quantitative raman spectroscopy: high...

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Journal of Non-Crystalline Solids 353 (2007) 4029–4042

Quantitative Raman spectroscopy: High-temperature speciationof potassium silicate melts

W.J. Malfait *, V.P. Zakaznova-Herzog, W.E. Halter

Institute of Isotope Geochemistry and Mineral Resources, ETH Zurich 8092, Zurich, Switzerland

Received 11 April 2007; received in revised form 12 June 2007Available online 1 August 2007

Abstract

In situ, high-temperature Raman spectroscopy was used to study the Qn speciation in binary potassium silicate melts. Over 300Raman spectra in the compositional range from 20 to 38 mol% K2O were collected at temperatures between 800 and 1200 K. Quanti-tative information on the relative abundances of species in melts was obtained from the Raman spectra through a quantification pro-cedure that does not require any a priori assumptions about the line shapes or external calibration of the Raman scatteringefficiencies for the various Qn species. The DH0 associated with the speciation reaction 2Q3 = Q4 + Q2 was found to be 33.1 ± 7.3 kJ/mol.� 2007 Elsevier B.V. All rights reserved.

PACS: 61.20.�p; 63.50.+x; 78.30.�j

Keywords: Raman scattering; Raman spectroscopy; Alkali silicates; Silicates; Structure; Short-range order; Thermodynamics

1. Introduction

Several decades of intense spectroscopic and diffractionstudies have demonstrated that the structure of silicateglasses and melts strongly influences their bulk properties[1,2]. It is also widely accepted that the structure of alkalisilicate melts and glasses at atmospheric pressure consistsof a three-dimensional network of SiO4 tetrahedra linkedby bridging oxygen atoms (BO). Addition of network mod-ifying cation oxides breaks up this network by generatingnon-bridging oxygen atoms (NBO). The short-range struc-ture of silicate glasses and melts can be described throughthe abundance of the different Qn species, where Q repre-sents a SiO4 tetrahedron and n is the number of bridgingoxygen atoms. The abundance of these Qn species is con-trolled by the following speciation reactions:

2Qn ¼ Qn�1 þ Qnþ1 ðn ¼ 3; 2; 1Þ: ð1Þ

0022-3093/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2007.06.031

* Corresponding author. Tel.: +41 44 6326137.E-mail address: [email protected] (W.J. Malfait).

Assuming that the activity coefficients are canceling out inthe speciation reaction, the equilibrium constants Kn ofreaction (1) are

Kn ¼½Qn�1� � ½Qnþ1�½Qn�2

:

The change in the Qn speciation of silicate melts as a func-tion of temperature, makes an important, albeit not domi-nant, contribution to the configurational heat capacity [3].Also, by using speciation information, Halter and Mysen[4] were able to model the phase diagram of the Na2O–SiO2 system. Furthermore, Malfait et al. [5] showed a linkbetween the speciation and the melt rheology in the K2O–SiO2 system. An accurate knowledge of the speciation insilicate melts, i.e. at high temperature, is thus an essentialprerequisite for any predictive model of the bulk meltproperties.

The abundances of the Qn species in alkali silicateglasses can be quantified by 29Si NMR spectroscopy [6].Unfortunately, in situ measurements of the speciation insilicate melts, i.e. at high temperature, are difficult with

mailto:[email protected]

Top view

to Volt meter

Pt wire

to p

ower

sou

rce

to Volt meter

Side view

zoom 5x

Legend

insulator steelbrass

0 2 4 cm

Fig. 1. Schematic representation of high-temperature heating stage.

4030 W.J. Malfait et al. / Journal of Non-Crystalline Solids 353 (2007) 4029–4042

29Si NMR because of the rapid exchange of the speciescompared to the time scales of the NMR experiment [7].Brandriss and Stebbins [3] investigated the effect of temper-ature on reaction (1) by applying 29Si NMR to a set ofglasses prepared with different quench rates. They observedthat the equilibrium in reaction (1) is shifted to the rightwith increasing temperature. The uncertainties in theirstudy were large, however, because of the low 29Si NMRsensitivity and the limited range in fictive temperatures(�100 K).

Because of its high sensitivity and the relative ease toperform in situ measurements, Raman spectroscopy hasgreat potential for providing information on the effect oftemperature on the speciation. Particularly, the spectralregion from 800 to 1250 cm�1, where the stretching vibra-tions for the different Qn species are present, is very infor-mative. However, obtaining quantitative information fromthe Raman spectra is not straightforward. Several strate-gies have been employed that fit the spectra with Gaussiancurves and calibrate the relative Raman sensitivities for thedifferent species. Mysen and Frantz [8–10], Maehara et al.[11] and Yano et al. [12] calibrated the Raman sensitivitieswith NMR results. Umesaki et al. [13,14] and You et al.[15] obtained Raman efficiencies from mass balance consid-erations. McMillan et al. [16] only quantified the effect oftemperature on the speciation, but not the speciation itself.There are several severe limitations to this type of approachhowever: (i) the assumption of Gaussian line shapes hasnot been tested, in fact, Zotov et al. [17] observed distinctlynon-Gaussian partial Raman spectra for the Qn species intheir ab initio calculations; (ii) different band assignmentshave been used by different authors and (iii) different cali-bration factors have been obtained by different authors.In a companion paper [18], we have developed a robustmethod to quantify the speciation from Raman spectrathat does not depend on any a priori assumptions aboutthe positions and shapes of the bands for the different spe-cies. The method determines the equilibrium constant ofreaction (1) from a large set of spectra from different com-positions at a given temperature. We used this method todetermine the speciation of potassium silicate glasses atroom temperature and tested the validity of the approachby comparing the results to 29Si NMR data.

In the present study, we apply this method to Ramanspectra of potassium silicate melts in situ at different tem-peratures to quantify the abundance of species and changesas a function of temperature. The results provide the firstrobust measurement of the Qn speciation in silicate meltsover a wide range in temperature.

2. Experimental

We acquired Raman spectra for potassium silicate meltsover a wide range of compositions and temperatures byusing an evaporation method: the composition of a potas-sium rich melt was modified in situ, by evaporation ofpotassium at high temperature and Raman spectra were

collected at regular time intervals. The composition wasdetermined by comparison of the room temperature spec-tra to a set of calibration glasses.

