Thermodynamics and Constitution of Silicate Melts The System PbO + PbF, + SiO, BY WILLIAM F. CALEY AND CHARLES R. MASSON" Atlantic Regional Laboratory, National Research Council of Canada, Halifax, Nova Scotia, Canada B3H 3Zl Received 28th February, 1978 Activities of PbFz in PbO + PbF2 and PbO + PbF2 + Si02 melts with up to 40 mol % PbF2 were determined at 1073-1173 K by means of an electrochemical cell with CaF2 as solid electrolyte. The results, together with previous measurements of the activity of PbO, were interpreted in terms of a theory in which the anionic constitution of the melts is represented by 02-, F- and an equilibrium array of silicate and fluorosilicate ions of formula Sin03n+l-mFk2n+ 2 - m)-. The equilibrium constant k' for the formation of fluorosilicate ions by the reaction F-+Si,03n+l-mF~2n+2-m)' = Si,03,-,F(2n+ m + l 1 - d - +02- was estimated to be 0.440.025.This allowed the anionic distribution to be evaluated for basic melts. In addition to 02- and F-, the main anionic constituents in melts with XpbO/XSi02 > 2.5 and XpbFz < 0.25 are SO$-, Si03F3-, SiOzFt-, Si03F-, Si,O$- and Siz06Fs-, with decreasing amounts of more highly fluorinated species. The volatile constituent SiF4 is also present in small amount and becomes increasingly significant as Xsioz/Xpbo is increased. Substitution of PbO by PbF2 causes a net decrease in the mean chain length of the anions. In the preceding communication theoretical expressions were derived for activi- ties of MO and MF, as functions of composition in ternary silicate melts MO+ MF, + Si02 whose anionic constitution was considered to be represented in terms of 02-, F- and an array of silicate and fluorosilicate ions of general formula Sin03n+l-mF(m2n+ 2 - m ) - in thermodynamic equilibrium.The purpose in the present study was to test the applicability of this theory for melts of the system PbO+PbF2 +SO,. Activities of PbO in such melts with up to 20 mol % PbF, have already been reported.2 Here we extend these studies to the measurement of activities of PbF2 over a similar range of compositions. Knowledge of these two activities allows an equilibrium constant k' to be derived for the equili- brium between fluoride, silicate, fluorosilicate, and oxide ions. This, together with an equilibrium constant k previously determined for the silicate-oxide ion equili- brium, provides a quantitative description of the system and allows the distribution of the polyions to be evaluated.The activities were determined by means of a concentration cell without transfer, with a solid CaF, electrolyte. The reliability of CaF, as an ionic conductor in cells of this type, in which the conduction is solely by F- ions, has been established in several investigation^.^-^ EXPERIMENTAL PREPARATION OF MELTS Yellow lead oxide (Fisher, " purified ") of stated purity 99.25 %, lead fluoride (B.D.H., " extra pure ") and silica, obtained by firing Mallinckrodt reagent grade silicic acid over- night at 1273 K, were used. Melts were prepared in Pt-20 % Rh crucibles by firing 50 g 2952W. F. CALEY AND C. R. MASSON 2953 of the mixed reagents in a preheated muffle furnace for 3 h ; firing temperatures were kept as close to the melting point as possible to avoid excessive volatilization. After firing, the melts were quenched between brass plates and crushed to a fine powder in an agate ball mill before use in the cell.CELLS The cells were of the type (A) The design is shown in fig. 1. A calcium fluoride crucible, M 1 cm i.d. x 3.8 cm long, prepared by slip-casting, was used as the solid electrolyte. This crucible contained the melt under investigation. A larger calcium fluoride crucible, M 1.9 cm i.d. x 4.1 cm long long, was used to contain the standard melt. The wall thickness of each crucible was approx. 