Impact of recently discovered sodium calcium silicate solutions on the phase diagrams of relevance for glass-ceramics in the Na2O-CaO-SiO2 system

examined in more detail. The fundamental data obtained can be employed for the thermodynamic reassessment of the Na 2 O-CaO-SiO 2 system. The present study also discusses the findings and their impact on melting and annealing processes during the manufacture of glass and glass-ceramics.


Introduction
Soda-lime-silica is the most important glass family in daily life because 90 % of the manufactured conventional glasses in the world belong to the Na 2 O-CaO-SiO 2 system [1].The Na 2 O-CaO-SiO 2 glass system is also vital in many medical applications, including several compositions used for tissue engineering and drug delivery [2,3].Understanding the behavior of the Na 2 O-CaO-SiO 2 system, e.g., the phase relations among those present at high temperatures, is therefore crucial for manufacturing these glasses and ceramics.One tool to help manufacturers in the essential task of successfully predicting the melting range of a particular mixture and the crystalline phases formed during any subsequent heat treatment is the detailed understanding of the phase diagram Na 2 O-CaO-SiO.However, the data used to construct this diagram is based on the classic papers by Kracek [4] and Morey and Bowen [5] in 1925 and further developed by Segnit [6], as resumed in the book of Phase Diagram for Ceramist [7].For the metallurgical industries, the system is vital for slags as Na 2 O could significantly decrease their melting point and increase a slag's capacity to remove impurities [8].For the incineration technology to process the Municipal Solid Waste (MSW), the system is important as the slag, accounted for 85 % by weight formed in the bottom of the reactors as the solid residue, contains considerable amounts of Na 2 O, CaO and SiO 2 [9,10] Morey and Bowen [5] experimentally investigated the phase relations of liquid with solid phases in the Na 2 O-CaO-SiO 2 system by using the melting-quenching technique.The samples were prepared from the mixture of CaCO 3 , Na 2 CO 3 and SiO 2 heated using platinum crucible to form a glass which was used for the phase equilibria measurement.The glass composition was analyzed before the equilibration to measure phase relations.The quenched phases were examined by using optical microscope.They reported SiO 2 , CaSiO 3 , Na 2 SiO 3 , Na 2 Si 2 O 5 , Na 2 Ca 2- Si 3 O 9 , Na 8 Ca 3 Si 5 O 17 , Na 4 CaSi 3 O 9 , and Na 2 Ca 3 Si 6 O 16 primary phase fields.Then, Segnit [6] used the same experimental method used by Morey and Bowen [5] extended the study to the area containing less SiO 2 and reported a new compound of Na 8 Ca 3 Si 5 O 17 and measured liquidus data in the new primary phase fields Na 8 Ca 3 Si 5 O 17 , Ca 2 SiO 4 , Ca 2 Si 2 O 7 , Na 2 CaSiO 4, and Na 2 Ca 2 Si 2 O 7 .He [6] experienced difficulty at high temperatures due to soda volatilization.Later, Sahid and Glasser [11] revised the diagram after finding new crystalline phases of Na 2 CaSi 5 O 12 and Na 6 Si 8 O 19 and measured their liquidus points employing the same methods as Morey and Bowen [5].
However, the chemical composition measurements of the glasses reported by Morey and Bowen [5], Segnit [7], Sahid and Glasser [11] were undertaken before the re-melting in the equilibration process during which liquidus of the mixtures was measured.The phases in the quenched samples were examined using optical microscopy.As Na 2 O is a volatile component, losing Na 2 O to the atmosphere during the melting is likely to change the concentration of Na 2 O compared to the initial mixture.With regard to this limitation, post-equilibrium chemical analysis of the sample by employing the Equilibration-Quenching-EPMA method may be the solution [12].Zhang et al. [13] also employed this method, although they quenched their samples in a nitrogen atmosphere that gives a slow quenching rate.As indicated in their results, the quenched liquid phases were not homogenous because they turned into microcrystalline phases during the quenching.This change proves that the liquid properties stable at high temperatures cannot be preserved to room temperature as the melt's composition might alter during the quenching process.Therefore, it is difficult to indicate the composition of the phases formed and phase relations from their results [13].
