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Abstract

Infrared (IR) spectra originate from transitions between vibrational energy levels of vibrating atomic groups and they are usually observed as absorption spectra. Molecules, atomic groups and even the whole lattice in crystals may interact with the electromagnetic field of light and absorb part of the energy carried by the light. The molecule interacts only with light that carries the right amount of energy to promote the molecule from one discrete energy level (ground state) to another. When it happens that IR radiation can be absorbed and a ground state molecule can be promoted to its first excited vibrational state, we say that the molecule has made a transition between the ground state and the excited state. Light of IR frequencies can generally excite molecules or functional atomic groups from one vibrational energy level to another. Hence, IR spectroscopy is called “vibrational spectroscopy”. Visible and UV radiation are higher energetic and can promote the redistribution of electrons in a molecule or atomic group, such that the electronic potential energy of the molecule is changed (“electronic spectroscopy”).

Theoretical background
Bohr’s frequency condition

Using the terminology of quantum mechanics, we have to state that if a molecule is placed in an electromagnetic field (IR light), a transfer of energy from the field to the molecule will occur only when Bohr’s frequency condition is satisfied:

Introduction

Infrared (IR) spectra originate from transitions between vibrational energy levels of vibrating atomic groups and they are usually observed as absorption spectra. Molecules, atomic groups and even the whole lattice in crystals may interact with the electromagnetic field of light and absorb part of the energy carried by the light. The molecule interacts only with light that carries the right amount of energy to promote the molecule from one discrete energy level (ground state) to another. When it happens that IR radiation can be absorbed and a ground state molecule can be promoted to its first excited vibrational state, we say that the molecule has made a transition between the ground state and the excited state. Light of IR frequencies can generally excite molecules or functional atomic groups from one vibrational energy level to another. Hence, IR spectroscopy is called “vibrational spectroscopy”. Visible and UV radiation are higher energetic and can promote the redistribution of electrons in a molecule or atomic group, such that the electronic potential energy of the molecule is changed (“electronic spectroscopy”).

Theoretical background

Bohr’s frequency condition

Using the terminology of quantum mechanics, we have to state that if a molecule is placed in an electromagnetic field (IR light), a transfer of energy from the field to the molecule will occur only when Bohr’s frequency condition is satisfied:

 

formula

where ΔE is the difference in the energy between two quantised states (energy levels), h is Planck’s constant (6.6262·10–34 Js) and v is the frequency of the light. If ΔE = E" – E', where E" is a quantised vibrational state of higher energy than E', the molecule absorbs radiation when it is promoted from E' to E" and emits radiation when it reverts from E" to E'. From the quantum mechanical point of view it must be additionally stated that a vibration is active in the IR spectrum (“IR activ”) if the dipole moment of the vibrating atomic group or molecule is changed. It is unimportant whether the molecule has a permanent dipole moment or not, only the change associated with the vibration is important. A vibrational mode is “Raman activ” if the polarisability of the molecule is changed during the vibration (Herzberg, 1967; Nakamoto, 1978; McMillan & Hofmeister, 1988).

According to its wave nature, electromagnetic radiation is characterised by two quantities: the wavelength λ and the frequency v. In the IR spectral region the wavelength is usually given in units of [μm] (1 μm = 10–4 cm = 103 nm). The frequency is given in units of [s–1] or hertz [Hz], 1 Hz = 1 s–1. The product of λ and v is the velocity of light (c = λv), which is 2.9979·1010 cm s–1 in vacuum. An additional parameter which is commonly used in vibrational spectroscopy instead of the frequency is the wavenumber forumla, defined as the reciprocal of the wavelength in cm [cm–1]. The following relation exists between the wavelength λ, the frequency v, the wavenumber forumla and the velocity of light c: forumla [cm–1] = 104/λ [μm] = v [s–1]/c [cm s–1]. The energy E of the electromagnetic radiation is proportional to its frequency and its wavenumber, but inverse to the wavelength λ: 

formula

Group theoretical basis

The classification of the vibrational quantum states and the description of the spectroscopic interaction are greatly simplified by exploiting the symmetry of the vibrating atomic groups. The mathematical framework of group theory is the basis of the quantitative description of the symmetry relations possessed by the vibrating groups, finally giving rise to the formulation of “selection rules”. As the symmetry of the atomic group increases, the number of different energy levels decreases. The degeneracy, i.e. the number of vibrational states which have the same energy, increases with increasing symmetry. The more symmetric the atomic group, the fewer different energy levels it has, and the greater the degeneracies of those levels. Symmetry helps us to decide which transitions between energy levels are possible. The symmetry must be compatible in order that the molecule may absorb light and the symmetry-based selection rules tell us which transitions are possible. This will be explained by an example in the Appendix of this chapter (Fateley et al., 1972; McMillan & Hess, 1988; Fadini & Schnepel, 1989).

Harmonic oscillator model

In the classical model of vibrational theory, point masses that are connected by elastic springs are allowed to undergo certain vibrational displacements about their equilibrium position. If the restoring force is directly proportional to the displacement of the point masses that represent the atoms of the vibrating group, then the vibrational motion is “harmonic” (“harmonic oscillator model”). In the simplest case, a diatomic molecule can be represented in a macroscopic model by two masses m1 and m2, connected by an elastic spring. This system will oscillate about the equilibrium distance re if it is first distorted by a distance Δr = rmaxre, and then released. The oscillation is caused by the restoring force K which is opposed to the distortion:

 

formula

The proportionality factor k, which in the model corresponds to the spring constant, is called the force constant in the case of vibrational spectroscopy and is a measure of the bond strength. Based on classical mechanics, the frequency v of the vibrating diatomic molecule is related to the force constant and the reduced mass μ = (m1·m2)/(m1 + m2), representing the atomic masses, by the equation

 

formula

Vibrational modes

In diatomic molecules the vibration of the point masses occurs only along the line connecting two atoms. In polyatomic groups (e.g. CO3, SiO4, PO4 groups) the situation is much more complicated because all the atoms perform their own harmonic oscillations. It can be shown that any of these extremely complicated vibrations of the atomic group may be represented as a superposition of fundamental or normal modes of vibration. The number of normal vibrations follows from simple considerations. A system of N atoms has 3 N degrees of freedom corresponding to the three independent coordinates, with respect to a Cartesian system of coordinates, of each of the N atoms. Three of these are just translations of the entire atomic group along the x, y, and z axes and another three are taken up by the rotation of the molecule about the three principal axes of inertia, passing through the centre of mass. Linear molecules have only two rotational degrees of freedom, as no rotational freedom exists around the molecular axis. The number of remaining vibrational degrees of freedom Z is identical to the number of fundamental or normal vibrations:

 

formula

for a non-linear molecule (e.g. three normal vibrations for the H2O molecule and nine normal vibrations for the tetrahedral SiO4 group) and

 

formula

for a linear molecule (e.g. four normal vibrations for the linear CO2 molecule; no rotation about the molecular axis).

The normal modes of vibration are usually classified by type and symmetry. Two main types can be distinguished: 1) valence or stretching vibrations (symbol v), characterised by changing bond lengths, and 2) planar bending vibrations (symbol δ), where one or more bond angles change, while bond lengths remain constant. Additionally, in out-of-plane bending vibrations (symbol γ), one atom oscillates through a plane defined by at least three neighbouring atoms (e.g. CO3 group). Stretching frequencies are usually higher than bending frequencies. There are also two symmetry modes: 1) symmetric vibrations (index s), where the symmetry of the atomic group is retained and 2) asymmetric vibrations (index as), where the symmetry changes during the vibration. In highly symmetric atomic groups degenerate vibrations occur. In this case two or more vibrations, depending on the degree of degeneracy, have different coordinates but the same energy, giving cause for absorptions at the same wavenumber.

Fig. 1.

Normal vibrations of the H2O and CO2 molecules. v1 represents the symmetric stretching and v3 the asymmetric stretching vibration, v2 represents the bending vibration. v2a and v2b are doubly degenerate bending vibrations of CO2.

Fig. 1.

Normal vibrations of the H2O and CO2 molecules. v1 represents the symmetric stretching and v3 the asymmetric stretching vibration, v2 represents the bending vibration. v2a and v2b are doubly degenerate bending vibrations of CO2.

The comparison of the normal vibrations of water, H2O, and carbon dioxide, CO2, illustrates the various vibrations of a non-linear and a linear molecule (Fig. 1). According to Equation 5 we have to expect three vibrations for H2O and according to Equation 6 four vibrations for CO2. Both molecules have two stretching vibrations, one symmetric vs (v1), where both bonds are stretched simultaneously, and one asymmetric vas (v3), where one bond is compressed, while the other is elongated. The H2O molecule has one bending vibration δ (v2), the CO2 molecule, as a consequence of its linearity, has two bending vibrations which are perpendicular to each other (v2a and v2b). Both bending vibrations of CO2 have the same energy, they are doubly degenerate. Any attempt to construct a second bending vibration for the H2O molecule would result in a rotation. For the CO2 molecule, v2 and v3 are IR active but not Raman active, whereas v1 is Raman active but not IR active (v1 = 1337 cm–1, v2 = 667 cm–1, v3 = 2349 cm–1; Nakamoto, 1978). In the case of H2O, all three vibrations are both IR and Raman active (for gaseous H2O, v1 = 3654 cm–1, v2 = 1595 cm–1, v3 = 3756 cm–1; Nakamoto, 1978). Figure 2 represents the normal modes of vibration of a tetrahedral TO4 group (e.g. SiO4, PO4 etc.). v1 and v3 correspond to symmetric and asymmetric stretching, v2 and v4 to the corresponding bending vibrations. As we have to expect nine vibrational modes (Eqn. 5), v2 is doubly degenerate, v3 and v4 are triply degenerate. All vibrations are Raman active, whereas only v3 and v4 are IR active (for the SiO4 group, v1 = 819 cm–1, v2 = 340 cm–1, v3 = 956 cm–1, v4 = 527 cm–1; Nakamoto, 1978).

Fig. 2.

Normal modes of vibration of a tetrahedral TO4 group. v1 and v3 represent the symmetric and asymmetric stretching modes, respectively, v2 and v4 the corresponding bending vibrations.

Fig. 2.

Normal modes of vibration of a tetrahedral TO4 group. v1 and v3 represent the symmetric and asymmetric stretching modes, respectively, v2 and v4 the corresponding bending vibrations.

Two further types of vibrations have to be distinguished from the normal vibrations: 1) combination bands that are obtained by adding or subtracting the frequencies of one or more fundamental (stretching and/or bending) vibrations (simplified: vc = v1 ± v2), and 2) overtones that occur at approximately twice or three times the frequencies of the respective fundamental vibrations (simplified: vo = nv1). Combination modes and overtones have usually much lower intensities than the respective normal vibrations. This can be illustrated by a simplified model for H2O: absorptions around 3600 and 1600 cm–1 are due to stretching and bending vibrations (normal modes), respectively. A weak band at 5200 cm–1 corresponds to the combination mode and a weak band at 7200 cm–1 to the first overtone of the stretching mode.

Group frequencies

Changes in the number or position of IR absorption bands are mostly analysed in terms of structural changes. In order to make a full correlation between vibrational spectra and structure, it would be necessary to know the atomic displacements associated with each vibrational mode. A reliable approach for discerning the origin of particular IR absorption bands of minerals, is to combine theoretical considerations based on the mathematical framework of group theory, with empirical observations of phases having the same structure but differing in composition. By simply using the “harmonic oscillator model” for the energetics of IR-active vibrations, the substitution of one element by another will shift the wavenumber of a vibration according to the masses and the bonding behaviour of the respective atoms and will also modify the shape of the respective absorption band. The relationship in Equation 4 between the vibrational frequency v, the bond strength (expressed by the force constant k) and the atomic mass (expressed by the reduced mass μ), allows a first coarse classification of the IR absorption spectrum. The wavenumber increases with increasing bond strengths and decreasing atomic masses. It is important to note that in a crystal some functional atomic groups can be treated, in a first approximation, as independent oscillators. Characteristic normal vibrations are then localised in distinct spectral regions and can be assigned to the respective structural group (e.g. CO3, SiO4, PO4 etc.), described by the vibrations of the relevant atoms. Since these vibrations are treated as being largely independent of neighbouring atoms, their frequencies appear in a relatively narrow region of the spectrum. Characteristic “group frequencies” can be observed in the spectra of all compounds that contain the respective functional groups and can be used for their identification. Frequencies of atomic groups relevant for mineral phases and inorganic compounds are compiled in Table 1.