1.6 111111. These crucibles were suspended concentrically in the hot zone of the furnace by means of an alumina pin H which passed through slots cut in the wall of each crucible and in the lower end of the refractory tube E.The standard melt was a liquid slag of composition 70 mol % PbO, 30 mol %lPbF2 for which the activity of PbF2 had first been determined in Ir,Ar,Pb~), me1 t 1 CaF2(&t andard melt, Pbg,Ar,Ir t o P o t e n t i o m e t e r TC FIG. 1.-Design of cell. A iridium wire, B serum bottle caps, C brass flange, D mullite tube, E ceramic tube to hold crucibles, F alumina tubes, G kanthal shield, H alumina pin, J PbO + PbFz + SiOz slag, K PbO + PbF2 standard slag, L liquid Pb, M CaFz crucibles, N pedestal, P swagelok fitting, Q alumina pushrod, R cooling water, TC thermocouple.29 54 THERMODYNAMICS OF PbO+PbF, +SiO, MELTS the same apparatus by using pure PbFz as the standard melt.NN 6 g slag and 4 g Pb were used in the inner crucible ; the outer crucible contained 12 g Pb and 12 g standard slag. The cell was flushed continuously with argon at atmospheric pressure. Tem. peratures were measured with a Pt/Pt-13 % Rh thermocouple located in the pedestal N- E.rn.f. values were measured by a Leeds and Northrup volt-potentiometer, and could be estimated to kO.01 mV. The cell was held in a platinum-wound resistance furnace controlled to f 1°C. FABRICATION OF CALCIUM FLUORIDE CRUCIBLES The technique used for fabricating the crucibles was similar to that described previo~sly.~ Absolute ethanol was used to suspend the particles rather than an acidic medium as reported elsewhere.O This simplified their manufacture. Fisher " certified " calcium fluoride, used to prepare the slips, was ball milled under absolute ethanol until 75 % of the particles were in the size range 1 to 4pm. The firing temperature was 1233 K, and the shrinkage was of the order of 10.5 %. Final density of the articles was 97 % of theoretical. To avoid formation of a Ca(OH)2 skin, the k e d crucibles were held in a desiccator until ready for use. Thermal stresses were minimal, as only 5 % of the crucibles were lost due to cracking on firing. Thermal expansion in the temperature range of the experiments (1073-1173 K) was of the order of 2 %. A.c. resistivity measurements on the final ceramics were in good agreement with published values [5 x cm-l at 923 K, 1592 Hz (present work) ; 8.5 x R-l cm-I at 923 K, 1592 Hzll]. ELECTRON MICROPROBE ANALYSES At the conclusion of each experiment the cells was sectioned and an electron microprobe was used to examine the contents and the walls of the crucibles.Analyses were performed for calcium in the melt and lead in the crucible. The results yielded supplementary informa- tion concerning the time and compositional range over which the CaF2 electrolyte could operate reliably in contact with corrosive melts of this nature. RESULTS CRUCIBLE-MELT INTERACTIONS The most severe attack of the CaF, electrolyte occurred during experiments with pure liquid PbF2 in the cell and it was for this reason that most of the work was done with a standard PbO+PbF2 melt which contained 30 mol % PbF2 as the refer- ence.Five separate experiments, varying in time from 5 to 10 h, were performed in which the e.m.f. of the standard slag was measured against pure liquid PbF,. Maxi- mum Ca found in the PbF, melt was 3 wt % at the crucible-melt interface; this decreased to a value of 1 % in the slag at a distance of 1 mm from the interface. Pb contamination