Abstract
A critical evaluation and thermodynamic optimization of all available experimental data of the CaO-P2O5 system was performed to obtain a set of thermodynamic functions which can reproduce all available and reliable experimental phase diagram and thermodynamic data. The modified quasichemical model, which takes into account short range ordering, was employed to describe the thermodynamic properties of the liquid phase. Discrepancies observed in the Gibbs energy of formation of the compounds were resolved and phase diagram and thermodynamic data of all the solid and liquid phases were well reproduced within experimental errors limits including the sharp liquidus of Ca3(PO4)2.
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Introduction
The CaO-P2O5 system is an important key binary system in numerous research fields of industrial interest. This is particularly the case for optical glasses[1,2] and glasses and glass–ceramics employed as hard tissue implants and drug carriers.[3–8] The CaO-P2O5 system is also important in the steelmaking process to refine phosphorus in molten steel,[9–11] in cement production,[12] in phosphate fertilizers,[13,14] etc. To improve current process conditions and develop new processes and products, a good knowledge of its phase diagram and thermodynamic properties is critical. This can be achieved by using the CALPHAD (CALculation of PHADiagram) technique.
In the thermodynamic “optimization” of a system, all available thermodynamic and phase equilibrium data are evaluated simultaneously in order to obtain a set of model equations for the Gibbs energies of all phases as functions of temperature and composition. Thermodynamic property data, such as activity data, can aid in the evaluation of the phase diagram, and phase diagram measurements can be used to deduce thermodynamic properties. From the Gibbs energy equations, all the thermodynamic properties and phase diagrams can be back-calculated. In this way, all the data are rendered self-consistent and consistent with thermodynamic principles. Discrepancies in the available data can often be resolved, and interpolations and extrapolations can be made in a thermodynamically correct manner. The thermodynamic database resulting from the optimization can be self-consistently built from low order to high order systems and applied to industrial processes.
In spite of the importance of the CaO-P2O5 system, the only attempt to optimize its thermodynamic properties and phase diagram was done recently by Serena et al.,[15,16] who used an associate model to describe the thermodynamic properties of the CaO-P2O5 liquid. Several associate species were employed for the liquid phase and the properties of the solid compounds were taken from the compilation of Barin.[17] Unfortunately, the phases Ca10(PO4)6O2 and Ca4P6O19 (trömelite) were ignored, some polymorphic transitions and numerous phase equilibrium and thermodynamic data were not taken into account, and the phase diagram was not well reproduced.
Recently, we performed a new assessment of the thermodynamic properties and phase diagram of pure P2O5 to resolve inconsistencies in the SGTE database[18] and present new thermodynamic data for various solid polymorphs and liquid phases of P2O5.[19] We also performed the thermodynamic optimization of the SiO2-P2O5 system using literature data and new phase diagram experimental data.[20] In the present study, we have performed the critical evaluation of all the experimental data of the phase diagram and thermodynamic properties of the CaO-P2O5 system. This is part of a large research project to develop the thermodynamic database of the Na2O-CaO-MgO-FeO-Fe2O3-MnO-Al2O3-SiO2-P2O5 system.
Review of Literature Experimental Data
A total of eight intermediate compounds are known to exist in the CaO-P2O5 binary: Ca4(PO4)2O (C4P), Ca10(PO4)6O2 (C10P3), Ca3(PO4)2 (C3P), Ca2P2O7 (C2P), Ca4P6O19 (C4P3), Ca(PO3)2 (CP), Ca2P6O17 (C2P3), and CaP4O11 (CP2). Most of these compounds undergo polymorphic transitions. Structural and experimental data relevant to the stability field of each polymorph are detailed in Section II–A below which permits to confirm the existence of each phase. All the non-standard space groups were converted into standard notation according to the International Union for Crystallography.[21] For the sake of clarity, a summary of structural data is given in Table I while melting and polymorphic transition temperatures are reported in Tables II through VI and invariant points involving the liquidus are listed in Table VII. Melting points measured by Dieckmann and Houdremont[22] were rejected because they are usually much lower than the ones determined in other studies; the presence of water and impurities is probably the source of error. The phase diagram of the CaO-P2O5 system is shown in Figure 1 with experimental data. Phase equilibrium and thermodynamic data are reviewed in Sections II–B and II–C, respectively.
The binary CaO-P2O5 system along with experimental data of Nielsen,[117] Trömel,[36] Behrendt and Wentrup,[37] Frear,[118] Hill et al.,[91] Trömel and Fix,[40] Welch and Gutt,[41] Trömel and Fix,[119] Berak and Znamierowska,[73] Maciejewski et al.,[120] and other studies (1911 to 2008) from Tables 2 through 6. Abbreviations are the same as the ones listed in the tables
Structural Data and Phase Transformations of Compounds
Ca4(PO4)2O (C4P)
Ca4(PO4)2O was discovered by Hilgenstock[23] in slags from Hörde (Wesphalia). It is sometimes named hilgenstockite, which is not recognized as an official mineral name.[24] Ca4(PO4)2O exists in two polymorphic forms. The high temperature form, α-Ca4(PO4)2O, has an orthorhombic structure[23,25–31] and crystallizes in the P2221[28,29] or P21212[30,31] space group. The only discordant result is from Schneiderhohn[32] who reported that it belongs to the triclinic system based on optical microscopic observations. The low temperature form, β-Ca4(PO4)2O, was first thought to crystallize in the orthorhombic[27] and triclinic[33] systems but it is now known to belong to the monoclinic P21 space group.[30,31,34]
The first experimental studies[35–38] report that α-Ca4(PO4)2O melts congruently while the most recent ones[39–41] state that it melts peritectically. More credit is given to the last two studies[40, 41] because they employed an in situ (heating microscopy) technique to measure the melting point, which is observed at 1983 K to 1993 K (1710 °C to 1720 °C). According to Cieśla[31] and Cieśla and Rudnicki,[42] the transition between α and β occurs in the temperature range of 873 K to 943 K (600 °C to 670 °C). Melting temperatures reported in the literature are presented in Table II together with the temperatures of the α–β polymorphic transition.
Ca10(PO4)6O2 (C10P3; Oxyapatite)
The existence of oxyapatite, Ca10(PO4)6O2, has been debated for a long time (see Trombe and Montel[43] for a review), but it is now recognized as a valid species due to the work of Trombe and Montel[43–45] and Trombe,[46] who used X-ray diffraction (XRD), thermogravimetric analysis (TGA), infrared spectroscopy (IR), and chemical analysis to characterize it. The structure was only determined recently by Henning et al.[47] with the help of high-resolution electron microscopy (HREM): it is hexagonal and belongs to the \( P\bar{6} \) space group. In their first publications,[44–46] Trombe and Montel place the stability field of oxyapatite between 1073 K and 1273 K (800 °C and 1000 °C), while in the later,[43] they put it between 1123 K and 1323 K (850 °C and 1050 °C) (Table II).
Ca3(PO4)2 (C3P)
Ca3(PO4)2, and more specifically β-Ca3(PO4)2, are sometimes named whitlockite or Ca-whitlockite, a mineral found in the Palermo quarry, New Hampshire (USA). The mineral was first described by Frondel[48] as Ca3(PO4)2 based on chemical analysis. Later, Frondel[49] showed that Ca-whitlockite and synthetic β-Ca3(PO4)2 are the same phase due to their identical XRD patterns and optical constants. Currently, whitlockite is rather considered as a mineral with the general chemical formula Ca9(Mg, Fe2+)(PO4)6(PO3OH).[24,50]
Ca3(PO4)2 exists in three polymorphic forms. The high temperature phase, α′-Ca3(PO4)2, was investigated by high-temperature neutron diffraction by Knowles et al.[51] and Yashima and Sakai[52] who determined that it belongs to the hexagonal P63/mmc and trigonal \( P\bar{3}m1 \) space groups, respectively. According to Mackay,[53] Mathew et al.[54] and Yashima and Sakai,[52] the intermediate temperature phase, α-Ca3(PO4)2, crystallizes in the monoclinic space group P21/c. Frondel[48] determined by XRD that the low temperature polymorph, β-Ca3(PO4)2, belongs to the trigonal system and probably to the \( R\bar{3}c \) space group; using XRD, Mackay[55] found the same space group. The structure was later refined by Dickens et al.[56] and Calvo and Gopal[57] using XRD and Yashima et al.[58] using neutron diffraction and the belonging to the trigonal system was confirmed but the space group was changed to R3c. Based on luminescence and calorimetric measurements at low temperatures, Koelmans et al.[59] identified two additional phase transformations between 233 K and 308 K (−40 °C and 35 °C). Unfortunately, due to the sluggishness of these transitions, they were unable to resolve them. According to Koelmans et al.,[59] the transformations might be related to some cation ordering in the structure; they are not taken in consideration in the present optimization.
The α′-Ca3(PO4)2 phase melts congruently. In general, the earliest studies (Table III) report rather low melting temperatures [e.g., 1823 K (1550 °C)] while the most recent ones give high melting temperatures [e.g., 2083 K (1810 °C)]; our preference went to the most recent investigations.
Temperatures reported in the literature for the polymorphic transitions are summarized in Table III. Remarkably, the whole spectrum of transition temperatures lies between 1553 K and 1813 K (1280 °C and 1540 °C) for the α′–α transition and between 1273 K and 1773 K (1000 °C and 1500 °C) for the α–β one. Fasting and Haraldsen[60] and Ando[61] were the first to point out these differences and to propose that small amounts of impurities can change considerably the transition temperature of α- to β-Ca3(PO4)2. Their experiments show that a small addition of Na2O or BaO to Ca3(PO4)2 decreases the transition temperature by stabilizing the α phase while a small addition of MgO, FeO or SiO2 increases the transition temperature by stabilizing the β phase. Among the oxides investigated, the effect of MgO is the most intense one. This later observation is corroborated by numerous studies.[56,62–67] On the other hand, Bredig et al.[68] showed that very small amounts of moisture and excess CaO can modify the temperature of the polymorphic transformation. By taking in consideration these observations, our preference went to the α′–α and α–β transitions data located around 1743 K and 1398 K (1470 °C and 1125 °C), respectively.
