky M H 1983 Raman scattering in amorphous semiconductors. In: Cardona M (ed.) Light Scattering in Solids 1. Springer, Berlin, pp. 205–51 Efimov A M 1995 Optical Constants of Inorganic Glasses. CRC Press, Boca Raton, FL Exarhos G J 1983 Vibrational studies of glass structure and localized interactions. In: Walrafen G E, Revesz A G (eds.) Structure and Bonding in Noncrystalline Solids. Plenum Press, New York, pp. 203–17 Galeener F L, Leadbetter A J, Stringfellow M W 1983 Comparison of the neutron, Raman, infrared vibrational spectra of vitreous SiO , GeO , BeF . Phys. Re. B 27, 1052–78 # # # Genge M J, Jones A P, Price G D 1995 An infrared and Raman study of carbonate glasses: Implications for the structure of carbonatite magmas. Am. Min. 59, 927–37 Konijnendijk W L 1975 The Structure of Borosilicate Glasses. Philips Research Reports Supplements, No. 1. Centrex Publishing, Co. Eindhoven, The Netherlands Lespade P, Al-Jishi R, Dresselhaus M S 1982 Model of Raman scattering from incompletely graphitized carbons. Carbon 20, 427–31 Lucas J 1999 Infrared glasses. Curr. Opin. Solid State Mater. Sci. 4, 181–7 McMillan P F, Wolf G H 1995 Vibrational spectroscopy of silicate liquids. In: Stebbins J F, McMillan P F, Dingwell D B (eds.) Structure, Dynamics and Properties of Silicate Melts. Mineralogy Society of America, Washington, DC, pp. 247–315 Simmons J H, Simmons C J, Wright A C 1991 Fluoride glass structure. In: Aggarwal I D, Lu G (eds.) Fluoride Glass Fiber Optics. Academic Press, Boston, pp. 37–84 Tauc J 1975 Infrared and Raman spectroscopy of amorphous semiconductors. In: Bendow B, Mitra S S (eds.) Optical Properties of Highly Transparent Solids. Plenum Press, New York, pp. 525–40 Wong J, Angell C A 1976 Glass Structure by Spectroscopy. Dekker, New York
P. F. McMillan
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Amorphous Materials: Vibrational Spectroscopy
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 251–256 6
1. Infrared and Raman Spectroscopy In infrared spectroscopy, a change in electric dipole moment ∆µ(t) associated with a vibrational mode of the sample interacts with the oscillating electric field E(t) of the incident infrared beam, giving rise to an absorption signal. IR studies of amorphous materials are readily carried out using powder transmission, in which ground aliquots of sample are pressed into discs along with IR-transparent support material (nujol, KBr), or by carrying out transmission experiments directly on thin films. Quantitative information on optical constants, including real and imaginary parts of the refractive index (n, k), dielectric constant (εh and εhh), and the absorption coefficient α(), is best obtained from IR reflectivity studies (Efimov 1995). Raman scattering spectroscopy is an inelastic light scattering technique, in which the electric field (Eo) of the incident light oscillates at much higher frequency (*) than the vibrational modes (frequencies i). The incident light causes instantaneous displacements of the electron density relative to the nuclei, causing an induced dipole, µ] ind l α] E:α is the molecular polarizability (Brodsky 1983). For small vibrational displacements qi, µind(t) l E
E
Eo αo cos 2π*tj F
G
G
1 dα q cos 2π(*pi)t 2 F dq H o i H "
(1)
The time-dependent terms result in re-emission of light not only at the Rayleigh-scattered incident frequency *, but also at the Raman-shifted frequencies *ki and *ji. Raman spectroscopy is carried out by passing a laser beam (frequency *) through the sample, and recording the vibrational spectrum of frequency shifts (*pi).