of the crucible was of the order of 6 wt % at the crucible-melt interface, and 2.8 wt % at a distance of 0.5 mm inside the crucible. Interaction between the crucible and the standard slag resulted in 0 to 5.6 wt % Ca in the slag and 0 to 3 wt % Pb in the ceramic at the slag-crucible interface. In no case was Ca or Pb detected in the slag or electrolyte respectively at a distance of more than 0.5 mm from the interface. For the other melt compositions investigated, slag-crucible interactions occurred only in those samples which contained 20 mol % or more S O 2 or PbF2.Maximum Pb found in the ceramic at the ceramic-slag interface was 2 wt % (60 mol % PbO, 40 mol % PbF2 slag) ; maximum Ca in the slag was 1 % for the same sample. For all other slag compositions, only trace Pb and Ca contamination was found, with no contamination detected more than 0.5 mm inside the slag or ceramic phases. In order to minimize effects due to the crucible-melt reaction, experiments with a particular cell were not allowed to exceed 5 h, during which the cells gave resultsW. F. CALEY AND C. R. MASSON 2955 reproducible to within +1 mV. Temperatures were kept in the range 1097-1137 K. For all experiments reported, the e.m.f.was reversible with respect to temperature and independent of the flow rate of argon. Prolonged use of a cell above 1173 K eventually resulted in a drift of the e.m.f. of the order of 2 mV h-l, which increased with temperature and time. CALIBRATION OF STANDARD MELT The melting point of the standard slag was 913 K. The results of five separate experiments with the cell in the range 1097-1173 K yielded the following expression for the e.m.f., E : These values were reproducible to & 1.5 mV, with a standard deviation of 0.5 mV, when the experiments were performed in accordance with the limitations discussed in the previous section. The e.m.f. values reported below for cells C and D are the measured values, with the appropriate sign, plus the e.m.f.of cell B at the temperature of measurement, as given by eqn (1). All values have thus been corrected to yield the e.m.f. values which correspond to pure PbF2 as the reference melt. (-)Ir,Ar,Pb(l,, standard melt ]CaF,olPbF2(l,,Pb(l,,Ar,Ir'f' (B) E(mV) = -36.53+0.10T (1) THE SYSTEM PbO f PbF2 The results of experiments with the cell Ir,Ar,Pb(l,, (PbO + PbF2),l,ICaF2(s,l(standard melt),Pb(l,,Ar,Ir (C) corrected for the e.m.f. of the standard melt by eqn (1) are shown in fig. 2. The maximum PbFz content for which reliable data could be obtained was 40 mol % ; greater amounts of PbFz resulted in excessive crucible-slag interaction. The equations for each mixture together with their statistical data are given in table 1. TABLE ~.-E.M.F. DATA FOR THE SYSTEM PbO+PbFz (CELLS B AND C) E = A+BTmV standard maximum XPbO XPbFz A B deviationlmv deviationlrnv 0.95 0.05 - 2.7865 0.2172 0.4 1 .o 0.90 0.10 -25.3403 0.1741 0.1 0.2 0.80 0.20 - 32.3270 0.1260 0.1 0.5 0.70 0.30 - 37.0737 0.1020 0.5 1.3 0.60 0.40 - 47.9320 0.0907 0.2 0.4 Activities of PbF2 were calculated from the data by means of the relationship : RT E = - 2F In aPbFz where E is the combined e.m.f. of cells B and C , T is the temperature and 2F is the Faraday constant.These are plotted in fig. 3 as a function of the PbO content at 1173 K. In order to provide an approximate check on the PbF2 activities, a Gibbs-Duhem graphical integration was performed on the PbO activities previously obtained with CaO+ZrO, solid electrolyte cells for the same system., The integra- tion was in terms of activity coefficients,12 and the results are given in fig.3 for com- parison. The excellent agreement between the calculated activities and those deter- mined from the present data provides a check on the reliability of the cells.2956 250 200 > a Q-i E 6 ' 1 150 I I I I I I 1 I - *PbFZ= B+o*O-OO: 0..05 -0- - - - - - 0.10 , ~ o - ~ o ' - ' - : 4-0-0- - -. - - 0.20 o--""--- o ~ o ~ o - o - o 0.4 0.3 0.2 c 0. I 0 0.30 +o-o~~o-O-o-o-o-----o 0.40 5o o - o ~ o - c c c - c - o c c L L o - - ------ - I100 1120 I140 1160 , , , i 0.6 0.7 0.8 0.9 I .o XPbO 1173 FIO. 3.