The existence of two solid solutions in the ternary system was reported by Moir and Glasser [14] when they reexamined the stability of combeite (Na 2 Ca 2 Si 3 O 9 ) and Na 4 CaSi 3 O 9 compounds characterized by using XRD analysis for the samples synthesized using Morey and Bowen's techniques [5].They showed that combeite was not a stoichiometric compound of Na 2 Ca 2 Si 3 O 9, neither Na 4 CaSi 3 O 9 .These compounds form solid solutions existing in the pseudo-binary Na 2 SiO 3 -CaSiO 3 system.Combeite has a compositional range of Na 2 SiO 3 between 28.5 and 53.5 mol-%, whereas the Na 4 CaSi 3 O 9 has a much smaller range.They also reported solid solution of β-CaSiO 3 that can dissolve up to 2 mol-% Na 2 SiO 3 .Fedorov and Brodkina [15] outlined a solid solution of β-Ca 2 SiO 4 in the pseudo-binary Ca 2 SiO 4 and Na 2 CaSiO 4 .β-Ca 2 SiO 4 was found to dissolve up to 10 wt-% Na 2 CaSiO 4 at 1300 • C at which the sample was annealed and then characterized by XRD method.Toropov and Arakelyan [16]  In terms of thermodynamic modeling, Thermo-Calc [18] was employed by L. Zhang et al. [17] to assess the Na 2 O-CaO-SiO 2 system.The sub-lattice model was used to describe the Gibbs energy of liquid.Later, Z. Zhang et al. [19] assessed the system using a modified associated species model to evaluate the Gibbs energy of the liquid phase and employing FactSage using FToxid database [20] for the calculation.Some disagreements were obvious between the results in these two works by Z. Zhang et al. and L. Zhang et al.For example, in the diagram produced by L. Zhang et al. [17], the pseudo-binary Na 2 SiO 3 -CaSiO 3 section was much more complicated than the one presented by Z. Zhang et al. [19].It is because the computed quasi-binary diagram by L. Zhang et al. [17] did not indicate the stability of the Ca 2 SiO 4 , Na 2 Si 6 O 7 , and Na 2 Ca 2 Si 3 O 9 compounds.However, these compounds were stable in the computed quasi-binary diagram by Z. Zhang et al. [19].
Kahlenberg et al. [21] recently reported the Na 2 Ca 6 Si 4 O 15 compound.Its liquidus data have not been available in the literature.Therefore, the inclusion of this compound in the thermodynamic assessment of the Na 2 O-CaO-SiO 2 system will affect the computed phase diagrams.They [21] synthesized the compound by using Na 2 CO 3 -Ca-CO 3 -SiO 2 placed in a platinum container and heated 1300 • C and then quenched.The sample was characterized by using EPMA to measure chemical compositions and by employing X-ray diffractometer to collect crystallographic data.The existence of some compounds, such as Na 8 Ca 3 Si 5 O 17 , Na 2 Ca 3 Si 2 O 8 and Na 2 CaSi 5 O 12 , was questioned [22] as they cannot be reproduced experimentally by using the crystallization approach and solid-state syntheses.
It is obvious that there is a lack of reliable experimental liquidus data for mixtures with higher Na 2 O contents.The omission of liquidus data for the newly reported crystals is evident.Disagreement among the authors [17,19] is also apparent.To conclude the above analysis, to better understand the formation of suggested additional crystalline phases and their liquidus, experimental reinvestigation of the system Na 2 O-CaO-SiO 2 is required.In the present study, the Equilibration-Quenching-EPMA/EDS method was employed to study the Na 2 O-CaO-SiO 2 system over a wide composition range of SiO 2 from 33.33 to 84.2 mol-% and Na 2 O up to 47.5 mol-% between 1000 and 1400 • C. The primary phase fields were explored to derive the saturation boundary lines of the compounds.Furthermore, liquidus with double saturation was also studied to obtain the univariant lines, which are the boundary lines between two adjacent primary phase fields.Comparison of the data obtained in the present work to previous research, as well as the computed phase diagram was undertaken.The results are discussed in relation to the manufacturing of the glass.

