Thermodynamic Assessment of the P2O5-Na2O and P2O5-MgO Systems

Knowledge about the thermodynamic equilibria of the P2O5-Na2O and P2O5-MgO systems is very important for controlling the phosphorus content of steel materials in the process of steelmaking dephosphorization. The phase equilibrium and thermodynamic data of the P2O5-Na2O and P2O5-MgO systems were critically evaluated and re-assessed by the CALPHAD (CAlculation of PHAse Diagram) approach. The liquid phase was described by the ionic two-sublattice model for the first time with the formulas (Na+1)P(O−2, PO3−1, PO4−3, PO5/2)Q and (Mg+2)P(O−2, PO3−1, PO4−3, PO5/2)Q, respectively, and the selection of the species constituting the liquid phase was based on the structure of the phosphate melts. A new and improved self-consistent set of thermodynamic parameters for the P2O5-Na2O and P2O5-MgO systems was finally obtained, and the calculated phase diagram and thermodynamic properties exhibited excellent agreement with the experimental data. The difference in the phase composition of invariant reactions from the experimentally determined values reported in the literature is less than 0.9 mol.%. The present thermodynamic modeling contributes to constructing a multicomponent oxide thermodynamic database in the process of steelmaking dephosphorization.


Introduction
As society progresses, industries advance to higher developmental stages, leading to more demanding usage of steel materials and increased quality requirements for steel materials across various sectors.Phosphorus, as one of the detrimental elements in steel, serves as a critical indicator of steel quality.Therefore, the control of phosphorus content in steel remains a crucial target for enterprise development.In the steelmaking process, the inclusion of alkaline earth metal oxide fluxes such as MgO can effectively diminish phosphorus in liquid steel, while alkali metal oxide fluxes like Na 2 O also exhibit a strong dephosphorization effect [1].The phase diagrams and thermodynamic properties of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems are essential to effectively control the dephosphorization effect of slags and to understand the phosphorus distribution ratio between liquid iron and oxide slags such as Na 2 O and MgO.Furthermore, good thermodynamic descriptions provide phase diagrams and thermodynamic data that can also effectively provide a theoretical basis for material design [2][3][4][5][6].
Xie et al. [7] utilized the modified quasi-chemical model to describe the liquid phase and firstly optimized the thermodynamic parameters of the P 2 O 5 -Na 2 O system based on the reliable experimental phase diagram and thermodynamic properties, and their calculations were in good agreement with the experimental data, while the description of the enthalpy of formation of Na 5 P 3 O 10 was inaccurate.In 2015, Ding et al. [8] evaluated a P 2 O 5 -MgO system by using the modified quasi-chemical model to describe the liquid phase, and PO 4  3− was considered the basic unit of P 2 O 5 in the liquid phase, but the calculations showed significant discrepancies with the experimental data.Furthermore, a set of thermodynamic data describing the liquid phase with the modified quasi-chemical model does not simultaneously describe both the oxide and metal liquid phases, which limits the study of the phosphorus distribution ratio between liquid iron and oxide slags.Therefore, it is meaningful to construct a set of multicomponent thermodynamic databases that can describe both oxide and metal liquids using appropriate thermodynamic models to guide the addition of oxide fluxes in the steelmaking dephosphorization process.The ionic two-sublattice model allowing one set of the thermodynamic parameters to simultaneously describe both the oxide and metallic liquid [9] was used to describe the liquid phase for the first time in the current work.Additionally, the ionic two-sublattice model can not only rationally describe the phosphate melt structure but also adequately reproduce the thermodynamic properties of complex liquids such as slag [10,11].This is highly beneficial to the construction of a slag system multivariate database to guide steelmaking dephosphorization.
This work aimed to conduct a phase diagram thermodynamic optimization of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems using the CALPHAD (CAlculation of PHAse Diagram) approach through establishing suitable thermodynamic models.The crystal structure, limited measured phase diagram and thermodynamic properties were optimized to construct a Gibbs energy expression for each phase in the systems to obtain a set of thermodynamic parameters reasonably describing the phase diagrams, covering the whole composition range using Thermo-Calc software.