2.1. High-temperature Raman stage

A custom-made wire-loop heating stage [19,20] was usedfor the in situ, high-temperature Raman measurements. Adrawing of the stage is shown in Fig. 1. A Pt wire (1 mm Ø)is put in place between two brass rods that are connected tothe power supply; the wire is flattened in the middle. Thesample is suspended in a 0.8 mm Ø hole that is drilledthrough the flattened area. The temperature is raised byresistive heating of the Pt wire by sending an alternatingcurrent through it. The voltage over the wire is measuredwith two 0.1 mm Ø Pt wires welded on both sides to the

Urea

KNO3

KINaCl

Na2SiO3

Li2SiO3

CaMgSi2O6

200 400 600 800 1000 1200

Voltage (mV)

400

600

800

1000

1200

1400

1600

Tem

pera

ture

(K

)

Fig. 2. Temperature calibration line: the data for known melting pointsamples is fitted by a second order polynomial. The standard deviationbetween the data and the fit is 8.5 K.

Time

TEvaporation TEvaporation

TRaman TRaman

RT

T

RTRTRTRT200

400

600

800

1000

1200

1400

1600

Tem

pera

ture

(K

)

Fig. 3. Schematic temperature profile for the collection of a series ofRaman spectra. The K2O content is decreased in a stepwise manner bydwells at Tevaporation. Room temperature (RT) and high-temperaturespectra (TRaman) are collected intermittently.

W.J. Malfait et al. / Journal of Non-Crystalline Solids 353 (2007) 4029–4042 4031

1 mm Ø wire. The contacts between the Pt wire and thebrass rods have to fulfill two criteria: the Pt wire has tobe easy to remove for cleaning in hydrofluoric acid betweenruns and the electrical contact has to be reproducible toallow a proper temperature calibration. The design asshown in Fig. 1 worked best to fulfill these conditions:the Pt wire is placed in a triangular groove in the brassrod and squeezed between the rod and a brass plate bytightening two screws. With these reproducible electricalcontacts, the temperature can be calibrated as a functionof the voltage across the Pt wire using samples with knownmelting point [10]. The following materials were used forthe calibration: urea (408 K), KNO3 (610 K), KI (954 K),NaCl (1073 K), Na2SiO3 (1361 K), Li2SiO3 (1474 K), diop-side (1664 K). Such a calibration curve is shown in Fig. 2.The standard deviation between the calibration points andthe fit is 8.5 K for this calibration.

Fig. 4. Evaporation of K2O from potassium silicate melts for two differentseries, in air at 1500 K. For each evaporation series, the evaporation timescorresponding to the composition of the calibration glasses are determinedby comparing their spectra to the spectra from the evaporation series (seeinset Raman spectra for an example). Then, the compositions for theRaman spectra from the evaporation series are determined from theexponential fit to the reference spectra (y = y0 + AÆe�x/t).

2.2. Sample preparation: evaporation method

In order to efficiently collect a large dataset of Ramanspectra for a given temperature, the evaporation methodof Zakaznova-Herzog et al. [18] was applied. The composi-tion of a potassium rich sample was changed purposely andcontinuously at high temperature (typically �1500 K) byevaporation of K2O; a schematic temperature profile fora high-temperature run is shown in Fig. 3. In order to col-lect the Raman spectra, the dwell at high temperature,TEvaporation, was interrupted ca. 40 times by turning offthe power to the wire furnace (estimated quench rate�100–200 K/s). In order to check for sample homogeneity,Raman spectra were collected from different spots of thesample: no differences between spectra from different spotswere observed. First, a room temperature spectrum is col-lected. The temperature was then raised to a fixed temper-ature TRaman (ranging from 793 to 1198 K) to collect a

high-temperature Raman spectrum. The sample wasquenched to room temperature again to verify no K2Owas lost during the acquisition phase. No evaporation ofpotassium was observed at temperatures below 1300 K.The evaporation series were done under the Raman probein the heating stage. The composition of the melts was cal-ibrated as a function of dwell time at high temperature(Fig. 4). For each evaporation series, the evaporation timescorresponding to the composition of the calibration glassesare determined by comparing their spectra to the roomtemperature spectra from the evaporation series (see inset


in Fig. 4 for an example). Then, the compositions for theRaman spectra from the evaporation series are obtainedfrom an exponential fit to the reference spectra (y = y0 +

AÆe�x/t). Different evaporation rates for different series areobserved, these are related to the sample size, with fasterevaporation from smaller samples. With this evaporation

Table 1Sample compositions, PCA results and equilibrium constants for the different

Series c d e

T (K) 1002 1002 1189

Spectra 1 24.97 24.62 27.022 26.29 24.97 27.303 27.73 25.39 27.60

K2O (mol%) 4 29.10 25.78 27.915 30.12 26.22 28.246 31.24 26.61 28.597 32.05 27.05 28.968 32.90 27.53 29.369 33.57 27.91 29.77

10 34.04 28.33 30.2111 34.52 28.71 30.5712 34.95 29.10 30.9613 35.27 29.52 31.3614 35.59 30.34 31.7715 35.79 30.74 32.2116 35.99 31.15 32.6717 36.19 31.59 33.0218 36.39 32.52 33.5219 36.60 32.89 33.9020 36.74 33.28 34.3021 36.88 33.68 34.6422 37.02 34.10 34.9923 37.16 34.53 35.2824 37.30 34.83 35.5725 37.44 35.13 35.8726 37.59 35.44 36.1027 37.66 35.76 36.3428 37.74 36.01 36.4929 37.81 36.26 36.6530 37.88 36.42 36.8131 37.96 36.59 36.9832 36.77 37.1433 36.94 37.3134 37.12 37.3935 37.30 37.4836 37.48 37.5637 37.66 37.6538 37.75 37.7339 37.8240 37.914142

Cumulative PCA results 1 94.41 92.40 93.832 99.70 99.58 99.753 99.94 99.93 99.944 99.96 99.96 99.965 99.98 99.97 99.97

Log K3 �2.16 �2.01 �1.76

No usable sets of high-temperature Raman spectra were collected for series a* Value for logK3 is very dependent on the used compositional interval.