Methods
When investigating the equilibrium properties of phases occurring at high temperatures, the phases must be preserved by rapid cooling in a cold medium.Then, the composition and homogeneity of the phases can be examined under a microanalyzer.The liquid must be preserved as a glassy phase, and also the solid phase composition must be maintained.In the present investigation, the sample preparation challenges, were met by utilizing the Equilibration-Quenching-EPMA/EDS technique.

Sample preparation
The high purity chemicals presented in Table 1 were used for the preparation of the initial mixtures.The chemicals were weighed and mixed carefully using an agate mortar and pestle, then pressed to form a 0.15 g pellet.It was important to know the degree of Na 2 O volatilization during the equilibration process; thus, the excess amount of Na 2 O in the samples was specified accurately to obtain the targeted phase relations.Failing to take into account the volatilization would result in unwanted phase equilibria as the evaporation changes the location of the tie lines and the proportions between equilibrium phases.
Na 2 O concentration in the mixture was adjusted to form a liquid saturated with one or several crystalline phases.Otherwise, if the mixture formed upon quenching only amorphous phase(s), the liquidus boundaries would not be revealed.For this purpose, the diagram computed by FactSage using FToxid database [20] and MTDATA [23] using MTOX database [24] were used as the initial guidance for the mixtures.

Equilibration process
The pellets were placed in a platinum container and held by a platinum wire in the center of the hot zone of the reaction tube with 30 mm inner diameter, made from impervious recrystallized alumina, inside a furnace (Nabertherm RHTV 120-150/18, heated with MoSi 2 heating element, Germany) to equilibrate the samples.The arrangement of the furnace and the design of the Pt crucible can be seen in Figs. 1 and 2, respectively.The top of the reaction tube was equipped with two holes for the thermocouple sheath and one for a mini tube to protect the wire.
A calibrated S-type thermocouple of Pt/Pt-10 wt-% Rh (Johnson-Matthey, UK) was placed close to the samples and connected to a multimeter (Keithley, USA), which was linked to a computer program (NI LabView) to continuously measure and document the temperature of the samples every 5 s.Temperature uncertainty of ±2 • C was achieved.The bottom of the reaction tube was open to the air.

Equilibrium confirmation
Equilibrium attainment can be ensured from three different criteria: time, the direction of approach, and homogeneity.An equilibrium has been reached if samples heated at different equilibration times but at the same temperature locate on the same liquidus line.Therefore, samples in the present investigation were equilibrated at different holding times, and the results showed that the sample could reach equilibrium after 1 h or 2 days depending on temperature and the specific type of equilibria.The second criterion means that the same equilibrium state must be reachable either by heating the sample directly to the targeted temperature or by pre-melting, i.e., overheating the sample and then cooling it down to the targeted temperature.Also, the criterion is satisfied if different compounds used as the initial mixture can produce the same equilibrium condition.In the present investigation, mixtures of Na 2 CO 3 -CaO-SiO 2 or Na 2 SiO 3 -CaO-SiO 2 were employed (used as the main mixtures) to ensure that the solid phase in the final state was formed by chemical reactions, not from the unreacted oxides in the initial mixture.
The equilibrium state can be attained as well from the direction of the right side with lower Na 2 O content and from the left side with higher Na 2 O content.For example, the equilibrium state of Na According to the third criterion, no concentration gradient in any phase is allowed.Hence, the liquidus microanalyses were undertaken at multiple locations to ensure an equal concentration throughout the phases.

Quenching
After the equilibrium was achieved, the sample was dropped to cooled water by pulling upward the platinum wire that holds the sample.The quenched samples were then dried immediately using hot flash air and mounted in epoxy resin.The sample was polished by using a dry technique, carbon coated and sent for chemical analysis.There was no difficulty to obtain samples which contained glassy phase.

Phase examination
The samples were analyzed using EPMA (JXA-8530 F Plus Hyper Probe, Jeol, Japan) at Center for Material Analysis, University of Oulu and EDS (ThermoFisher Scientific UltraDry, USA) installed in SEM (Tescan Mira3, Tescan, Czech Republic) at Aalto University.Optimized instrument parameters were needed because of matrix modification resulted from the sodium ion migration in the sample during measurement.For the EPMA measurement 15 kV, 15 μm and 10 s of accelerating voltage, beam diameter, measuring time, respectively, were selected to measure the glass/amorphous phases.For the EDS measurement, area analysis of 100-200 μm 2 , 15 kV accelerating voltage and 420 nA current were employed.Tugtupite (Na 4 BeAlSi 4 O 12 Cl), calcite (CaCO 3 ) and quartz (SiO 2 ) minerals were used as Na, Ca and Si standards, respectively.ZAF correction was used for EPMA and EDS analyses.A comparison of results between EDS measured values and true stoichiometric values are presented in Table 2. Table 3 shows a comparison of the result obtained with EDS and EPMA analyses of the Na 2 CaSiO 4 ss compound and its amorphous phase representing the liquid phase at the high      temperature equilibrium condition.
It can be seen in Table 2 that the EDS results are in very close agreement with the theoretical values.They are also in good agreement with the EPMA results, as indicated in Table 3.The maximum uncertainties obtained were less than 1 mol-%.In the present study, EDS analysis results of liquid phase are presented together with the results of solid phase analysis, in Table 4. Therefore, the analysis accuracy of each amorphous phase, i.e., liquid phase at the high temperature, also can be checked from the results of the respective solid phase.The method is summarized in Fig. 3.