Other phase transitions were reported for Ca3(PO4)2: one at 1687 K (1414 °C),[69] one at 1681 K (1408 °C),[70] one at 1623 K (1350 °C),[71–74] one at 1603 K (1330 °C),[69] one at 1326 K (1103 °C),[70,72,73] one at 1370 K (1097 °C),[69] one at 1313 K (1040 °C),[74] and one at 1283 K (1010 °C),[69,74] all using thermal analysis and XRD. Each transition is considered as minor by the authors and might be due to the purity of the starting materials; consequently, none of them are considered here. Recently, Belik et al.[75] reported a new transition at 1193 K (920 °C) using electrical-conductivity measurements. No other details are reported for this transformation and for this reason it is also discarded.
Solid solution was initially reported for the α′-, α-, and β-C3P phases in the CaO-P2O5 system by Welch and Gutt[41] but a careful XRD study performed by Kreidler and Hummel[76] showed that tricalcium phosphate is stoichiometric; according to them, loss of P2O5 probably occurred during Welch and Gutt’s experiments. This diagnostic was confirmed by Wallace and Brown[77] who heated some CaO-P2O5 mixtures ranging from about 0.25 to 0.33 mol fraction P2O5 at 973 K and 1173 K (700 °C and 900 °C) and found no solid solution in the C3P phase. For Berak and Znamierowska,[72] who used thermal analysis, and Riboud,[78] who employed the quenching method, no solid solution was observed either. Recently, Jungowska[79] also reported some solid solution in α- and β- Ca3(PO4)2 using the quenching method and XRD but P2O5 loss may have occurred during their rather long (3 to 170 hours) experiments in open crucibles between 1173 K and 1523 K (900 °C and 1250 °C).
Ca2P2O7 (C2P)
The compound Ca2P2O7 exists in three polymorphic forms. The high temperature polymorph, α-Ca2P2O7, was studied by Ranby et al.[80] and Calvo[81] using XRD. The first study reports that it crystallizes in the orthorhombic system while the second one assigns it to the monoclinic space group P21/c. The intermediate form, β-Ca2P2O7, was first investigated by Schneiderhohn.[32] He performed optical microscopic observations on crystals and deduced that they belong to the tetragonal system. This diagnostic was confirmed by XRD studies made by Corbridge,[82] Keppler,[83] Webb,[84] and Boutin et al.[85] who determined that β-Ca2P2O7 crystallizes in the tetragonal space group P41. For Schneider et al.[86] though, X-ray data rather indicate that this phase belongs to the monoclinic space group P21/c. The structure of the low temperature form, γ-Ca2P2O7, is not known yet. McIntosch and Jablonski[87] and Parodi et al.[88] measured its X-ray pattern but they did not determine the structure. Recently, Cornilsen and Condrate[89] shown that the Raman and X-ray patterns of γ-Ca2P2O7 are similar to, but well less defined than β-Ca2P2O7, which suggests that both phases are structurally related.
A large consensus exists for the melting point of α-Ca2P2O7. In the most recent studies,[40,41,72,73,90–94] it is systematically detected around 1623 K (1350 °C; see Table IV). The α–β transition (Table IV) was observed over the temperature range of 1173 K to 1523 K (900 °C to 1250 °C) and clusters around 1448 K (1175 °C). For the β–γ transition, the temperature ranges between 828 K and 1473 K (555 °C and 1200 °C), but most data lie between 900 K and 1123 K (627 °C and 850 °C).
Solid solution was initially reported for α- and β-Ca2P2O7 in the CaO-P2O5 system by Hill and al.[91] but the careful XRD study performed by Kreidler and Hummel[76] showed that dicalcium phosphate is stoichiometric.
Ca4P6O19 (C4P3)
Hill et al.[91] were the first to report the existence of this compound; they gave it the name trömelite in honor of Gerhard Trömel, who made the first systematic study of the CaO-P2O5 system. However, trömelite was never found in nature and for this reason it is not considered as a valid mineral name.[24] According to Hill et al.’s[91] quenching method, optical microscopy and XRD study, trömelite is a pentapolyphosphate (Ca7P10O32; C7P5). This diagnostic was supported by paper chromatographic investigations made by Van Wazer and Ohashi[95,96] who also identified the phase as a pentapolyphosphate. However, further chromatographic experiments by Wieker et al.[97] showed that the phase is in fact a hexapolyphosphate of the likely composition Ca4P6O19 (C4P3). This was later confirmed by a 31P NMR analysis performed by Gard.[98]
No polymorphs are known for this compound. XRD data collected by Wieker et al.[97] reveal that Ca4P6O19 has a triclinic unit cell. The structure was refined recently by Höppe[99] using XRD; according to him, Ca4P6O19 crystallizes in the triclinic \( P\bar{1} \) space group. For Hill et al.,[91] Ca4P6O19 melts incongruently to β-Ca2P2O7 and liquid at 1258 K (985 °C). Recently, Szuszkiewicz[100] determined the peritectic melting point by DTA and found 1273 K (1000 °C), which is in good agreement with Hill’s data. Hill et al.[91] reported some solid solution in trömelite and a lower limit of stability at 1168 K (895 °C). Kreidler and Hummel[76] demonstrated by XRD that no such solid solution exists and that the phase is stable as low as 1073 K (800 °C). Szuszkiewicz[100] confirmed the absence of solid solution and showed by DTA and XRD that Ca4P6O19 is stable down to room temperature. All these data are summarized in Table V.
Ca(PO3)2 (CP)
This compound was first synthesized by Maddrell.[101–103] It is known to exist in four polymorphic forms, α, β, γ, and δ. The highest temperature polymorph, α-Ca(PO3)2, was examined with an optical microscope by Schneiderhohn[32]; he deduced that it fits the hexagonal system. A recent XRD and solid-state 31P NMR study made by Weil et al.[104] rather shows that α-Ca(PO3)2 crystallizes in the monoclinic Cc space group. The intermediate temperature polymorph, β-Ca(PO3)2, was studied by Corbridge[105] and Rothammel and Burzlaff[106] with XRD. Their investigations revealed that β-Ca(PO3)2 crystallizes in the monoclinic P21/c space group. A recent high temperature X-ray diffraction (HTXRD) study conducted by Viting et al.[107] confirms the belonging to the monoclinic system. The next low temperature polymorph was first investigated by Boullé[108] using XRD but no structure was derived. Hill et al.[91] attributed the prefix γ to the phase examined by Boullé[108] following an XRD study of various monocalcium phosphates. The structure of γ-Ca(PO3)2 was determined recently by Jackson et al.[109] using XRD; it belongs to the monoclinic Cc space group. The lowest temperature polymorph in the series was first synthesized by Bale et al.[90] and the prefix δ was later attributed to it by Hill et al.[91]. Based on XRD data collected by Bale et al.,[110] δ-Ca(PO3)2 crystallizes in the tetragonal system.
The melting point of α-Ca(PO3)2 is congruent and lies only between 1233 and 1293 K (960 and 1020 °C), which is rather small. The same is true for the α–β transition where the observed temperatures range between 1200 K and 1251 K (927 °C and 978 °C). For the β–γ transition, the temperatures mentioned in the literature vary between 673 K and 993 K (400 and 720 °C; Table V). The highest temperatures [963 K to 993 K (690 °C to 720 °C)] were reported by Jackson et al.[109] using DSC, TGA and XRD. We discarded their data because they measured at 963 K to 993 K (690 °C to 720 °C) an enthalpy of transition of 24 ± 1 kJ mol−1, an unreasonable large value for such a polymorphic transformation. The remaining data range mostly between 773 K and 823 K (500 °C and 550 °C) and our preference went to them. The temperature of the γ–δ transformation is not known; for this reason, and due to the fact that no thermodynamic information is known for δ-Ca(PO3)2, the polymorph is not considered in the present study.
Some solid solution was initially reported for the α- and β-Ca(PO3)2 phases by Hill et al.[91] but the careful XRD study performed by Kreidler and Hummel[76] demonstrated that Ca(PO3)2 is stoichiometric.
Ca2P6O17 (C2P3)
No polymorphs are known for this compound. According to Stachel[111] and Meyer et al.,[112] who used XRD, Ca2P6O17 crystallizes in the monoclinic P21/c space group. Hill et al.[91] employed the quenching technique, optical microscope, and XRD and found that Ca2P6O17 melts incongruently to β-CaP2O6 and liquid at 1047 K (774 °C). Using DTA, Meyer et al.[112] obtained 1053 K (780 °C) but did not specify if the melting was congruent or not. The only discordant data is from Viting et al.,[107] who observed by HTXRD that α-CaP4O11 (CP2, see next compound below) decomposes very slowly to γ-Ca(PO3)2 (γ-CP) and P2O5 above about 673 K (400 °C). Consequently, Ca2P6O17 (C2P3) could only be stable up to about 668 K (395 °C) where it would decompose to γ-CaP2O6 (γ-CP) and P2O5. This data was not considered because quenching experiments performed by Hill et al.[91] in the CaO-P2O5 binary show that starting materials containing more than 0.612 mol fraction P2O5 cannot remain homogeneous in open crucibles due to P2O5 loss by volatilization. Samples investigated by Viting et al.[107] were typically subjected to 1 to 5 hours (and even longer) thermal treatments in air, which may have resulted in excessive P2O5 loss and produced the discordant results reported by them. The data are summarized in Table V.