In addition to the usually broad features caused by vibrational excitations, Raman spectra of glasses typically show a temperature-dependent low-frequency maximum that results from the combined Tand -dependence of the Raman scattering. At low frequency, amorphous materials show a near-continuum of vibrational states. The temperature dependence of the Raman scattered intensity gives rise to a multiplying factor which increases exponentially at small wavenumber. The two effects combine to give an apparent maximum in the Raman spectrum, which disappears if the sample is cooled well below room temperature, or if the spectra are ‘‘reduced’’ by multiplying the observed intensities by the Bose factor \[n(, T )j1] (n l 1\exp(h\kT )k1). A distinct ‘‘boson peak’’ feature is also found in inelastic scattering spectra of amorphous polymers and inorganic systems. This feature occurs at low wavenumber (2–15 cm−") and is not removed by any ‘‘reduction’’ procedures. This feature and its temperature dependence is indicative of the mesoscopic disordered structure of the glass. It is thought that excitations associated with the boson peak play a role in defining the properties of the system at the glass transition (Angell 1995) (see Amorphous Materials: Boson Peak). In resonance Raman spectroscopy, the incident laser excitation frequency corresponds nearly with electronic absorption transitions of the sample. The intensity of particular Raman-active modes is greatly enhanced, and the technique provides a powerful probe of local structure and vibrational–electronic coupling in the sample. Resonance Raman spectroscopy is used extensively in studies of semiconducting glasses, for example, GeSe or As S . Hyper-Raman # spectrum # $ spectroscopy, in which the is recorded around twice the laser frequency (at 2*pi), is used to study polar modes in glasses.
2. Amorphous Tetrahedral Semiconductors Vibrational excitations in a-Si and a-Ge are studied mainly by Raman scattering spectroscopy (Tauc 1975; Brodsky 1983). The structures consist of covalently bonded tetrahedral units, linked into a continuous random network (CRN). The Raman spectra have principal maxima at 460 cm−" (a-Si) and 240 cm−" (aGe), and resemble broadened vibrational density of states g() functions of the crystalline semiconductors. This observation is due to loss of translational symmetry in the disordered semiconductors. The same process results in loss of inversion symmetry, and the vibrations of the amorphous solids are IR-active. Raman spectroscopy is highly sensitive for studying the onset of crystallization in a-Si or Ge, and for studies of disordering (caused by e.g., irradiation damage) of the crystals. Vibrational spectroscopy is useful for characterizing SiHx and GeHx sites in 1
Amorphous Materials: Vibrational Spectroscopy hydrogenated amorphous alloys (see Amorphous Silicon and Germanium). Disordered carbon-based materials have structures based upon sp#-bonded sheets as in crystalline graphite, which has its principal Raman mode at 1575 cm−". With increasing disorder, this band broadens and moves to " 1600 cm−", and a broad band at " 1355 cm−" grows in intensity. The result is interpreted as a gradual loss of crystalline selection rules and more of the crystalline phonon branches appear in the Raman spectrum as the average ‘‘unit cell’’ becomes larger (Lespade et al. 1982). The 1355 cm−" feature lies close to the Raman peak of tetrahedrally coordinate diamond, and some workers assign part of its intensity to sp$-bonded regions. Differences in band width, shape, and relative intensities of " 1600 cm−" and "1355 cm−" features distinguish a-C samples with differing degree and type of disorder. In amorphous III-V semiconductors, features in Raman and IR spectra are interpreted as broadened ‘‘crystalline’’ g() functions within a CRN model, as for a-Si and a-Ge. The a-(III-V) spectra show additional broadening caused by separation of transverse and longitudinal modes in the polar semiconductor. The spectra also give information on local structure. In a-InP, a band near 440 cm−" is assigned to P P linkages, revealing the presence of ‘‘wrong bonds’’ in the amorphous semiconductor. a-SixGe"−x alloys show features near 500 cm−", 250 cm−", and 370 cm−", assigned to Si Si, Ge Ge, and Si Ge bonds. The relative intensities vary systematically with Si:Ge ratio. This example of ‘‘two-mode’’ behavior demonstrates how the CRN ‘‘density of states’’ model for a-Si and a-Ge is extended to a more local ‘‘molecular’’ interpretation, in intermediate compounds. Raman spectra of a-SixC −x samples show " bands at 525 cm−" and 1430 cm−", assigned to Si Si and C C bonds in the sample. In this case, the C C bonding is planar sp#, unlike the tetrahedral sp$ bonding of the a-Si network.