Computational phase diagram
The computed phase diagrams presented were calculated by FactSage 7.3.using FToxid database [20] and MTDATA [23] using MTOX database, version 8.2 [24].The obtained phase diagrams were then compared with the experimental data.

Result and discussion
The compositional analyses of the amorphous (liquid) and solid phases using EDS are reported in Table 4.In the present study, 10 primary phase fields were obtained since altogether 10 solid compounds were found to exist in equilibrium with the liquid phase and verified in the quenched samples.These were the phase fields of SiO   fields along the univariant lines drawn as a solid black line in Fig. 11.
The microstructures are represented by the amorphous phase in equilibrium with two solid phases in Fig. 5.In the isothermal sections, this liquid is depicted by the tie triangle connecting the liquid with the two solid compounds.Altogether, 18 different phase assemblages of the quenched samples were obtained in the present study.These assemblages are collected in Comparisons between the experimental data and the calculated phase diagrams by FToxid database [20] are presented in Figs. 13 and 14 as CaSiO 3 -Na 2 SiO 3 and Ca 2 SiO 4 -Na 4 SiO 4 pseudo binary diagrams, respectively.Figs.[15][16][17] show comparisons between the computed diagrams by FToxid [20] and MTOX databases [24] and the data at 1000, 1200 and 1400 • C, respectively.

Behavior of Na 2 O
The study of the Na 2 O evaporation was similar to that used in an earlier study of K 2 O [25].Fig. 18 shows how the tie lines move due to the evaporation of Na 2 O.The remaining Na 2 O content in the equilibrium phase at a specific temperature depended on the equilibration time and the concentration of Na 2 O in the initial mixture.If Na 2 O evaporates gradually, the composition will also change gradually following the evaporation line toward the CaO-SiO 2 side, drawn as a dashed line.As shown in Fig. 18, Na 2 O concentration in sample NCS-81 decreased from 42.5 mol-% to 31 mol-% after being equilibrated for just 6 h at 1200 • C.However, sample NCS-13 with Na 2 O concentration of 10 mol-% in the initial mixture decreased to 7.5 mol-% after 44 h equilibration.Therefore, to obtain a particular final equilibrium assemblage, the specific concentration in the initial mixture must be carefully adjusted.

Primary phase field of SiO 2
The liquidus point data in SiO 2 primary phase field at 1000 • C are in good agreement with the FToxid database [20] and have slightly lower Na 2 O solubility than that calculated with the MTOX database [24] (Fig. 15).The data agree with those reported by Santoso and Taskinen [12], who measured the liquidus data at SiO 2 saturation in the binary Na 2 O-SiO 2 system.MTDATA and its MTOX database [24] used the data by Kracek [4] and Morey and Bowen [5] in its assessment where the calculated liquidus line will have higher Na 2 O concentration.Thus, the measured liquidus line should be lower in Na 2 O content compared to the MTOX database simulation due to some Na 2 O evaporation in the experiments by Kracek [4] and Morey and Bowen [5].The present study reports liquid data in double saturation of SiO 2 and CaSiO 3 (Fig. 5A), thus providing data to locate the intersection between the SiO 2 and CaSiO 3 primary phase fields.The locations of intersection between SiO 2 and CaSiO 3 in the ternary diagram has a higher CaO content than calculated by the FToxid database [20], as indicated in Figs.16 and 17.

Primary phase field of CaSiO 3
Between 1200 and 1400 • C, liquidus point data at CaSiO 3 saturation are lower in Na 2 O content than the liquidus line predicted by FToxid [20] and MTOX databases [24] (Figs.16 and 17).This difference can be explained by the fact that these two softwares are, again, based on Kracek [4] and Morey and Bowen [5]  (Fig. 5I) were obtained at 1300 and 1400 • C, meaning that the intersection location between primary phase fields of CaSiO 3 and Ca 3 Si 2 O 7 is known in the ternary diagram.

Primary phase field of Ca 3 Si 2 O 7
The primary phase field of Ca 3 Si 2 O 7 obtained in the present study is very narrow, as shown in Fig. 11.The width of the liquidus contours is relatively constant at low and high Na 2 O concentrations, which agrees  with the Segnit [6] report and the values computed with the MTOX database [24].This kind of feature of the Ca 3 Si 2 O 7 primary phase field was also found to be typical to the Ca 3 Si 2 O 7 primary phase field in the Ka 2 O-CaO-SiO 2 system [25].It differs, however, from the line computed with the FToxid data [20].The computed field becomes much wider toward the Na 2 O-SiO 2 direction.Nevertheless, as shown in Fig. 17, the location of the intersection between the Ca 2 SiO 3 and Ca 3 Si 2 O 7 primary phase fields is in good agreement with the predictions of FToxid [20] and MTOX databases [24].