Table 1.

Characteristic group frequencies in cm–1 of functional atomic groups relevant for common minerals (after Farmer, 1974; Nakamoto, 1978).

GroupStretching vibrationsBending vibrationsGroupStretching vibrationsBending vibrations

MOH3700–29001300–400POforumla1100–950600–550
H2O3700–29001650–1600SiOforumla1000–800550–400
COforumla1600–1300950–650SixOforumla1200–900800–400
NOforumla1500–1250900–700AsOforumla900–750400
BOforumla1300–1200800–600VOforumla900–750400
SOforumla1200–1050700–600WOforumla850–750350–300
GroupStretching vibrationsBending vibrationsGroupStretching vibrationsBending vibrations

MOH3700–29001300–400POforumla1100–950600–550
H2O3700–29001650–1600SiOforumla1000–800550–400
COforumla1600–1300950–650SixOforumla1200–900800–400
NOforumla1500–1250900–700AsOforumla900–750400
BOforumla1300–1200800–600VOforumla900–750400
SOforumla1200–1050700–600WOforumla850–750350–300

In the case of crystal structures where it is not useful to discern structural groups (e.g. halite, fluorite, spinel etc.), the whole crystal lattice has to be considered, resulting in a more complex theoretical treatment. Within the lattice, the vibration of each atom about its equilibrium position is strongly influenced by the vibrational motion of its neighbouring atoms. The vibrational modes take the form of displacement waves travelling through the crystal lattice. These lattice waves may be described as longitudinal, where the atomic displacements are parallel to the wave propagation direction, and transverse, where the displacements are perpendicular to the wave propagation direction. These motions can generate a changing dipole moment which interacts with light, giving rise to absorptions. The lattice vibrations which can be IR and/or Raman active are generally described as “optic modes”. The number of vibrational modes is Z = 3N–3, where N is the number of atoms in the primitive unit cell (compare Eqns. 5 and 6 for functional groups).

Characterisation of cordierite and mullite ceramic precursors

Due to the great technical importance of cordierite and mullite as phases occurring frequently in ceramic materials, a large amount of IR spectroscopic work has been done on the structural characterisation of their precursor phases (cordierite precursors: Saha & Pramanik, 1995; Pal et al., 1996; Voll & Beran, 2002; mullite precursors: Voll et al., 1998; Beran et al., 2001). Cordierite is distinguished by its extraordinarily low coefficient of thermal expansion and its consequently good resistance to thermal shock. For advanced applications it has gained considerable importance in electronic packaging because of its low dielectric constants (Pal et al., 1996). Mullite exhibits low thermal expansion, low thermal conductivity, excellent creep resistance and strength retention up to about 1500 °C. Besides its importance for conventional ceramics (tableware, refractories), mullite has become a widely used engineering material in advanced structural and functional ceramics (electronic substrates, optical materials) and in oxide based composites (hot gas filters, thermal protection systems for gas turbine engines; Schneider et al., 1994a). Since the crystallisation paths of high-purity and ultrafine precursor powders significantly influence the properties of the ceramics, detailed knowledge on the temperature-dependent structural development of the precursors is required. Sol-gel processing provides a conventional method for the synthesis of cordierite and mullite precursor powders with relatively low sintering temperatures.

Preparation of the precursors

Cordierite precursor

The composition of cordierite can be described in the system MgO–Al2O3–SiO2 as ternary compound 2MgO·2Al2O3·5SiO2. Several types of cordierite precursor syntheses by sol-gel routes were discerned. Most cordierite ceramic precursors were synthesised by using tetraethoxysilane, TEOS, and aluminium sec-butoxide, Al(OBus)3, as sources for silicon and aluminium, respectively. As magnesium source, magnesium ethoxide, Mg(OEt)2, magnesium sec-butoxide, Mg(OBus)2, and magnesium acetate tetrahydrate were reported (Gensse & Chowdhry, 1986; Selvaraj et al., 1990; Kumta et al., 1994). Magnesium metal flakes were used as magnesium source by Fukui et al. (1993) and Voll & Beran (2002). TEOS and hydrates of aluminium nitrate and magnesium nitrate were used by Saha & Pramanik (1995) as starting materials for the precursor synthesis.

From room temperature up to about 800 °C the precursors remain non-crystalline. Above this temperature they crystallise to metastable hexagonal μ-cordierite, which is structurally analogous to “stuffed β-quartz” with a partial substitution of Si by Al and Mg entering the structural channels. As the sintering temperature increases the structure transforms to hexagonal α-cordierite (Babonneau et al., 1990; Pal et al., 1996; Okada et al., 1998). The crystal structure of α-cordierite is characterised by (Si,Al)6O18 rings which are alternately rotated and stacked over each other along the c axis. The rings are interconnected by three additional (Al,Si) cations in tetrahedral coordination and by two Mg cations in a distorted octahedral coordination, thus forming a three-dimensional framework which has nearly ideal disorder in the (Si,Al) occupancy of the tetrahedral sites (Armbruster, 1985).

Mullite precursor

The composition of mullite is commonly described as a solid solution series, Al2(Al2+2x Si2 – 2x)O10–x, with x ranging from about 0.2 to 0.8. The Al-poor end-member is structurally closely related to sillimanite, Al2SiO5, i.e. x = 0, while the Al-rich endmember is close to a hypothetical alumina phase, ı-Al2O3, i.e. x = 1. The frequently observed solid solution compositions with x = 0.25 and x = 0.40 are designated as 3:2 mullite (3Al2O3·2SiO2) and 2:1 mullite (2Al2O3·1SiO2), respectively. Phase development and thermal behaviour of the mullite precursors show considerable differences, which depend on the reaction conditions during synthesis and the nature of the starting materials. Three main types of mullite formation processes were described by Schneider et al. (1993, 1994b). All precursor types were synthesised by sol-gel routes using mixtures of TEOS and Al(OBus)3 as starting materials. Type I mullite precursors were produced by slow air humidity hydrolysis, type II precursors by rapid hydrolysis with excess H2O under strongly basic pH conditions and type III precursors by rapid hydrolysis at moderately basic conditions. From room temperature up to 900 °C, type I and type III precursors remain non-crystalline. Above this temperature type I precursors crystallise to alumina-rich mullite, while type III precursors partially transform to γ-Al2O3. In both cases a silica-rich amorphous phase is coexisting with the crystalline phases, though in different amounts. Mullite formation in type III precursor starts at temperatures of 1200 °C. Type II precursors consist of a non-crystalline SiO2-rich phase and poorly crystalline pseudo-boehmite, transforming to γ-Al2O3 at about 350 °C, while mullite crystallisation occurs above 1200 °C.

Dehydration behaviour

As described by Beran et al. (2001) and Voll & Beran (2002) the produced gels of the cordierite and mullite precursor types, dried at 150 °C for 15 h, represent the “as-prepared” precursor samples. Separated as-prepared cordierite and mullite precursor samples were differently treated by 15 h heating steps at temperatures of 200, 300, 400, 500, 600, 700, 800, 900, and 1000 °C. The analytical water content of the as-prepared and preheated precursor samples was determined with a modified Du Pont moisture evolution analyser, MEA 903H, working on the basis of water electrolysis in a P2O5 cell. For weight loss determinations a Mettler thermobalance TG 50 equipped with a TA 4000 thermoanalysis system was used.

A continuous decrease of the hydrous component in the cordierite precursors is evident from Figure 3 showing the analytical water content of the preheated precursor phases in comparison with the thermogravimetrically determined weight losses. The substantially higher weight loss values up to preheating temperatures of 500 °C are due to additional decomposition of the organic starting materials used for the syntheses. Above preheating temperatures of 700 °C only very minor amounts of water are detectable in the cordierite precursors. In precursor samples heat-treated at 900 °C the crystallisation of a hexagonal μ-cordierite phase occurs. The 1000 °C sample consists solely of α-cordierite (Voll & Beran, 2002). Figure 3 also shows a continuously decreasing analytical water content for the mullite type I precursor. Type III precursors are characterised by a more discontinuous decrease of the analytical water content compared to that of type I precursors. At preheating temperatures of 900 °C, the type I precursor contains only 1.8 wt% H2O+, while the type III precursor contains 13.7 wt%. At 1000 °C type III precursors still contain essential amounts of water (Beran et al., 2001).

Fig. 3.

Analytical water contents (open symbols) and weight losses (full symbols) in wt% for cordierite (triangle), mullite type I (circle) and mullite type III (square) precursors, as-prepared (150 °C dried) and preheated at temperatures from 200 to 1000 °C in intervals of 100 °C (after Beran et al., 2001 and Voll & Beran, 2002).

Fig. 3.

Analytical water contents (open symbols) and weight losses (full symbols) in wt% for cordierite (triangle), mullite type I (circle) and mullite type III (square) precursors, as-prepared (150 °C dried) and preheated at temperatures from 200 to 1000 °C in intervals of 100 °C (after Beran et al., 2001 and Voll & Beran, 2002).

Absorption features assigned to the hydrous components

The FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared samples and of the differently preheated precursor samples are presented in Figure 4 for cordierite precursors (Voll & Beran, 2002) and in Figures 5 and 6 for mullite type I and mullite type III precursors, respectively. KBr micropellets with a sample/KBr weight ratio of 0.004 for cordierite precursors and 0.0025 for mullite precursors were produced for the FTIR powder measurements. A sample/KBr weight ratio of 0.05 was exclusively used for measurements of the H2O and M–OH combination modes in the near-IR region. Both powdered samples and KBr were dried at 110 °C for 2 hours prior to pressing. FTIR powder spectra were recorded by means of a FTIR spectrometer equipped with a TGS detector and a CsI microfocus accessory. Background and sample spectra were obtained from 64 scans each, with a nominal resolution of 4 cm–1 (Griffiths & de Haseth, 1986).

Fig. 4.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared cordierite precursor and the cordierite precursors preheated at temperatures from 200 to 1000 °C, forming μ-cordierite at 900 °C and α-cordierite at 1000 °C (Voll & Beran, 2002).

Fig. 4.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared cordierite precursor and the cordierite precursors preheated at temperatures from 200 to 1000 °C, forming μ-cordierite at 900 °C and α-cordierite at 1000 °C (Voll & Beran, 2002).

Fig. 5.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type I precursor and the type I precursors preheated at temperatures from 200 to 1000 °C, forming mullite at 1000 °C.

Fig. 5.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type I precursor and the type I precursors preheated at temperatures from 200 to 1000 °C, forming mullite at 1000 °C.

Fig. 6.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type III precursor and the type III precursors preheated at temperatures from 200 to 1000 °C. Note that no mullite formation occurs at 1000 °C.

Fig. 6.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type III precursor and the type III precursors preheated at temperatures from 200 to 1000 °C. Note that no mullite formation occurs at 1000 °C.

The great difference in the band intensities between the stretching mode region of the H2O molecules and OH groups centred around 3430 cm–1 and the bending mode region of H2O molecules centred around 1640 cm–1 indicates the presence of both H2O and OH. As shown in Figure 7 for cordierite and in Figure 8 for mullite type I precursors, this consideration is confirmed by the absorption properties in the region of the H2O and M–OH combination modes around 5200 and 4500 cm–1, respectively. The two weak combination bands centred around 5170 and 4540 cm–1 in cordierite and around 5160 and 4540 cm–1 in mullite precursors prove the presence of H2O molecules and OH groups as structural components of the precursors.

Cordierite precursors

The upper part of Figure 9 shows the integral absorbances of the H2O combination bands, revealing for the cordierite precursor a more or less continuous decrease up to 800 °C preheating temperature, similar to that obtained from the analytical water content and weight loss determination (Fig. 3). The lower part of Figure 9, representing the equivalent diagram of the M–OH combination mode, shows a significantly different dehydration behaviour with nearly constant or even slightly increasing absorbance values up to preheating temperatures of 500 °C, followed by an abrupt decrease up to 800 °C. Consequently, with a continuous loss of the total analytical water content, the OH/H2O ratio of the preheated cordierite precursors increases continuously up to 500 °C, whereas at higher temperatures the contents of both species strongly decrease. At preheating temperatures above 800 °C, H2O molecules and OH groups are detectable in only very minor amounts.

