This viscoelastic deformation is presented as the real and imaginary components of the shear modulus as a function of frequency. A maximum in imaginary part of the shear modulus (energy loss) appears at the frequency at which part of the melt structure moves. This maximum is accompanied by an increase in the real (storage) part of the modulus. One expects 3 peaks to occur in sodium aluminosilicate melts (Fig. 49). Based on a simplistic model of the rates of motion of the different atoms in the melt there should be the slowest motion of Si-O (with the longest bond lifetime); the fast motion of Na+ atoms (based upon diffusion data Na-O bonds are assumed to have the shortest lifetime) and at frequencies between these two there should be a peak for the lifetime of Al-O bonds.
Fig. 49. The known change in modulus with log10ωτM for the motion of Si and O atoms in silicate melts together with theoretically expected loss modulus associated with the motion of Al3+ and Na+ atoms in the present melts.
Shear modulus, G (GPa)
log 10 ω τΜ
REAL COMPONENT
IMAGINARY COMPONENT
4. RESULTS
4.1. Composition
The compositions of investigated samples were determined by microprobe and are presented in the Table 8. Fe2+ was measured with the KMnO4 titration method (Heinrichs
& Herrmann, 1998; Herrmann, 1975). Fe2O3total was determined by spectral photometry and did not differ from microprobe data.
Tab. 8. Measured glass compositions in wt%. The compositions were determined by microprobe (JEOL JXA 8900 RL): 15 kV voltage, 10 µm beam diameter, 12 nA current. Data are the average of 10 analyses of each glass. Errors are 1σ values. Anorthite, albite and hematite were used as standards.
G8 56.3±0.3 12.2±0.1 28.5±0.1 2.54±0.05 G9 56.9±0.8 12.9±0.2 23.5±0.5 7.12±0.24 G10 59.1±0.5 13.0±0.2 20.8±0.3 6.86±0.16 G11 58.7±1.5 14.0±0.4 20.0±1.0 7.08±0.32 G12 59.2±1.2 15.1±0.2 18.2±0.8 7.49±0.33 G13 59.1±0.5 16.0±0.2 17.7±0.3 7.20±0.12 G14 60.5±0.3 17.5±0.1 14.7±0.1 6.98±0.10 Tab. 9. Calculated glass compositions in mol%. The compositions of SiO2, Na2O and Al2O3 were determined by microprobe (Tab. 8); FeO was measured with a titration method, Fe2O3 was measured by microprobe and confirmed by spectral photometry (data are the average of 10 analyses of each glass). Errors are 1σ values. Anorthite, albite and hematite were used as standards. NBO/T value was determined follow the Eq. 7; and γ from the Eqs. 9&10. Σatoms/mol presents the number of atoms (times Avogadro’s Number) in one mol of melt. Fe2+/Fe total is an atomic ratio between Fe2+ and the total amount of iron in the sample.
mol % G8 65.5±0.1 13.8±0.1 19.6±0.1 0.188±0.015 0.96±0.02 -0.105 0.41 3.411 0.098 G9 66.0±0.8 14.6±0.3 16.2±0.4 0.845±0.011 2.99±0.12 -0.014 0.46 3.394 0.141 G10 68.3±0.5 14.6±0.2 14.1±0.2 0.458±0.025 2.97±0.08 -0.039 0.47 3.350 0.077 G11 67.7±1.3 15.7±0.5 13.6±0.8 0.256±0.016 3.00±0.15 -0.013 0.49 3.337 0.043 G12 67.8±1.0 16.8±0.3 12.3±0.6 0.137±0.012 2.93±0.16 0.035 0.53 3.302 0.023 G13 67.4±0.4 17.6±0.2 11.9±0.2 0.331±0.008 2.98±0.05 0.063 0.55 3.301 0.056 G14 68.2±0.1 19.1±0.1 9.75±0.1 0.111±0.007 2.92±0.04 0.140 0.60 3.255 0.019
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Peraluminous sample G8 has only 1 mol% of Fe2O3, otherwise it will crystallize.
From the reason of composition and Fe2O3 content, properties of these melts differ sometimes from the others and the points can lie out of the drawn trends (especially G8).
Figure 50 shows the atomic ratio between the number of Fe2+ and total amount of atomic Fe as a function of Fe2O3 total (in mol%). Peralkaline Fe-bearing samples have lower Fe2+/Fe total (atoms) ratio than peraluminous melts. Fe2+/Fe total (atoms) ratio does not depend on the Fe2O3 total (Fig. 50), but there is a relationship between this ratio and composition of the melt (Fig. 51). Webb (2005b) suggested that this behaviour is connected with the difference in charge balancing between peraluminous and peralkaline melts. In peraluminous melts, when there is not enough Na+ to compensate negative charge of Al3+- and Fe3+-tetrahedra, the role of charge balancer is played by Fe2+.
The very characteristic breaking point in all of the physical properties trends indicates minimal number of non-bridging oxygens occurring in the melt and that is in the moment, when peralkaline melt changes into peraluminous (see Table 9). This is shown in Figure 52 (glass transition temperature at log10η=12 as a function of NBO/T). As there is dependence between structure, composition and physical and thermodynamic properties of the melts, this behaviour will appear also in the visualisation of other data.
The maximum in Tg12 occurs slightly on the peraluminous side of the melt composition; and not exactly at NBO/T=0. In the investigated melts there is no sample which has NBO/T equals zero. The localization of the breaking point has been marked out between samples G3 and G4 in Fe-free melts and between samples G9 and G10 in Fe-bearing melts.