Primary phase field of Ca 2 SiO 4
In the present study, the primary phase field Ca 2 SiO 4 was observed at 1300 and 1400 • C. At 1400 • C, Ca 2 SiO 4 dissolved 3.1 mol-% Na 4 SiO 4 and appears in the pseudo-binary Ca 2 SiO 4 -Na 4 SiO 4 section (Fig. 14).It means that Ca 2 SiO 4 formed a solid solution extending to the direction of Na 2 CaSiO 4 ss, and the maximum solubility of Na 4 SiO 4 can be greater than 3.1 mol-% Na 4 SiO 4 .This is consistent with the results of Fedorov and Brodkina [15].The primary phase field of Ca 2 SiO 4 intersects with the Na 2 Ca 6 Si 4 O 15 field at 1300 and 1400 • C, as well as the Ca 3 Si 2 O 7 field, whereas FToxid [20] and MTOX databases [24] predict that at 1300 and 1400 • C, Ca 2 SiO 4 directly crosses the CaO primary phase field.Liquidus at Ca 2 SiO 4 saturation obtained in the present investigation is in good agreement with the MTOX database [24] computation.

Primary phase field of Na 2 Ca 6 Si 4 O 15
Na 2 Ca 6 Si 4 O 15 crystals were formed in the sample equilibrated at 1300 and 1400 • C, thus confirming the observations by Kohlenberg [21].In addition, the present study successfully measured novel liquidus data at Na 2 Ca 6 Si 4 O 15 saturation.The intersection between the Na 2 Ca 6- Si 4 O 15 and Na 2 CaSiO 4 ss primary phase fields between 1300 and 1400 • C was finally confirmed since the liquid phase in the double saturation of Na 2 Ca 6 Si 4 O 15 and Na 2 CaSiO 4 ss was verified (Fig. 5F).This compound, Na 2 Ca 6 Si 4 O 15, is not present in FToxid database [20] and MTOX database [24].

Primary phase field of combeite
As can be seen in Fig. 13, the combeite phase obtained was located in the pseudo-binary section of Na 2 SiO 3 and CaSiO 3 , ranging for CaSiO 3 concentration from 50 to 73 mol-%.The solubility of CaSiO 3 in combeite increased with increasing temperature when it in equilibrium with CaSiO 3 .This observation agrees with the computational phase equilibria of the FToxid database [20] and the data by Moir and Glasser [14].The liquidus point data obtained in the present investigation are in good agreement with the FToxid database [20] between 1000 and 1200 • C and the MTOX database [24] at 1000 • C (Figs. 15 and 16).MTOX database [24] regards combeite as a stoichiometric compound of Na 2 Ca 2 Si 3 O 9 .Its computed liquidus line at 1200 • C (Fig. 16) is in poor

Table 5
Phase assemblages and their microstructures in the present investigation.agreement with the data obtained in the present investigation.Liquid compositions with the double saturation of combeite with Na 2 Ca 3 Si 6 O 16 (Fig. 5B), Na 4 CaSi 3 O 9 ss (Fig. 5C), CaSiO 3 (Fig. 5D), and Na 2 Ca 2 Si 2 O 7 ss (Fig. 5E) were obtained in the present investigation.It means that the locations of the intersections and phase boundaries between combeite with the mentioned primary phase fields are now known in the diagram for the temperature range between 1000 and 1200 • C.

Primary phase field of Na 2 Ca 2 Si 2 O 7 ss
The present study indicates that Na 2 Ca 2 Si 2 O 7 is not a stoichiometric compound but forms a solid solution, Na 2 Ca 2 Si 2 O 7 ss, for which the Na 2 O concentration in the solution varies from 17.6 to 26.5 mol-% at 1200 • C.This finding provides novel experimental verification showing that Na 2 Ca 2 Si 2 O 7 ss can form a solid solution.MTOX database [24] considered Na 2 Ca 2 Si 2 O 7 as a stoichiometric compound, and the computed liquidus line at 1200 • C is in poor agreement with the data obtained in the present investigation (Fig. 16).FToxid database [20] predicted that Na 2 Ca 2 Si 2 O 7 ss primary phase field does not exist at 1200 • C (Fig. 16).Liquid at double saturation of Na 2 Ca 2 Si 2 O 7 ss with Na 2 Ca-SiO 4 ss (Fig. 5H) was observed in the present investigation and, thus, the location where these two primary phase fields cross each other can be located in the ternary diagram.