Fig. 7.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared cordierite precursor and the precursors preheated from 200 to 1000 °C (Voll & Beran, 2002).

Fig. 7.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared cordierite precursor and the precursors preheated from 200 to 1000 °C (Voll & Beran, 2002).

Fig. 8.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared mullite type I precursor and the precursors preheated from 200 to 900 °C (after Voll et al., 1998).

Fig. 8.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared mullite type I precursor and the precursors preheated from 200 to 900 °C (after Voll et al., 1998).

Fig. 9.

Absorbance values of as-prepared and preheated cordierite (open triangle), mullite type I (full circle) and mullite type III (open square) precursors for the H2O combination band (upper part) and for the M–OH combination band (lower part) (after Voll et al., 1998, Beran et al., 2001 and Voll & Beran, 2002).

Fig. 9.

Absorbance values of as-prepared and preheated cordierite (open triangle), mullite type I (full circle) and mullite type III (open square) precursors for the H2O combination band (upper part) and for the M–OH combination band (lower part) (after Voll et al., 1998, Beran et al., 2001 and Voll & Beran, 2002).

Mullite precursors

The upper part of Figure 9 shows the integral absorbances of the H2O combination bands of type I and type III mullite precursors. A practically continuous and strong decrease of the absorbance values of precursor samples preheated up to 600 °C and an abrupt increase at 700 °C are the characteristic features of the mullite precursor type I. The equivalent diagram of the M–OH combination band in the lower part of Figure 9 shows slightly changing trends of absorbances up to 600 °C, followed by an increasing negative slope for the precursors preheated at higher temperatures. Compared to type I precursors, type III precursors show a slighter and more continuous decrease of the H2O absorbances with practically constant values between 500 and 700 °C and a further strong decrease at 1000 °C. The corresponding M–OH combination mode shows a continuous decrease of the OH absorbances up to 900 °C, followed by a strong decrease at 1000 °C. Consequently the OH/H2O ratio of type III precursors is continuously increasing over the whole range of preheating temperatures. This is in contrast to type I precursors that show a strong increase of the OH/H2O ratio up to 600 °C and an apparent recombination of OH groups to H2O molecules above 600 °C. Essential amounts of H2O molecules and OH groups are still present in type III precursors at preheating temperatures of 1000 °C.

Specification of the hydrous component

The strong and broad absorptions centred around 3430 cm–1 are due to stretching vibrations of H2O molecules and OH groups. Starting with reasonable wavenumber values, best observed as maxima and shoulders in the spectra of precursors preheated at higher temperatures, the deconvolution of the absorption band in the stretching vibrational region, which was provided by the program PeakFit (Jandel Scientific) on the basis of Gaussian-shaped absorption bands, reveals four peaks designated as I, II, III, and IV. The fitted bands for the cordierite precursors are shown in Figure 10 and for the mullite type I and type III precursors in Figure 11. The corresponding wavenumber values are listed in Table 2. In cordierite precursors band II, representing the strongest absorption, and band IV, which is the weakest band, are continuously decreasing, whereas bands I and III remain nearly constant up to 500 °C. The absorption behaviour of these two band groups (II + IV) and (I + III) in the preheated samples corresponds to that of the H2O and M–OH combination modes.

Fig. 10.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 500, 700 and 800 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands I–IV (Voll & Beran, 2002). Note the different absorbance scales. For band notation and band positions see Table 2.

Fig. 10.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 500, 700 and 800 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands I–IV (Voll & Beran, 2002). Note the different absorbance scales. For band notation and band positions see Table 2.

Table 2.

Band notation, band positions in cm–1 and band assignment to dominating vibrational modes of cordierite precursors, mullite type I and mullite type III precursors from as-prepared samples (as-prep) and samples preheated at 500, 800 °C (cordierite precursors) and 900 °C (mullite precursors), respectively (“stretch”: stretching vibration, “bend”: bending vibration).

Band notationCordierite Band assignmentMullite type IMullite type III
Band assignmentBand positionsBand assignment
as-prep.500 °C800 °Cas-prep.900 °Cas-prep.900 °C

I358435833580OH stretch3588353435743580OH stretch
II341534343428H2O stretch3435342634343434H2O stretch
III321632353234OH stretch3220313532283217OH stretch
IV304730403072H2O stretch2999290830003000H2O stretch
A113711501187Si–O stretch (SiO4)1104116211171135Si–O stretch (SiO4)
B102010251085Si–O stretch (SiO4)1005106210141028Si–O stretch (SiO4)
C872886926Al–O stretch (AlO4)858865863868Al–O stretch (AlO4)
D792Al–O stretch (AlO4)772Al–O stretch (AlO4)
E710727695(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend702678711721(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend
F572583572Al–O stretch (AlO6) + O–Al–O bend (AlO4)567558576571Al–O stretch (AlO6) + O–Al–O bend (AlO4)
G437441433Mg–O stretch (MgO6) + O–Si–O bend (SiO4)441433449450O–Si–O bend (SiO4)
Band notationCordierite Band assignmentMullite type IMullite type III
Band assignmentBand positionsBand assignment
as-prep.500 °C800 °Cas-prep.900 °Cas-prep.900 °C

I358435833580OH stretch3588353435743580OH stretch
II341534343428H2O stretch3435342634343434H2O stretch
III321632353234OH stretch3220313532283217OH stretch
IV304730403072H2O stretch2999290830003000H2O stretch
A113711501187Si–O stretch (SiO4)1104116211171135Si–O stretch (SiO4)
B102010251085Si–O stretch (SiO4)1005106210141028Si–O stretch (SiO4)
C872886926Al–O stretch (AlO4)858865863868Al–O stretch (AlO4)
D792Al–O stretch (AlO4)772Al–O stretch (AlO4)
E710727695(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend702678711721(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend
F572583572Al–O stretch (AlO6) + O–Al–O bend (AlO4)567558576571Al–O stretch (AlO6) + O–Al–O bend (AlO4)
G437441433Mg–O stretch (MgO6) + O–Si–O bend (SiO4)441433449450O–Si–O bend (SiO4)

The four fitted bands of mullite precursors reveal an intensity distribution which corresponds to that of the cordierite precursors, and the four bands are also attributed to two different types of H2O molecules and two different types of OH groups. Differences are evident in the (H2O,OH) absorption pattern of type I and type III precursors preheated at 900 °C (Fig. 11). While the absorption features of the 900 °C treated type III precursor are similar to that of the as-prepared precursor, the 900 °C treated type I precursor reveals significant changes in its absorption pattern compared to the as-prepared phase. However, band I around 3580 cm–1 is also strikingly present in the high-T pretreated type I precursor.

Absorption features assigned to lattice vibrations

Cordierite precursors

Figure 4 demonstrates that at temperatures of 1000 °C the cordierite precursors are transformed to α-cordierite, which presents its characteristic absorption pattern in the 1400–400 cm–1 region (Langer & Schreyer, 1969; Putnis & Bish, 1983; Güttler et al., 1989). The spectrum of the precursor preheated at 900 °C resembles that shown by Langer & Schreyer (1969) for stuffed high-quartz. The 800 °C spectrum closely corresponds to that reported for cordierite glass (Langer & Schreyer, 1969; Güttler et al., 1989).

Fig. 11.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 700 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands I–IV (after Voll et al., 1998 and Beran et al., 2001). Note the different absorbance scales. For band notation and band positions see Table 2.

Fig. 11.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 700 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands I–IV (after Voll et al., 1998 and Beran et al., 2001). Note the different absorbance scales. For band notation and band positions see Table 2.

Starting with wavenumber values observed in the spectrum of the as-prepared precursor, the deconvolution of the absorptions in the 1400–400 cm–1 region reveals six fitted bands, which are labelled with capital letters A–C and E–G, respectively. For precursors with preheating temperatures above 600 °C an additional band D must be introduced (Voll & Beran, 2002). The spectra of the deconvoluted as-prepared samples and of the precursor samples preheated at 700, 800, and 900 °C are presented in Figure 12 and the wavenumber values are summarised in Table 2. With increasing preheating temperatures, the band group centred in the as-prepared precursors around 1020 cm–1 broadens and finally separates into two distinct band groups, best observed in the 800 °C preheated precursor with maxima at 1085 and 926 cm–1. The spectrum of this non-crystalline sample shows already striking similarities to that of the 900 °C treated crystalline μ-cordierite sample (Figs. 4 and 12). Along with the separation of these bands, a significant shift to higher wavenumbers is evident from Figure 14, which confirms the relation between the preheating temperature and the band position.

Mullite precursors

Close similarities exist in the pattern of the FTIR powder spectra in the 1400–400 cm–1 vibrational region between type I and type III mullite precursors up to heating temperatures of 800 °C. Significant differences are evident at preheating temperatures of 900 °C, where the spectrum of the type III precursor still corresponds to that of the 800 °C spectrum, while the type I precursor reveals a spectrum with features also present in the spectrum of mullite (Figs. 5 and 6). At temperatures of 1000 °C, type I precursors are transformed to mullite which shows its characteristic absorption bands in the 1200–1100, 1000–700, and 650–400 cm–1 region (see the section “IR band assignment of mullit” below). The spectrum of type III precursors preheated at 1000 °C resembles that of the 900 °C treated type I precursors, but is strongly influenced by absorptions due to the presence of γ-Al2O3 with maxima in the 800–550 cm–1 range and the amorphous SiO2-rich phase with maxima around 1110 and 470 cm–1. The deconvolution of the absorptions reveals six fitted bands with half widths of about 150 cm–1 (Fig. 13). The wavenumber positions of the bands of the as-prepared samples and of the samples preheated at 800 and 900 °C, labelled with capital letters A–C and E–G, are summarised in Table 2. Analogously to the high-temperature treated cordierite precursor, an additional band D for the 900 °C treated mullite type I precursor must be introduced. For bands A and B around 1110 and 1010 cm–1, a weak and continuous increase of the wavenumber with increasing preheating temperatures up to 800 °C and with an abrupt increase of the wavenumber at 900 °C is evident from Figure 15. The spectra of both precursor types are characterised by a strong increase of the intensity of band C around 860 cm–1 with increasing preheating temperatures up to 900 °C. Apparently, the intensities of bands E and F around 705 and 570 cm–1, respectively, decrease with increasing temperature.

Fig. 12.

FTIR powder spectra in the lattice vibrational region of as-prepared and 700, 800 and 900 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands A–G (Voll & Beran, 2002). For band notation and band positions see Table 2.

Fig. 12.

FTIR powder spectra in the lattice vibrational region of as-prepared and 700, 800 and 900 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands A–G (Voll & Beran, 2002). For band notation and band positions see Table 2.

Fig. 13.

FTIR powder spectra in the lattice vibrational region of as-prepared and 800 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands A–G. For band notation and band positions see Table 2.

Fig. 13.

FTIR powder spectra in the lattice vibrational region of as-prepared and 800 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands A–G. For band notation and band positions see Table 2.

Assignment of absorption bands

The absorption features assigned to vibrations of the silicate framework change significantly with increasing preheating temperatures. The proposed band assignment (Table 2) is essentially based on empirical observations which were made as a result of the heat treatment and on spectroscopic data obtained from silicate melts and glasses (McMillan et al., 1992; Mysen, 1995). Important deductions were also made from band assignments performed on crystalline cordierite phases (Langer & Schreyer, 1969; Putnis & Bish, 1983) and on crystalline mullite compounds (MacKenzie, 1972; Voll et al., 2001, 2002; see section “IR band assignment of mullit”). It should be noted that on the basis of theoretical considerations, the number of IR-active modes has been worked out by Güttler et al. (1989) for the hexagonal cordierite structure to 6A2u + 16E1u. For “ideal” mullite (with x = 0) we also have to expect 22 IR-active modes (4B1u + 9B2u + 9B3u) (Michel et al., 1996) or 32 (6B1u + 13B2u + 13B3u) for a more adequate mullite structure (Rüscher, 1996).