-Activity of PbF2 plotted against mol fraction of PbO for PbO + PbF2 and PbO + PbFz + SiOz melts at 1173 K. PbFz/SiOz = (A)m, (B) 4, (C) 1, @) 0.5. (0) 0.2. x , from apbo by Gibbs- Duhem.T = 1173 K.W . F. CALEY AND C . R . MASSON 2957 2 2 0 200 I80 I60 > E 'u: 140 Ei d - 120 100 ao 60 I080 I100 1120 I140 I I60 1173 temperature /I( to the following compositions : FIG. 4.-E.m.f. plotted against temperature for PbO+PbF2 + Si02 melts. The curves correspond curve XPbO XPbFz xSi02 0.85 0.05 0.10 0.90 0.08 0.02 0.86 0.07 0.07 0.70 0.05 0.25 0.80 0.07 0.13 0.80 0.10 0.10 0.70 0.10 0.20 curve Xpbo (8) 0.80 (9) 0.70 (10) 0 0.66 (11) 0 0.60 (12) 0.70 (13) 0.60 (14) 0.60 XPbF2 xSi02 0.16 0.04 0.15 0.15 0.17 0.17 0.13 0.27 0.24 0.06 0.20 0.20 0.32 0.082958 THERMODYNAMICS OF PbO+PbF2+Si02 MELTS THE SYSTEM PbO + PbF2 + Si02 The temperature dependence of the cell e.m.f. values for fourteen slag compositions (D) with the cell Ir,Ar,Pb(l), (PbO + PbF2 + Si02)(,,lCaF2,,,I(standard melt), Pb(l,,Ar,Ir corrected for the e.m.f.of the standard melt by eqn (1) are shown in fig. 4. The equations corresponding to the lines in fig. 4 are given in table 2, along with the maximum and standard derivations. Activities of PbF2 in these melts, as calculated also by eqn (2), are included in fig. 3 for four PbF2/Si02 ratios, with PbO levels ranging from 60 to 95 rnol %. Error bars for each slag are included in the graph. Because of the high melting points (about 1153 K), and consequent high volatil- ization rates of the slags, the cells containing 94 mol % PbO + 3 rnol % PbF2 + 3 mol % Si02 and 94 mol % PbO +2 mol % PbF2 +4 mol % Si02 were operated only between 1163 and 1178 K. The activities of PbF2 at 1173 K for these compositions are shown also in fig.3. From this figure it may be seen that the PbF2 activity increases with addition of PbF2, at constant PbO levels. Also, for a constant PbF2/Si02 ratio, the activity of PbF2 increases steadily with decreasing PbO content. ISOACTIVITY PROFILES The results in fig. 3 were used to construct isoactivity contours for eight PbF2 activity levels at 1173 K. These are shown in fig. 5, along with the isoactivity con- tours determined previously for PbO. The profiles are slightly concave toward the PbO apex at low PbF2 activities, and away from the PbO apex at higher levels. The contour for apbFz = 0.1 is approximately linear. Table 3 presents the PbF2 activity data taken from fig. 3. XPbO FIG. 5.-Isoactivity contours for -, PbO [ref.(2)] and -a-, PbFz (this work) for the system PbO + PbFz + SiOp at 11 73 K.W. F. CALEY AND C. R . MASSON 2959 TABLE 2,-E.M.F. DATA FOR THE SYSTEM PbO+PbFz+SiOz (CELLS B AND D) XPbO 0.60 0.60 0.60 0.66 0.70 0.70 0.70 0.70 0.80 0.80 0.80 0.85 0.86 0.90 XPbFz 0.32 0.20 0.13 0.17 0.24 0.15 0.10 0.05 0.16 0.10 0.07 0.05 0.07 0.08 x~i02 0.08 0.20 0.27 0.17 0.06 0.15 0.20 0.25 0.04 0.10 0.13 0.10 0.07 0.02 E = A+BT/mV A - 55.6079 -66.1121 - 71.5736 - 70.3822 - 45.0980 - 51.2591 - 41 3220 - 40.7704 - 24.9363 - 4.828 1 - 28.2726 - 7.0429 - 3.6840 24.3271 0.1023 0.1242 . 0.1477 0.1466 0.1150 0,1444 0.1580 0.1945 0.1329 0.1435 0.1833 0.2055 0.1451 0.1716 standard deviahon/mV 0.3 0.6 0.5 0.1 0.1 0.2 0.7 0.7 0.2 0.5 0.2 0.4 0.6 0.5 maximum deviation/mV 0.5 0.9 0.8 0.2 0.2 0.5 1.3 1.4 0.4 0.1 0.4 0.7 1.3 1 .o TABLE 3.