CaP4O11 (CP2)
The compound CaP4O11 exists in two polymorphic forms, α and β. The high temperature polymorph, α-CaP4O11, was studied by Schneider et al.[113] using XRD; it was found to crystallize in the orthorhombic Aea2 space group. The belonging to the orthorhombic system was recently confirmed by a high temperature XRD investigation made by Viting et al.[107] According to the XRD studies of Meyer et al.,[112] Schneider et al.,[113] Beucher,[114] and Tordjman et al.,[115] the low temperature polymorph, β-CaP4O11, crystallizes in the monoclinic space group P21/c. In his high temperature XRD investigation, Viting et al.[107] concluded as well that α-CaP4O11 is monoclinic.
Melting temperatures reported in the literature (Table V) for α-CaP4O11 are in very good agreement with each other; they lie between 1063 K and 1083 K (790 °C and 810 °C). The only data at odd with these are from Viting et al.[107] As explained above for the C2P3 phase, the high-temperature XRD study of Viting et al.[107] shows that α-CaP4O11 decomposes very slowly in air to γ-Ca(PO3)2 and P2O5 above 673 K (400 °C); this data was not used because P2O5 loss probably occurred during their experiments.
The polymorphic transition between α- and β-CaP4O11 was first detected by Churakova et al.[116] who observed a weak endothermic effect at 613 K (340 °C) on a DTA profile collected with CaP4O11. This effect was also seen at 613 K (340 °C) by Viting et al.[107] using high temperature XRD and was interpreted as a polymorphic transition. Using the same technique, Schneider et al.[113] located the same transformation at 358 K (85 °C) in nitrogen. Results reported by Churakova et al.[116] and Viting et al.[107] at 613 K (340 °C) were selected because they were performed in air.
Liquidus and Solidus Phase Diagram Data
In addition to the melting and polymorphic transition data listed in Tables II through VI, numerous phase equilibrium data, such as liquidus and solidus data, are also available. These data were obtained by Nielsen[117] using thermal analysis between 0.250 and 0.500 mol fraction P2O5, by Trömel[36] using thermal analysis, optical microscopy, and XRD between 0.161 and 0.53 mol fraction P2O5, by Behrendt and Wentrup[37] using thermal analysis between 0.119 and 0.245 mol fraction P2O5, by Frear et al.[118] using the quenching method and optical microscopy between 0.291 and 0.323 mol fraction P2O5, by Barrett and McCaughey[38] using oxy-acetylene flame, pyrometer, quenching method, optical microscopy, and XRD between about 0.20 and 0.30 mol fraction P2O5 (note that they only measured the temperatures of some peritectic and eutectic points; the compositions of the points were not determined), by Hill et al.[91] using the quenching method, optical microscopy, and XRD between 0.334 and 0.949 mol fraction P2O5, by Trömel and Fix[40] using the quenching method, heating microscopy, thermal analysis, and XRD between 0.195 and 0.334 mol fraction P2O5, by Welch and Gutt[41] using heating microscopy between 0.20 and 0.334 mol fraction P2O5, by Trömel and Fix[119] using the quenching method and optical microscopy between 0.202 and 0.209 mol fraction P2O5, by Berak and Znamierowska[73] using thermal analysis, optical microscopy, and XRD between 0.25 and 0.335 mol fraction P2O5, and by Maciejewski et al.[120] using DSC, TGA, and XRD between 0.248 and 0.333 mol fraction P2O5. All these data are in general in good agreement with each other. The only data discarded are the ones collected by Welch and Gutt[41] along the liquidus. According to the XRD study of Kreidler and Hummel,[76] P2O5 lost probably occurred during Welch and Gutt’s experiments, which make their results unreliable. Invariant points involving the liquidus are reported in Table VII.
Thermodynamic Data
Thermodynamic properties of end-members are listed in Table VIII. All available enthalpy, entropy, and heat capacity data are summarized in Tables IX through XII. Details about data selection are given below for each compound and experimental data are depicted in Figures 2 through 7. As far as we know, no thermodynamic data are available for Ca10(PO4)6O2 (C10P3), Ca4P6O19 (C4P3), and Ca2P6O17 (C2P3).
Optimized heat content \( H_{\text{T}} - H_{{298.15 {\text{K}}}}^{^\circ } \) of α-Ca4(PO4)2O along with experimental data of Sokolov et al.[123]
Optimized (a) heat content \( H_{\text{T}} - H_{{298.15 {\text{K}}}}^{^\circ } \) of α-, β-, and γ-Ca2P2O7 and its glass and (b) heat capacity C P of β-Ca2P2O7 along with experimental data of Egan and Wakefield[158] and Soga et al.[153] The polymorph employed by Soga et al.[153] to make their measurements is unknown
Optimized (a) heat content \( H_{\text{T}} - H_{{298.15 {\text{K}}}}^{^\circ } \) of β-Ca(PO3)2 and its glass and (b) heat capacity C P of β-Ca(PO3)2 along with experimental data of Egan and Wakefield[165] and Soga et al.[153] The polymorph employed by Soga et al.[153] to make their measurements is unknown
Optimized standard Gibbs energies of formation of (a) Ca4(PO4)2O (C4P), Ca3(PO4)2 (C3P), Ca2P2O7 (C2P) and Ca(PO3)2 (CP) from the elements along with experimental data of Bookey et al.,[125] Bookey,[126] Ban-Ya and Matoba,[127] Aratani et al.,[128] Iwase et al.,[129,130] Tagaya et al.,[131,132] Sandström et al.,[162] Nagai et al.,[133] and Yamasue et al.,[134] (b) Ca3(PO4)2 (C3P) from Ca4(PO4)2O (C4P) and Ca2P2O7 (C2P) from Ca3(PO4)2 (C3P), with experimental data of Yama-zoye et al.[154,155] and Hoshino et al.,[161] and (c) Ca10(PO4)6O2 (C10P3), Ca4P6O19, Ca2P6O17, and CaP4O11 from the elements
Calculated activity of CaO(s) and P2O5(l) in CaO-P2O5 system at 1923 K (1650 °C) with experimental data of Schwerdtferger and Engell[169]
CaO and P2O5
Thermodynamic data for the end-members CaO and P2O5 were taken from previous optimizations that can be found in FactSage FToxide database (Bale et al.[121]) and Jung and Hudon,[19] respectively. The data are listed in Table VIII.
Ca4(PO4)2O (C4P)
Martin et al.[122] used isothermal calorimetry to measure the standard heat of formation of α-Ca4(PO4)2O at 310.55 (37.4 °C) and obtained −717.072 kJ mol−1 from the oxides. The heat content \( H_{\text{T}} - H_{{298.15\,{\text{K}}}}^{^\circ } \) of α-Ca4(PO4)2O (Figure 2) was determined between 679 K and 1611 K (406 °C and 1338 °C) using adiabatic calorimetry and an equation for the heat capacity was derived from the measurements by Sokolov et al.[123] The only thermodynamic data available for β-Ca4(PO4)2O is the standard heat of formation which was measured by Jeffes (unpublished result cited in Pearson et al.[124]) using hydrochloric acid solution calorimetry. He found −723.455 kJ mol−1 at 348 K (75 °C) from the oxides.