The bands in as-prepared cordierite precursors centred at 1137 cm–1 (band A) and 1020 cm–1 (band B) and in mullite precursors at around 1110 and 1010 cm–1 are assigned to Si–O stretching vibrations of the SiO4 tetrahedral units (Table 2). Band C around 872 cm–1 in cordierite precursors and around 860 cm–1 in the mullite precursors is assigned to Al–O stretching vibrations of AlO4 tetrahedral units. Band D, only appearing in cordierite precursors preheated at temperatures above 500 °C and in 900 °C treated mullite type I precursors, is also assigned to stretching modes of AlO4 tetrahedra. No absorption equivalent to band D is observed in the spectrum of μ-cordierite. Band E is essentially determined by (Si,Al)–O–(Si,Al) bending vibrations. It is highly probable that in low-temperature preheated precursors this band is overlapped by (Si,Al)–OH bending modes, also occurring in this energy region. Band F centred around 570 cm–1 in all precursor phases is assigned to Al–O stretching modes of AlO6 octahedral units and to O–Al–O bending modes of the AlO4 tetrahedral units. The strong absorption centred around 440 cm–1 (band G) in cordierite precursors is due to MgO6 octahedral units and to O–Si–O bending vibrations of the SiO4 tetrahedra. In mullite precursors this band, occurring with an essentially lower intensity, is primarily caused by the O–Si–O bending modes. Probably this absorption is also influenced by Al–O–Al bending modes of neighbouring AlO6 octahedra.

Structural behaviour of the hydrous component

IR absorption bands due to H2O and M–OH combination modes prove the presence of both H2O molecules and OH groups as structural components in cordierite and mullite precursors. In cordierite precursors preheated up to 500 °C, the constant OH content provokes a continuous increase of the OH/H2O ratio with increasing preheating temperatures. Precursors preheated above 500 °C show a strong decrease in both H2O and OH, with H2O molecules remaining the dominating form of water. In type I mullite precursors preheated up to 600 °C the OH/H2O ratio increases continuously with increasing preheating temperature. Above 600 °C a recombination of OH groups to H2O molecules is indicated. According to Voll et al. (1998) the formation of H2O molecules represents an initial stage to the complete dehydration of the type I precursor phase. It is proposed that some of this “recombination produced” H2O is trapped in newly formed closed micropores. Above 800 °C opening of micropores due to microfracturing occurs and, as a consequence, H2O evaporates. This process proceeds rapidly and at 900 °C the precursor is nearly H2O-free. This is in contrast to the dehydration behaviour of type III precursors which show a slight and continuous increase of the OH/H2O ratio up to only about 400 °C, followed by a nearly constant to slightly decreasing OH/H2O ratio. However, even at 1000 °C, type III compositions contain essential amounts of structural OH groups and H2O molecules.

On the basis of the relation between OH stretching band positions and O–H…O distances (Novak, 1974; for minerals see Libowitzky, 1999), bridging and non-bridging H2O molecules and OH groups are discernible in the cordierite and mullite precursors. The deconvolution of the broad and strong absorption in the (H2O, OH) stretching region reveals four bands attributed to two different types of H2O molecules and two different types of OH groups. Since most of the analytical water in the as-prepared and high-T pretreated precursors is present as H2O molecules, the strong band II around 3415 cm–1 in cordierite and 3435 cm–1 in mullite precursors is assigned to the stretching vibration of one type of H2O molecules. The weaker bands I and III, both remaining practically constant in cordierite precursors preheated up to 500 °C, are assigned to the stretching vibrations of two types of OH groups. In precursors preheated at lower temperatures, H2O and OH should be present in more or less comparable amounts. In further agreement with the deduced band assignment for cordierite and mullite precursors, band IV, which is weak and continuously decreasing within the preheating temperature range, is attributed to a second type of H2O. The high-energy band positions I (OH) and II (H2O) require practically no hydrogen bonding, whereas the low-energy OH band position III and the low-energy H2O band position IV require strong hydrogen bonding with O–H… O distances of about 2.70 and 2.65 Å, respectively. A similar scheme of H2O and OH bonding is described in glasses, where in addition to extremely short O–H… O distances, strongly bonded and free H2O molecules and OH groups are discerned (Scholze, 1991). As a general feature, the (H2O,OH) spectra of the high-temperature treated precursors are dominated by band II assigned to the stretching vibration of non-hydrogen bonded H2O. In addition, lower concentrations of non-hydrogen bonded OH groups are present. Mullite type III precursors also contain essential amounts of strongly hydrogen bonded OH groups at 900 °C. In addition it should be noted that H2O molecules occur in naturally formed cordierite as trace constituents of the structural channels (Aines & Rossman, 1984; Winkler, 1996).

Structural ordering phenomena

Cordierite precursors

The increase in the intensities for bands C and D along with the slight decrease for band F with increasing preheating temperatures demonstrates a clear preference of Al for a four-fold coordinated structural position in the precursors preheated at high temperatures. Apparently no Al atoms in octahedral coordination are present in μ-cordierite. The lack of the D band indicates a more pronounced uniformity of the AlO4 tetrahedral size. Figure 12 evidently shows that the bands in μ-cordierite are more structured than those of the non-crystalline precursors. The enhanced number of bands in the stretching vibrational region of SiO4 and AlO4 tetrahedral units is due to the crystalline state of μ-cordierite, controlled by a higher degree of Si/Al ordering. Apparently the band at 1047 cm–1 is related to band B, the bands at 996 and 846 cm–1 are explained by a splitting of the C band, forming a band triplet. The band at 665 cm–1 is probably related to band E, implying the formation of a doublet band; an additional weak component in this energy region of μ-cordierite could be caused by the O–Al–O bending vibration of AlO4 tetrahedra. As evident from Figure 14, bands A, B and C above 500 °C show a significant shift to higher wavenumbers with increasing preheating temperature. The positions of these bands, especially of the dominating B and C bands of the 800 °C preheated samples, come close to the positions of the corresponding Si–O and Al–O stretching bands in crystalline μ-cordierite. This band shift is a strong indication for an increasing degree of network condensation, including changes in the Si–O and Al–O distances to SiO4 and AlO4 tetrahedron dimensions similar to those occurring in crystalline cordierite. It should be noted that according to literature data (Putnis & Bish, 1983; Güttler et al., 1989), no significant band shifts occur in differently annealed crystalline cordierite phases. The slightly decreasing wavenumbers of band E, primarily assigned to (Si,Al)–O–(Si,Al) bending modes, with increasing preheating temperatures above 500 °C indicates a lowering of the values of (Si,Al)–O–(Si,Al) angles within the tetrahedral network. In μ-cordierite the corresponding band is centred at essentially higher wavenumbers, indicating different (Si,Al)–O–(Si,Al) angles in the crystalline phase. The significant shift of band F above 500 °C to lower wavenumbers is probably indicating somewhat larger Al–O distances in the AlO6 units. However, this band shift could also be caused by the reduced absorption of the Al–OH bending modes occurring in this energy region. Apparently, the appearance of band D above 500 °C, which is assigned to an Al–O stretching mode of additionally formed AlO4 units, must be related to the strong decrease of the water content in form of both H2O molecules and OH groups.

Fig. 14.

Diagram relating the preheating temperature and the wavenumber positions for bands A–G of the cordierite precursors. The isolated symbols present the wavenumber positions of bands B, C and E of the 900 °C treated sample (μ-cordierite) (after Voll & Beran, 2002). For band notation see Table 2.

Fig. 14.

Diagram relating the preheating temperature and the wavenumber positions for bands A–G of the cordierite precursors. The isolated symbols present the wavenumber positions of bands B, C and E of the 900 °C treated sample (μ-cordierite) (after Voll & Beran, 2002). For band notation see Table 2.

Fig. 15.

Diagram relating the preheating temperature and the wavenumber positions for Si–O stretching bands A and B of mullite type I (full circle) and mullite type III precursors (open square) (after Beran et al., 2001). For further band notation see Table 2.

Fig. 15.

Diagram relating the preheating temperature and the wavenumber positions for Si–O stretching bands A and B of mullite type I (full circle) and mullite type III precursors (open square) (after Beran et al., 2001). For further band notation see Table 2.

Mullite precursors

The similar absorption behaviour of mullite type I and type III precursors preheated up to 800 °C (Fig. 13) is interpreted in terms of similar structural arrangements in both precursor types. This is of interest, taking into account the different transformation behaviour of the two precursor types. Bands A and B centred around 1110 and 1010 cm–1, respectively, which are assigned to Si–O stretching vibrations, are strongly shifted in 900 °C treated type I precursors to higher wavenumbers (Fig. 13). The position of these two bands is close to the position of the Si–O stretching bands in mullite at around 1170, 1130, and 990 cm–1 (Voll et al., 2001). This band shift is a strong indication for an increasing degree of network condensation and for changes in the Si–O distances in the 900 °C treated precursor to SiO4 tetrahedron dimensions similar to those occurring in mullite, characterised by one short (Si,Al)–O distance of about 1.667 Å (Angel & Prewitt, 1986). In type III precursors no striking changes in the band positions are observed up to 900 °C. A slight shift to higher wavenumbers is evident in samples preheated to 1000 °C. The increasing intensity of band C around 860 cm–1 in both precursor types and the appearance of band D in mullite type I precursor with increasing preheating temperatures indicates a strong increase of AlO4 tetrahedra present as structural units in precursors preheated at higher temperatures. The slightly decreasing intensity of band F around 570 cm–1 (related to AlO6 octahedral units) with increasing preheating temperatures, along with the strongly increasing intensity of band C around 860 cm–1, demonstrates a clear preference of Al for a four-fold coordinated structural position in the precursors preheated at high temperatures. The assignment of band E around 705 cm–1 to the (Si,Al)–O–(Si,Al) bending modes of the tetrahedral framework is in agreement with the proposed T–O–T bending mode for the band at 737 cm–1 in mullite. Under this assumption, the low wavenumber would be indicative for relatively low (Si,Al)–O–(Si,Al) angles within the tetrahedral network. An overlapping of this band with (Si,Al)–OH bending modes would explain the relatively weak intensity of band E in the 900 °C treated type I precursor having a very low water content, compared to the relatively strong intensity of this band in the equivalent type III precursor with its essentially higher water content. As described for the cordierite precursor, the appearance of band D in mullite type I precursor preheated at 900 °C, which is assigned to an Al–O stretching mode of AlO4 units, must be related to the strong decrease of the water content.

Conclusion

Great similarities exist between the absorption features of the cordierite precursor and that of both types of mullite precursors, especially of mullite type I precursor. In analogy to the structural development of the cordierite precursor, it can be concluded that also in the low-temperature state of the heat-treated mullite precursors, AlO6 octahedra are the dominating structural units and that with increasing temperature AlO4 tetrahedra become more dominant. This structural development is correlated to the dehydration process and indicates the inhibiting role of H2O and especially of OH for the formation of AlO4 units and the subsequent network condensation. The crystallisation of μ-cordierite at relatively low preheating temperatures is related to the presence of SiO4 and AlO4 tetrahedra and MgO6 octahedra as tailored structural elements, thus providing preordering prior to crystallisation. The Al–O stretching vibrations in crystalline mullite are centred at 909 and 828 cm–1 for AlO4 tetrahedral units and at 578 cm–1 for AlO6 octahedral units. The band assigned to the AlO6 octahedra is a striking feature of the mullite spectrum (see section “IR band assignment of mullit”). Apparently the crystallisation of mullite is related to newly formed AlO6 octahedra, whereas SiO4 and AlO4 tetrahedra are already available structural units. It is evident that structural changes in mullite type I precursors occur at significantly lower temperatures as in type III precursors. This different behaviour is essentially caused by the strong retainment of H2O molecules and OH groups in type III precursors in the 400–700 °C preheating temperature range.