-ISOACTIVITY DATA TAKEN FROM FIG.3 FOR CONSTANT apbF2 AT 1173 K aPbF2 XPbO 0.30 0.585 0.61 5 0.20 0.604 0.670 0.700 0.15 0.583 0.646 0.718 0.750 0.10 0.640 0.700 0.775 0.807 0.05 0.71 5 0.772 0.838 0.870 XPbF2 0.332 0.385 0.198 0.264 0.300 0.139 0.177 0.226 0.250 0.120 0.150 0.180 0.193 0.095 0.114 0.130 0.130 0.198 0.066 qbF2 XPbO 0.025 0.700 0.785 0.844 0.888 0.906 XPbF2 0.050 0.072 0.078 0.090 0.094 XSioZ 0.250 0.143 0.078 0.022 0.278 0.177 0.056 0.02 0.805 0.866 0.900 0.91 5 0.065 0.67 0.080 0.085 0.130 0.067 0.020 0.240 0.150 0.045 0.190 0.1 14 0.032 - - 0.01 0.860 0.900 0.940 0.047 0.050 0.060 0.093 0.050 DISCUSSION Following the theoretical treatment outlined in the accompanying communica- tion,l ionic distributions of silicate and fluorosilicate anions in the ternary PbO + PbF2 + Si02 may be calculated from the activities of PbO and PbF2 for each melt composition, if the equilibrium constants k and k’ are known. The equilibrium constant k has the value 0.196,13 and the PbO and PbF2 activities for any melt com- position may be obtained from fig.5. Knowing these three parameters, the follow- ing procedure was used to evaluate k’. Values of apbo (= N02-) and aPbFz (= N$) corresponding to the point of inter- section of a pair of isoactivity lines in fig. 5 were first selected. These values were substituted along with the value of k (= 0.196) and an arbitrary value of k’ in eqn2960 THERMODYNAMICS OF PbO+PbF, +SO, MELTS (19) and (23)-(25) of ref. (1) to yield a calculated value for the composition of the melt.The process was repeated with other values of k‘ until a value was found which yielded a composition close to the experimental value at the point of intersection of the isoactivity lines. The value of k’ thus determined was then used to calculate compositions corresponding to other points of intersection in fig. 5. This value was then adjusted so as to provide the best fit with the bulk of the experimental data over the entire range of compositions. TABLE $.-CALCULATED AND EXPERIMENTAL MELT COMPOSITIONS FOR VARIOUS VALUES OF apbO AND aPbF2 (k = 0.196, k’ = 0.40) UPbO aPbF2 0.4 0.3 0.2 0.15 0.1 0.05 0.025 0.5 0.2 0.15 0.1 0.05 0.025 0.6 0.1 0.05 0.025 0.7 0.05 0.025 0.02 0.8 0.025 0.02 0.01 calculated XPbO 0.564 0.579 0.596 0.620 0.648 0.666 0.665 0.670 0.681 0.697 0.707 0.746 0.749 0.753 0.812 0.807 0.806 0.877 0.873 0.865 XPbFz 0.370 0.268 0.21 5 0.158 0.098 0.063 0.273 0.21 5 0.157 0.097 0.063 0.169 0.102 0.065 0.113 0.071 0.062 0.081 0.070 0.046 Xsioz 0.066 0.153 0.189 0.222 0.254 0,271 0.062 0.115 0.162 0.206 0.230 0.085 0.149 0.182 0.075 0.122 0.132 0.042 0.057 0.089 experimental XPbO 0.578 0.590 0.602 0.615 0.640 0.660 0.670 0.675 0.682 0.693 0.705 0.740 0.744 0.746 0.810 0.802 0.800 0.878 0.873 0.860 XPbFz 0.322 0.191 0.147 0.109 0.060 0.030 0.265 0.192 0.179 0.088 0.050 0.165 0.104 0.061 0.122 0.074 0.060 0.088 0.077 0.046 x5i02 0.100 0.219 0.251 0.276 0.300 0.310 0.065 0.133 0.139 0.219 0.245 0.095 0.152 0.193 0.068 0.124 0.140 0.034 0.050 0.094 In these calculations, which were performed with the aid of a computer, the moles C moles PbO + moles PbFz +moles SiOz following relationship was also required : xc = (3) where C represents PbO, PbF2 or SO2.The value of k’ found by this iterative procedure was 0.40+0.025. The results of these computations are given in table 4, which shows the calculated and experi- mental melt compositions corrresponding to the points of intersection of the iso- activity lines in fig. 5. Fig. 6 illustrates the range of applicability of the theory. The solid lines are the experimentally-determined isoactivity lines for PbO, as shown in fig. 5, and the points, taken from table 4, are calculated compositions for melts of selected aPbO for which the aGtivities of PbO and PbF, were obtained from fig. 5. The agreement between theory and experiment is reasonable for melts with aPbO >, 0.5.In this range ofW. F. CALEY AND C . R. MASSON 2961 XPbO FIG. 6.