Review of Literature Data
The experimental phase diagram information and thermodynamic property data of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems are systematically evaluated.The crystal structures of the solid phases in the systems are listed in Table 1.

System
Compound Crystal System Space Group Reference Pmc2 1 [33] α/β/γ: the polymorph from high temperature to low temperature.[34][35][36][37][38][39].Partridge et al. [34], using thermal, microscopic and X-ray diffraction (XRD) analysis, determined the liquidus of the NaPO 3 -Na 4 P 2 O 7 system and confirmed the presence of the Na 5 P 3 O 10 compound.Two invariant reactions of L = β − NaPO 3 + α − Na 5 P 3 O 10 and L + α − Na 4 P 2 O 7 = α − Na 5 P 3 O 10 were reported to occur at 824 K and 893 K, respectively.And the melting points of NaPO 3 , Na 5 P 3 O 10 and Na 4 P 2 O 7 were 898 K, 788 K and 1258 K, respectively.In their work [34], the Na 4 P 2 O 7 and NaPO 3 phases exhibited a lot of phase transitions from room temperature to melting point.The transition temperatures of Na 4 P 2 O 7 were found to be 673 K, 783 K, 793 K and 818 K by differential thermal analysis (DTA).Two phase transitions of NaPO 3 at 677 K and 783 K were detected.Subsequently, Morey and Ingerson [35] also studied the phase equilibria of the NaPO 3 -Na 4 P 2 O 7 system in good agreement with the work of Partridge et al. [34].Two invariant reactions L = β − NaPO 3 + α − Na 5 P 3 O 10 and L + α − Na 4 P 2 O 7 = α − Na 5 P 3 O 10 were measured to have reaction temperatures of 825 K and 895 K, and the melting points of NaPO 3 and Na 4 P 2 O 7 were observed to be 901 K and 1262 K, respectively, but the third structure of NaPO 3 was not found.Turkdogan et al. [36], using the thermal, microscopic, and DTA methods, determined the phase diagram of the NaPO 3 -Na 3 PO 4 system and did not report the presence of Na 5 P 3 O 10 .Three invariant reaction temperatures of L = β − NaPO 3 + α − Na 5 P 3 O 10 , L + α − Na 4 P 2 O 7 = α − Na 5 P 3 O 10 and L = α − Na 4 P 2 O 7 + β − Na 3 PO 4 in the NaPO 3 -Na 3 PO 4 system were suggested to be 763 K, 893 K and 1218 K by Markina et al. [37], respectively.In 1970, Osterheld et al. [38] determined the phase transition temperature of the Na 4 P 2 O 7 -Na 3 PO 4 system below 1573 K by thermal analysis and high-temperature microscopy.They reported that the eutectic reaction L = α − Na 4 P 2 O 7 + β − Na 3 PO 4 occurred at 1225 K, and two compounds (Na 4 P 2 O 7 and Na 3 PO 4 ) melted congruently at 1271 K and 1785 K, respectively.In 1972, Berak et al. [39] observed three invariant reactions in the liquidus study of the Na 2 O-P 2 O 5 system.The liquidus data obtained from these works for the P 2 O 5 -Na 2 O system were in reasonable agreement and were used in the optimization process of the current work.The four compounds NaPO 3 , Na 5 P 3 O 10 , Na 4 P 2 O 7 and Na 3 PO 4 have polymorphic phase transitions, and the thermodynamic description of the phase transition of the compounds in the P 2 O 5 -Na 2 O system by Xie et al. [7] based on the reliable literature is more complete, which was considered in the thermodynamic assessment of the present work with refinement and improvement.It is worth noting that there is less information about the experimental phase relation of the P 2 O 5 -rich and Na 2 O-rich regions in the P 2 O 5 -Na 2 O system, which still needs to be further determined experimentally.
In 1909, Mixter [40] determined the enthalpy of formation of NaPO 3 from its elements using solution calorimetry (SCA).In 1967, Irving et al. [41] also utilized SCA to measure the enthalpy of formation of Na 3 PO 4 from its elements at 298 K. Subsequently, in 1968, Irving et al., [42,43] Krivtsov et al., [44] and Zhuang et al. [45] determined the enthalpies of formation of Na 4 P 2 O 7 , Na 5 P 3 O 10 and NaPO 3 from their elements using the SCA method.In 2011, Khaled et al. [46] measured the standard enthalpy of formation of Na 4 P 2 O 7 from its elements using the SCA method.These experimental results were incorporated into the present study with consideration for possible error margins.Andon et al. [47] determined the heat capacities of NaPO 3 , Na 5 P 3 O 10 , Na 4 P 2 O 7 and Na 3 PO 4 using adiabatic calorimetry within the temperature range of 10 to 320 K. Ashcroft et al. [48] measured the heat capacities of Na 4 P 2 O 7 and NaPO 3 from 298 to 620 K and determined the low-temperature transition enthalpy of Na 4 P 2 O 7 .Lazarev et al. [49] used DSC to measure the heat capacity of Na 4 P 2 O 7 in the temperature range from 300 to 1000 K and measured the low-temperature enthalpy of transition of the Na 4 P 2 O 7 .Grantscharova et al. [50] used DSC to determine the heat capacity of NaPO 3 between 468 and 675 K, but their measurements were much higher than those reported by Ashcroft et al. [48].Considering the above-reported heat capacity data, the data reported by Andon et al. [47], Ashcroft et al. [48] and Lazarev et al. [49] were considered in the present work to optimize the heat capacities of Na 4 P 2 O 7 and NaPO 3 .