0.35 0.40 0.45 0.50 0.55 0.60 0.65
0.00
Fig. 50. Plot of the atomic ratio between the number of Fe2+ and Fe total as a function of Fe2O3 total (in mol%).
Fig. 51. Plot of the atomic ratio between the number of Fe2+ and Fe total as a function of the composition. The trend-line is a guide to the eye.
Fig. 52. Glass transition temperature at log10η=12 as a function of the parameter NBO/T.
Between NBO/T values and
γ
for both the Fe-free and Fe-bearing melts there is a linear relationship described by an equation NBO T/ = −0.65 1.31+γ
with R2 = 0.976 (Fig. 53). Sodium silicate sample G0 is not described by this correlation. To connect samples G1-G7 and G8-G14 with NS2 melt a curve needs to be drawn (Fig. 53).Fig. 53. Parameter NBO/T for all of the samples as a function of their composition. The linear relationship between Fe-free
(G1-G7) and Fe-bearing samples (G8-G14) is indicated by a solid grey straight line. Dashed grey curve connects Fe-free and Fe-bearing melts with NS2 melt.
-0.15 0.00 0.15 0.30 0.45 0.60
400
0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 -0.15
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The oxidation state of Fe in melts G8-G14 is controlled by: (1) composition of the melt, (2) temperature and (3) oxygen fugacity (Jeoung et al., 2001; Berry et al., 2003) (the samples were made in air and measured in air-nitrogen atmosphere).
Neither microscopic observation nor microprobe analyses indicated the presence of crystals in Fe-free and Fe-bearing melts. The only one problem was with samples G8 and G9. During viscosity measurements the surface oxidized very fast, what required a polishing the surface before every new measurement.
4.2. Density
The densities of the glasses (see Table 10) as a function of composition together with their standard deviations from 10 measurements are shown in Figure 54. Density decreases as network-modifying Na+ is removed from the peralkaline glass; and begins to increase as charge-balancing Na+ is removed from the peraluminous glass. The same situation occurs in Fe-free as well in the Fe-bearing glasses. Fe-bearing glasses are denser and the trend-line is steeper. The characteristic minimum on the density plot is marked by samples G4 for Fe-free glasses and G11 for Fe-bearing glasses.
Figure 55 shows density data of the glasses from the system Na2O-Al2O3-SiO2 containing 67 mol% SiO2 and 75 mol% SiO2. The presented data of Hunold & Brückner (1980), Webb et al. (2007) and Fe-free samples from this study (G1-G7) create trends of the same shape. The dashed line drawn through the present data is simply a guide for the eye. A minimum in density is observed in all of these studies at γ~0.5.
The data of Day & Rindone (1962) show a similar minimum for 75 mol% SiO2 glasses. The ±0.01 g cm-3 difference between the densities of the 67 mol% SiO2 glasses may be due to small differences in SiO2 content; or to differences is cooling rate. The present glasses were cooled down in three stages process:
- between 1650-700°C at 10°C min-1; - between 700-550°C at 1°C min-1; - between 550-25°C at 10°C min-1;
while those of Webb et al. (2007) were cooled at 5 and 10°C min-1. Thus the glasses do not have the same fictive temperatures, but a change in density vs. composition trend is seen as the melt changes form peralkaline to peraluminous, and there is no longer enough Na+ to charge-balance all of the Al3+ in tetrahedral coordination.
Tab. 10. Densities, molar mass and molar volume of the glasses G0-G14 at room temperature. The standard deviations are calculated from 10 measurements.
melt density @25°C molar mass molar volume number g cm-3 g mol-1 cm3 mol-1
G0 2.485±0.005 60.650±0.078 24.407±0.051 G1 2.419±0.006 68.658±0.076 28.383±0.051 G2 2.412±0.003 67.524±0.129 27.995±0.083 G3 2.414±0.001 67.819±0.075 28.094±0.048 G4 2.409±0.003 67.774±0.113 28.134±0.073 G5 2.415±0.001 67.027±0.223 27.755±0.144 G6 2.432±0.003 67.048±0.175 27.569±0.112 G7 2.444±0.003 66.370±0.106 27.156±0.068 G8 2.460±0.004 69.638±0.077 28.301±0.050 G9 2.493±0.011 70.701±0.410 28.363±0.261 G10 2.485±0.010 69.193±0.284 27.839±0.181 G11 2.445±0.010 69.146±0.707 28.278±0.453 G12 2.485±0.008 68.755±0.608 27.665±0.386 G13 2.496±0.015 68.438±0.220 27.421±0.143 G14 2.512±0.003 67.496±0.146 26.874±0.092
Fig. 54. Measured densities of the glasses as a function of their compositions. Sample G8 has less Fe3+ than other Fe-bearing samples.
0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 2.38
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Fig. 55. Measured densities of the Fe-free sodium aluminosilicate glasses as a function of their compositions. Four sets of data have been used: black points – Falenty (samples G1-G7 – from this study); open circles – Webb (2007); open squares – Day & Rindone (1962); open triangles – Hunold & Brückner (1980). The trend-line is a guide to the eye.
Figure 56 shows molar volume of the NS2 glass (blue point), Fe-free (black points) and Fe-bearing (red points) glasses as a function of composition. Here the effect of changing structure is not as clear as in the density plot. Data show that the structural units take up different volumes of space in peraluminous and peralkaline melts; the trend-line is similar to that in Figure 52.
Fig. 56. Molar volume of the glasses as a function of composition.
24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0
NS2 sample (G0) Fe-free samples Fe-bearing samples
Molar volume (cm3 mol-1 )