IR band assignment of mullite

Mullite crystallises in the orthorhombic space group Pbam and its structure is best described in relation to the sillimanite structure (Winter & Ghose, 1979). Sillimanite possesses columns of edge-sharing AlO6 octahedra forming chains parallel to [001]. The octahedral columns are cross-linked by tetrahedrally coordinated Si and Al on T sites, forming double chains that run in the same direction. In deriving the mullite structure from that of sillimanite, some bridging oxygen atoms of the tetrahedral pairs must be removed from their Oc sites, which results in a displacement of the two adjacent T cation sites to the T* positions. The non-vacant Oc site is then displaced towards the T* site to the new Oc* position, forming T3O groups with 2T + 1T* (Fig. 16). Along with these structural changes occurs a partial substitution of Al for Si on the T site (Saalfeld & Guse, 1981; Angel & Prewitt, 1986; Fischer et al., 1994; Voll et al., 2001). Rietveld refinements on mullite-type alkali aluminates revealed Na and K atoms to reside in the vacant Oc sites, with Na on a split site off the special position. Due to crystal chemical constraints, the number of alkali atoms is restricted to 2/3 per unit cell (Fischer et al., 2001).

Fig. 16.

Schematic representation of the average structure of mullite along the c axis.

Fig. 16.

Schematic representation of the average structure of mullite along the c axis.

For a simplified structural model, MacKenzie (1972) calculated the number of IR-active band frequencies of 3:2 mullites on the assumption of independently vibrating AlO6, AlO4 and SiO4 structural units. Based on MacKenziE's band assignment, Cameron (1977) and Rüscher et al. (1996) proposed the intensity variations of the absorptions in the 1200–1100 cm–1 range to be a useful empirical scale for the determination of mullite compositions. However, Rüscher (2001) has shown that band intensity distribution in this energy region can also be provided without compositional changes. IR spectra of Al-Si, Al-Ge and Ga-Ge mullites with a schematic classification of absorption features were published by Schneider (1981). A band assignment for mullite was also presented by Padmaja et al. (2001) discussing structural changes as a function of temperature. IR reflection spectra and back-scattered Raman spectra of 2:1 mullite single crystals were measured by Rüscher (1996), analysing the number of IR-active modes for an adequate structure to 6B1u + 13B2u + 13B3u. On the basis of Raman spectroscopic investigations a band assignment for mullite was discussed by McMillan & Pirou (1982) and a Raman spectroscopic study of mullite compounds in the Al2O3–GeO2 system was reported by Michel et al. (1996).

Voll et al. (2001, 2002) established a modified band assignment for mullite on the basis of polarised FTIR microspectroscopy of oriented ultrathin 2:1 mullite single-crystal slabs and on FTIR powder spectroscopy of polycrystalline mullite-type compounds in the silicate and germanate systems Al2O3–SiO2, Al2O3–GeO2, Ga2O3–GeO2 and in the aluminate and gallate systems Al2O3–Na2O, Al2O3–K2O, Al2O3–Rb2O, Ga2O3–Rb2O. As precise structural data are an important basis for the assignment of absorption bands, the investigated mullite-type compounds were characterised by single-crystal X-ray crystallography or by XRD Rietveld refinements (Fischer et al., 2001; Voll et al., 2001). The 2:1 mullite single crystal was synthesised by the Czochralski technique using SiO2 and Al2O3 powders as starting materials (Guse & Mateika, 1974). The mullite powder samples were prepared by heat treatment of sol-gel derived precursor powders (Al-Si mullite, aluminate and gallate compounds) and by reaction sintering of oxide powders (Al-Ge, Ga-Ge mullites) (Mazza et al., 1992; Beran et al., 2001; Voll et al., 2001, 2002).

FTIR powder spectroscopy

KBr micropellets with a sample/KBr weight ratio of 0.0025 were used for the powder measurements in the mid-IR region. Polyethylene pellets with a sample/polyethylene ratio of 0.1 were used for the measurements in the far-IR region. FTIR powder spectra in the mid-IR region were recorded by means of an FTIR spectrometer equipped with a TGS detector and a CsI microfocus accessory, in the far-IR region by means of an FTIR spectrometer equipped with a DTGS (FIR) detector. The FTIR powder spectra in the 1400–400 cm–1 region of Al-Si, Al-Ge, Ga-Ge mullite as well as of Rb aluminate and Rb gallate mullite are shown in Figure 17. The spectra of the Al-Si, Al-Ge and Ga-Ge mullites are characterised by three band groups labelled after Schneider (1981) (a), (b) and (c). For Al-Si mullite these band groups are centred in the 1200–1100, 1000–700 and 650–400 cm–1 regions, respectively. For Al-Ge mullite, group (a) bands are centred in the 1100–1000 cm–1 region, group (b) bands in the 950–650 cm–1 region and group (c) bands in the 600–400 cm–1 region. For Ga-Ge mullite the corresponding band systems are in the 1050–950, 850–600 and 550–400 cm–1 ranges. The spectra of the Rb-Al and Rb-Ga mullite-type compounds are characterised by the two band groups (b) and (c), centred in the 950–650/600–400 cm–1 range and in the 800–550/500–400 cm–1 range, respectively. The FTIR powder spectra for the end-members of the mullite-type K aluminate–Na aluminate binary and of intermediate compositions are presented in the left part of Figure 18, showing a slight but significant and continuous change of their spectral features. Analogous to the Rb-Al compounds the spectra are characterised by band groups (b) and (c) centred in the 950–650 and 600–400 cm–1 region. It is evidently seen that the bands of the Na-Al compound are more structured than those of the K-Al compound, indicating structural changes due to the split Na site. The FTIR powder spectra in the 450–50 cm–1 region of the K aluminate–Na aluminate series, shown in the right part of Figure 18, also reveal more structured bands in the Na dominated aluminate compounds. On the basis of clearly observable band maxima and shoulders, the deconvolution of the absorption features of Al-Si mullite requires a minimum of 10 fitted bands, that of Al-Ge and Ga-Ge mullite of nine fitted bands (Fig. 19) with values of absorption maxima given in Table 3. In contrast to the Al-Ge and Ga-Ge compounds the Al-Si mullite shows an additional band in the group (a) band system. The spectrum of K aluminate mullite requires a minimum of nine fitted bands, that of Na aluminate mullite 10 bands (Fig. 20). A band notation with capital letters A–I is related to the fitted spectrum of Al-Si mullite. Bands A and B belong to band group (a), bands C–F to band group (b) and G–I to band group (c). Al-Ge and Ga-Ge mullite reveal a strong shift for A and B bands to lower wavenumbers; these bands are completely lacking in the alkaline aluminate and Rb gallate spectra (Figs. 17, 18). A strong shift to lower wavenumbers is also evident for the band groups (b) and (c) in the spectra of Ga-Ge mullite and Rb gallate, compared to equivalent bands of Al-Si, Al-Ge mullite and the alkaline aluminate compounds. Only slight changes of the wavenumbers for the D–F bands can be observed for Al-Si, alkaline aluminate and Al-Ge mullites. For the Ga bearing compounds, the G and H bands are significantly shifted to lower wavenumbers compared to the Al bearing compounds. The detailed trends of the band shift are plotted on the correlation diagram given in Figure 21.

Fig. 17.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Rb-Al, Al-Ge, Ga-Ge and Rb-Ga mullites. The spectra are subdivided in three band groups (a), (b) and (c), marked by the shaded areas (Voll et al., 2002). For band positions see Table 2. The sharp weak bands around 1375 and 985 cm–1, marked by asterisks, are due to stretching vibrations of residual nitrate groups of the starting material used for the synthesis.

Fig. 17.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Rb-Al, Al-Ge, Ga-Ge and Rb-Ga mullites. The spectra are subdivided in three band groups (a), (b) and (c), marked by the shaded areas (Voll et al., 2002). For band positions see Table 2. The sharp weak bands around 1375 and 985 cm–1, marked by asterisks, are due to stretching vibrations of residual nitrate groups of the starting material used for the synthesis.

Fig. 18.

FTIR powder spectra for members of the K aluminate (0Na1K)–Na aluminate (1Na0K) mullite-type binary in the 1400–400 cm–1 range (left part) and in the 450–50 cm–1 range (right part) (after Voll et al., 2002).

Fig. 18.

FTIR powder spectra for members of the K aluminate (0Na1K)–Na aluminate (1Na0K) mullite-type binary in the 1400–400 cm–1 range (left part) and in the 450–50 cm–1 range (right part) (after Voll et al., 2002).

Fig. 19.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Al-Ge and Ga-Ge mullite, deconvoluted into single Gaussian-shaped bands A–I (Voll et al., 2001). For positions of band maxima see Table 3. The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17.

Fig. 19.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Al-Ge and Ga-Ge mullite, deconvoluted into single Gaussian-shaped bands A–I (Voll et al., 2001). For positions of band maxima see Table 3. The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17.

FTIR single-crystal spectroscopy

For single-crystal measurements with transmitted non-polarised and polarised light, two slabs oriented parallel to (100) and (001) from the mullite single crystal were cut and coplanar, self-supporting plates with a thickness of about 100 μm were produced. Further thinning to a final thickness of 3 μm was provided by ion milling. The FTIR single-crystal spectra were recorded with a rectangular sample aperture of 50 × 30 μm2 on a FTIR microscope equipped with 0.60 numerical aperture mirror lenses (Cassegrains), a liquid nitrogen cooled MCT detector and a gold wire grid polariser. Polarised single-crystal spectra in the 1400–600 cm–1 range of the oriented Al-Si 2:1 mullite slabs are shown in Figure 22. The strongly orientation-dependent bands can be largely correlated with bands (A–H) of the powder spectrum. Group (a) bands are strongly polarised parallel to [100] and [010] and show no essential component parallel to [001]. The presence of a third group (a) band on the low-wavenumber side (B’) is confirmed by the polarised single-crystal spectra. The three bands are centred at 1161, 1135 and 1116 cm–1. Apparently, bands C and D show minimum absorption when the vector E of the polarised radiation vibrates parallel to [001]; band C has also a minor component parallel to [100], band D has an essential component parallel to [010]. The maximum of the C band is centred around 970 cm–1, the D band shows a maximum at around 890 cm–1. An additional band, not revealed by the powder spectra, is centred at 1040 cm–1. Probably this band is caused by an additional Si–O stretching mode. Compared to the powder spectrum, band E is significantly shifted to lower wavenumbers with maximum absorption in the [100] spectrum centred at 800 cm–1. This band has also a significant component parallel to [001]. Band F is polarised parallel to [010] and shows a maximum at 720 cm–1. The generally observed differences in the band positions and intensities between single-crystal and powder spectra are probably caused by coupling of vibration frequencies and are also inherent in the preparation characteristics. Apparently the shape of the powder grains did not resemble that of spherules, which influences diffuse reflection and which could be responsible for a shift of the absorption maxima. Also the grain size could influence the position of absorption maxima.

Table 3.

Notation of band groups and individual bands with wavenumber positions in cm–1 for the mullite-type compounds Al-Si mullite (Al-Si), Na aluminate (Na-Al), K aluminate (K-Al), Rb aluminate (Rb-Al), Al-Ge mullite (Al-Ge), Ga-Ge mullite (Ga-Ge) and Rb gallate (Rb-Ga). Band assignment is related to the band positions of Al-Si mullite (“stretch”: stretching vibration, “bend”: bending vibration, “in-plan” and “out-of-plan” vibrations are related to the (001) plane of the mullite structure).

Band groupBand notationAl-SiNa-AlK-AlRb-AlAl-GeGa-GeRb-GaBand assignment

A116810681010Si–O stretch (SiO4), in–plane
(a)B11311034978Si–O stretch (SiO4), in–plane
B’1107

C988889831Si–O stretch (SiO4), out–of–plane
D”791
D909876868864831735726Al–O stretch (AlO4), out–of–plane
(b)D’858842821
E828772761762779673671Al–O stretch (AlO4), in–plane
F”739730734
F737702699699709620611T–O–T bend (TO4), in–plane
F’656552

G620623629629593549514O–Al–O bend (AlO4)
H”582583584
(c)h578538538536541493454Al–O stretch (AlO6)
I482482484485469O–Si–O bend (SiO4) and Al–O–Al bend (AlO6)
Band groupBand notationAl-SiNa-AlK-AlRb-AlAl-GeGa-GeRb-GaBand assignment

A116810681010Si–O stretch (SiO4), in–plane
(a)B11311034978Si–O stretch (SiO4), in–plane
B’1107

C988889831Si–O stretch (SiO4), out–of–plane
D”791
D909876868864831735726Al–O stretch (AlO4), out–of–plane
(b)D’858842821
E828772761762779673671Al–O stretch (AlO4), in–plane
F”739730734
F737702699699709620611T–O–T bend (TO4), in–plane
F’656552

G620623629629593549514O–Al–O bend (AlO4)
H”582583584
(c)h578538538536541493454Al–O stretch (AlO6)
I482482484485469O–Si–O bend (SiO4) and Al–O–Al bend (AlO6)
Fig. 20.