** Compositions could not be accurately determined between 38 and 35 mol%

method, a set of spectra for 40 compositions and two tem-peratures (room temperature and TRaman) can be collectedin a day. A comprehensive set of Raman spectra, spanninga wide composition and temperature range, was acquired,the compositions and temperatures of which are given inTable 1 and shown in Fig. 5.

high-temperature Raman series

f g h i i* j**

855 1093 793 793 1189 1189

23.71 24.25 22.58 21.28 21.28 20.4623.95 24.26 22.78 21.88 21.88 21.0124.13 24.28 23.00 22.48 22.48 21.7424.35 24.31 23.23 23.12 23.12 22.4224.52 24.36 23.53 23.65 23.65 23.2724.72 24.42 23.78 24.26 24.26 23.9324.94 24.49 24.08 24.80 24.80 24.6925.19 24.58 24.44 25.41 25.41 25.3325.47 24.67 24.75 25.91 25.91 26.0425.80 24.77 25.10 26.44 26.44 26.8226.16 24.90 25.51 27.02 27.02 27.3926.58 25.06 25.97 27.65 27.65 28.0026.81 25.25 26.50 28.33 28.33 28.6527.05 25.49 27.11 28.81 28.81 29.3527.31 25.78 27.80 29.32 29.32 30.0927.59 26.14 28.59 29.85 29.85 30.4828.20 26.46 29.49 30.42 30.42 30.8928.89 26.84 30.16 31.01 31.01 31.3129.27 27.13 30.90 31.64 32.29 31.7429.67 27.45 31.70 32.29 32.64 32.1930.10 27.80 32.13 32.64 33.35 32.6530.56 28.19 32.57 32.99 33.72 33.1331.05 28.63 33.04 33.35 34.10 33.6331.57 29.11 33.53 33.72 34.49 34.1432.12 29.64 34.04 34.10 34.89 34.6733.34 29.93 34.57 34.49 35.30 34.9434.73 30.24 35.13 34.89 35.7235.49 30.56 36.33 35.72 36.3736.30 30.90 36.96 36.82 36.5937.16 31.25 36.15 36.82

31.63 36.37 37.0532.02 36.59 37.2832.44 36.8232.88 37.0533.34 37.2833.8334.3434.8835.4536.0536.6837.34

95.77 94.07 94.31 91.61 91.01 97.5799.69 99.66 99.40 99.27 99.51 99.8799.92 99.95 99.90 99.89 99.91 99.9399.95 99.98 99.97 99.97 99.96 99.9699.96 99.98 99.98 99.97 99.97 99.97

�2.43 �2.04 �2.60 �2.41 �2.60 �1.76

and b.

K2O due to irregular evaporation rate.

10 15 20 25 30 35 40 45 50

400

600

800

1000

1200

1400

1600

K2O (mol%)

Tem

pera

ture

(K

)

series c and d

series e, i and j

series f

series g

series h and i

Figures 6 & 14

¦¦v

(2007)

calibration glasseshigh temperature seriesevaporation series

Fig. 5. Compositions and temperatures for which Raman spectra werecollected, a comprehensive set of Raman spectra, spanning a wide range incompositions and temperatures, was collected.


2.3. Preparation of calibration glasses

Fourteen K-silicate glasses were prepared in the range15–50 mol% K2O; this set of glasses was also used in twoprevious studies [5,18]. The glasses were prepared in 4 gbatches from reagent grade SiO2 and K2CO3; 0.1 wt% ofFe2O3 was added to the samples for the NMR spectro-scopic measurements that were performed on the sameset of samples [5]. Comparison with spectra of iron freesamples shows that this had no effect on the Raman spec-tra. The mixtures were decarbonated for 3–12 h at 800 �Cand were subsequently molten in Pt crucibles for three con-secutive 1-h periods at 100 K above their respective liqui-dus temperatures. The dwell time at high temperaturewas limited to three consecutive dwells of 20 min for themore alkali rich samples to avoid unnecessary alkali evap-oration. Two intermediate crushings under acetone wereperformed to ensure sample homogeneity. The glasses werequenched by dipping the bottom of the crucible in water(quench rate of 200–500 K/s). Since, most of the glassesare very hygroscopic, all handling after quenching was donein an argon atmosphere and the samples were kept in anargon filled container, placed inside a desiccator prior tothe Raman analysis. The K2O/SiO2 ratio of the sampleswas measured by XRF analysis and the results correspondto the nominal compositions within analytical error.

2.4. Raman spectroscopy

The Raman spectra of the melts were collected with aconfocal LabRam system in back scatter geometry, usingthe 488 nm line of an external argon laser with typically330 mW of laser power at the sample surface. The spectrawere collected with 2–4 acquisitions of 30 s each.

The background was removed by fitting a second orderpolynomial to the spectral region of 1250–1800 cm�1,extrapolating it to lower wavenumbers and subtracting itfrom the spectrum. Subsequently, a temperature-frequencycorrection for the first order Raman intensities [21] wasapplied. The spectra were not corrected for the tempera-ture-frequency dependence of the overtone bands, because(i) the contribution of overtone bands is expected to be rel-atively small for the temperature range studied and (ii) afully accurate correction for the overtone intensities isnot possible, despite a commendable attempt by Danielet al. [22].

3. Quantification procedure

The procedure to extract quantitative speciation infor-mation from a set of Raman spectra has been describedin detail before [18]; in the present paper, we will onlydescribe the main principles of the approach.

The method is based on the following assumptions:

1. All Qn species have different partial Raman spectra(PRS), i.e. the contribution to the Raman spectrum ofan individual species.

2. Each Raman spectrum is a linear combination of thepartial Raman spectrum of each species: in matrix formthis can be written as

Aij ¼ Qik � ekj; ð2Þ

where i, j, k are the number of spectra, wavenumbersand species, respectively; Aij is the matrix of the Ramanintensities as a function of wavenumber; Qik is a matrixof the abundances of the Raman species and ekj containsthe partial Raman spectra for the individual species.

3. The shape of the partial Raman spectrum for each spe-cies is independent of the concentration of the species.

NMR studies have shown that there are two differenttypes of Q2 species in potassium silicate glasses at highK2O content [5,6] and two different types of Q3 species atlow K2O content (<16 mol%) [23]. However, these differenttypes of Q2 and Q3 do not represent a conflict with assump-tion 3 because (i) these additional species were mostlyobserved outside of the compositional range of the currentstudy and (ii) the results from the Principal ComponentAnalysis indicate the presence of three species only (seebelow).

Because absolute intensities in Raman spectra dependon analytical conditions, the spectra need to be normalizedto their appropriate relative intensities. This is done byintroducing a set of normalization factors ni into Eq. (2),which can then be rewritten as

ni � Aij ¼ Qik � ekj: ð3Þ

In a first step, Principal Component Analysis (PCA) isused to determine the number of independent contributionsto the Raman spectra. In our case, this is the minimum


number of components needed to explain more than 99.8%of the variance of A. Application of PCA to our data setyielded the results given in Table 1. For all series exceptj, the first two Principal Components (PC) account for lessthan 99.8% of the variance, while the first three compo-nents always explain more than 99.9% of the variance.The remaining PC (only first 5 PC are shown) are consid-ered as noise. Thus, the number of species determined byPCA is three, consistent with the number expected fromthe Qn speciation model described by reaction (1). Thisconsistency indicates that our starting assumptions aboutthe partial Raman spectra are correct.