3. Chalcogenide Glasses The second large family of amorphous semiconductors is that of amorphous chalcogenides (X l S, Se, Te), and their binary (GeSx, AsSx), ternary, and more complex (Ge-As-X, etc.) compounds. These have applications as optical materials (Lucas 1999). Liquid S just above its melting point shows a rich Raman spectrum with peaks at 474 cm−", 218 cm−", 151 cm−", and 77 cm−" (Brodsky 1983). The spectrum resembles that of the orthorhombic crystal, with ‘‘isolated’’ S ring units held together by van der Waals forces. The) Raman spectrum of the liquid is thus given a ‘‘molecular’’ interpretation, contrasting with the CRN interpretation of a-Si and a-Ge. As temperature is increased, the S chains begin to open into Sn poly) and the viscosity increases. The meric chain units, 2
Raman spectrum of a-Se is dominated by a band at 235 cm−", with a prominent shoulder at 255 cm−". These features correspond to the Se Se stretching peaks of the trigonal (helical Se_ chains) and monoclinic (Se rings) crystalline forms. The IR spectrum shows pairs) of bands in the 220–260 cm−" and 90–150 cm−" ranges, assigned to Se Se stretching and bending modes within chain and ring units. The glass consists of Sen chain units with some proportion of Se rings. In the ) case of a-Te, the Raman spectrum is dominated by a − " broad band at " 160 cm , with a weaker feature appearing at " 85 cm−". Although the spectrum is usually given a ‘‘density of states’’ interpretation like a-Si, it does not correspond to a broadened g() function for known crystalline forms of Te. Crystalline As S and As Se have planar structures # $ AsX# (X $ l S, Se) units linked containing pyramidal $ by bridging X atoms. The Raman spectrum of a-As S # $ has a strong, polarized band at 360 cm−" due to As S stretching, whereas the IR spectrum is dominated by a band at 310 cm−". The complementarity between IR and Raman spectra indicate that the pyramidal AsX molecular units have high symmetry. The units vibrate$ ‘‘independently’’ because the AsXAs angle is narrow (90–100m). The polarized Raman band is assigned to symmetric ( ) AsS breathing, and the IR band to " ) stretching. $ asymmetric ( Weaker features in the $ 130–150 cm−" range are due to bending vibrations. A CRN ‘‘density of states’’ interpretation could equally well be applied to a-As S and a-As Se , in that # $ $ the glass spectra resemble broadened g()# functions derived from the crystalline materials. This observation illustrates convergence between the two ‘‘extreme’’ models for interpreting spectra of amorphous materials. When phonon branches show little dispersion, as in c-As S , they correspond to ‘‘localized’’ # $ and they give rise to sharp vibrational excitations, peaks and rich structure in the vibrational spectra of the amorphous material that are readily interpreted in terms of ‘‘molecular’’ structures. When crystal dispersion is large, as is the case in c-Si and c-Ge, a range of frequency-dependent coherence lengths occurs in the corresponding amorphous material, and detailed information on local ‘‘molecular’’ structure is difficult to extract from the vibrational spectra. In binary As-S glasses, Raman and resonance Raman studies reveal the presence of As As (peak at 231 cm−") and S S (490 cm−") linkages, including S ring units at high sulfur content. The glasses contain) As S molecular units, identified by their spectroscopic % % signature peaks at 220 cm−" and 190 cm−". These units undergo light-initiated polymerization upon prolonged exposure to the laser beam. Amorphous GeX (X l S, Se, Te) systems consist # essentially of tetrahedral GeX units linked by two% coordinated X atoms, as in the crystalline materials. aGeS shows a strong, polarized Raman mode at # −", assigned to symmetric stretching ( ) of GeS 342 cm groups in the structure. The corresponding" mode% $
Amorphous Materials: Vibrational Spectroscopy (asymmetric stretching) is found in the IR spectrum at 367 cm−". In GexS −x glasses with x 0.67, the charac" of S rings (470 cm−") is observed teristic Raman mode ) by IR data. At high Ge in the spectra, confirmed concentrations, broadening of the Ge S stretching band and increased intensity in the 300 cm−" region reveals the formation of Ge Ge linkages in partly substituted Ge(Ge,S) tetrahedral units. %
This large class of amorphous materials is significant for geology as well as glass science (McMillan and Wolf 1995). a-SiO consists of a three-dimensional # (3-D) network of corner-shared SiO tetrahedra. The % vibrational spectrum measured by neutron scattering resembles g() of crystalline SiO polymorphs, and is # dominated by broad bands at " 1100 cm−", 800 cm−", and 350 cm−" (Galeener et al. 1983; Fig. 1). The Raman and IR spectra contain similar bands, assigned to Si O stretching and OSiO, SiOSi bending vibrations within the tetrahedral network. Much discussion has been concerned with the cooperative nature (i.e., correlation length) of these excitations. Hyper-Raman experiments indicate that the highest frequency modes are highly localized, but vibrational coherence exists for the lowest frequency excitations, from neutron studies. The Raman