The standard Gibbs energy of formation of Ca4(PO4)2O was first measured by Bookey et al.[125] from the reaction 2P in Fe + 5O in Fe + 4CaO(s) = Ca4(PO4)2O(s) between 1833 K and 1873 K (1560 °C and 1600 °C). Liquid iron, containing phosphorus and oxygen, was equilibrated with a mixture of solid CaO and Ca4(PO4)2O (in a crucible made of CaO and Ca4(PO4)2O) under an oxygen partial pressure controlled by H2 and H2O. The Gibbs energy of formation of Ca4(PO4)2O was also determined by Bookey[126] using the reaction 4Ca4(PO4)2O(s) + 5H2(g) = 4CaO(s) + P2(g) + 5H2O(g) between 1523 K and 1773 K (1250 °C and 1500 °C). Measurements consisted of passing a known volume of hydrogen over C3P(s), contained in a molybdenum boat within an impervious alumina tube, and the determination of the amount of H2O(g) in the exit gas. Although a certain amount of Mo3P was formed during the experiment, this had no effect on the determination of the Gibbs energy of the reaction above. Ban-Ya and Matoba[127] determined the Gibbs energy of formation of Ca4(PO4)2O from the reactions 4CaO(s) + 2P in Fe + 5CO2(g) = Ca4(PO4)2O(s) + 5CO(g) and 4CaO(s) + 2P in Fe + 5CO(g) = Ca4(PO4)2O(s) + 5C in Fe between 1803 K and 1858 K (1530 °C and 1585 °C). Fe-C-P melts were equilibrated with solid CaO and Ca4(PO4)2O in CaO or Ca4(PO4)2O crucibles under a controlled CO-CO2 gas mix. Aratani et al.[128] determined the Gibbs energy of formation from the reactions 4CaO(s) + 2Pin Fe + 5H2O(g) = Ca4(PO4)2O + 5H2(g) and H2(g) + Oin Fe = H2O(g) between 1813 K and 1873 K (1540 °C and 1600 °C). Iron melts containing phosphorus were equilibrated in CaO crucibles under a controlled H2-H2O atmosphere. Iwase et al.[129,130] employed two techniques to determine the Gibbs energy of formation. First, they measured the emf of the electrochemical cell Mo/Mo + MoO2//ZrO2(MgO)//(Cu + P)alloy + (CaO + CaCl2 + P2O5)slag + CaO + Ca4(PO4)2O/Mo between 1423 K and 1523 K (1150 °C and 1250 °C) and second, they equilibrated the reaction 4CaO(s) + 2P in Cu + 5CO(g) = 4Ca4(PO4)2O(s) + 5C(s) at 1473 K (1200 °C. In this last experiment, molten copper was brought to equilibrium with solid CaO and Ca4(PO4)2O in a graphite crucible under a stream of CO gas. Both techniques gave consistent results. Tagaya et al.[131,132] measured the Gibbs energy of formation between 1473 K and 1598 K (1200 °C and 1325 °C) using the reactions 3Ca4(PO4)2O(s) + 2P in Ag + 5CO(g) = 4Ca3(PO4)2(s) + 5C(s) and Ca3(PO4)2(s) + Ca in Ag + CO(g) = Ca4(PO4)2O(s). Mixtures of Ca3(PO4)2(s) and Ca4(PO4)2O(s) were equilibrated with silver-phosphorus alloys in graphite crucibles under CO and Ar mixtures. The Gibbs energy of formation of Ca4(PO4)2O(s) was also measured by Nagai et al.[133] between 1523 K and 1623 K (1250 °C and 1350 °C) using double Knudsen cell mass spectrometry. Recently, Yamasue et al.[134] determined the Gibbs energy of formation from the reaction Ca4(PO4)2O(s) + 5C(s) = 4CaO(s) + P2(g) + 5CO(g) between 1373 K and 1573 K (1100 °C and 1300 °C). Measurements consisted of passing a known volume of Ar-CO gas over C4P(s), contained in a graphite chamber, and the determination of the amount of P2(g) in the exit gas. All the Gibbs energies of the reactions obtained experimentally were converted to 4Ca(l) + P2(g) + 4.5O2(g) = Ca4(PO4)2O(s) using Gibbs energy of the reactions Ca(l) + O2(g) = CaO(s) from FactSage (Bale et al.[121]), 2.5O2(g) = 5O in Fe from Sakao and Sano[135] and Elliot and Gleiser,[136] P2(g) = 2P in Fe from Yamamoto et al.[137], and 0.5P2(g) = P in Ag from Ban-Ya and Suzuki[138] and Yamamoto et al.[139] The resultant Gibbs energy of formation of Ca4(PO4)2O from all the experiments are depicted in Figure 6(a).
Ca3(PO4)2 (C3P)
Butylin et al.[140] used the Knudsen effusion method to determine the ΔH f°298.15 K and S°298.15 K of α′-Ca3(PO4)2 and found −449.502 kJ mol−1 (from the oxides) and 233.886 J mol−1 K−1, respectively. By investigating the system CaO-P2O5 at various water pressures, Riboud[141] used the Clausius–Clapeyron relation to estimate the enthalpy of transition from α- to α′-Ca3(PO4)2 at 1748 K (1475 °C). He found 73.220 kJ mol−1, which is rather high for this kind of transformation; we consider his data as doubtful.
Smirnova et al.[142] employed hydrochloric acid solution calorimetry to measure the standard enthalpy of formation of α-Ca3(PO4)2 at 298.15 K (25.15 °C) and obtained −681.714 kJ mol−1 from the oxides. Martin et al.[122] found a slightly higher value, −686.262 kJ mol−1 at 310.55 (37.4 °C), using isothermal calorimetry. The heat capacity of α-Ca3(PO4)2 (Figure 3) was determined by low temperature adiabatic calorimetry between 15 K and 287 K (−258 °C and 14 °C) by Southard and Milner[143] and the entropy S°298.15 K was found to be 240.91472 J mol−1 K−1. Britzke and Veselovskii[144] measured the heat content of β- and α-Ca3(PO4)2 between 871 K and 1512 K (598 °C and 1239 °C) using solution calorimetry and heat capacity data at high temperature were derived. Despite the fact that Britzke and Veselovskii[144] corrected their raw data to make them in line with those of Southard and Milner,[51] their heat capacity data are very scattered as can be seen in Figure 3. Britzke and Veselovskii’s heat capacity data were fitted by Kelley[145] using a polynomial equation which we adopted as it is. Britzke and Veselovskii[144] also estimated (with some reserves) the enthalpy of transition between β- and α-Ca3(PO4)2 at 1373 K (1100 °C) to be 18.828 kJ mol−1.
For β-Ca3(PO4)2, Berthelot[146–148] measured the heat of neutralization of phosphoric acid by calcium hydroxide and obtained from the oxides a standard enthalpy of formation at 298.15 K (25.15 °C) of −687.572 kJ mol−1 (values recalculated by Smirnova et al.[142]). Matignon and Séon[149] measured the heat of solution of Ca3(PO4)2, CaO, and H3PO4 in 2N HCl and the heat of mixing of CaO and H3PO4; the data were then used by Richardson et al.[150] to derive a standard enthalpy of formation at 298.15 K (25.15 °C) for β-Ca3(PO4)2 of −686.176 kJ mol−1. Jeffes (unpublished result cited in Pearson et al.[124]) obtained a value of −680.653 kJ mol−1 at 348 K (75 °C) by hydrochloric acid solution calorimetry. Using the same technique, Smirnova et al.[142] found −702.634 kJ mol−1 while Meadowcroft and Richardson[151] obtained −706.259 ± 8.4 kJ mol−1 at 308 K (35 °C). Jacques et al. (personal communication cited in Meadowcroft and Richardson[151]) used solution calorimetry as well and reported a ΔH f°298.15 K of −717.954 ± 16.7 kJ mol−1. More recently, Abdelkader et al.[152] reported a much lower value, −645.762 kJ mol−1, by measuring the heat of solution of β-Ca3(PO4)2 in a 9 wt pct nitric solution with an isoperibol calorimeter. The standard entropy at 298.15 K (25.15 °C), S°298.15 K, was determined by Southard and Milner[143] with low temperature adiabatic calorimetry between 15 K and 300 K (−258 °C and 27 °C); they reported a value of 235.9776 J mol−1 K−1 by integrating their heat capacity data. Soga et al.[153] prepared Ca3(PO4)2 by crystallizing a glass of the same composition; unfortunately, they did not indicate which polymorph (α′-, α-, or β-Ca3(PO4)2) was obtained. Using low temperature adiabatic calorimetry, they then determined the heat capacity between 80.1 K and 279.2 K (−192.9 °C and 6.2 °C) but did not calculate S°298.15 K. As can be seen in Figure 3, their C P data are lower than those of Southard and Milner.[143] By integrating the data of Soga et al.,[153] one can obtain 177.247 J mol−1 K−1, which is about 59 J mol−1 K−1 lower than the value measured by Southard and Milner[143] for β-Ca3(PO4)2.
The standard Gibbs energy of formation of Ca3(PO4)2 was measured by Bookey[126] between 1523 K and 1773 K (1250 °C and 1500 °C) using the reaction 4α-Ca3(PO4)2(s) + 5H2(g) = 3Ca4(PO4)2O(s) + P2(g) + 5H2O(g). As for Ca4(PO4)2O, he determined the Gibbs energy of the reaction by passing a known volume of hydrogen over C3P(s) and measuring the amount of H2O(g) in the exit gas. Yama-zoye et al.[154,155] determined the Gibbs energy of formation between 1423 K and 1523 K (1150 °C and 1250 °C) from the reaction 3Ca4(PO4)2O(s) + P2(g) + 5/2O2(g) = 4Ca3(PO4)2(s). Molten copper contained in a graphite crucible was brought to equilibrium with C4P(s) and C3P(s) under a stream of pure CO gas at 1 atm. The Gibbs energy of formation of Ca3(PO4)2 was also measured by Tagaya et al.[131,132] between 1473 K and 1598 K (1200 °C and 1325 °C) using the reactions 3Ca4(PO4)2O(s) + 2P in Ag + 5CO(g) = 4Ca3(PO4)2(s) + 5C(s) and Ca3(PO4)2(s) + Ca in Ag + CO(g) = Ca4(PO4)2O(s). Mixtures of Ca3(PO4)2(s) and Ca4(PO4)2O(s) were equilibrated with silver-phosphorus alloys in graphite crucibles under CO and Ar mixtures. Recently, Nagai et al.[133] determined the ΔG f° between 1523 K and 1623 K (1250 °C and 1350 °C) using double Knudsen cell mass spectrometry. All the experimental data are converted to the standard Gibbs energy of formation of Ca3(PO4)2 in Figures 6(a) and (b).
Ca2P2O7 (C2P)
Butylin et al.[140] employed the Knudsen effusion method at 1555 K (1282 °C) and estimated the ΔH f°298.15 K of α-Ca2P2O7 to be −526.028 kJ mol−1 from the oxides; the standard entropy at 298.15 K (25.15 °C), S°298.15 K, was estimated to be 197.485 J mol−1 K−1. Using the same technique between 1409 K and 1560 K (1136 °C and 1287 °C), Lopatin[156] obtained a ΔH f°298.15 K of −567.852 kJ mol−1, but recently, Lopatin[157] revised this result and reported a value of −548.852 kJ mol−1. Egan and Wakefield[158] measured the heat content of α-Ca2P2O7 between 1473 K and 1626 K (1200 °C and 1353 °C) by drop calorimetry (Figure 4(a)) and the heat of fusion at 1626 K (1353 °C) was found to be −100.851 kJ mol−1. Despite the fact that Egan and Wakefield[158] did not observe directly the β–α transition, they reported a heat of transition of 6.786 kJ mol−1 at 1413 K (1140 °C). Similar enthalpy of transition was found by Mesmer and Irani[159] using DTA and Jacob et al.[160] using DSC; they obtained 6.360 kJ mol−1 at 1493 K (1220 °C) and 6.551 ± 0.7 kJ mol−1 at 1435 K (1162 °C), respectively.