-Comparison of experimental iso-PbO activity contours (-) with theoretical melt compositions a for melts of selected QpbO and aPbF2, corresponding to the points of intersection of the isoactivity lines in 6g. 5. The compositions were calculated for k = 0.196, k’ = 0.400. 1.0 i XPbF, = O ..- 0. a 0.6 0.2 0.1.0 - I I I I 0.1 0.2 0.3 0.4 XSiOz lXPb0 FIG. 7.-Calcuiated on fractions of 02- and F- in PbO+PbF, +SOz melts at 1173 K.2962 THERMODYNAMICS OF PbO+PbF2+Si02 MELTS compositions the theoretical expressions derived previously are applicable and may be used to evaluate ionic distributions in this system.IONIC DISTRIBUTIONS Calculated ion fractions for 02- and F- are plotted in fig. 7 against XSi02/XpbO for various values of &bF2. These were obtained by interpolation from the experi- mental isoactivity curves in fig. 5, with No2- = apbo and NF = atbF2. 0.25 0.20 0.1 5 I VP 0 .I s 0.10 0.0 5 0 Xsioz lxpw FIG. 8.-Calculated ion fractions of SiOd- in PbO+PbFz+SiOz melts at 1173 K. Values of N02- and NF- from fig. 7 were substituted, along with k = 0.196 and k' = 0.4, in eqn (19) and (13) of ref. (1) to yield the ion fractions of silicate and fluoro- silicate anions. The results for SiO$- and Si20$- are shown in fig. 8 and 9. The addition of relatively small amounts of PbF2 to a melt of fixed Si02/Pb0 ratio causes a marked lowering in the ion fractions of these species.In addition, the maximum in these distributions (which, in the absence of PbF2, occurs at &ioz/&bo = 0.5 for SiOt- and 0.667 for Si20$-) is displaced to lower xsiOz/&bO ratios as XpbF2 is increased. The calculated ion fractions of the monofluorosilicate ions Si03Fi- and Si206F5- are shown in fig. 10 and 11. There is evidence that these ion fractions also exhibit maxima at specific Si02/Pb0 ratios but, except for melts with XPbF2 = 0.15, the results are not sufficiently extensive to illustrate this feature.xSiO2 lXPb0 FIG. %-Calculated ion fractions of Si20:- in PbO + PbF2 + Si02 melts at 1173 K. xSiO2/xPbO FIG. 10.-Calculated ion fractions of Si03F3- in PbO+PbFz+SiOz melts at 1173 K.2964 THERMODYNAMICS OF PbO+PbF2+SiOa MELTS TABLE 5 .-CALCULATED ION FRACTIONS OF OXIDE, FLUORIDE, SILICATE AND FLUOROSILICATE IONS IN MELTS WITH XSiOz = 0.2 ion 02- F- SiO$- Si03F3- Si02F3- SiOF, SiF4 ion fractions for melt compositions (N 3 0.0001) x s i o z = 0.2 xsio2 = 0.2 0.4150 0.693 0.5200 0.2449 0.4472 0.280 0.1780 0.0767 0.0335 0.0330 0.0063 0.0142 0.001 2 0.006 1 0.0002 0.0026 xsio2 = 0.2 XPbo = 0.7 XPbo = 0.6 XPbo = 0.8 XpbF2 = 0.1 XpbFz = 0.2 si2067 - 0.022 0.01 19 0.0028 Siz06F5- 0.0023 0.001 2 Siz05 Fi- 0.0004 0.0005 Si204F:- 0.0001 0.0002 Si203Fa- - o.oO01 Si202F; - - Si20F6 - - Si30:; 0.001 8 0.0008 0.0001 si309~7- 0.0002 - Si308@- I - si40; $j- 0.0001 o.Ooo1 - x 0.005 0.004 0.003 I n % 0, .* z 0.002 0.9969 0.9999 0.9997 X P b F , = 0.10 1 O.OO' 1- xSiOz/xPbO FIG.ll.