spectrum contains sharp peaks at 606 cm−" and 492 cm−" that are not predicted by structural models based on known polymorphs. These features are due to three and four membered siloxane rings present as ‘‘defect’’ species within the glass. Their formation enthalpies are " 42 kJ mol−" and " 15 kJ mol−", and the Raman intensities are a useful indicator of the state of thermal equilibration of the glass. Ring formation has a negative ∆V, so that the three-ring peak intensity increases both with density, and also in glasses prepared from gels or from the vapor phase. The Raman spectrum is dominated by a polarized 430 cm−" band due to symmetric SiOSi bending in intertetrahedral linkages. The frequency is dependent upon the intertetrahedral (SiOSi) angle, and it shows anomalous behavior with temperature caused by anharmonicity below the glass transition and structural relaxation at high temperature. Adding alkali or alkaline earth metal oxide components (MxOy) to SiO causes depolymerization of # the framework and ‘‘nonbridging oxygens’’ (NBOs) appear with increased O:Si ratio. Silicon is a strong Lux–Flood acid, so that all O atoms are usually bound to at least one Si. Exceptions include Pb O Pb linkages occurring in lead silicate glasses and liquids and Al O Al linkages in aluminosilicates (characteristic Raman peaks at " 200 cm−" and " 570 cm−"). Changing polymerization of the silicate framework results in the successive appearance of silicate units with 1, 2, 3, and 4 NBO, labeled Qn (4kn is the number of NBOs present). Characteristic Raman
Arbitrary units (a)
8
4
0
RAMAN 0.3 Counts
4. Silicate and Aluminosilicate Glasses
12
0.2
HH
0.1 HV (b)
0.0
0.8 0.6 R 0.4 0.2 (c)
0.0
0
500 1000 Wavenumber (cm–1)
Figure 1 Comparison of the IR reflectance (c), polarized (HH and HV) Raman (b) and inelastic neutron scattering (a) spectra of SiO glass, redrawn from Galeener et al. (1983). The # sharp ‘‘defect’’ peaks at 500 cm−" and 600 cm−" are clearly visible in the HH Raman spectrum. The strongly IR-active modes above 1000 cm−" are assigned to tetrahedral Si O stretching vibrations: the highly polarized Raman band at 430 cm−" is assigned to symmetric SiOSi linkage bending vibrations.
peaks at " 1100 cm−", 1000 cm−", 900 cm−", and 850 cm−" are assigned to symmetric Si O stretching vibrations of Q$, Q#, Q", and Q! species. Coexistence of Qn-species at a given composition in equilibria like 2Q$ l Q%jQ# is studied by Raman and NMR spectroscopy. The reactions are endothermic, with ∆Hm " 15–30 kJ mol−". In IR reflectance, the strong 3
Amorphous Materials: Vibrational Spectroscopy SiO glass band at " 1150 cm−" decreases rapidly in # reflectivity with added ‘‘modifier’’ oxide component, accompanied by the growth in intensity of a band near 1075 cm−". This band shifts to lower frequency as SiO is decreased, and it is joined by a second component at# 1000–900 cm−". These features correspond to asymmetric Si O stretching in structures dominated by Q$ and Q#. Features at 800–900 cm−" in spectra of glass compositions with lower silica contents are due to asymmetric stretching of Q" and Q! species. The vibrational bands of aluminosilicate glasses are broader than for silicates because of a greater distribution in structural environments, and the perturbing effect of Al on silicate vibrations. ‘‘Charge-balanced’’ SiO -MAl O (M l 2M+ or M#+) glasses have structures #based #on% a polymerized network of SiO and AlO . Magnesium-containing glasses % % have very broad spectra, and contain five and six coordinated Al. The spectra between 850 cm−" and 1250 cm−" contain unresolved bands due to (Si,Al) O stretching vibrations of the tetrahedral framework: components are assigned to ‘‘Q% (n Al)’’ species, in which SiO tetrahedra share up to four linkages with Al atoms.% At high SiO content, Raman spectra # Al-rich domains occurs, indicate that clustering of consistent with positive deviations from ideality found in heats of mixing in M#+-bearing systems. IR and Raman bands in the 400–600 cm−" region are assigned to TOT or OTO (T l Si, Al) bending. Pure aluminates are highly ‘‘fragile’’ (nonArrhenian) liquids that are marginal glass formers (Angell 1995). CaO–(Ga,Al) O bulk glasses and fibers # $ are useful IR-transmitting materials. The three dimensional network of corner-linked AlO tetrahedra in a% CaAl O is analogous to SiO , ‘‘stuffed’’ with Ca#+ # % Raman spectrum contains # ions. The a strong polarized − " band at 580 cm due to AlOAl bending. The band is sharper than its counterpart in SiO because the range # (average AlOAl in intertetrahedral angles is smaller angle " 135m). For CaO:Al O 1, Raman and IR # $ spectra indicate depolymerization of the tetrahedral network analogous to binary silicates. In glasses with CaO:Al O 1, AlO and AlO species appear, and $ &of vibrational ' extreme# broadening spectra occurs. Similar broadening is found in Raman and IR spectra of SiO –Al O glasses. Here, the Raman signature of # regions # $ SiO -rich is superimposed on a background # due to the featureless vibrational ‘‘density of states’’ of an alumina-rich matrix, consistent with the observation of unmixing in the system.