For the β-Ca2P2O7 phase, no experimental measurements of the standard enthalpy of formation exist. The standard entropy at 298.15 K (25.15 °C), S°298.15 K, was determined to be 189.330 J mol−1 K−1 by Egan and Wakefield[158] using data obtained between 10 K and 305 K (−273 °C and 32 °C) with low temperature adiabatic calorimetry (Figure 4(b)). Egan and Wakefield[158] also determined the heat content between 298 K and 1473 K (25 °C and 1200 °C) using drop calorimetry (Figure 4(a)), which allowed them to derive heat capacities at high temperatures. These heat capacity data were fitted by Kelley[145] using a polynomial equation which is adopted in the present study. The enthalpy of transition from γ- to β-Ca2P2O7 was measured by Mesmer and Irani[159] using DTA and Jacob et al.[160] using DSC; they obtained 1.674 kJ mol−1 at 1123 K (850 °C) and 1.074 ± 0.2 kJ mol−1 at 1074 K (801 °C), respectively.
Little thermodynamic data exist for γ-Ca2P2O7. Mesmer and Irani[159] determined the heat of solution of γ-Ca2P2O7 in 6N HCl at 308 K (35 °C) and derived a standard enthalpy of formation at 298.15 K (25.15 °C) of −571.116 ± 7.5 kJ mol−1 from the oxides. Egan and Wakefield[158] measured the heat content of γ-Ca2P2O7 at 673 K, 773 K, and 873 K (400 °C, 500 °C, and 600 °C) and found that it is essentially the same as the β-form. Soga et al.[153] prepared Ca2P2O7 by crystallizing a glass of the same composition; unfortunately, they did not indicate which polymorph (α-, β-, or γ-Ca2P2O7) was obtained. Using low temperature adiabatic calorimetry, they then determined the heat capacity between 80.2 K and 280.4 K (−192.8 °C and 7.4 °C) but did not calculate S°298.15 K. As can be seen in Figure 4(b), their C P data are lower than those of Egan and Wakefield.[158] By integrating the data of Soga et al.,[153] one can obtain 149.040 kJ mol−1, which is about 40 J mol−1 K−1 lower than the value measured by Egan and Wakefield[158] for β-Ca2P2O7.
Recently, the standard Gibbs energy of formation of Ca2P2O7, ΔG f°, was measured by Hoshino et al.[161] between 1423 K and 1523 K (1150 °C and 1250 °C) and by Sandström et al.[162] between 898 K and 1004 K (625 °C and 731 °C); both studies employed the solid-state emf method. Experimental data are compared in Figures 6(a) and (b).
Ca(PO3)2 (CP)
No thermodynamic data exist for α-Ca(PO3)2.
The standard enthalpy of formation at 298.15 K (25.15 °C) of β-Ca(PO3)2 was estimated from Knudsen effusion experiments at 1180 K and 1100 K (907 °C and 827 °C) by Rat’kovskii et al.[163] and Butylin et al.,[140] respectively; they both reported a value of −336.870 kJ mol−1 from the oxides. Using the same technique, Rat’kovskii et al.[164] and Lopatin[156] estimated the ΔH f°298.15 K to be −315.950 and −342.942 kJ mol−1, respectively. Later, Lopatin[157] revised his data to −329.942 kJ mol−1. The S°298.15 K was determined by Egan and Wakefield[165] using low temperature adiabatic calorimetry between 10 K and 306 K (−263 °C and 33 °C). The entropy measured by them is 146.940 J mol−1 K−1, which is similar to the values obtained by Rat’kovskii et al.[163,164] and Butylin et al.[140] with the Knudsen effusion method: that is 146.440 and 152.298 J mol−1 K−1, respectively. Yaglov and Volkov[166] investigated the dehydration of Ca(H2PO4)2·H2O by DTA and found the S°298.15 K for β-Ca(PO3)2 to be 136.817 ± 18.8 J mol−1 K−1. Egan and Wakefield[165] measured the heat content of β-Ca(PO3)2 between 375.80 K and 1253 K (102.65 °C and 979.85 °C) using drop calorimetry (Figure 5(a)) and derived its heat capacity data. These data were fitted by Kelley[145] using a polynomial equation which is used in this study. The enthalpy of transition between γ- and β-Ca(PO3)2 at 963 K to 993 K (690 °C to 720 °C) was determined by Jackson et al.[109] using DSC; they found 24 ± 1 kJ mol−1, a rather unreasonable value for this kind of transformation.
The standard enthalpy of formation at 298.15 K (25.15 °C) of γ-Ca(PO3)2 was determined by Volkov et al.[167] who studied the dehydration of Ca(H2PO4)2·H2O by DTA; they obtained −340.636 kJ mol−1 from the oxides. Soga et al.[153] prepared Ca(PO3)2 by crystallizing a glass of the same composition; unfortunately, they did not indicate which polymorph (α-, β-, or γ- Ca(PO3)2) was obtained. Using low temperature adiabatic calorimetry, they then determined the heat capacity between 80.3 K and 280.7 K (−192.7 °C and 7.7 °C) but did not calculate S°298.15 K. As can be seen in Figure 5(b), their C P data are lower than those of Egan and Wakefield.[165] By integrating the data of Soga et al.,[153] one can obtain 119.371 kJ mol−1, which is about 28 J mol−1 K−1 lower than the value measured by Egan and Wakefield[165] for β-Ca(PO3)2.
The standard Gibbs energy of formation of Ca(PO3)2 between 840 K and 1140 K (567 °C and 867 °C) was measured by Sandström[162] using a solid-state emf cell. Experimental data are depicted in Figure 6(a).
CaP4O11 (CP2)
No thermodynamic data exist for α-CaP4O11.
The standard enthalpy of formation of β-CaP4O11 at 298.15 K (25.15 °C) was estimated by Golubchenko[168] (cited and recalculated by Lopatin[157]) using the Knudsen effusion method at 808 K to 923 K (535 °C to 650 °C); he obtained a value of −392.97 kJ mol−1 from the oxides.
Liquid
Using a galvanic cell, Schwerdtfeger and Engell[169] measured the activity of CaO(s) in the CaO-rich part of liquid CaO-P2O5 at 1923 K (1650 °C). Experimental data (Figure 7) show a sharp decrease in the CaO activity at 0.25 mol fraction of P2O5.
Thermodynamic Model
Stoichiometric Compounds
The Gibbs energy of stoichiometric compounds can be described by:
where \( \varDelta H_{{298.15 {\text{K}}}}^{^\circ } \) is the enthalpy of formation of a given species from pure elements (\( \varDelta H_{{298.15 {\text{K}}}}^{^\circ } \) of elemental species stable at 298.15 K (25.15 °C) and 1 atm are assumed as 0 J/mol; reference state), \( S_{{298.15 {\text{K}}}}^{^\circ } \) is the entropy at 298.15 K (25.15 °C), and C P is the heat capacity.
Liquid Phase
The modified quasichemical model (MQM),[170] which takes into account the short-range-ordering (SRO) of second-nearest-neighbor (SNN) cations in liquid silicate, is used to describe the thermodynamics of the liquid oxide melt. Since oxygen is always connected to cations in oxide melt systems, the breakage of the P2O5 network by CaO can be simulated by consideration of SRO of SNN cations. In the CaO-P2O5 liquid solution, both PO4 3− and P2O7 4− are the basic building units of P2O5. Strictly speaking, both P2O7 4− and PO4 3− can exist in the liquid phase, but for the sake of simplicity in the present thermodynamic modeling, we use only P2O7 4−. We already used this for the SiO2-P2O5 system and successfully explained the phase diagram and in particular the liquidus of SiO2.[20]
In order to adopt P2O7 4− as a building unit of P2O5 in the MQM, P2O3 4+, which can be surrounded by four broken oxygen to form P2O7 4− (this is similar to Si4+ surrounded by four broken oxygen to form SiO4 4−), was used as a cation species for the P2O5 component. To reproduce the short range ordering (minimum enthalpy of mixing of liquid) occurring at the Ca3P2O8 composition, the coordination numbers of the cations were set in the model to be 1.37745 for Ca2+ and 4.1322 for P2O3 4+. The quasichemical reaction between cations in liquid CaO-P2O5 can be expressed as:
where \( \varDelta g_{{{\text{Ca - P}}_{2} {\text{O}}_{3} }} \) is the Gibbs energy of the quasichemical Reaction [4].