Primary phase field of Na 2 CaSiO 4 ss
The details of the location of Na 2 CaSiO 4 ss in the diagram are presented in Fig. 14.As can be seen in Fig. 14, Na 2 CaSiO 4 ss is stable in the pseudo-binary Na 4 SiO 4 and Ca 2 SiO 4 systems.In the ternary diagram, the solid solution is located at a constant SiO 2 concentration of 33.33 mol-%.Between 1100 and 1400 • C, the maximum solubility of Na 4 SiO 4 concentration in the solid solution is between 55.8 and 66.4 mol-% and it

Table 6
Invariant points and the respective phases obtained in present study, pervious investigation [19] and computation [20]   increases with increasing temperature.FToxid [20] and MTOX databases [24] regard Na 2 CaSiO 4 ss as a stoichiometric compound in their assessments.Thus, the computed liquidus at Na 2 CaSiO 4 saturation is in poor agreement with the data obtained in the present investigation.As can be seen in Fig. 15, at 1200 • C, the FToxid database [20] predicts that the ternary liquid can contain CaO up to around 53 mol-%.In contrast, according to the present investigation, the maximum CaO concentration in the ternary liquid is only 27.2 mol-%.This can be explained by Na 2 CaSiO 4 ss being stable within a wide composition range.Thermodynamically, it will reduce the fully liquid region in the ternary diagram.Therefore, the insertion of Na 2 CaSiO 4 ss to the thermodynamic evaluation of the Na 2 O-CaO-SiO 2 system will significantly change the phase assembly of the computed phase diagrams.Accordingly, it is highly recommended that this phase is taken into account as the diagrams in this ternary system are employed in many industrial applications.

Primary phase field of Na 4 CaSi 3 O 9 ss
It can be seen in Fig. 15 that Na 4 CaSi 3 O 9 ss is stable at 1000 • C and the liquidus contours obtained in the present investigation are in good agreement with FToxid [20] and MTOX database [24] calculations.Na 4 CaSi 3 O 9 ss (Fig. 13) was also observed to form a solid solution in a narrow range of compositions, as also reported by Moir and Glasser [12].Since the liquidus contour at double saturation of Na 4 CaSi 3 O 9 ss and Na 2 Ca 2 Si 2 O 7 ss (Fig. 5G) was analysed in the present investigation, these solid solutions will be in equilibrium with each other along the univariant lines at different temperatures.However, the FToxid database [20] predicts that the Na 4 CaSi 3 O 9 ss primary phase field does not connect to the Na 2 Ca 2 Si 2 O 7 ss field, but to Na 8 Ca 3 Si 5 O 17 , as reported previously by Segnit [6].

Primary phase field of Na 2 Ca 3 Si 6 O 16
It can be seen in Fig. 15 that the liquidus data at Na 2 Ca 3 Si 6 O 16 saturation obtained at 1000 • C are in good agreement with the computation using the FToxid database [20].In contrast, the MTOX database [24] predicts the liquid phase domain at Na 2 Ca 3 Si 6 O 16 saturation to be narrower than the data obtained in the present investigation (Fig. 15).

Invariant points
By definition, a invariant reaction has zero degrees of freedom in given conditions.Thus, it is almost impossible to determine the exact location of an invariant point at a certain total pressure and temperature in the ternary diagram by experimentation, as the starting mixture already fixes the compositions of the equilibrium phases.Thus, the locations of invariant points were interpolated from temperature and composition data in the ternary diagram.The solid phases analyzed are plotted in Fig. 12 to examine the Alkemade lines [26,27] used to determine the type of the invariant point.The Alkemade lines connectingtwo crystalline compounds were drawn as solid red lines.The lines can only be drawn if the phase fields of the two crystals intersect each other, i.e., they share a common univariant line.Fig. 12 shows the lines of intersection between two adjacent primary phase fields, drawn as black solid lines with arrows indicating the direction of decreasing temperature.
Fig. 12 shows the Alkemade lines of Na Three Alkemade lines inside the ternary system cross their respective boundary lines of two primary phase fields.Firstly, the boundary between primary phase fields of combeite and Ca 3 Si 2 O 7 crosses the Alkemade line of combeite and Ca 3 Si 2 O 7 at point X 1 .Secondly, the Alkemade line of combeite and Na 2 Ca 6 Si 4 O 15 crosses the boundary between the fields of combeite and Na 2 Ca 6 Si 4 O 15 at point X 2 .Thirdly, the boundary between the primary phase fields of combeite and CaSiO 3 crosses the Alkemade line of combeite and CaSiO 3 at point X 3. Thus, according to the Alkemade theorem [26,27], points X 1 , X 1 and X 3 must be the local maximum points at which temperatures start to decrease in two opposite directions in the lines connecting two adjacent fields.