5. Carbonate and Nitrate Glasses Carbonate glasses are studied because of their importance for understanding carbonatite magmas in mantle geochemistry. IR and Raman spectroscopy show that the glasses are based upon the CO#− anion, $ and that different types of carbonate environment 4
exist within the glass (Genge et al. 1995). Similar IR and Raman studies show that nitrate glasses (e.g., KNO –Ca(NO ) ) contain NO#− anions. The Raman$ # stretching ( $) vibration is particuactive$ symmetric " planar units. IR and larly characteristic of the trigonal Raman spectroscopy can detect small concentrations ( 50 ppm) of these species dissolved in glass.
6. Borate and Phosphate Glasses Glasses based upon B O form a large class of # $ materials (Konijnendijk technologically important 1975, Wong and Angell 1976). The Raman spectrum of a-B O is dominated by a narrow, polarized band at 808 cm#−" $ caused by symmetric breathing of B O # $ ‘‘boroxol’’ rings within the glass structure based upon linked trigonal BO units. The IR spectrum shows a $ cm−", due to B O stretching, strong band at " 1250 and a weaker band at " 700 cm−" due to OBO\BOB bending. As metal–oxide ‘‘modifier’’ component is added to B O , the boroxol ring peak in the Raman $ spectrum is# replaced by a feature at " 770 cm−" and broad B O stretching vibrations at 1400–1500 cm−" become prominent. These changes indicate the appearance of tetrahedral BO groups in the glass. The % earth borosilicate and structures of alkali and alkaline boroaluminate glasses have been investigated using Raman and IR spectroscopy. In borosilicates close to a ‘‘charge balanced’’ join (SiO –M+BO ), the glass # # structures are analogous to aluminosilicates, with tetrahedral B$+ replacing Si%+ in the network. For ternary glasses with high B O contents, the boroxol # in $ the spectra indicating ring peak becomes prominent the presence of BO units. Phosphate glasses$ have applications in biomedicine, in high-power lasers, and in semiconductor packaging. Hygroscopic a-P O has a network structure based on tetrahedral PO , #in &which three oxygens are bridging (POP linkages) %and the fourth is terminal (P O). The Raman spectrum is dominated by a polarized narrow band at 1390 cm−" due to P O stretching, and strong IR and Raman bands in the 650–800 cm−" region characteristic of POP linkages. Bulk glasses and fibers are easily formed from melts around the metaphosphate (-PO#) to pyrophosphate (P O%) compositions. $ # ( of PO tetraMetaphosphates are based upon chains % per hedra, with two bridging oxygens and two NBO tetrahedron (i.e., PO units). The IR and Raman # spectra show peaks at 1100–1200 cm−" and " 700 cm−" due to P O stretching and POP bending, respectively. The width and frequency of each peak is sensitive to the number and type of counter ion present. Lowfrequency (far-IR) peaks are due to characteristic cation modes decoupled from the phosphate glass framework (Exarhos 1983). Vibrational spectroscopy is useful in studies of phase separation and fluorine incorporation in silicophosphate glasses for laser applications. Characteristic P F and Si F stretch-
Amorphous Materials: Vibrational Spectroscopy ing vibrations are observed in the 750–900 cm−" region of the spectra.