FTIR powder spectra in the 1400–400 cm–1 range of K-Al and Na-Al mullites, deconvoluted into single Gaussian-shaped bands D–I (Voll et al., 2002). The band notation corresponds to that of Figure 19. For positions of band maxima see Table 3.

Fig. 20.

FTIR powder spectra in the 1400–400 cm–1 range of K-Al and Na-Al mullites, deconvoluted into single Gaussian-shaped bands D–I (Voll et al., 2002). The band notation corresponds to that of Figure 19. For positions of band maxima see Table 3.

Fig. 21.

Relation diagram showing the band position of absorption bands A–I of Al-Si mullite and mullite-type compounds Na aluminate (Na-Al), K aluminate (K-Al), Rb aluminate (Rb-Al), Al-Ge mullite (Al-Ge), Ga-Ge mullite (Ga-Ge) and Rb gallate (Rb-Ga) (Voll et al., 2002).

Fig. 21.

Relation diagram showing the band position of absorption bands A–I of Al-Si mullite and mullite-type compounds Na aluminate (Na-Al), K aluminate (K-Al), Rb aluminate (Rb-Al), Al-Ge mullite (Al-Ge), Ga-Ge mullite (Ga-Ge) and Rb gallate (Rb-Ga) (Voll et al., 2002).

Fig. 22.

Polarised FTIR spectra of oriented ultrathin 2:1 Al-Si mullite single-crystal slabs, deconvoluted into single Gaussian-shaped bands, and compared with a non-polarised FTIR single-crystal spectrum (top: dashed line) and an FTIR powder spectrum (top: full line), which corresponds to that of Figure 19. The spectra with E vibrating parallel to [100] and [010] were measured on a (001) slab, the spectrum with E parallel to [001] was measured on a (100) slab, both 3 μm thick. Vertical dotted lines indicate band positions (Voll et al., 2001).

Fig. 22.

Polarised FTIR spectra of oriented ultrathin 2:1 Al-Si mullite single-crystal slabs, deconvoluted into single Gaussian-shaped bands, and compared with a non-polarised FTIR single-crystal spectrum (top: dashed line) and an FTIR powder spectrum (top: full line), which corresponds to that of Figure 19. The spectra with E vibrating parallel to [100] and [010] were measured on a (001) slab, the spectrum with E parallel to [001] was measured on a (100) slab, both 3 μm thick. Vertical dotted lines indicate band positions (Voll et al., 2001).

The absorption behaviour is in good agreement with the data published by Rüscher (1996) on the basis of polarised reflection spectra of 2:1 mullite. The reported band positions for the high-energy triplet are at 1162, 1133 and 1108 cm–1. The band at 1040 cm–1 is only weakly recognisable in the reflection spectra. The C, D, E and F bands are centred at 978, 900, 795 and 723 cm–1, respectively. Slight differences between the spectra measured in transmittance and in reflectance also exist in the relative band intensities. Polarised OH absorption spectra of mullite single-crystal plates hydroxylated at 1600 °C in an Ar/H2O gas mixture at 100 kPa were reported by Rüscher et al. (2002).

Interpretation of the FTIR spectra

The strong shift of group (a) absorption bands in going from Si to Ge mullites along with the complete lack of group (a) bands in alkaline aluminate and gallate mullite-type compounds clearly proves their assignment to Si-O or Ge-O stretching vibrations of the SiO4 or GeO4 tetrahedral units in Al-Si, Al-Ge and Ga-Ge mullites. The similar behaviour of band C and its relatively weak intensity indicates that this band is also caused by Si-O and Ge-O stretching vibrations (Table 3). The band shift perfectly agrees with the increase of the mean T–O distances of Al-Ge and Ga-Ge mullite as compared to that of Al-Si mullite (Voll et al., 2001). The lack of an absorption component of group (a) bands in the polarised single-crystal spectra parallel to [001] (Fig. 22) is interpreted as a result of bands A and B (and B’ in Al-Si mullite) being essentially determined by high-energy stretching vibrations, as can be expected from the extremely short Si(Ge)–Oc tetrahedral bond within (001). According to the structural refinement of sillimanite by Winter & Ghose (1979) the Si–Oc distance amounts to 1.574 Å. From the close relationship with the crystal structure of sillimanite and with its absorption spectrum (Fig. 23), a very similar distance can be expected also for the distorted structure of mullite. The lack of significant absorption bands at around 1000 cm–1 in the alkaline aluminates and Rb gallate confirms this assignment. The weak but broad absorption in K and Na aluminate spectra centred around 1050 cm–1 could be explained by the first overtone of the strong absorption in the 530 cm–1 region (Fig. 20). Derived from the fact that the intensity ratio (1130/1170 cm–1), which is equivalent to the B/A band ratio, strongly increases with an increasing Al2O3 content (Cameron, 1977; Rüscher et al., 1996), it is a possible conclusion that the B band is related to the Si–O stretching vibration in the tetrahedral T3O groupings of the mullite structure, indicating that a significant amount of Si enters the tricluster units. Models for different Si configurations in the triclusters were also discussed, providing a changing intensity distribution of the group (a) bands without changing the chemistry (Rüscher, 2001). The similar shift behaviour of band C with that of group (a) bands and its relatively weak intensity indicates that this band is also determined by tetrahedral stretching vibrations. Its strong component parallel to [001] is probably due to Si–O stretching modes vibrating roughly along the direction of the tetrahedral double chains, e.g. the elongated Od–T–Od bonds connecting the edge sharing MO6 polyhedra along the c axis.

The IR spectra of α-Al2O3 (corundum) with Al solely in octahedral coordination and of γ-Al2O3 with Al in octahedral and tetrahedral coordination show that octahedrally coordinated Al causes absorptions in the range of 650–450 cm–1 while bands associated with tetrahedrally coordinated Al appear in the 900–750 cm–1 range (Tarte, 1965). The structural parameters (Voll et al., 2001) imply a strong decrease of vibrational force constants from the Al-Si to the Al-Ge and to the Ga-Ge mullite due to the strong increase of the respective cation-oxygen distances. From the strong shift of group (b) and (c) bands of the Ga-Ge mullite, it is concluded that the bands D and E belong to stretching vibrations of Al and Ga on T sites. The pleochroic behaviour of the D band, which is polarised essentially parallel to [001], and of the E band, polarised essentially parallel to [100], is in agreement with Al(Ga)–O stretching vibrations along the tetrahedral chain axis and with Al(Ga)–O stretching modes occurring essentially parallel to the direction of the a axis. The F band with its most intense component parallel to [010] is attributed to T–O–T bending vibrations of the TO4 tetrahedra. It is possible that the relatively strong intensity of the F band in Al-Si and Ga-Ge mullite reflects the assumed mixed occupancy of Al/Si and Ga/Ge on the T site (Voll et al., 2001).

Fig. 23.

FTIR powder spectrum of Al-Si mullite with band assignment A–I (dotted line), compared with the powder spectrum of sillimanite (continuous line). The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17 (Voll et al., 2001).

Fig. 23.

FTIR powder spectrum of Al-Si mullite with band assignment A–I (dotted line), compared with the powder spectrum of sillimanite (continuous line). The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17 (Voll et al., 2001).

The predominant band H of group (c) bands is assigned to stretching vibrations of the M cations in the octahedral coordination. This is in accordance with the continuous change of the polyhedral bond angles due to an elongation of the octahedral chain along the c axis with a reduction of the length of Oab–Oab common edges and an increase of the Oab–Oab bond lengths along [001]. The G band which is strongly overlapped by band H is assigned to O–Al(Ga)–O bending vibrations of the respective tetrahedra and band I to O–Si(Ge)–O bending vibrations of the tetrahedral units. Probably this band is influenced by M–O–M bending vibrations of the respective octahedra.

The quite similar positions of group (b) and (c) bands for the Al-Si, Al-Ge and alkaline aluminate mullites on the one hand and their similar positions for the Ga-Ge and Rb gallate mullites on the other hand, indicate that these bands are due to vibrations of Al–O and Ga–O, respectively. The higher-energy band group (b) must be essentially determined by Al–O or Ga–O stretching vibrations of the tetrahedral TO4 units. It is interesting to note that the deconvolution procedure yields a splitting of D, F and H bands of the alkaline aluminates into doublet and even triplet bands. The significant differences in the absorption pattern of K aluminate and Na aluminate, both phases crystallising in space group Pbam (Fischer et al., 2001), can be explained by the presence of one K site, but of a split Na site with two symmetrically equivalent Na atoms. The continuous change of the spectra in the mid-IR and far-IR region (Fig. 18) clearly indicates and supports the idea that K and Na aluminate mullites form a continuous solid solution series. In band group (c) the band positions of the alkaline aluminates perfectly agree with the bands of the Al-Si and Al-Ge mullites and there is also a good agreement in the band position between Rb gallate and Ga-Ge mullite. Obviously, this lower energetic band group is essentially caused by M–O vibrations of the octahedral MO6 units. The slightly but significantly lower wavenumbers of the D and especially of the E and F bands in the alkaline aluminates could be explained by the greater number of larger sized T*O4 tetrahedra contributing to the stretching vibrations of the tetrahedral units. Probably the relatively strong intensity of the F band in the alkaline aluminates and gallate is related to the high T3O cluster concentration in these compounds (Fischer et al., 2001; Voll et al., 2001). The band shifts due to the replacement of Si by Ge agree with the significant increase of the mean T–O distance of Al-Ge and Ga-Ge mullite as compared to that of Al-Si mullite and the same holds for the replacement of Al by Ga determining the strong increase of the mean M–O distances from Al-Ge to Ga-Ge mullite.

Conclusion

Considering the results obtained from the studies on the mullite-type compounds along with the polarised single-crystal IR spectroscopic study of 2:1 Al-Si mullite by Voll et al. (2001, 2002), the IR band assignment can be set on a new base. A and B bands of band group (a) are assigned to Si–O stretching vibrations within the (001) plane (“inplan” vibration; Table 3) and band C to Si–O stretching vibrations roughly perpendicular to this plane (“out-of-plan” vibration). Bands D and E of band group (b) are related to the stretching modes of AlO4 tetrahedra vibrating essentially parallel and perpendicular to the tetrahedral chain axis, respectively. Band F is assigned to T–O–T bending vibrations of the tetrahedral units with a strong influence of the T3O triclusters, especially in the aluminate and gallate compounds. Band G which is strongly influenced by band H is assigned to O–T–O bending vibrations of the tetrahedral units. The predominant band H of band group (c) is assigned to stretching vibrations of Al or Ga in the octahedral coordination. Apparently, band I is caused by both, O–Si–O bending vibrations of the SiO4 tetrahedra in Al-Si mullite and Al–O–Al bending vibrations of the octahedral units (Table 3).

The FTIR spectrum of sillimanite

On the basis of the present band assignment it is interesting to compare the IR spectrum of mullite with that of the structurally related sillimanite. Figure 23 demonstrates the close similarities between the sillimanite and the 3:2 Al-Si mullite spectrum. The irreducible representations for sillimanite (Salje & Werneke, 1982) explain the enhanced number of bands. On the basis of theoretical considerations we expect 40 IR-active modes (10B1u + 15B2u + 15B3u) compared to a reduced number of 22 for an “ideal” mullite with x = 0 (4B1u + 9B2u + 9B3u) (Michel et al., 1996) or 32 (6B1u + 13B2u + 13B3u) for a more adequate mullite structure (Rüscher, 1996).