Implications of the results on the glass and ceramic manufacture
A typical manufacturing process of glass-ceramics is presented schematically in Fig. 19 [28].It involves melting an oxide mixture in a refractory-lined container to homogenize the melt.The viscous melt is formed to the desired shape, after which the sample is thermally treated to nucleate (T N , Fig. 19) the desired crystalline phases.Then, the temperature is increased to value providing growth of the crystals (T G , Fig. 19).Finally, the glass-ceramic sample is annealed to room temperature.The melting container size can be as large as an Olympic swimming pool if melting, for example, 1600 tons per day.Depending on the original mixture composition, the melting temperatures can be as high as 1600 • C [28] to produce a melt with a low enough viscosity needed to eliminate the gaseous inclusions and dissolve all the crystalline species in the original mixture.
For a glass-ceramic in the ternary system Na 2 O-CaO-SiO 2 , the ternary invariant point and liquidus temperatures can be employed to estimate the commencement of melting (0% L) and the exact melting point of the mixture (100 % L).The data generated in the present work can also be used to figure out the crystalline phases that form in the thermal treatments of glass-ceramics.However, it should be pointed out that the actual melting temperatures of viscous melts for glasses and glassceramics are also affected by the fining and homogenizing criteria.
Fig. 20 shows the liquidus contour compared with the values based on the FTOxid [20] database.The compositions of typical glasses for daily applications e.g., for windows and container glass are also marked in the figure as a large grey circle [28].Information about the eutectic points is critical for designing the glass since it quantifies the compositions which fully melt at the lowest temperature.This information might be useful when designing compositions with reduced energy and manufacturing costs.Fig. 20 shows that the melting point of a typical glass is actually lower if predicted by the data obtained in the present study than those predicted by FTOxid [20].The difference is around 50 • C and increases up to 100 • C if the concentration of the mixture located in the Na 2 Ca 3 Si 6 O 16 primary phase field moves toward primary phase field of CaSiO 3 as it showed that liquidus of 1300 • C from present study combined with liquidus of 1400 • C from FTOxid [20].Present data also can be used to predict the crystal phases and their proposition during annealing more accurately.For example, if the annealing is undertaken in sub-liquidus at certain temperature and as in the field of CaSiO 3 the liquidus surfaces obtained in the present study is lower it means that the proposition of crystal to liquid is also smaller than that predicted by FTOxid [20].Thus, data obtained in present study can be used for process optimization during melting and annealing.

Conclusion
Equilibration-quenching-EPMA/EDS method suggested solid solutions of Na 2 CaSiO 4 and Na 2 Ca 2 Si 2 O 7 in a wide range of compositions in the system Na2O-CaO-SiO2.The impact of the solid solutions on the ternary diagram was investigated together with the primary phase fields of SiO Five new invariant points were suggested based on the data obtained.The liquidus lines at saturation with two different crystalline phases as functions of temperature indicated the locations of the univariant lines as intersections between two adjacent primary phase fields.Comparisons of the data with previous investigations, assessment and computational results by FToxid database [20] databases and MTOX database [24] were also undertaken.Implications of current findings on the manufacturing of the glass and glass ceramics were discussed.The results suggest that Na 2 O-CaO-SiO 2 system needs to be reassessed as the many new stable compounds are likely to significantly change many features of the phase properties and the computationally predicted phase equilibria.This study provides fundamental data to be included in the thermodynamic databases.

2 ,
Na 2 Ca 3- Si 6 O 16 , combeite (Na 2 Ca 2 Si 3 O 9 ), Na 4 CaSi 3 O 9 ss, CaSiO 3 , Na 2 CaSiO 4 ss, Na 2 Ca 2 Si 2 O 7 ss, Na 2 Ca 6 Si 4 O 15 , Ca 3 Si 2 O 7 and Ca 2 SiO 4 .The micrographs of a liquid saturated with a single and two types of crystals are presented in Figs. 4 and 5 respectively.The detailed relation among the phases obtained is presented as isothermal sections at 1000, 1100, 1200, 1300 and 1400 • C in Figs.6-10, respectively.In the isothermal sections, this liquid is represented by tie lines connecting the liquid with the solid compound.The liquid phase is graphically presented as liquidus projections in Fig. 11.The solid phases connected by Alkemade lines are reported in Fig. 12.Each primary phase field intersects with the adjacent
data.Evaporation of Na 2 O should have shifted their data systematically away from the Na 2 O corner.According to Moir and Glasser [14], CaSiO 3 can dissolve Na 2 SiO 3 up to 5 mol-%.However, the present investigation proved that solid CaSiO 3 obtained at 1200 and 1300 • C contains only a negligible amount of Na 2 O. Liquid compositions at double saturation of CaSiO 3 and Ca 3 Si 2 O 7

Fig. 19 .
Fig. 19.A schematic diagram showing the steps in the manufacturing of the glass-ceramics [28].