The normalization factors ni, the concentration matrixQik and the partial Raman spectra ekj are all unknownsin Eq. (3). Using mass and charge balance considerations,we can calculate Qik for a value of the equilibrium constantKn of reaction (1). Linear programming is used to solvesimultaneously for ni and ekj for a given value of Kn by min-imizing the absolute deviation between the measured andcalculated spectra, summed over all spectra and all wave-numbers; the objective function to be minimized is

F ¼ minni ;ej

XI

i¼1

XJ

j¼1

niAij � Qijekj

�� ( )( ): ð4Þ

The objective function F, which is basically a goodness offit parameter, is calculated for a range of Kn values and dis-

400 800 1200

49.42

46.67

43.5

39.05

36.39

33.82

31.96

28.65

24.33

17.4

12.4

K2O

Inte

nsity

(a.u

.)

(mol%)

400 500 600

(b)

Raman

(a) RT glasses

(b) RT glasses

Fig. 6. (a) Room temperature Raman spectra as a function of K2O content; onlon the low frequency region from (a). (c) Raman spectra as a function of tempecollected spectra are shown for clarity. (d) Zoom on the low frequency region

plays a minimum at the true value for Kn. This approachallows us to simultaneously extract the speciation (Kn),the partial Raman spectra (ekj) and the normalization fac-tors (ni) from a set of measured spectra (Aij).

4. Results

Changes in the Raman spectra with composition andtemperature are described qualitatively in Section 4.1.The speciation results from the quantification procedurefrom Section 3 are given in Section 4.2.

4.1. Raman spectra – qualitative description

A set of room temperature spectra for different K2Ocontents is shown in Fig. 6(a) and in more detail in (b).A set of spectra for the disilicate sample for different tem-peratures is shown in Fig. 6(c) and in more detail in (d).There is a broad asymmetric peak at �500 cm�1, this peakis a composite peak due to bending vibrations of the silicatenetwork [24] and four-membered rings. This peak decreasesin intensity and shifts to lower wavenumbers with increas-ing temperature (Fig. 6(d)) and decreases in intensity andshifts to higher wavenumbers with increasing K2O content(Fig. 6(b)). A relatively sharp peak is present at �590 cm�1.This peak has been attributed to three-membered rings [25–27]. The peak area increases strongly with increasing K2O

400 800 1200

298

455

646

792

855

927

1005

1152

1220

1299

1357

T (K)

400 500 600

(d)

shift (cm )

(c) 33.3 mol% K2O

(d) 33.3 mol% K2O

y 11 out of more than 300 collected spectra are shown for clarity. (b) Zoomrature for potassium disilicate sample (33.3 mol% K2O); only 11 out of 64from (c). All spectra were scaled to the same maximum.


content (Fig. 6(b)) and increases moderately with increas-ing temperature (Fig. 6(d)) above the glass transition(Tg � 800 K). Its peak position is more or less constantwith temperature. The increased intensity with increasingpotassium content of this 590 cm�1 peak is consistent withthe data by Malfait et al. [5], who observed abundant three-membered rings in potassium silicate glasses by NMRspectroscopy at high potassium content. An increasingabundance of three-membered rings with increasing potas-sium content or temperature has been inferred previouslyfrom Raman spectroscopy [16,28] and reverse Monte Carlosimulations to neutron diffraction data [29] and is con-firmed by our data. The high degree of peak overlap in thisregion makes a robust deconvolution difficult. There also isa lack of knowledge about the Raman scattering efficiencies.Thus, the quantification of the abundance of three-mem-bered rings through a fit with Gaussian lines has not beenattempted. Quantification with the approach from Section3 is also not possible, since no appropriate chemical modelis at our disposal that describes the abundances of all spe-cies contributing to the Raman intensity in this region. Athigh SiO2 content, there is a broad feature of relatively lowintensity around 800 cm�1. This peak probably is the resultof Si–O stretching vibrations with a large Si displacement [30].

The remainder of this paper will focus on the spectralregion between 850 and 1250 cm�1, this is the region wherethe stretching vibrations of the different Qn species are pres-ent. Several spectral changes occur with increasing K2Ocontent (Fig. 6(a)). The shoulder at 1150 cm�1, which isoften assigned to Q4, e.g. [10], decreases in intensity withincreasing K2O content and disappears near the disilicatecomposition. The position of the 1100 cm�1 peak, whichis generally assigned to Q3 [9,16] remains constant untilthe disilicate composition is reached and apparently shiftsto lower wavenumbers at higher K2O contents. Please notethat there are two main bands at �1070 and �930 cm�1 inthe spectrum of the �50 mol% sample; an explanation forthis will be given below. A peak at �930 cm�1, which canbe unambiguously assigned to Q2 [9,16] appears at ca.27 mol% K2O, this peak grows in intensity and is at a max-imum at 50 mol% K2O. A small peak at �830 cm�1 is pres-ent at K2O contents above 43 mol%, this peak can beassigned to Q1 [21]. Several spectral changes occur withincreasing temperature (Fig. 6(c)). There is a clear increasein the intensity with increasing temperature of the930 cm�1 peak above Tg (�800 K). Both the 1100 andthe 930 cm�1 peaks shift to lower wavenumbers withincreasing temperature.

The Raman spectra and the fits obtained from the math-ematical treatment (see Section 4.2) for a few selected tem-peratures are shown in Fig. 7. It can be seen on the Ramanintensity maps that the peak at �930 cm�1, increases inintensity with increasing temperature. At high temperature,the peak is also present at lower potassium contents. Foreach temperature, the position of the main band at�1100 cm�1 remains constant for the potassium contentsfor which there is no peak at �930 cm�1; the peak gradu-

ally shifts to lower wavenumbers at higher potassium con-tents. The onset of this peak shift occurs roughly at thepotassium content where the Q2 peak at �930 cm�1

appears. This is at lower potassium contents for higher tem-peratures. The 1150 cm�1 shoulder decreases in intensitywith increasing temperature. In the next paragraph, it willbe shown that these apparent peak shifts can be explainedas the result of changes in the relative intensities of highlyoverlapping peaks of the different Qn species, rather thanthe result of changes of the Qn peak positions themselves.

4.2. Speciation

The quantification method described in Section 3 wasapplied in order to extract quantitative speciation informa-tion from the Raman spectra (Fig. 7). The compositionalrange from 20 to 38 mol% K2O was used for the calcula-tions: this range does not include the ranges where phaseseparation (around 10 mol% K2O [31]) or crystallization(typically observed above 38 mol% K2O) could be a prob-lem. There is an excellent agreement between the fits andthe measured spectra. The contributions for the differentQn species are shown for a few compositions. It is clearfrom the fits of the spectra around the disilicate composi-tion (�33.3 mol% K2O) that the contributions from Q2

and Q4 increase with increasing temperature, consistentwith a shift of the equilibrium in reaction (1) to the rightwith increasing temperature.