From the comparison of the spectra it can be deduced that the “isolated” absorption centred at around 1200 cm–1 (i.e. group (a) bands) is solely caused by stretching vibrations of the structural SiO4 units which are determined by the very short Si–Oc distance of 1.574 Å in sillimanite (Winter & Ghose, 1979). The bands grouped in the 1000–650 cm–1 region must also be due to vibrations of tetrahedral units, essentially to stretching vibrations of AlO4 tetrahedra and to T–O–T bending vibrations. From the similar band positions of group (b) bands it can be concluded that the mean size of the SiO4 and AlO4 tetrahedra in mullite is very close to that of SiO4 and AlO4 in sillimanite with 1.627 and 1.763 Å, respectively (Winter & Ghose, 1979). Accordingly the mean T–O distances in the average Al-Si mullite structures determined by X-rays as 1.702 Å for 3:2 (Saalfeld & Guse, 1981) and 1.709 Å for 2:1 mullite (Voll et al., 2001) fit exactly between these values. The bands around 600 cm–1 are due to Al–O stretching vibrations of the AlO6 octahedral units. The practically identical size of the AlO6 octahedra in mullite and sillimanite with mean Al–O distances of 1.908 Å and 1.912 Å, respectively, is expressed by the almost identical position of band H. The sharp and splitted bands in the 550–450 cm–1 region are assigned to O–Si–O bending modes and Al–O–Al bending modes of the AlO6 octahedra. The two sharp sillimanite bands at 700 and 450 cm–1, not evident in the spectrum of mullite, must be exclusively controlled by Si-Al ordering effects over the T sites.

Appendix

How can we determine that for a tetrahedral TO4 group the vibrational degrees of freedom are

 

formula

First we have to know the meaning of the symbols. The capital A denotes vibrations that are symmetrical and B denotes vibrations that are anti-symmetrical with respect to a rotation about the principal axis of the atomic group. E and F are the symbols for doubly and triply degenerate vibrations. Subscripts g and u specify vibrations that are symmetrical and anti-symmetrical with respect to inversion, and the superscripts’ and “specify vibrations symmetrical and anti-symmetrical with respect to a mirror plane (e.g. Bg or A”). Now it is obvious that we have to expect nine vibrations (1 + 2 + 2·3 = 9). This number must agree with Equation 5 for the number of normal vibrational modes, but Equation A1 evidently contains additional information on the symmetry species of the vibrations.

Then we have to use the “point group character tabl” for point group Td to which the TO4 group refers and which is shown in Figure 24. In spectroscopy the Schoenflies notation is preferred: symbol I means identity and is required as a neutral symmetry element; Cp is the axis of rotation, where the subscript p denotes the order of the rotation; σ represents the symbol for a mirror plane with the subscripts h, v and d for horizontal, vertical and diagonal position, respectively. The symbol i stands for centre of inversion and Sp for an improper rotation axis. Symmetry operations can be described in form of matrices where the sum of the diagonal elements of a matrix, called the “character” of the matrix, is usually denoted as χ. Figure 25 shows the reducible matrix representation of the symmetry operations determining the point group Td. Character tables contain irreducible characters and represent the effects that symmetry operations have on the positions of vibrating atoms; they make the connections between the symmetry of an atomic group and the spectral behaviour of its vibrations. There are theorems which tell us how to find the characters for any irreducible representation of any point group. The respective character tables are given in many textbooks dealing with basics of spectroscopy (e.g. Fateley et al., 1972; Nakamoto, 1978; Wilson et al., 1980; Harris & Bertolucci, 1989).

Fig. 24.

Character table for the point group Td. Additional information is given in the last three lines (usually not contained in the character tables) with respect to the procedure of calculating the vibrational degrees of freedom.

Fig. 24.

Character table for the point group Td. Additional information is given in the last three lines (usually not contained in the character tables) with respect to the procedure of calculating the vibrational degrees of freedom.

Fig. 25.

Matrix representation of the symmetry operations used in the point group Td. Note the sum of the diagonal elements as the character of the matrix, specified in Figure 24 as “Contribution to χR”.

Fig. 25.

Matrix representation of the symmetry operations used in the point group Td. Note the sum of the diagonal elements as the character of the matrix, specified in Figure 24 as “Contribution to χR”.

In the upper first line of the character table for point group Td (Fig. 24), the number and the type of the symmetry operations are specified. The summed up number of symmetry operations represents the “order of the point group” (in the present example: 1 + 8 + 3 + 6 + 6 = 24). The first column comprises the classification of the symmetry species to which the normal vibrations can belong (see meaning of the symbols). Between the upper horizontal line and the column we find the array of the irreducible characters forumla.(+)1 means that a vibration is symmetrical with respect to the symmetry operation, i.e. the corresponding symmetry element remains intact during the vibration; –1 means that a vibration is antisymmetrical with respect to the symmetry operation, i.e. the symmetry element is lost during the vibration.

A fast way to define the distribution of the normal modes in dependence of their symmetry is to use the following equation:

 

formula

where ai is a positive integer that indicates the number of times the irreducible representation of the corresponding symmetry species appears in the reducible representation; R expresses the type of symmetry operations and g the number; h = Σg denotes the order of the point group. forumla represents the character of R in the irreducible representation, and χR the character of R in the reducible representation. This means that in addition to the information we derive from the point group character table, in order to get the reducible representation we have to know the character of the matrices of the respective symmetry operations presented in Figure 25. The values (sum of the diagonal elements) are specified in Figure 24 under “Contribution to χR” (3 0 –1 –1 1). Then we have to consider the number of atoms lying on each symmetry element, which corresponds to the number of atoms that are not shifted by the symmetry operations. These numbers, (5 2 1 1 3), are specified inFigure 24 under “Number of unshifted atoms”. We simply multiply the corresponding numbers, resulting in the values for the reducible representation χR (15 0 –1 –1 3).

Now we can start with the calculations according to Equation A2:

ai (A1) = 1/24 [(1·1·15) + (8·1·0) + (3·1·–1) + (6·1·–1) + (6·1·3)] = 1

ai (A2) = 1/24 [(1·1·15) + (8·1·0) + (3·1·–1) + (6·–1·–1) + (6·–1·3)] = 0

ai (E) = 1/24 [(1·2·15) + (8·–1·0) + (3·2·–1) + (6·0·–1) + (6·0·3)] = 1

ai (F1) = 1/24 [(1·3·15) + (8·0·0) + (3·–1·–1) + (6·1·–1) + (6·–1·3)] = 1

ai (F2) = 1/24 [(1·3·15) + (8·0·0) + (3·–1·–1) + (6·–1·–1) + (6·1·3)] = 3

Consequently, we obtain the total degrees of freedom (total number of vibrations)

 

formula

From the point group character tables it is found that the x, y, z translations (Tx, Ty, Tz) of the entire atomic group are triply degenerate and belong to the symmetry species F2, while the three degenerated rotational modes (Rx, Ry, Rz) belong to F1. The substraction of these six vibrations leaves, in accordance with Equation 5, the vibrational degrees of freedom for TO4 (total number of internal vibrations) as

 

formula

All vibrations are Raman active, only the 2F2 vibrations are IR active: correlating these results with the deductions made for the vibrational modes, one of the two triply degenerate F2 vibrations corresponds to v3 and the other to v4 (A1 corresponds to v1 and E to v2; Fig. 2).

Acknowledgements

Financial support by the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” is acknowledged.

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Figures & Tables

Fig. 1.

Normal vibrations of the H2O and CO2 molecules. v1 represents the symmetric stretching and v3 the asymmetric stretching vibration, v2 represents the bending vibration. v2a and v2b are doubly degenerate bending vibrations of CO2.

Fig. 1.

Normal vibrations of the H2O and CO2 molecules. v1 represents the symmetric stretching and v3 the asymmetric stretching vibration, v2 represents the bending vibration. v2a and v2b are doubly degenerate bending vibrations of CO2.

Fig. 2.

Normal modes of vibration of a tetrahedral TO4 group. v1 and v3 represent the symmetric and asymmetric stretching modes, respectively, v2 and v4 the corresponding bending vibrations.

Fig. 2.

Normal modes of vibration of a tetrahedral TO4 group. v1 and v3 represent the symmetric and asymmetric stretching modes, respectively, v2 and v4 the corresponding bending vibrations.

Fig. 3.

Analytical water contents (open symbols) and weight losses (full symbols) in wt% for cordierite (triangle), mullite type I (circle) and mullite type III (square) precursors, as-prepared (150 °C dried) and preheated at temperatures from 200 to 1000 °C in intervals of 100 °C (after Beran et al., 2001 and Voll & Beran, 2002).

Fig. 3.

Analytical water contents (open symbols) and weight losses (full symbols) in wt% for cordierite (triangle), mullite type I (circle) and mullite type III (square) precursors, as-prepared (150 °C dried) and preheated at temperatures from 200 to 1000 °C in intervals of 100 °C (after Beran et al., 2001 and Voll & Beran, 2002).

Fig. 4.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared cordierite precursor and the cordierite precursors preheated at temperatures from 200 to 1000 °C, forming μ-cordierite at 900 °C and α-cordierite at 1000 °C (Voll & Beran, 2002).

Fig. 4.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared cordierite precursor and the cordierite precursors preheated at temperatures from 200 to 1000 °C, forming μ-cordierite at 900 °C and α-cordierite at 1000 °C (Voll & Beran, 2002).

Fig. 5.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type I precursor and the type I precursors preheated at temperatures from 200 to 1000 °C, forming mullite at 1000 °C.

Fig. 5.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type I precursor and the type I precursors preheated at temperatures from 200 to 1000 °C, forming mullite at 1000 °C.

Fig. 6.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type III precursor and the type III precursors preheated at temperatures from 200 to 1000 °C. Note that no mullite formation occurs at 1000 °C.

Fig. 6.

FTIR powder spectra in the 4000–400 cm–1 range of the as-prepared mullite type III precursor and the type III precursors preheated at temperatures from 200 to 1000 °C. Note that no mullite formation occurs at 1000 °C.

Fig. 7.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared cordierite precursor and the precursors preheated from 200 to 1000 °C (Voll & Beran, 2002).

Fig. 7.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared cordierite precursor and the precursors preheated from 200 to 1000 °C (Voll & Beran, 2002).

Fig. 8.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared mullite type I precursor and the precursors preheated from 200 to 900 °C (after Voll et al., 1998).

Fig. 8.

FTIR powder spectra in the 5500–4000 cm–1 range of the as-prepared mullite type I precursor and the precursors preheated from 200 to 900 °C (after Voll et al., 1998).

Fig. 9.

Absorbance values of as-prepared and preheated cordierite (open triangle), mullite type I (full circle) and mullite type III (open square) precursors for the H2O combination band (upper part) and for the M–OH combination band (lower part) (after Voll et al., 1998, Beran et al., 2001 and Voll & Beran, 2002).

Fig. 9.

Absorbance values of as-prepared and preheated cordierite (open triangle), mullite type I (full circle) and mullite type III (open square) precursors for the H2O combination band (upper part) and for the M–OH combination band (lower part) (after Voll et al., 1998, Beran et al., 2001 and Voll & Beran, 2002).

Fig. 10.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 500, 700 and 800 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands I–IV (Voll & Beran, 2002). Note the different absorbance scales. For band notation and band positions see Table 2.

Fig. 10.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 500, 700 and 800 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands I–IV (Voll & Beran, 2002). Note the different absorbance scales. For band notation and band positions see Table 2.

Fig. 11.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 700 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands I–IV (after Voll et al., 1998 and Beran et al., 2001). Note the different absorbance scales. For band notation and band positions see Table 2.

Fig. 11.

FTIR powder spectra in the (H2O,OH) stretching vibrational region of as-prepared and 700 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands I–IV (after Voll et al., 1998 and Beran et al., 2001). Note the different absorbance scales. For band notation and band positions see Table 2.

Fig. 12.

FTIR powder spectra in the lattice vibrational region of as-prepared and 700, 800 and 900 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands A–G (Voll & Beran, 2002). For band notation and band positions see Table 2.

Fig. 12.

FTIR powder spectra in the lattice vibrational region of as-prepared and 700, 800 and 900 °C treated cordierite precursors, deconvoluted into single Gaussian-shaped bands A–G (Voll & Beran, 2002). For band notation and band positions see Table 2.

Fig. 13.

FTIR powder spectra in the lattice vibrational region of as-prepared and 800 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands A–G. For band notation and band positions see Table 2.

Fig. 13.

FTIR powder spectra in the lattice vibrational region of as-prepared and 800 and 900 °C treated mullite type I (left part) and mullite type III precursors (right part), deconvoluted into single Gaussian-shaped bands A–G. For band notation and band positions see Table 2.

Fig. 14.