Fig. A3 .
Fig. A3.Phase transformations of sample V during cooling from the melt to 1200 • C and further to room temperature, respectively.
identified two new compounds in the Ca 2 SiO 4 and Na 2 CaSiO 4 system, hexagonal Na 4 Ca 8 Si 5 O 20 and Na 4 Ca 4 Si 3 O 12 .However, according to Fedorov and Brodkina [15], Na 4 Ca 8 Si 5 O 20 is actually a β-Ca 2 SiO 4 solid solution and Na 4 Ca 4 Si 3 O 12 does not exist.

Table 1
Chemicals used in the present Investigation.
2 Ca 2 Si 2 O 7 solid solution (Na 2 Ca 2 Si 2 O 7 ss) can be reached from the Na 2 Ca 2 Si 3 O 9 solid solution (combeite) or the Na 2 CaSiO 4 solid solution (Na 2 CaSiO 4 ss).From the thermodynamic point of view, if the equilibria of liquid-Na 2 Ca 2 Si 2 O 7 ss exist, the equilibria of liquid-Na 2 Ca 2 Si 2 O 7 ss-Na 2 CaSiO 4 ss and equilibria of liquid-Na 2 Ca 2 Si 2 O 7 ss-combeite must exist as well.

Table 2
Comparison between EDS analysis results and stoichiometric values of the formed crystalline compounds.
Analysis Na

Table 3
Comparison between EDS and EPMA analysis results of the solid and liquid phases.

Table 4
Phase compositions measured by EDS analysis.
(continued on next page) I.Santoso et al.

Table 4
(continued ) (continued on next page) I.Santoso et al.
(1)]eans that B is a new ternary eutectic of liquid + combeite + Na 2 Ca 6 Si 4 O 15 + Ca 3 Si 2 O 7 located at the temperature close to 1285 • C. Point C is the ternary eutectic point of liquid + CaSiO 3 + combeite + Ca 3 Si 2 O 7 located close to 1280 • C. FToxid database[20]calculated Point C to be 1287.69•C,although it was predicted as peritectic, not as eutectic point.However, Z. Zhang et al.[19]estimated it to be close to 1400 • C.Furthermore, the present study suggests the existence of the following peritectic points:(1)liquid + Ca 3 Si 2 O 7 + Na 2 Ca 6 Si 4 O 15 + Ca 2 SiO 4 (Point A) close to 1295 • C; (2) liquid + Na 2 Ca 2 Si 2 O 7 ss + Na 2 Ca 6 Si 4 O 15 + Na 2 CaSiO 4 ss (Point D) at 1275 • C; (3) liquid + Na 2 Ca 2 Si 2 O 7 ss + Na 2 Ca 6 Si 4 O 15 + combeite at 1220 • C (Point F) and (4) liquid + Na 2 Ca 2 Si 2 O 7 ss + Na 4 CaSi 3 O 9 ss + combeite (Point G), located 1130 • C. Peritectic points of liquid + Na 2 Ca 3 Si 6 O 16 + CaSiO 3 + combeite (Point H) at 1050 • C, and liquid + Na 2 Ca 3 Si 6 O 16 + SiO 2 + CaSiO 3 (Point I) at 1030 • C are suggested in the present study.Points H and I were calculated using the FToxid database [20] to be at 1046.11 and 1027.88 • C, respectively.The invariant points and their phases are summarized in Table 6.Furthermore, Figs.11 and 12 show that the ternary compounds of Na 2 Ca 6 Si 4 O 15 , Na 2 Ca 2 Si 2 O 7 ss, Na 4 CaSi 3 O 9 ss and Na 2 Ca 3- Si 6 O 16 are located not in their own phase field, meaning that they melt incongruently.As can be seen in Figs.11 and 12, crystals of Na 2 Ca 6- Si 4 O 15 , Na 2 Ca 2 Si 2 O 7 ss, Na 4 CaSi 3 O 9 ss and Na 2 Ca 3 Si 6 O 16 are located in the fields of Ca 2 SiO 4 , Na 2 Ca 6 Si 4 O 15, combeite and CaSiO 3 , respectively.