During the quantification procedure, we calculated thevalue of the objective function (4) for a range of valuesfor the equilibrium constant, K3, of reaction (1). The resultsfor various temperatures are shown in Fig. 8. The equilib-rium constants providing the best fit to the Raman spectra,are given in Table 1 and plotted as a function of tempera-ture in Fig. 9. Log K3 increases as a function of temperaturein the equilibrium regime, i.e. above the glass transition.One point does not fit the trend: the logK3 for series i at1189 K is small compared to the other measurements.The exact reason for this is not entirely clear, but the valuefor logK3 for this series does show an anomalously strongdependence on the compositional interval that is chosen forthe calculations. Two more series of spectra were collectedat this temperature to make sure the result of series i couldbe discarded, which will be done for the remainder of thepaper. The value for logK3 at 793 K is slightly lower thanthe room temperature values. This is probably due to therelatively high fictive temperature of the glasses becauseof the fast quench rate (�100–200 K/s). In contrast, thestructure was able to relax to the actual, lower temperatureduring the dwell time of �100 s before the in situ, measure-ments at 793 K. The speciation is plotted as a function ofcomposition in Fig. 10. The speciation becomes more ran-dom with increasing temperature, e.g. less Q3 and more Q2

and Q4 at the disilicate composition with increasing tem-perature. The quantitative results on the speciation areconsistent with the qualitative observations on the Ramanspectra.

Fig. 7. (a) Raman intensity maps and stacked Raman spectra for room temperature, 793 K and 855 K. All spectra were scaled to a maximum intensity of100. The numbers to the right of the stacked spectra correspond to the compositions given in Table 1. For each temperature, all spectra were fittedsimultaneously with the method described in Section 3. The collected Raman spectra are shown by the symbols; the fitting envelope for each spectrum isshown as a line. The contributions from the Qn species to the Raman spectrum are shown below a few selected spectra, the compositions for those aregiven in mol% below the fitted spectra. The decrease in intensity for the 930 cm�1 peak from 793 to 855 K for the �37 mol% spectrum, is probably due touncertainties in the composition. As the effect of composition on the relative peak intensities is much larger than the effect of temperature, even smalluncertainties on the composition will dominate over the temperature effect. (b) Raman intensity maps and stacked Raman spectra for 1002 K, 1093 K and1189 K. All spectra were scaled to a maximum intensity of 100. The numbers to the right of the stacked spectra correspond to the compositions given inTable 1. For each temperature, all spectra were fitted simultaneously with the method described in Section 3. The collected Raman spectra are shown bythe symbols; the fitting envelope for each spectrum is shown as a line. The contributions from the Qn species to the Raman spectrum are shown below a fewselected spectra, the compositions for those are given in mol% below the fitted spectra.


Fig. 7 (continued)


4.3. Thermodynamic interpretation

Thermodynamic data can be extracted from the specia-tion information: the standard state enthalpy of the speci-ation reaction, DH0, is related to the equilibrium constantthrough the van t Hoff equation:

DH 0 ¼ �R � o ln K3

oT�1; ð5Þ

with R being the gas constant. The natural logarithm of theequilibrium constant, lnK3, is plotted as a function of the

200 400 600 800 1000 1200

logK

3

Temperature (K)

Z H et al. (2007)

2 points

series i

-2.6

-2.4

-2.2

-2

-1.8

-1.6

Fig. 9. LogK3 as a function of temperature, the room temperature resultsfrom Zakaznova-Herzog et al. [18] are also plotted (Z-H). The error barsrepresent 1 SD on the room temperature data. Apart from the outlier at�1200 K from series i, logK3 increases monotonically with increasingtemperature. The values for logK3 at �800 K are slightly lower than atroom temperature [18]. This is due to the fast quench rates for the roomtemperature glasses, i.e. for the room temperature glasses, the speciationwas frozen in at a high fictive temperature, while for the �800 K liquids,the structure had sufficient time to relax to its equilibrium state prior to theRaman analysis.

logK3

793h

855f

1002c

1093g

1189e

T (K)series

-2.8 -2.6 -2.4 -2.2 -2-3 -1.8 -1.6 -1.4

F /

Fm

in

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

1.014

Fig. 8. Normalized value of the objective function (F/Fmin) as a functionof logK3 for a few selected temperatures. The minima occur at highervalues for logK3 with increasing temperature.


inverse temperature in Fig. 11. With this Arrhenius plotand following Eq. (5), the enthalpy of the speciationreaction can easily be calculated from the slope of thedata: DH0 = 33.1 ± 7.3 kJ/mol. Using the fit to lnK3 inthe Arrhenius plot, we can calculate the Qn speciation fora wide range of temperature and composition (Table 2,Fig. 12).

K2O (mol%)

Spe

cies

abu

ndan

ce (

%)

h 793 K

f 855 K

c 1002 K

g 1093 K

e 1189 K

Q3

Q4

Q2

22 24 26 28 30 32 34 36 380

10

20

30

40

50

60

70

80

90

100

Fig. 10. Qn speciation as a function of composition for a few selected temperatures. The symbols denote the compositions at which a Raman spectrum wascollected. The speciation becomes more random with increasing temperature, e.g. less Q3 and more Q2 and Q4 at the disilicate composition with increasingtemperature.

4.4

.E

rror

calcu

latio

n

Th

eu

ncertain

tyo

nlo

gK

3at

high

temp

erature

isco

nsid

-ered

tob

eth

esam

eas

the

un

certainty

for

the

roo

mtem

per-

ature

glasses.T

his

isb

asedo

nth

esim

ilarn

oise

levelsin

the

Ram

ansp

ectra,th

esam

ep

recision

with

wh

ichth

eco

mp

o-

sition

sare

kn

ow

nan

dth

eh

ighp

recision

with

wh

ichth

etem

peratu

reis

kn

ow

n.

Th

eerro

rb

arso

nF

igs.9

and

11are

determ

ined

by

the

stand

ardd

eviation

of

the

measu

re-m

ents

inglasses:

0.10in

log

un

its,0.23

inln

un

its[18].