The molar Gibbs energy of the liquid CaO-P2O5 solution in the MQM can then be expressed as:
where, \( G_{\text{CaO}}^{^\circ } \) and \( G_{{{\text{P}}_{2} {\text{O}}_{5} }}^{^\circ } \) are the molar Gibbs energies of pure liquid CaO and P2O5, \( \varDelta S^{\text{conf}} \) is the configurational entropy of mixing given by a random distribution of the (Ca-Ca) (P2O3-P2O3) and (Ca-P2O3) pairs in the one-dimensional Ising approximation, \( n_{\text{CaO}} \) and \( n_{{{\text{P}}_{2} {\text{O}}_{5} }} \) are the numbers of moles of CaO and P2O5, and \( n_{{{\text{Ca - P}}_{2} {\text{O}}_{3} }} \) is the number of moles of (Ca-P2O3) pairs in one mole of CaO-P2O5 solution. The term \( \varDelta g_{{{\text{Ca - P}}_{2} {\text{O}}_{5} }} \) is the model parameter to reproduce the Gibbs energy of the liquid phase of the binary CaO-P2O5 system, which is expanded as a polynomial in terms of the pair fractions, as follows:
where \( \varDelta g_{{{\text{Ca - P}}_{2} {\text{O}}_{3} }}^{0} \), \( g_{{{\text{Ca - P}}_{2} {\text{O}}_{3} }}^{i0} \) and \( g_{{{\text{Ca - P}}_{2} {\text{O}}_{3} }}^{0j} \) are adjustable model parameters which can be functions of temperature. The details of the model including the expression of \( \varDelta S^{\text{conf}} \) can be found elsewhere.[170]
Thermodynamic Optimization
Thermodynamic optimization (modeling) of the present system was carried out based on the critical evaluation of all the experimental data discussed in Section II using the thermodynamic model described in Section III. Since thermodynamic data for the liquid are scarce and those for the solid compounds are abundant, the thermodynamic properties of the solid phases were first determined followed by the preliminary optimization of the model parameters of the liquid phase to reproduce the phase diagram. In the final stage, the thermodynamic parameters of both solids and liquid were optimized to reproduce all reliable experimental data within experimental error limits as much as possible. In the case of the solid phases C10P3, C4P3, C2P3, and CP2 for which little or no thermodynamic data are available, heat capacities were first evaluated by summing the C P of known adjacent compounds as listed in Table XII. The \( \varDelta H_{{298.15 {\text{K}}}}^{{^\circ }} \) and \( S_{{298.15 {\text{K}}}}^{^\circ } \) of the compounds were then evaluated to reproduce the phase diagram. The results of the optimization are compared with experimental data in Figures 1 through 7 and Tables II through VII and IX through XII. In general, all the experimental data are well reproduced within experimental error limits.
The phase diagram data of the CaO-P2O5 system are in general well reproduced in the present optimization except for the liquidus of C4P; the melting temperature of C4P being reproduced slightly outside experimental error limits. Optimized liquid model parameters are listed in Table XIII. In order to reproduce the sharp liquidus of C3P, relatively large temperature dependent terms were needed for the \( \varDelta g_{{{\text{Ca - P}}_{2} {\text{O}}_{3} }}^{0} \) parameter.
During the optimization, we were also able to resolve the discrepancies observed in the Gibbs energy of formation of the compounds. Figure 6 shows the calculated Gibbs energy of formation of intermediate compounds in the CaO-P2O5 system along with experimental data. Some original experimental data[125–134] were given as the Gibbs energy of formation from CaO, O in Fe or P in Fe; they were converted to the Gibbs energy of formation from elemental references using the Gibbs energy changes of the reactions Ca(l) + O2(g) = CaO(s) from FactSage (Bale et al.[121]), 2.5O2(g) = 5O in Fe from Sakao and Sano[135] and Elliot and Gleiser,[136] P2(g) = 2P in Fe from Yamamoto et al.,[139] and 0.5P2(g) = P in Ag from Ban-Ya and Suzuki[138] and Yamamoto et al.[139] The Gibbs energy of formation can be indirectly calculated from known \( \varDelta H_{{298.15 {\text{K}}}}^{^\circ } \), \( S_{{298.15 {\text{K}}}}^{^\circ } \), and heat capacity. According to our optimization, the experimental Gibbs energy of formation of C4P and C3P measured by Bookey et al.[126] and Nagai et al.[133] are more consistent with other experimental thermodynamic property data in Tables IX through XII than those by Bookey et al.,[125] Ban-Ya and Matoba,[127] Iwase et al.,[129,130] Tagaya et al.,[131,132] and Yamasue et al.[134] The experimental emf data of C2P determined by Sandström et al.[162] are also consistent with other data in Tables IX through XII. However, the Gibbs energy of formation of CP from the emf measurements of Sandström et al.[162] is inconsistent with the enthalpy, entropy and heat capacity data of the same compound listed in Tables IX through XII. The optimized Gibbs energy of CP is about 50 kJ mol−1 higher than the experimental data reported by Sandström et al.[162]
As can be seen in Figure 8(a), the optimized enthalpies of formation of the compounds at 298.15 K (25.15 °C) (here given for 1 mol of components CaO plus P2O5) are in good agreement with experimental data except for the enthalpy measured by Butylin et al.[140] for α′-Ca3(PO4)2 (α′-C3P), which is far off from the trend observed for other data. The optimized enthalpies of formation reach a minimum of about −180 kJ mol−1 at the Ca2P2O7 (C2P) composition. This is almost four times more negative than that for the CaO-SiO2 system.[171] The optimized entropies of formation of the compounds at 298.15 K (25.15 °C) (Figure 8(b); also here given for one mole of components CaO plus P2O5) are also in good agreement with experimental data except for the entropy of β-Ca(PO3)2 (β-CP) determined by Yaglov and Volkov[166] using DTA (a not reliable technique for entropy determination) and, again, by Butylin et al.[140] for α′-C3P. It is not clear why Butylin et al.[140] failed to obtain reliable enthalpy and entropy of formation for α′-C3P using the Knudsen effusion method.
Calculated and experimentally determined (a) enthalpies of formation at 298.15 K (25.15 °C) with experimental data of Berthelot,[146–148] Richardson et al.,[150] Jeffes cited in Pearson et al.,[124] Smirnova et al.,[142] Meadowcroft et al.,[151] Jacques et al. cited in Meadowcroft and Richardson,[151] Rat’kovskii et al.,[163] Rat’kovskii et al.,[164] Butylin et al.,[140] Volkov et al.,[167] Golubchenko,[168] Lopatin,[156] Lopatin,[157] Martin et al.,[122] and Ben Abdelkader et al.,[152] and (b) entropies of formation at 298.15 K (25.15 °C) of the compounds with experimental data of Southard and Milner,[143] Egan and Wakefield,[165] Egan and Wakefield,[158] Rat’kovskii et al.,[163] Rat’kovskii et al.,[164] Butylin et al.,[140] and Yaglov and Volkov.[166] The solid lines are calculated values connecting the polymorphs stable at 298.15 K (25.15 °C). Note that the reference state of P2O5 is hexagonal P2O5 (strictly speaking, hexagonal P2O5 is metastable at 298.15 K (25.15 °C) but is the most commonly used polymorph as a reference state for solid P2O5). Note also that the enthalpies and entropies of formation are here given for one mole of components CaO plus P2O5
The enthalpies of fusion of C2P and CP are well reproduced as shown in Figures 4 and 5. The enthalpy of mixing of the liquid phase at 1773 K (1500 °C) is calculated from the present optimization in Figure 9; like the enthalpies of formation of the solid compounds, the liquid shows a minimum at 0.25 mol fraction of P2O5 and reaches −225 kJ mol−1. Unfortunately, there is no experimental enthalpy data for the liquid. However, our calculated enthalpy must be reasonable as judged from the well reproduced enthalpies of melting of Ca2P2O7 and CaP2O6 in Figures 4 and 5. The sharp change in the enthalpy of mixing of the liquid phase at 0.25 mol fraction of P2O5 is also consistent with the activity of CaO in Figure 7 and the sharp liquidus of C3P as shown in the phase diagram of Figure 1. For the sake of clarity, the optimized binary CaO-P2O5 system is depicted in Figure 10 without experimental data.
Calculated enthalpy of mixing of the liquid phase at 1873 K (1600 °C)
The optimized binary CaO-P2O5 system. Temperatures are in degree Celsius
A final note must be made about the CaO melting point that was employed in this study. Using quasi-containerless laser heating in various controlled atmospheres, Manara et al.[172] just recently located the CaO melting point at 3222 ± 25 K (2949 ± 25 °C), which is 377 K (377 °C) above the value (2845 K; 2572 °C) we used in our optimization of the CaO-P2O5 system. The new melting point obtained by Manara et al.[172] is in agreement with earlier measurements performed by Foex[173] [3223 K (2950 °C)], Traverse and Foex[174] [3200 K (2927 °C)] and Yamada[175] [3178 K (2905 °C)] and the value recommended in the JANAF Tables[176] [3200 K (2927 °C)] whereas the melting point employed by us is in agreement with previous determinations made by Noguchi et al.[177] [(2863 K) 2590 °C)], Panek[178] [2890 K (2617 °C)], Shevchenko[179] [2833 K (2560 °C)], and Hlaváč[180] [2886 K (2613 °C)]. According to Manara et al.,[172] the difference observed between the two experimental datasets [one with temperatures around 3200 K (2927 °C) and one with temperatures around 2868 K (2595 °C)] is due to the oxidizing/reducing conditions in which the CaO melting point was measured in the various studies. In this regard, the Ca-O binary system provides some clues about the CaO melting point. In this system, the CaO liquidus, which is metastable, was experimentally determined by Bevan and Richardson[181] using thermal analysis, by Fischbach[182] using DTA and the quenching method, and by Zaitsev and Mogutnov[183] using the quenching method. Data collected by Fischbach[182] are slightly at odds with those of Bevan[181] and Zaitsev and Mogutnov[183] but according to Fischbach[182] himself, this may be caused by segregation effects in his samples. Extrapolation of the metastable CaO liquidus data toward pure CaO points to a melting temperature of about 2800 K (2527 °C), which is in agreement with the value [2845 K (2572 °C)] we used in our optimization of the CaO-P2O5 system. The melting point employed by us is actually based on the optimization of the CaO-SiO2 system by Pelton and Blander,[184] the CaO-MgO, CaO-FeO, and CaO-MnO systems by Wu et al.,[185] and the Ca-O system by Lindberg and Chartrand.[186] In these phase diagram assessments, the CaO melting point was obtained by extrapolating CaO liquidus data, collected at low temperatures, toward pure CaO; this points to a melting temperature of 2845 K (2572 °C).