associated with increased Zr coordination and degree of polymerization (Aasland et al. 1996). See also: Excitations
Amorphous
Materials:
Vibrational
7. Fluoride Glasses a-BeF has a tetrahedral network structure based # upon tetrahedral BeF units linked by bridging F ions (Galeener et al. 1983;% Brawer 1985). Fluorides based upon fluorozirconate (ZrF ) and fluorohafnate (HfF ) components give rise to a %wide range of binary (ZrF% BaF ), ternary (ZrF –BaF –NaF:ZBN) and complex% % # (ZrF# –BaF –LaF –NaF:ZBLAN) glass forming com% # applications $ positions with as IR-transmitting fibers (Lucas 1999). The liquids are highly fragile (Angell 1995), and vibrational spectroscopy is used to study changes in glass and liquid structure with temperature and composition (Simmons et al. 1991, Aasland et al. 1996). Fluorozirconate glasses and liquids have structures containing Zr polyhedra in six-, seven-, and eight-fold coordination, linked by bridging fluoride ions. The ‘‘doubly-bridged’’ Zr–(F,F)–Zr unit formed by edge sharing between adjacent ZrFn polyhedra is also important. Systematic variations in glass properties with composition are explained by changes in the Zr coordination and the relative numbers of bridging and nonbridging fluorines. The main Raman peak at 570–590 cm−" is assigned to symmetric stretching (s) of terminal Zr F bonds within ZrFn polyhedra. The IR band at 490–520 cm−" is due to asymmetric (as) Zr F stretching, involving bridging and nonbridging fluorines. The Raman bands at 330–490 cm−" are assigned to Zr F stretching within Zr F Zr linkages. The lowest frequency bands (180–200 cm−" in the Raman spectrum, and 250–285 cm−" in the IR spectrum) are assigned to ZrFn bending vibrations, as well as counter-cation vibrations. The stretching frequencies (s and as) in fluorozirconate glasses occur at lower frequency than in corresponding melts, indicating that the average Zr coordination number is greater in the glass. This is achieved by increased formation of Zr F Zr linkages on vitrification. The rapid structural change with temperature is used to rationalize the extreme fragility in these systems. Both s and as frequencies also decrease with increasing F\Zr ratio for glasses and melts. This observation indicates increased average Zr F distance, as shorter, stronger terminal Zr F bonds are replaced by longer Zr F Zr bridges
Bibliography Aasland S, Einarsrud M A, Grande T, McMillan P F 1996 Spectroscopic investigations of fluorozirconate glasses in the ternary systems ZrF –BaF –AF (A l Na, Li). J. Phys. Chem. % # 100, 5457–63 Angell C A 1995 Formation of glasses from liquids and biopolymers. Science 267, 1924–35 Brawer S A 1985 Relaxation in Viscous Liquids and Glasses. American Ceramic Society. Columbus, OH Brodsky M H 1983 Raman scattering in amorphous semiconductors. In: Cardona M (ed.) Light Scattering in Solids 1. Springer, Berlin, pp. 205–51 Efimov A M 1995 Optical Constants of Inorganic Glasses. CRC Press, Boca Raton, FL Exarhos G J 1983 Vibrational studies of glass structure and localized interactions. In: Walrafen G E, Revesz A G (eds.) Structure and Bonding in Noncrystalline Solids. Plenum Press, New York, pp. 203–17 Galeener F L, Leadbetter A J, Stringfellow M W 1983 Comparison of the neutron, Raman, infrared vibrational spectra of vitreous SiO , GeO , BeF . Phys. Re. B 27, 1052–78 # # # Genge M J, Jones A P, Price G D 1995 An infrared and Raman study of carbonate glasses: Implications for the structure of carbonatite magmas. Am. Min. 59, 927–37 Konijnendijk W L 1975 The Structure of Borosilicate Glasses. Philips Research Reports Supplements, No. 1. Centrex Publishing, Co. Eindhoven, The Netherlands Lespade P, Al-Jishi R, Dresselhaus M S 1982 Model of Raman scattering from incompletely graphitized carbons. Carbon 20, 427–31 Lucas J 1999 Infrared glasses. Curr. Opin. Solid State Mater. Sci. 4, 181–7 McMillan P F, Wolf G H 1995 Vibrational spectroscopy of silicate liquids. In: Stebbins J F, McMillan P F, Dingwell D B (eds.) Structure, Dynamics and Properties of Silicate Melts. Mineralogy Society of America, Washington, DC, pp. 247–315 Simmons J H, Simmons C J, Wright A C 1991 Fluoride glass structure. In: Aggarwal I D, Lu G (eds.) Fluoride Glass Fiber Optics. Academic Press, Boston, pp. 37–84 Tauc J 1975 Infrared and Raman spectroscopy of amorphous semiconductors. In: Bendow B, Mitra S S (eds.) Optical Properties of Highly Transparent Solids. Plenum Press, New York, pp. 525–40 Wong J, Angell C A 1976 Glass Structure by Spectroscopy. Dekker, New York
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Amorphous Materials: Vibrational Spectroscopy
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