P 2 O 5 -MgO System
The phase diagram of the P 2 O 5 -MgO system in the composition ranges from 0 to 50 mol.%P 2 O 5 was investigated by Berak [51] using thermal, microscopy and XRD analyses.In this concentration range, three intermediate compounds were observed: Mg 3 P 2 O 8 , Mg 2 P 2 O 7 and MgP 2 O 6 with melting points at 1630 K, 1655 K and 1438 K, respectively.These phases were considered as line compounds.The temperature of three eutectic reactions L = MgO + Mg 3 P 2 O 8 , L = Mg 3 P 2 O 8 + α − Mg 2 P 2 O 7 and L = α − Mg 2 P 2 O 7 + MgP 2 O 6 were found to be 1598 K, 1555 K and 1423 K, respectively.Additionally, Mg 3 P 2 O 8 with two polymorphic forms was confirmed, and its transition temperature was 1328 K. Subsequently, Bobrownicki and Slawski [52] also measured the melting temperature of Mg 3 P 2 O 8 to be 1628 K and the structural transition temperature to be 1323 K.However, these two studies did not give data such as the lattice parameter and the structural transition of Mg 3 P 2 O 8 , which have not been reported in subsequent studies [53,54].Therefore, the optimization process of the present work did not consider the phase transformation of Mg 3 P 2 O 8 .Bookey [55], using thermal analysis, investigated the eutectic reaction L = MgO + Mg 3 P 2 O 8 by means of cooling curves, which yielded a reaction temperature of 1603 K.The results were consistent with the data reported by Berak [51].The melting points of Mg 3 P 2 O 8 and Mg 2 P 2 O 7 were investigated, and the presence of the phase transition in the Mg 2 P 2 O 7 was determined by Czupinska et al. [53] and Oetting et al. [54] using thermal analysis.Combined with the data obtained by Roy et al. [56] and Calvo et al. [57], only the structural transformation of the Mg 2 P 2 O 7 in the low-temperature region was considered in the present work.MgP 4 O 11 was reported to melt congruently at 1183 K by Meyer et al. [32] using DTA.Rakotomahanina-Rolaisoa et al. [58] investigated the melting point of MgP 2 O 6 by DTA.
In 1897, Berthelot [59] determined the enthalpy of formation of Mg 3 P 2 O 8 from elements using SCA.In 1952, Bookey et al. [55] investigated the enthalpy of formation of Mg 3 P 2 O 8 .In 1954, the enthalpy of formation of Mg 3 P 2 O 8 from elements was measured by Stevens and Turkdogan [60] using SCA.In 1986, Lopatin et al. [61] studied the standard enthalpies of formation of Mg 2 P 2 O 7 and MgP 2 O 6 from elements using the Knudsen cell mass spectrometry (KCMS) approach.In 1989, Lopatin et al. [62] used the KCMS method to determine the enthalpy of formation of Mg 3 P 2 O 8 from elements.In 1999, Abdelkader et al. [63] measured the standard enthalpy of formation of Mg 3 P 2 O 8 from elements using the SCA approach.These experimental data on the enthalpies of formation of the compounds in the P 2 O 5 -MgO system described above were accepted for the present work.Oetting and Mcdonald [54] measured the heat capacities of Mg 3 P 2 O 8 and Mg 2 P 2 O 7 using an adiabatic calorimeter and determined the heat contents of Mg 3 P 2 O 8 and Mg 2 P 2 O 7 in the temperature range from 0 to 1700 K. Furthermore, the energy change in the low-temperature phase transition of Mg 2 P 2 O 7 was determined.Iwase et al. [64] investigated the activity of P 2 O 5 in liquid P 2 O 5 -MgO mixtures using solid oxide galvanic cell techniques at 1673 K. Given that the reported data were obtained from indirect calculations, the data on the activity were not used in the current work.