Summary
The CaO-P2O5 system was successfully optimized by performing a comprehensive evaluation of all available experimental phase diagram and thermodynamic data. The CaO-P2O5 system is one of the most energetically negative oxide systems among all well-known binary solid oxide systems. In the present study, the Gibbs energy of the liquid phase was well described by the MQM taking into account the short range ordering in the liquid state. The discrepancies in the Gibbs energy of formation of the compounds were also resolved as the results of the thermodynamic optimization. Phase diagram data are well reproduced except for the liquidus of Ca4(PO4)2O (C4P) which is slightly away from the experimental error range. The model with optimized model parameters can be used to calculate any thermodynamic properties in the system. The obtained thermodynamic database is being expanded to the multicomponent system Na2O-MgO-CaO-FeO-Fe2O3-MnO-Al2O3-SiO2-P2O5 for applications related to the glassmaking and steelmaking processes.
References
Y. Abe, H. Hosono, W.H. Lee, and T. Kasuga: Phys. Rev. B: Condens. Matter. Mater. Phys., 1993, 48 (21), pp. 15621-25.
N. Vedeanu, O. Cozar, I. Ardelean, and S. Filip: J. Optoelectron. Adv. Mater., 2006, vol. 8 (3), pp. 1135-39.
F. de Mestral and R.A.L. Drew: J. Eur. Ceram. Soc., 1989, vol. 5 (1), pp. 47-53.
L.L. Hench: J. Am. Ceram. Soc., 1991, vol. 74, pp. 1487-1510.
K. Franks, I. Abrahams, and J.C. Knowles: J. Mater. Sci. Mater. Med., 2000, vol. 11 (10), pp. 609-14.
V. Salih, K. Franks, M. James, G.W. Hastings, J.C. Knowles, and I. Olsen: J. Mater. Sci. Mater. Med., 2000, 11 (10), 615-20.
R.Z. LeGeros and J.P. LeGeros: J. Wuhan Univ. Technol. Mater. Sci. Ed., 2005, vol. 20 (Suppl), pp. 1–6.
V.I. Putlyaev and T.V. Safronova: Glass Ceram., 2006, vol. 63 (3–4), p. 99102.
[9] F. Pahlevani, S.Y. Kitamura, H. Shibata, and N. Maruoka: ISIJ Int., 2010, vol. 50 (6), pp. 822-29.
H. Matsuura: Materia, 2011, vol. 50 (10), pp. 446-49.
I.H. Jung and Y. Zhang: JOM, 2012, vol. 64 (8), pp. 973-81.
T. Ifka, M.T. Palou, and M, Z. Bazelova: Ceram.-Silik., 2012, 56 (1), pp. 76-84.
U.K. Alimov, A.M. Reimov, T.A. Sattarov, Sh.S. Nazarov, and B.M. Beglov: Khym. Prom. (St. Petersburg, Russian Federation), 2011, vol. 88 (6), pp. 271-76.
S.Z. Li, Z.H. Wang, and B.A. Stewart: Adv. Agron., 2011, vol. 110, pp. 125-249.
[15] S. Serena, L. Carbajal, M.A. Sainz, and A. Caballero: J. Am. Ceram. Soc., 2011, 94 (9), pp. 3094-103.
S. Serena, L. Carbajal, M.A. Sainz, and A. Caballero: J. Am. Ceram. Soc., 2011, vol. 94 (11), p.4089.
I. Barin: Thermochemical Data of Pure Substances, Part I—II, Weinheim, Federal Republic of Germany, New York, VCH, 1993.
A.T. Dinsdale: CALPHAD, 1991, vol. 15 (4), 1991, pp. 317-425.
[19] I.H. Jung and P. Hudon: J. Am. Ceram. Soc., 2012, vol. 95 (11), pp. 3665-72.
M. Rahman, P. Hudon, and I.H. Jung: Metall. Mater. Trans. B, 2013, 44 (4), pp. 837-52.
T. Hahn: in International Tables for Crystallography Volume A: Space Group Symmetry, H. Fuess, T. Hahn, H. Wondratschek, U. Müller, U. Shmueli, E. Prince, A. Authier, V. Kopský, D. Litvin, M. Rossmann, E. Arnold, S. Hall, and B. McMahon, eds., Springer, Dordrecht, 2002, pp. 111–717.
T. Dieckmann and E. Houdremont: Z. Anorg. Chem., 1921, vol. 120 (1), pp. 129-49.
G. Hilgenstock: Stahl Eisen, 1883, vol. 9, p. 498.
J.W. Anthony, R.A. Bideaux, K.W. Bladh, and M.C. Nichols, eds.: Handbook of mineralogy, Mineralogical Society of America, Chantilly, 2012.
A. von Groddeck and K. Broockmann: Stahl Eisen, 1884, vol. 3, pp. 141-42.
H. Bücking and G. Linck: Stahl Eisen, 1887, vol. 4, pp. 245-49.
H.A. Miers: J. Chem. Soc. London, 1887, vol. 51, pp. 608-10.
G. Trömel and C. Zaminer: Arch. Eisenhuettenwes., 1959, vol. 30 (4), pp. 205-9.
H. Bauer and W. Balz: Z. Anorg. Allg. Chem., 1965, vol. 340, pp. 225-31.
[29] W.E. Brown and E.F. Epstein: J. Res. Nat. Bur. Std. A, 1965, vol. 69, pp. 547-51.
[30] K. Cieśla: Prace Naukowe Akademii Ekonomicznej imienia Oskara Langego we Wroclawiu, 1984, vol. 267, pp. 418-21.
H. Schneiderhohn: Mitt. Kaiser-Wilhelm Inst. Eisenforsch. Duesseldorf, 1932, vol. 14, 34-36.
A. Schleede, W. Schmidt, and H. Kindt: Z. Elektrochem. Angew. Phys. Chem., 1932, vol. 38, pp. 633-41.
B. Dickens, W.E. Brown, G.J. Kruger, and J.M. Stewart: Acta Cryst. B, 1973, vol. 29, pp. 2046-56.
H. Blome: Stahl Eisen, 1911, vol. 30, pp. 2161-67.
G. Trömel: Mitt. Kaiser-Wilhelm Inst. Eisenforsch. Duesseldorf, 1932, vol. 14, pp. 25-34.
G. Behrendt and H. Wentrup: Arch. Eisenhuettenwes., 1933, vol. 7 (2), pp. 95-102.
R.L. Barrett and W.J. McCaughey: Am. Mineral., 1942, vol. 27 (10), pp. 680-95.
G. Trömel: Stahl Eisen, 1943, vol. 63 (2), pp. 21-30.
G. Trömel and W. Fix: Arch. Eisenhuettenwes., 1961, vol. 32 (4), pp. 209-12.
J.H. Welch and W.H. Gutt: J. Chem. Soc., 1961, pp. 4442–44.
K. Cieśla and R. Rudnicki: Polish J. Chem., 1988, vol. 62, pp. 683-91.
J.C. Trombe and G. Montel: J. Inorg. Nucl. Chem., 1978, vol. 40, pp. 15-21.
J.C. Trombe and G. Montel: Compt. Rend. Acad. Sci. Paris, Série C, 1971, vol. 273, pp. 462-65.
J.C. Trombe and G. Montel: Compt. Rend. Acad. Sci. Paris, Série C, 1972, vol. 274, pp. 1169-72.
J.C. Trombe: Ann. Chim., 1973, vol. 8, pp. 251-69.
P.A. Henning, A.R. Landa-Cànovas, A.K. Larsson, and S. Lidin: Acta Cryst. B, 1999, vol. 55, pp. 170-76.
C. Frondel: Am. Mineral., 1941, vol. 26, pp. 145-52.
C. Frondel: Am. Mineral., 1943, vol. 28, pp. 215-32.
R. Gopal and C. Calvo: Nature Phys. Sci., 1972, vol. 237, pp. 30-32.
J.C. Knowles, I.R. Gibson, and I. Abrahams: in Bioceramics Volume 12: Proc. 12th Int. Sympos. Ceram. Med., H. Ohgushi, G.W. Hasting, T. Yoshikawa, eds., World Scientific, Nara, 1999, pp. 341–44.
M. Yashima and A. Sakai: Chem. Phys. Lett., 2003, vol. 372, pp. 779-83.
A.L. Mackay: Acta Cryst., 1953, vol. 6, pp. 743-44.
M. Mathew, L.W. Schroeder, B. Dickens, and W.E. Brown: Acta Cryst., 1977, vol. B33, pp. 1325-33.
A.L. Mackay: Ph.D. Thesis, Birkbeck College, London University, London, 1952.
B. Dickens, L.W. Schroeder, and W.E. Brown: J. Solid State Chem., 1974, vol. 10, pp. 232-48.
C. Calvo and R. Gopal: Am. Mineral., 1975, vol. 60, pp. 120-33.
M. Yashima, A. Sakai, T. Kamiyama, and A. Hoshikawa: J. Solid State Chem., 2003, vol. 175, pp. 272-77.
H. Koelmans, J.J. Engelsman, and P.S. Admiraal: J. Phys. Chem. Solids, 1959, vol. 11, pp. 172–73.
J.P. Fasting and H. Haraldsen: Tidsskr. Kjemi Bergv. Metall., 1943, vol. 3 (5), pp. 48-55.
J. Ando: Bull. Chem. Soc. Japan, 1958, vol. 31, pp. 196-201.
I.R. Gibson, M. Akao, S.M. Best, and W. Bonfield: in 9th International Symposium on Ceramics in Medicine Proceedings, T. Kokubo, T. Nakamura, and F. Miyaji, eds., Pergamon Press, Otsu, 1996, pp. 173–76.