-Calculated ion fractions of Si20sF5- in PbO+PbF2+Si02 melts at 1173 K.W.F. CALEY AND C. R. MASSON 2965 In the melts under consideration, ion fractions of higher fluorosilicate ions (SiO,Fg-, SOFT, Si205Fi-, Si,O,F3-, etc.) are generally very low, but become increasingly significant as XPbF2 is increased. Table 5 shows the calculated ion fractions of various species when PbF2 is substituted for PbO in a melt of original composition X,,, = 0.8, Xsioz = 0.2. Ion fractions < 0.0001 are not reported. The bulk of the fluorosilicate ions are of low molecular weight, as might be expected for highly basic melts of this nature. Replacing PbO by PbFz leads to an increase in the sum of the free oxide and fluoride ions and a corresponding decrease in the sum of the ion fractions of the " monomeric ", " dimeric ", and higher silicate and fluoro- silicate ions.The net effect of substituting PbFz for PbO at constant silica content is thus to cause a decrease in the mean chain length of the anions, a result which might be anticipated and which is in line with viscosity and other considerations. The calculated ion fractions shown in table 5 together constitute 99.69-99.99 % of the total. 0.08 0.07 0.0 6 0.05 R 8 0.04 & .3 u d .I 0.03 0.02 0.0 I 0 XSiOZ/XPbO FIG. 12.-Calculated ion fractions of Si0.+mFg,4-m) - in PbO + PbFz + Si02 melts with XpbF2 = 0.2 at 1173 K.2966 THERMODYNAMICS O F PbO+PbF,+SiO, MELTS Fig. 12 and 13 show the calculated ion fractions of the monomeric Si04-,,tFc-m-) and dimeric Si,O,-,Fg-")- species in melts for which XPbF2 = 0.2.At the highest silica content (Xsio2/Xpbo = 0.333) these ions constitute 13.74mol % of the total, the remainder being essentially 0,- (41.50 %) and F- (44.72 %). An interesting feature is the emergence of the uncharged molecular species SiF4 as a small but signifi- cant constituent when the silica content of the melt is increased. As this species is volatile, the equilibrium will be displaced. This may partly account for the difficulty in obtaining steady e.m.f. values for melts with higher PbFz contents. The result is in line with the observation of Mitchell l4 that SiF4 is lost from CaO + CaF, + SiO, melts of high CaF, content and of Kumar et a l l 5 that the loss of SiF4 from CaO + CaF, + SO2, Na,O + NaF + SiO, and MgO + CaF, + SiO, melts is strongly dependent on the basicity.0.003C O.OC25 0.00 20 d 2 0.0015 E .- U .- 0.0 0 l o 0.0005 XSiOz/XPbO FIG. 13,-Calculated ion fractions of Si207-mF(,6 in PbO+ PbF2 + SiOz melts with XpbFz = 0.2 at 1173 K. (Ion fractions of Si20F6 were too small for illustration). In view of the simplifying assumptions in the theory, the calculated ionic-distribu- tions reported here must be regarded as approximate, and subject to refinement. An important limitation is the assumption that the reactivity of the 0- groups is not influenced by their degree of substitution by F on the silicate ions. This cannot beW. F. CALEY AND C. R. MASSON 2967 expected to hold rigorously, in view of the difference in electronegativity between the 0 and F atoms (3.5 and 4.0, respectively), so that the value of k’ must vary, to same extent, with the value of m.In addition, restriction of the treatment to linear chains confines the theory to highly basic melts. The results, however, provide a basis for a more complete description of these systems and yield some insight into the factors which govern their thermodynamic properties. The conclusion that discrete fluorosilicate ions are present in PbO + PbF2 + Si02 melts is supported by the results of a recent investigation l6 in which these ions were identified chromatographically as their trimethylsilyl derivatives in extracts of PbO + PbF2 + Si02 glasses by a method described elsewhere?’ We thank Dr. A. E. Grau, who participated in the early stages of this work, and Miss N. Morrison for experimental assistance. We also thank Dr. G. K. Muecke for the microprobe analyses. C. R. 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