Thermodynamic Modeling
The CALPHAD method is used to formulate a comprehensive thermodynamic model to describe each phase in a system, drawing upon experimental data encompassing phase diagrams, thermodynamic properties and crystal structures.This method rationally selects undetermined parameters to represent each phase of the system as a Gibbs free energy function of variables such as temperature, pressure and composition.Ultimately, the phase diagrams and thermodynamic properties are derived through the utilization of a thermodynamic database containing these Gibbs free energy expressions.In the present study, the thermodynamic assessment of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems will be conducted using Thermo-Calc software.Employing the least-squares method, Thermo-Calc software endeavors to align the calculated values with the observed data, seeking optimized variable values that minimize the sum of squared differences between calculated and experimental data.Hence, the formulation of an appropriate thermodynamic model lays the groundwork for an excellent thermodynamic database.
The following thermodynamic models were used to model the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems in the present work.The constructed thermodynamic models used for two binary systems are listed in Table 2 and will be described below in more detail.

Pure Unary Component
The Gibbs energy G i (T) of pure unary component i can be expressed as follows: where H i SER is the standard molar enthalpy of pure unary component i at 298.15 K and 101,325 Pa, J•mol −1 ; a~h are the parameters to be optimized; T is the thermodynamic temperature, K.

Liquid Phase
In the current assessment, the ionic two-sublattice model is used to describe the liquid phase of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems.The ionic two-sublattice model assumes that cations only mix with each other, and anions only mix with each other.This model comprises two sublattices: one for cations and the other for anions, neutrals, and vacancies.
In the liquid phase of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems, the content of anions such as PO 3 −1 , P 2 O 7 −4 , PO 4 −3 varies with the composition of the system oxides [8].To simplify the thermodynamic model by reducing the thermodynamic parameters, only the two anions (PO 3 −1 and PO 4 −3 ) are considered in the optimized modeling process.Therefore, the thermodynamic models of the liquid phase of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems are (Na +1 ) P (O −2 , PO 3 −1 , PO 4 −3 , PO 5/2 ) Q and (Mg +2 ) P (O −2 , PO 3 −1 , PO 4 −3 , PO 5/2 ) Q , where P and Q denote the total valence of the anion sublattice and the total valence of the cation sublattice, respectively.To maintain the electroneutrality of the liquid phase of the systems, the stoichiometric factors P and Q are allowed to change with the composition of the system oxides.Taking the P 2 O 5 -Na 2 O system as an example, the Gibbs energy of the liquid phase is expressed as follows: where H i SER is the molar enthalpy of the pure unary component in the reference state of the standard element at 298.15 K and 101,325 Pa, J•mol −1 ; y is the site fraction of each species in the liquid phase in their respective sublattices; G is the Gibbs energy for the formation of the end-member, J•mol −1 ; R is the gas constant (R = 8.314 J•(mol is the