Th

estan

dard

deviatio

nb

etween

the

speciatio

nd

ata,

Table 2

Qn speciation (%) as a function of temperature (K) and K2O content (mol%), determined from the Arrhenius plot in Fig. 11. The errors correspond to half of the difference between the speciation for the upper and lower bounds of the 90%

confidence interval on the Arrhenius plot (Fig. 11)

K2O 800 k 900 K 1000 K 1100 K 1200 K

Q4 Q3 Q2 Q4 Q3 Q2 Q4 Q3 Q2 Q4 Q3 Q2 Q4 Q3 Q2

20 50.15 ± 0.04 49.7 ± 0.1 0.15 ± 0.04 50.26 ± 0.04 49.5 ± 0.1 0.26 ± 0.04 50.4 ± 0.1 49.2 ± 0.1 0.4 ± 0.1 50.6 ± 0.1 48.9 ± 0.2 0.6 ± 0.1 50.7 ± 0.2 48.5 ± 0.3 0.7 ± 0.2

21 47.02 ± 0.04 52.8 ± 0.1 0.18 ± 0.04 47.15 ± 0.04 52.5 ± 0.1 0.31 ± 0.04 47.3 ± 0.1 52.2 ± 0.1 0.5 ± 0.1 47.5 ± 0.1 51.8 ± 0.2 0.7 ± 0.1 47.7 ± 0.2 51.4 ± 0.4 0.9 ± 0.2

22 43.8 ± 0.1 56.0 ± 0.1 0.2 ± 0.1 44.0 ± 0.1 55.7 ± 0.1 0.4 ± 0.1 44.2 ± 0.1 55.3 ± 0.2 0.6 ± 0.1 44.4 ± 0.1 54.8 ± 0.3 0.8 ± 0.1 44.6 ± 0.2 54.3 ± 0.4 1.1 ± 0.2

23 40.5 ± 0.1 59.2 ± 0.1 0.3 ± 0.1 40.7 ± 0.1 58.8 ± 0.1 0.4 ± 0.1 40.9 ± 0.1 58.4 ± 0.2 0.7 ± 0.1 41.2 ± 0.2 57.8 ± 0.3 1.0 ± 0.2 41.5 ± 0.3 57.2 ± 0.5 1.3 ± 0.3

24 37.2 ± 0.1 62.5 ± 0.1 0.3 ± 0.1 37.4 ± 0.1 62.1 ± 0.2 0.5 ± 0.1 37.7 ± 0.1 61.5 ± 0.2 0.8 ± 0.1 38.0 ± 0.2 60.9 ± 0.4 1.2 ± 0.2 38.4 ± 0.3 60.1 ± 0.6 1.5 ± 0.3

25 33.7 ± 0.1 65.9 ± 0.2 0.4 ± 0.1 34.0 ± 0.1 65.3 ± 0.2 0.7 ± 0.1 34.3 ± 0.1 64.7 ± 0.3 1.0 ± 0.1 34.7 ± 0.2 63.9 ± 0.4 1.4 ± 0.2 35.1 ± 0.4 63.1 ± 0.7 1.8 ± 0.4

26 30.2 ± 0.1 69.3 ± 0.2 0.5 ± 0.1 30.5 ± 0.1 68.6 ± 0.2 0.8 ± 0.1 31.0 ± 0.2 67.8 ± 0.3 1.2 ± 0.2 31.4 ± 0.3 66.9 ± 0.5 1.7 ± 0.3 31.9 ± 0.4 65.9 ± 0.8 2.2 ± 0.4

27 26.6 ± 0.1 72.8 ± 0.3 0.6 ± 0.1 27.0 ± 0.1 71.9 ± 0.3 1.0 ± 0.1 27.5 ± 0.2 71.0 ± 0.4 1.5 ± 0.2 28.1 ± 0.3 69.9 ± 0.6 2.1 ± 0.3 28.7 ± 0.5 68.7 ± 1.0 2.6 ± 0.5

28 23.0 ± 0.2 76.2 ± 0.3 0.8 ± 0.2 23.5 ± 0.2 75.2 ± 0.4 1.3 ± 0.2 24.1 ± 0.2 74.0 ± 0.5 1.9 ± 0.2 24.7 ± 0.4 72.7 ± 0.7 2.5 ± 0.4 25.4 ± 0.6 71.4 ± 1.1 3.2 ± 0.6

29 19.3 ± 0.2 79.7 ± 0.4 1.0 ± 0.2 19.9 ± 0.2 78.4 ± 0.4 1.6 ± 0.2 20.7 ± 0.3 77.0 ± 0.6 2.4 ± 0.3 21.4 ± 0.4 75.4 ± 0.9 3.1 ± 0.4 22.2 ± 0.6 73.8 ± 1.3 3.9 ± 0.6

30 15.6 ± 0.3 83.0 ± 0.6 1.3 ± 0.3 16.4 ± 0.3 81.4 ± 0.5 2.1 ± 0.3 17.3 ± 0.3 79.7 ± 0.7 3.0 ± 0.3 18.2 ± 0.5 77.9 ± 1.0 3.9 ± 0.5 19.1 ± 0.7 76.0 ± 1.5 4.8 ± 0.7

31 12.0 ± 0.4 86.1 ± 0.7 1.9 ± 0.4 13.0 ± 0.3 84.1 ± 0.7 2.9 ± 0.3 14.1 ± 0.4 82.0 ± 0.8 3.9 ± 0.4 15.1 ± 0.6 79.9 ± 1.1 5.0 ± 0.6 16.1 ± 0.8 77.9 ± 1.6 6.0 ± 0.8

32 8.6 ± 0.5 88.6 ± 0.9 2.8 ± 0.5 9.9 ± 0.4 86.2 ± 0.8 4.0 ± 0.4 11.1 ± 0.4 83.7 ± 0.9 5.2 ± 0.4 12.3 ± 0.6 81.4 ± 1.3 6.4 ± 0.6 13.4 ± 0.9 79.1 ± 1.8 7.5 ± 0.9

33 5.8 ± 0.5 90.0 ± 1.1 4.3 ± 0.5 7.1 ± 0.4 87.2 ± 0.9 5.6 ± 0.4 8.5 ± 0.5 84.6 ± 1.0 7.0 ± 0.5 9.7 ± 0.7 82.1 ± 1.3 8.2 ± 0.7 10.9 ± 0.9 79.8 ± 1.8 9.4 ± 0.9

34 3.7 ± 0.5 89.7 ± 1.0 6.7 ± 0.5 5.0 ± 0.4 87.0 ± 0.9 8.0 ± 0.4 6.3 ± 0.5 84.4 ± 0.9 9.3 ± 0.5 7.5 ± 0.7 81.9 ± 1.3 10.5 ± 0.7 8.7 ± 0.9 79.6 ± 1.8 11.7 ± 0.9