Diagram relating the preheating temperature and the wavenumber positions for bands A–G of the cordierite precursors. The isolated symbols present the wavenumber positions of bands B, C and E of the 900 °C treated sample (μ-cordierite) (after Voll & Beran, 2002). For band notation see Table 2.

Fig. 14.

Diagram relating the preheating temperature and the wavenumber positions for bands A–G of the cordierite precursors. The isolated symbols present the wavenumber positions of bands B, C and E of the 900 °C treated sample (μ-cordierite) (after Voll & Beran, 2002). For band notation see Table 2.

Fig. 15.

Diagram relating the preheating temperature and the wavenumber positions for Si–O stretching bands A and B of mullite type I (full circle) and mullite type III precursors (open square) (after Beran et al., 2001). For further band notation see Table 2.

Fig. 15.

Diagram relating the preheating temperature and the wavenumber positions for Si–O stretching bands A and B of mullite type I (full circle) and mullite type III precursors (open square) (after Beran et al., 2001). For further band notation see Table 2.

Fig. 16.

Schematic representation of the average structure of mullite along the c axis.

Fig. 16.

Schematic representation of the average structure of mullite along the c axis.

Fig. 17.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Rb-Al, Al-Ge, Ga-Ge and Rb-Ga mullites. The spectra are subdivided in three band groups (a), (b) and (c), marked by the shaded areas (Voll et al., 2002). For band positions see Table 2. The sharp weak bands around 1375 and 985 cm–1, marked by asterisks, are due to stretching vibrations of residual nitrate groups of the starting material used for the synthesis.

Fig. 17.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Rb-Al, Al-Ge, Ga-Ge and Rb-Ga mullites. The spectra are subdivided in three band groups (a), (b) and (c), marked by the shaded areas (Voll et al., 2002). For band positions see Table 2. The sharp weak bands around 1375 and 985 cm–1, marked by asterisks, are due to stretching vibrations of residual nitrate groups of the starting material used for the synthesis.

Fig. 18.

FTIR powder spectra for members of the K aluminate (0Na1K)–Na aluminate (1Na0K) mullite-type binary in the 1400–400 cm–1 range (left part) and in the 450–50 cm–1 range (right part) (after Voll et al., 2002).

Fig. 18.

FTIR powder spectra for members of the K aluminate (0Na1K)–Na aluminate (1Na0K) mullite-type binary in the 1400–400 cm–1 range (left part) and in the 450–50 cm–1 range (right part) (after Voll et al., 2002).

Fig. 19.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Al-Ge and Ga-Ge mullite, deconvoluted into single Gaussian-shaped bands A–I (Voll et al., 2001). For positions of band maxima see Table 3. The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17.

Fig. 19.

FTIR powder spectra in the 1400–400 cm–1 range of Al-Si, Al-Ge and Ga-Ge mullite, deconvoluted into single Gaussian-shaped bands A–I (Voll et al., 2001). For positions of band maxima see Table 3. The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17.

Fig. 20.

FTIR powder spectra in the 1400–400 cm–1 range of K-Al and Na-Al mullites, deconvoluted into single Gaussian-shaped bands D–I (Voll et al., 2002). The band notation corresponds to that of Figure 19. For positions of band maxima see Table 3.

Fig. 20.

FTIR powder spectra in the 1400–400 cm–1 range of K-Al and Na-Al mullites, deconvoluted into single Gaussian-shaped bands D–I (Voll et al., 2002). The band notation corresponds to that of Figure 19. For positions of band maxima see Table 3.

Fig. 21.

Relation diagram showing the band position of absorption bands A–I of Al-Si mullite and mullite-type compounds Na aluminate (Na-Al), K aluminate (K-Al), Rb aluminate (Rb-Al), Al-Ge mullite (Al-Ge), Ga-Ge mullite (Ga-Ge) and Rb gallate (Rb-Ga) (Voll et al., 2002).

Fig. 21.

Relation diagram showing the band position of absorption bands A–I of Al-Si mullite and mullite-type compounds Na aluminate (Na-Al), K aluminate (K-Al), Rb aluminate (Rb-Al), Al-Ge mullite (Al-Ge), Ga-Ge mullite (Ga-Ge) and Rb gallate (Rb-Ga) (Voll et al., 2002).

Fig. 22.

Polarised FTIR spectra of oriented ultrathin 2:1 Al-Si mullite single-crystal slabs, deconvoluted into single Gaussian-shaped bands, and compared with a non-polarised FTIR single-crystal spectrum (top: dashed line) and an FTIR powder spectrum (top: full line), which corresponds to that of Figure 19. The spectra with E vibrating parallel to [100] and [010] were measured on a (001) slab, the spectrum with E parallel to [001] was measured on a (100) slab, both 3 μm thick. Vertical dotted lines indicate band positions (Voll et al., 2001).

Fig. 22.

Polarised FTIR spectra of oriented ultrathin 2:1 Al-Si mullite single-crystal slabs, deconvoluted into single Gaussian-shaped bands, and compared with a non-polarised FTIR single-crystal spectrum (top: dashed line) and an FTIR powder spectrum (top: full line), which corresponds to that of Figure 19. The spectra with E vibrating parallel to [100] and [010] were measured on a (001) slab, the spectrum with E parallel to [001] was measured on a (100) slab, both 3 μm thick. Vertical dotted lines indicate band positions (Voll et al., 2001).

Fig. 23.

FTIR powder spectrum of Al-Si mullite with band assignment A–I (dotted line), compared with the powder spectrum of sillimanite (continuous line). The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17 (Voll et al., 2001).

Fig. 23.

FTIR powder spectrum of Al-Si mullite with band assignment A–I (dotted line), compared with the powder spectrum of sillimanite (continuous line). The subdivision in the three band groups (a), (b) and (c) corresponds to that of Figure 17 (Voll et al., 2001).

Fig. 24.

Character table for the point group Td. Additional information is given in the last three lines (usually not contained in the character tables) with respect to the procedure of calculating the vibrational degrees of freedom.

Fig. 24.

Character table for the point group Td. Additional information is given in the last three lines (usually not contained in the character tables) with respect to the procedure of calculating the vibrational degrees of freedom.

Fig. 25.

Matrix representation of the symmetry operations used in the point group Td. Note the sum of the diagonal elements as the character of the matrix, specified in Figure 24 as “Contribution to χR”.

Fig. 25.

Matrix representation of the symmetry operations used in the point group Td. Note the sum of the diagonal elements as the character of the matrix, specified in Figure 24 as “Contribution to χR”.

Table 1.

Characteristic group frequencies in cm–1 of functional atomic groups relevant for common minerals (after Farmer, 1974; Nakamoto, 1978).

GroupStretching vibrationsBending vibrationsGroupStretching vibrationsBending vibrations

MOH3700–29001300–400POforumla1100–950600–550
H2O3700–29001650–1600SiOforumla1000–800550–400
COforumla1600–1300950–650SixOforumla1200–900800–400
NOforumla1500–1250900–700AsOforumla900–750400
BOforumla1300–1200800–600VOforumla900–750400
SOforumla1200–1050700–600WOforumla850–750350–300
GroupStretching vibrationsBending vibrationsGroupStretching vibrationsBending vibrations

MOH3700–29001300–400POforumla1100–950600–550
H2O3700–29001650–1600SiOforumla1000–800550–400
COforumla1600–1300950–650SixOforumla1200–900800–400
NOforumla1500–1250900–700AsOforumla900–750400
BOforumla1300–1200800–600VOforumla900–750400
SOforumla1200–1050700–600WOforumla850–750350–300
Table 2.

Band notation, band positions in cm–1 and band assignment to dominating vibrational modes of cordierite precursors, mullite type I and mullite type III precursors from as-prepared samples (as-prep) and samples preheated at 500, 800 °C (cordierite precursors) and 900 °C (mullite precursors), respectively (“stretch”: stretching vibration, “bend”: bending vibration).

Band notationCordierite Band assignmentMullite type IMullite type III
Band assignmentBand positionsBand assignment
as-prep.500 °C800 °Cas-prep.900 °Cas-prep.900 °C

I358435833580OH stretch3588353435743580OH stretch
II341534343428H2O stretch3435342634343434H2O stretch
III321632353234OH stretch3220313532283217OH stretch
IV304730403072H2O stretch2999290830003000H2O stretch
A113711501187Si–O stretch (SiO4)1104116211171135Si–O stretch (SiO4)
B102010251085Si–O stretch (SiO4)1005106210141028Si–O stretch (SiO4)
C872886926Al–O stretch (AlO4)858865863868Al–O stretch (AlO4)
D792Al–O stretch (AlO4)772Al–O stretch (AlO4)
E710727695(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend702678711721(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend
F572583572Al–O stretch (AlO6) + O–Al–O bend (AlO4)567558576571Al–O stretch (AlO6) + O–Al–O bend (AlO4)
G437441433Mg–O stretch (MgO6) + O–Si–O bend (SiO4)441433449450O–Si–O bend (SiO4)
Band notationCordierite Band assignmentMullite type IMullite type III
Band assignmentBand positionsBand assignment
as-prep.500 °C800 °Cas-prep.900 °Cas-prep.900 °C

I358435833580OH stretch3588353435743580OH stretch
II341534343428H2O stretch3435342634343434H2O stretch
III321632353234OH stretch3220313532283217OH stretch
IV304730403072H2O stretch2999290830003000H2O stretch
A113711501187Si–O stretch (SiO4)1104116211171135Si–O stretch (SiO4)
B102010251085Si–O stretch (SiO4)1005106210141028Si–O stretch (SiO4)
C872886926Al–O stretch (AlO4)858865863868Al–O stretch (AlO4)
D792Al–O stretch (AlO4)772Al–O stretch (AlO4)
E710727695(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend702678711721(Si,Al)–O–(Si,Al) bend + (Si,Al)–OH bend
F572583572Al–O stretch (AlO6) + O–Al–O bend (AlO4)567558576571Al–O stretch (AlO6) + O–Al–O bend (AlO4)
G437441433Mg–O stretch (MgO6) + O–Si–O bend (SiO4)441433449450O–Si–O bend (SiO4)
Table 3.

Notation of band groups and individual bands with wavenumber positions in cm–1 for the mullite-type compounds Al-Si mullite (Al-Si), Na aluminate (Na-Al), K aluminate (K-Al), Rb aluminate (Rb-Al), Al-Ge mullite (Al-Ge), Ga-Ge mullite (Ga-Ge) and Rb gallate (Rb-Ga). Band assignment is related to the band positions of Al-Si mullite (“stretch”: stretching vibration, “bend”: bending vibration, “in-plan” and “out-of-plan” vibrations are related to the (001) plane of the mullite structure).

Band groupBand notationAl-SiNa-AlK-AlRb-AlAl-GeGa-GeRb-GaBand assignment

A116810681010Si–O stretch (SiO4), in–plane
(a)B11311034978Si–O stretch (SiO4), in–plane
B’1107

C988889831Si–O stretch (SiO4), out–of–plane
D”791
D909876868864831735726Al–O stretch (AlO4), out–of–plane
(b)D’858842821
E828772761762779673671Al–O stretch (AlO4), in–plane
F”739730734
F737702699699709620611T–O–T bend (TO4), in–plane
F’656552

G620623629629593549514O–Al–O bend (AlO4)
H”582583584
(c)h578538538536541493454Al–O stretch (AlO6)
I482482484485469O–Si–O bend (SiO4) and Al–O–Al bend (AlO6)
Band groupBand notationAl-SiNa-AlK-AlRb-AlAl-GeGa-GeRb-GaBand assignment

A116810681010Si–O stretch (SiO4), in–plane
(a)B11311034978Si–O stretch (SiO4), in–plane
B’1107

C988889831Si–O stretch (SiO4), out–of–plane
D”791
D909876868864831735726Al–O stretch (AlO4), out–of–plane
(b)D’858842821
E828772761762779673671Al–O stretch (AlO4), in–plane
F”739730734
F737702699699709620611T–O–T bend (TO4), in–plane
F’656552

G620623629629593549514O–Al–O bend (AlO4)
H”582583584
(c)h578538538536541493454Al–O stretch (AlO6)
I482482484485469O–Si–O bend (SiO4) and Al–O–Al bend (AlO6)

Contents

GeoRef

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