excess Gibbs energy, J•mol −1 , which is denoted as follows: data from Andon et al. [47], Ashcroft et al. [48] and Lazarev et al. [49], which were treated as identical within this study.Subsequently, the formation enthalpies of the four intermediate phases were optimized using experimental data on formation enthalpies from elements [40][41][42][43][44][45][46].Then, the liquid parameters such as 0 L Liquid Na +1 :PO −1 3 ,PO −3   Utilizing the optimized thermodynamic parameters, the thermodynamic properties of the P 2 O 5 -Na 2 O system are computed.Figure 2a and b show the calculated heat capacities of Na 4 P 2 O 7 and NaPO 3 , respectively, obtained in this study, juxtaposed with experimental data measured by Andon et al. [47], Ashcroft et al. [48] and Lazarev et al. [49].The calculated results exhibit satisfactory agreement with the measured values.For Na 5 P 3 O 10 and Na 3 PO 4 , the Neumann-Kopp equation was employed to describe their heat capacities due to the limited experimental data available.The standard enthalpies of formation of the intermediate compounds from elements (BCC_A2 for sodium and white phosphorus) at 298 K are also calculated in this work, as depicted in Figure 3.The graph illustrates that our calculated results are generally consistent with the experimental values from Refs.[40][41][42][43][44][45][46].Considering experimental uncertainties, the calculations are deemed acceptable.Utilizing the optimized thermodynamic parameters, the thermodynamic properties of the P2O5-Na2O system are computed.Figure 2a and b show the calculated heat capacities of Na4P2O7 and NaPO3, respectively, obtained in this study, juxtaposed with experimental data measured by Andon et al. [47], Ashcroft et al. [48] and Lazarev et al. [49].The calculated results exhibit satisfactory agreement with the measured values.For Na5P3O10 and Na3PO4, the Neumann-Kopp equation was employed to describe their heat capacities due to the limited experimental data available.The standard enthalpies of formation of the intermediate compounds from elements (BCC_A2 for sodium and white phosphorus) at 298 K are also calculated in this work, as depicted in Figure 3.The graph illustrates that our calculated results are generally consistent with the experimental values from Refs.[40][41][42][43][44][45][46].Considering experimental uncertainties, the calculations are deemed acceptable.

P 2 O 5 -MgO System
The Gibbs energy functions for the components P 2 O 5 and MgO utilized in this study were sourced from Jung et al. [65] and Mao et al. [67], respectively.The heat capacities of Na 4 P 2 O 7 and NaPO 3 were modeled using experimental data from Oetting et al. [54].
In the present research, it is assumed that the heat capacities of both allotropic forms of Mg 2 P 2 O 7 were equal.The optimized phase diagram of the P 2 O 5 -MgO system, presented in Figure 4, is compared with experimental data [32,51,[53][54][55][56][57][58].Additionally, the temperature and phase composition details of invariant reactions are juxtaposed with the experimental data reported in the literature, as shown in Table 4.It is evident that the calculated phase boundaries align well with the experimental information found in the literature.The present study provides a better and more reasonable description of the experimental data for the P 2 O 5 -MgO system compared to the results of Ding et al. [8].