35 2.3 ± 0.4 87.6 ± 0.8 10.0 ± 0.4 3.5 ± 0.4 85.4 ± 0.7 11.2 ± 0.4 4.6 ± 0.4 83.1 ± 0.8 12.3 ± 0.4 5.7 ± 0.6 80.8 ± 1.2 13.4 ± 0.6 6.8 ± 0.9 78.7 ± 1.7 14.5 ± 0.9

36 1.5 ± 0.3 84.4 ± 0.6 14.0 ± 0.3 2.4 ± 0.3 82.7 ± 0.6 14.9 ± 0.3 3.4 ± 0.4 80.7 ± 0.7 15.9 ± 0.4 4.4 ± 0.5 78.8 ± 1.1 16.9 ± 0.5 5.3 ± 0.8 76.9 ± 1.5 17.8 ± 0.8

37 1.1 ± 0.2 80.4 ± 0.5 18.5 ± 0.2 1.7 ± 0.2 79.1 ± 0.5 19.2 ± 0.2 2.5 ± 0.3 77.6 ± 0.6 19.9 ± 0.3 3.3 ± 0.4 76.0 ± 0.9 20.7 ± 0.4 4.1 ± 0.7 74.3 ± 1.3 21.6 ± 0.7

38 0.8 ± 0.2 75.9 ± 0.3 23.3 ± 0.2 1.2 ± 0.2 74.9 ± 0.4 23.8 ± 0.2 1.8 ± 0.2 73.8 ± 0.5 24.4 ± 0.2 2.5 ± 0.4 72.5 ± 0.7 25.1 ± 0.4 3.1 ± 0.6 71.1 ± 1.1 25.7 ± 0.6

0.80.9

11.1

1.21.3

x 10-3

-6 -5 -4 -3 -2

2 points

lnK3

1/T (1/K

)

M.et al. (’04)

KS

2

This study (90% conf. bands)

M.&

F. (’94)

KS

4K

S3

KS

2

KS

3

Fig.

11.A

rrhen

ius

plo

tfo

rln

K3 .

Th

eerro

rb

arsrep

resent

1S

Do

nth

ero

om

temp

erature

data.

Th

eth

ickso

lidlin

eis

alin

earfi

tth

rou

ghth

ed

ata(ln

K3

=�

3978Æ(1/T)�

0.82).T

he

dash

edlin

esrep

resent

the

90%co

nfi

-d

ence

interval.T

he

enth

alpy

for

reaction

1,estimated

from

the

slop

eo

fth

eln

K3

asa

fun

ction

of

1/T,

is33.1

±7.3

kJ/m

ol.

Th

estan

dard

deviatio

nb

etween

the

data

and

the

fit

is0.18,

verysim

ilarto

the

stand

ardd

eviation

of

the

roo

mtem

peratu

red

atao

f0.23

[18].T

he

results

from

previo

us

stud

ies,tak

enfro

mth

ep

lotted

equ

ilibriu

mco

nstan

ts[11]

or

linear

fit

toth

eeq

uilib

rium

con

stants

[8]are

plo

ttedfo

rco

mp

arison

(M.&

F.

isM

ysenan

dF

rantz

[8];M

.et

al.is

Maeh

araet

al.[11]).

W.J

.M

alfa

itet

al.

/J

ou

rna

lo

fN

on

-Cry

stallin

eS

olid

s3

53

(2

00

7)

40

29

–4

04

24039

0102030

800

1000

1200

0

20

40

60

80

100

K2O (mol%)

T (K)

Inte

nsity

(a.

u.)

Q4Q3

Q2

Fig. 12. Speciation as a function of melt composition and temperature.The speciation was calculated from the fit to the Raman data in Fig. 11.

800 900 1000 1100 1200

793 K

855 K

1002 K

1093 K

1189 K

Inte

nsity

(a.

u.)

Q4

800 900 1000 1100 1200

793 K

855 K

1002 K

1093 K

1189 K

Inte

nsity

(a.

u.)

Q3

800 900 1000 1100 1200

793 K

855 K

1002 K

1093 K

1189 K

Raman shift (cm-1)

Inte

nsity

(a.

u.)

Q2

a

b

c

Fig. 13. Partial Raman spectra from the quantification procedure for Q4,Q3 and Q2 as a function of temperature. The offset between the spectra isscaled to the temperature at which they were collected.


lnK3, and the fit on the Arrhenius plot is 0.18 (ln units).This is nearly identical to the standard deviation from theroom temperature values for lnK3, indicating that theuncertainty for the high-temperature melts is indeed thesame as the uncertainty for the room temperature glasses.The 90% confidence bands for lnK3 for the fit on theArrhenius plot are shown in Fig. 11; the correspondinguncertainties for the speciation are shown in Table 2. Theerror on enthalpy of the speciation reaction DH0 corre-sponds to the 90% confidence interval for the slope of thelinear fit through the data.

4.5. Partial Raman spectra

The calculated partial Raman spectra for Q4, Q3 and Q2

for different temperatures are plotted in Fig. 13. Whencomparing the partial Raman spectra for different temper-atures, it should be kept in mind that Raman spectra fordifferent sets of compositions (Table 1) were used for differ-ent temperatures. This may result in differences in the par-tial Raman spectra if the partial Raman spectra for eachspecies are not entirely independent the species’ concentra-tion. Their general shape for Q2, Q3 and, to a lesser extent,Q4 remains fairly constant with varying temperature andclosely resembles the partial Raman spectra of the glassesat room temperature [18]. Because the bands in the PRSare strongly asymmetric and irregular in nature, the peakpositions and widths do not provide a full description ofthe peak shape. With increasing temperature, all peaks inthe partial Raman spectra shift to lower wavenumbers(Q4 from 1140 to 1120 cm�1, Q3 from 1095 to 1085 cm�1

and Q2 from 1070 to 1050 cm�1 and from 922 to920 cm�1) and the width of the peaks increases. Thedecrease in vibrational frequency with increasing tempera-ture is most likely related to the thermal expansion of theSiO4 tetrahedra. Because they change with increasing tem-

perature, the partial Raman spectra have to be determinedfor each temperature separately, i.e. for each temperatureunder investigation, a set of Raman spectra for many dif-ferent compositions has to be acquired.


5. Discussion

From the partial Raman spectra we obtained, it is clearthat the common assumption about Gaussian line shapesfor the Qn species is not valid. This significantly limits thepossibility of obtaining accurate speciation informationthrough the fitting of Raman spectra with Gaussian lines.The results of previous studies on the temperature depen-dence of the speciation in potassium silicate melts are com-pared to our results in Fig. 11. These previous studiesdepended on fitting the 800–1250 cm�1 region of high-tem-perature Raman spectra with a combination of Gaussianlines (at �930, �1060, �1100 and �1150 cm�1), but differ-ent band assignments have been used by different authors.The values obtained for DH0 in these previous studies scat-ter significantly and are generally lower than the valueobtained in this study (33.1 ± 7.3 kJ/mol).