P2O5-MgO System
The Gibbs energy functions for the components P2O5 and MgO utilized in this study were sourced from Jung et al. [65] and Mao et al. [67], respectively.The heat capacities of Na4P2O7 and NaPO3 were modeled using experimental data from Oetting et al. [54].In the present research, it is assumed that the heat capacities of both allotropic forms of Mg2P2O7 were equal.The optimized phase diagram of the P2O5-MgO system, presented in Figure 4, is compared with experimental data [32,51,[53][54][55][56][57][58].Additionally, the temperature and phase composition details of invariant reactions are juxtaposed with the experimental data reported in the literature, as shown in Table 4.It is evident that the calculated phase boundaries align well with the experimental information found in the literature.The present study provides a better and more reasonable description of the experimental data for the P2O5-MgO system compared to the results of Ding et al. [8].
The phase relationship in the composition range above 50 mol.%P2O5 remains to be definitively determined experimentally, owing to the limited available experimental data.In the optimization process, two eutectic reactions were predicted in this portion of the phase diagram.The calculated reaction temperatures are 1149 K for the reaction L = MgP2O6 + MgP4O11 and 773 K for the reaction L = MgP4O11 + O' − P2O5.Correspondingly, the calculated X(P2O5) values are 62 mol.% and 91 mol.%, respectively.[54], while the calculated melting enthalpy of Mg 2 P 2 O 7 (∆H melt = 160.03kJ•mol −1 ) is slightly higher than the experimental value.This brings the calculated values much closer to the experimental results compared to the study by Ding et al. [8].Additionally, the calculated enthalpy of transition from Mg 2 P 2 O 7 _β to Mg 2 P 2 O 7 _α at 340 K is determined to be 0.68 kJ•mol −1 .Figure 7 shows the calculated standard enthalpies of formation for the intermediate compounds from elements at 298 K compared with the experimental data [55,[59][60][61][62][63] and calculated results from the literature [8]; the reference states are the Mg of HCP_A3 and white phosphorus, which reproduce the standard enthalpy of formation for the compounds from elements very well.As can be seen, a precise description of the experimental thermodynamic properties of the system can be provided by utilizing the calculated thermodynamic parameters within the acceptable margin of error.from elements at 298 K compared with the experimental data [55,[59][60][61][62][63] and calculated results from the literature [8]; the reference states are the Mg of HCP_A3 and white phosphorus, which reproduce the standard enthalpy of formation for the compounds from elements very well.As can be seen, a precise description of the experimental thermodynamic properties of the system can be provided by utilizing the calculated thermodynamic parameters within the acceptable margin of error.

Conclusions
The CALPHAD method was utilized to critically evaluate and assess the P2O5-Na2O and P2O5-MgO binary systems.The main conclusions are summarized below: 1.A set of self-consistent thermodynamic parameters is derived for the P2O5-Na2O and P2O5-MgO binary systems based on a critical evaluation of the available phase diagram and thermodynamic property data.The calculated phase diagrams and thermodynamic properties employing the obtained thermodynamic parameters well reproduce the data reported in the literature.2. In comparison with the previous assessments using the modified quasi-chemical model for the liquid phase, the present study using the ionic two-sublattice model to express the liquid phase for the first time can describe the experimental data of the P2O5-Na2O and P2O5-MgO binary systems in a better and more reasonable way, par-

Conclusions
The CALPHAD method was utilized to critically evaluate and assess the P2O5-Na2O and P2O5-MgO binary systems.The main conclusions are summarized below: 1.A set of self-consistent thermodynamic parameters is derived for the P2O5-Na2O and P2O5-MgO binary systems based on a critical evaluation of the available phase diagram and thermodynamic property data.The calculated phase diagrams and thermodynamic properties employing the obtained thermodynamic parameters well reproduce the data reported in the literature.2. In comparison with the previous assessments using the modified quasi-chemical model for the liquid phase, the present study using the ionic two-sublattice model to express the liquid phase for the first time can describe the experimental data of the

Conclusions
The CALPHAD method was utilized to critically evaluate and assess the P 2 O 5 -Na 2 O and P 2 O 5 -MgO binary systems.The main conclusions are summarized below: 1.
A set of self-consistent thermodynamic parameters is derived for the P 2 O 5 -Na 2 O and P 2 O 5 -MgO binary systems based on a critical evaluation of the available phase diagram and thermodynamic property data.The calculated phase diagrams and thermodynamic properties employing the obtained thermodynamic parameters well reproduce the data reported in the literature.

2.
In comparison with the previous assessments using the modified quasi-chemical model for the liquid phase, the present study using the ionic two-sublattice model to express the liquid phase for the first time can describe the experimental data of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO binary systems in a better and more reasonable way, particularly the invariant reactions involving the liquid phase.The difference in the phase composition and temperature of invariant reactions from the experimentally determined values reported in the literature is less than 0.9 mol.% and 5K, respectively.

Figure 1 .
Figure 1.Calculated phase diagram of the P 2 O 5 -Na 2 O binary system compared with the experimental data [34-39].

Figure 3 .
Figure 3. Calculated enthalpies of formation for the intermediate compounds of the P2O5-Na2O binary system at 298.15 K from elements compared with the experimental data [40-46].

Figure 3 .
Figure 3. Calculated enthalpies of formation for the intermediate compounds of the P 2 O 5 -Na 2 O binary system at 298.15 K from elements compared with the experimental data [40-46].

Figure 7 .
Figure 7. Calculated enthalpies of formation for the intermediate compounds of the P2O5-MgO binary system at 298.15 K from elements compared with the experimental data [55,59-63] and calculated results from the literature [8].

Figure 7 .
Figure 7. Calculated enthalpies of formation for the intermediate compounds of the P2O5-MgO binary system at 298.15 K from elements compared with the experimental data [55,59-63] and calculated results from the literature [8].

Figure 7 .
Figure 7. Calculated enthalpies of formation for the intermediate compounds of the P 2 O 5 -MgO binary system at 298.15 K from elements compared with the experimental data [55,59-63] and calculated results from the literature [8].

Table 1 .
Crystal structures of all solid phases in the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems.
2.1.P 2 O 5 -Na 2 O SystemA phase diagram of the P 2 O 5 -Na 2 O system has been reported by several researchers

Table 2 .
The obtained thermodynamic parameters of the P 2 O 5 -Na 2 O and P 2 O 5 -MgO systems in the present work.

Table 3 .
Calculated invariant reactions involving the liquid phase in the P 2 O 5 -Na 2 O binary system.

Table 4 .
Calculated invariant reactions involving the liquid phase in the P 2 O 5 -MgO binary system.The phase relationship in the composition range above 50 mol.%P 2 O 5 remains to be definitively determined experimentally, owing to the limited available experimental data.In the optimization process, two eutectic reactions were predicted in this portion of the phase diagram.The calculated reaction temperatures are 1149 K for the reaction L = MgP 2 O 6 + MgP 4 O 11 and 773 K for the reaction L = MgP 4 O 11 + O' − P 2 O 5 .Correspondingly, the calculated X(P 2 O 5 ) values are 62 mol.% and 91 mol.%, respectively.The heat capacities of Mg 3 P 2 O 8 and Mg 2 P 2 O 7 obtained by optimization in this work are illustrated in Figure 5a,b.Reasonable agreement is obtained between our calculated results and the heat capacities of Mg 3 P 2 O 8 and Mg 2 P 2 O 7 in the temperature range from 298.15 K to 1800 K determined by Oetting et al. [54].To describe the heat capacities of MgP 2 O 6 and MgP 4 O 11 , the Neumann-Kopp equation was employed during the optimization process to sum the heat capacities of Na2O_γ and P2O5_H.Figure 6a,b present the calculated heat contents of Mg 3 P 2 O 8 and Mg 2 P 2 O 7 based on the obtained thermodynamic parameters, compared with the experimental data [54].The results indicate a close alignment with the experimental values, with acceptable deviations considering experimental errors.The calculated melting enthalpy of Mg 3 P 2 O 8 (∆H melt = 97.449kJ•mol −1 ) is slightly lower than the experimental value reported by Oetting et al.