The discrepancy in the results and the generally lowervalues for DH0 can be explained as follows. Zotov et al.[17] and Zakaznova-Herzog et al. [18] have shown thatthere are 2 peaks present for Q2, a peak at �930 cm�1

and a peak at �1080 cm�1; this also explains the doublepeak in the spectrum of the potassium metasilicate glass(50 mol% K2O) in Fig. 6(a). An increase in Q2 in theglass/melt will thus result in both an increase of the �930and the composite 1100 cm�1 peak. This can be seen clearlyin the Raman intensity map in Fig. 14: with increasing tem-perature above Tg, there is a simultaneous increase in

Fig. 14. (a) Fitted Raman spectrum of a 32.9 mol% K2O melt at 1002 K (spectrtemperature for a potassium disilicate sample (33.3 mol% K2O); the spectrawavenumbers with increasing temperature. The increased intensity at 930 cmincreased intensity at both 1050 and 1150 cm�1, as evidenced by a break in th

intensity, both at �930 and �1080 cm�1. In addition, Q4

also contributes to the Raman intensity at 1100 cm�1. Inour view, the break in slope of the contours at the high-wavenumber side of the 1100 cm�1 peak in Fig. 14 is theresult from a growing contribution of Q4 with increasingtemperature and not from a broadening of the Q3 peak.This is consistent with our assumption about the constancyof the PRS, which is confirmed by the observation that thevariation in the spectrum can be described by just 3 inde-pendent contributions. As a result, the approach followedby McMillan et al. [16] and to a lesser extent the one fol-lowed by Mysen and Frantz [8] and Maehara et al. [11],who consider the 1100 cm�1 peak to be mainly due toQ3, will yield a higher abundance of Q3 at high temperatureand a smaller temperature dependence of the speciationreaction. This leads to a smaller value of the DH0 of thespeciation reaction.

McMillan et al. [16] quantified the temperature depen-dence of the speciation, but not the speciation itself (hencenot shown in Fig. 11). They considered the ratio A950/(A1060 + A1100) to be proportional to the Q2/Q3 ratio,where Ax is the area of the peak at x cm�1 and obtaineda value for DH0 of 20.6 ± 5.5 kJ/mol for KS2. Because theyregarded the entire composite peak at 1100 cm�1 to resultfrom Q3, they derived a significantly lower temperaturedependence of the speciation reaction and DH0.

Mysen and Frantz [8] quantified the speciation throughcross calibration with NMR results. In contrast to McMillan

um 24 from series c); (b) Raman intensity as a function of Raman shift andare scaled to a maximum intensity of 100. Both peaks shift to lower�1 with increasing temperature above Tg (�800 K) is accompanied by

e slopes of the contour lines at Tg.


et al. [16], they considered the ratio A950/A1100 to be pro-portional to the Q2/Q3 ratio. They obtained values forDH0 of 27.6 ± 0.8, 20.7 ± 2.2 and 25.3 ± 3.0 kJ/mol forK2O Æ (SiO2)2 (KS2), K2O Æ (SiO2)3 (KS3) and K2O Æ (SiO2)4

(KS4), respectively. Because they considered only part of thecomposite 1100 cm�1 peak to be due to Q3, they obtained astronger temperature dependence of the speciation reactionand a higher DH0 than McMillan et al. [16]. Since the Q3 par-tial Raman spectrum is essentially Gaussian, fitting the com-posite 1100 cm�1 peak with Gaussian curves and subsequentsubtraction of the 1060 cm�1 and 1150 cm�1 peaks, yieldsessentially the same peak as our partial Raman spectrumfor Q3. As a consequence, there is a reasonable agreementbetween the results by Mysen and Frantz [8] and the presentstudy, despite the limitations of some of their startingassumptions. This indicates that, to some extent, their resultson other binary systems, e.g. Li2O–SiO2, Na2O–SiO2 [8],BaO–SiO2, SrO–SiO2, CaO–SiO2 [32], remain valid. Thisshould be particularly the case for relative changes in the spe-ciation and DH0 for different cations.

Maehara et al. [11] also quantified the speciationthrough cross calibration with NMR and used the sameband assignment as Mysen and Frantz [8]. Despite usingthe same quantification procedure, their results differ sig-nificantly from previous Raman results by Mysen andFrantz [8] and for the values at the glass transition, fromthe NMR results [5,6]. The values obtained for DH0 fromtheir Arrhenius plots are 39 and 20 kJ/mol for KS2 andKS3, respectively, which is different from the 58 and29 kJ/mol, they have reported in the text. Maehara et al.[11] gave no explanation for the discrepancy between theirresults and the results by Mysen and Frantz [8].

6. Conclusions

In this study, we obtained high quality data on the spe-ciation of silicate melts using Raman spectroscopy only.These results were obtained using the quantificationmethod developed by Zakaznova-Herzog et al. [18], whichdoes not require any a priori assumptions about the Qn lineshapes or any external calibration of the Raman scatteringefficiencies. This is the first application of this approach athigh temperatures and it appears to be the most accuratetechnique to investigate the Qn speciation in silicate melts.

The accurate and precise speciation informationobtained in this study can be used to extract high qualityinformation on thermodynamic properties of the Qn spe-cies. Because this method is directly applicable to a widerange in temperatures and melt compositions, it providesa key tool to systematically investigate the way metal cat-ions influence the properties and abundance of melt spe-cies. As a result, it will enhance our understanding of therelationship between the composition, the speciation andthe physical and chemical properties of melts.

Acknowledgments

This project was funded by a ETH grant (0-20168-04)and a Swiss National Science Foundation project (PP002-68687) to WH. Peter Ulmer and Lydia Zender are thankedfor help with the XRF analysis. We would like to thankUrs Menet and Donat Niederer for making the heatingstage and Yann Morizet for testing of the heating stage.Eric Reusser provided access to the Raman facility. ZoltanZajacz is thanked for many fruitful discussions.

References

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Cryst. Solids 205–207 (1996) 225.[15] J.L. You, G.C. Jiang, X. Kuangdi, J. Non-Cryst. Solids 282 (2001) 125.[16] P.F. McMillan, G.H. Wolf, B.T. Poe, Chem. Geol. 96 (1992) 351.[17] N. Zotov, I. Ebbsjo, D. Timpel, H. Keppler, Phys. Rev. B 60 (1999)

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