Y. Pan, J.L. Huang, and C.Y. Shao: J. Mater. Sci., 2003, vol. 38, pp. 1049-56.
R. Enderle, F. Götz-Neunhoeffer, M. Göbbels, F.A. Müller, and P. Greil: Biomaterials, 2005, vol. 26, pp. 3379-84.
R.G. Carrodeguas, A.H. De Aza, X. Turrillas, P. Pena, and S. De Aza: J. Am. Ceram. Soc., 2008, vol. 91 (4), pp. 1281-86.
L.W. Schroeder, B. Dickens, and W.E. Brown: J. Solid State Chem., 1977, vol. 22, pp. 253-62.
K.S. TenHuisen and P.W. Brown: J. Am. Ceram. Soc., 1999, vol. 82 (10), pp. 2813-18.
M.A. Bredig, H.H. Franck, and H. Füldner: Z. Elektrochem. Angew. Phys. Chem., 1933, vol. 39, pp. 959-69.
J. Berak and I. Tomczak-Hudyma: Prace Naukowe Akademii Ekonomicznej we Wroclawiu Chemia, 1972, vol. 31 (53), pp. 135-49.
J.M. Millet, R. Sassoulas, and A. Sebaoun: J. Thermal Anal., 1983, vol. 28, pp. 131-46.
J. Berak and G. Czupińska: Prace Naukowe Akademii Ekonomicznej imienia Oskara Langego we Wroclawiu, 1988, vol. 426, pp. 300-5.
J. Berak and T. Znamierowska: Prace Naukowe Akademii Ekonomicznej we Wroclawiu Chemia, 1972, vol. 31 (53), pp. 151-71.
J. Berak and T. Znamierowska: Rocz. Chem. Ann. Soc. Chim. Polonorum, 1973, vol. 47, pp. 1137-49.
J. Berak and I. Tomczak-Hudyma: Rocz. Chem. Ann. Soc. Chim. Polonorum, 1972, vol. 46, pp. 2157-64.
A.A. Belik, F. Izumi, S.Y. Stefanovich, A.P. Malakho, B.I. Lazoryak, I.A. Leonidov, O.N. Leonidova, and S.A. Davydov: Chem. Mater., 2002, vol. 14, pp. 3197-3205.
E.R. Kreidler and F.A. Hummel: Inorg. Chem., 1967, vol. 6 (5), 884-91.
B.M. Wallace and W.E. Brown: J. Dent. Res., 1971, vol. 50, pp. 343-46.
P. Riboud: Ph.D. Thesis, University of Paris VI, Paris, 1972.
W. Jungowska: Prace Naukowe Akademii Ekonomicznej imienia Oskara Langego we Wroclawiu, 2001, vol. 888, pp. 66-68.
P.W. Ranby, D.H. Mash, and S.T. Henderson: Brit. J. Appl. Phys. Suppl., 1955, vol. 4, pp. 18-25.
C. Calvo: Inorg. Chem., 1968, 7 (7), 1345-51.
D.E.C. Corbridge: Acta Cryst., 1957, vol. 10, p. 85.
U. Keppler: Naturwissenschaften, 1962: vol. 49, pp. 446-47.
N.C. Webb: Acta Cryst., 1966, vol. 21, pp. 942-48.
S. Boutin, S. Grandin, M.M. Borel, A. Leclaire, and B. Raveau: Acta Cryst. C, 1993, vol. 49, pp. 2062-64.
M. Schneider, K.H. Jost, and P. Leibnitz: Z. Anorg. Allg. Chem., 1985, vol. 527, pp. 99-104.
A.O. McIntosch and W.L. Jablonski: Anal. Chem. 1956, vol. 28 (9), pp. 1424-27.
J.A. Parodi, R.L. Hickok, W.G. Segelken, and J.R. Cooper: J. Electrochem. Soc., 1965, vol. 112 (7), pp. 688-92.
B.C. Cornilsen and R.A. Condrate Sr: J. Inorg. Nucl. Chem., 1979, vol. 41, pp. 602-5.
W.F. Bale, J.F. Bonner, H.C. Hodge, H. Adler, A.R. Wreath, and R. Bell: Ind. Eng. Chem. Anal. Ed., 1945, vol. 17, pp. 491-95.
W.L. Hill, G.T. Faust, and D.S. Reynolds: Am. J. Sci., 1944, vol. 242, pp. 457-77, 542-62.
V.A. Urikh, V.V. Tikhonov, D.Z. Serazetdinov, and A.B. Bekturov: Izv. Akad. Nauk SSSR Neorg. Mater., 1970, vol. 6 (11), pp. 2076-77.
J. Berak and T. Znamierowska: Rocz. Chem. Ann. Soc. Chim. Polonorum, 1972, vol. 46, pp. 1921-9.
A.A. Ismatov, S.Y. Azimov, and R.I. Akhmedov: Uzb. Khim. Zhur., 1985, vol. 4, pp. 66-69.
J.R. Van Wazer and S.A. Ohashi: J. Am. Chem. Soc., 1958, vol. 80, p. 1010.
S. Ohashi and J.R. Van Wazer: J. Am. Chem. Soc., 1959, vol. 81, pp. 830-32.
W. Wieker, A.R. Grimmer, and E. Thilo: Z. Anorg. Allg. Chem., 1964, vol. 330, pp. 78-90.
D.R. Gard: Phosphorus, Sulfur, and Silicon, 1993, vol. 76, pp. 231-34.
H.A. Höppe: Z. Anorg. Allg. Chem., 2005, vol. 631, 1272-76.
W. Szuszkiewicz: Mater. Chem. Phys., 1992, vol. 31, pp. 257-61.
R. Maddrell: Ann. Chem., 1847, vol. 61 (1), pp. 53-63.
R. Maddrell: Phil. Mag., 1847, vol. 30 (202), pp. 322-29.
R. Maddrell: Mem. Proc. Chem. Soc. London, 1847, vol. 3, pp. 273-80.
M. Weil, M. Puchberger, and J. Schmedt auf der Günne, and J. Weber: Chem. Mater., 2007, vol. 19, pp. 5067-73.
D.E.C. Corbridge: Acta Cryst. 1955, vol. 8, p. 520.
W. Rothammel and H. Burzlaff: Acta Cryst., 1989, vol. C45, pp. 551-53.
B.N. Viting, S.V. Golubchenko, and B.I. Laroryak: Rus. J. Inorg. Chem., 1994, vol. 39 (9), pp. 1364-66.
A. Boullé: Compt. Rend. Acad. Sci. Paris, 1936, vol. 202, pp. 1434-35.
L.E. Jackson, B.M. Kariuki, M.E. Smith, J.E. Barralet, and A.J. Wright: Chem. Mater., 2005, vol. 17, pp. 4642-46.
W.L. Hill, S.B. Hendricks, E.J. Fox, and J.G. Cady: Ind. Eng. Chem., 1947, vol. 39, pp. 1667-72.
D. Stachel: Z. Kristallogr., 1992, vol. 202, pp. 117-18.
K. Meyer, H. Hobert, A. Barz, and D. Stachel: Vibr. Spect., 1994, vol. 6, pp. 323-32.
M. Schneider, J. Bushmann, and P. Luger: Z. Anorg. Allg. Chem., 1994, vol. 620, pp. 766-70.
M. Beucher: Mat. Res. Bull., 1969, vol. 4, pp. 15-18.
I. Tordjman, M. Bagieu-Beucher, and R. Zilber: Z. Kristallogr., 1974, vol. 140, p. 145.
E.K. Churakova, A.I. Poloznikov, N.N. Shevtsova, R.G. Aziev, and S.I. Volfkovich: Vestn. Mosk. Univ. Ser. 2: Khim., 1980, vol. 21 (3), pp. 282-85.
O. Nielsen: Ferrum, 1913, vol. 10, pp. 97-111.
G.L. Frear, E.F. Deese, and J.W. Lefforge: Ind. Eng. Chem., 1944, vol. 36 (9), pp. 835-40.
G. Trömel and W. Fix: Arch. Eisenhuettenwes., 1962, vol. 33 (11), pp. 745-55.
M. Maciejewski, T.J. Brunner, S.F. Loher, W.J. Stark, and A. Baiker: Thermochem. Acta, 2008, vol. 468, pp. 75-80.
C.W. Bale, E. Bélisle, P. Chartrand, S.A. Decterov, G. Eriksson, K. Hack, I.H. Jung, Y.B. Kang, J. Melançon, A.D. Pelton, C. Robelin, and S. Petersen: CALPHAD, 2009, vol. 33, pp. 295-311.
R.I. Martin, K.S. TenHuisen, P. Leamy, and P.W. Brown: J. Phys. Chem. B, 1979, vol. 101, pp. 9375-79.
V.A. Sokolov, S.M. Rubinchik, E.I. Banashek, and E.E. Burovaya: Izv. Akad. Nauk SSSR, Neorg. Mater., 1966, vol. 2 (4), pp. 717-20.
J. Pearson, E.T. Turkdogan, and E.M. Fenn: J. Iron Steel Inst., 1954, vol. 176, pp. 441-44.
J.B. Bookey, F.D. Richardson, and A.J.E. Welch: J. Iron Steel Inst., 1952, vol. 171, pp. 404-12.
J.B. Bookey: J. Iron Steel Inst., 1952, vol. 171, pp. 61-66.
S. Ban-Ya and S. Matoba: Tetsu-to-Hagane, 1963, vol. 49 (4), pp. 666-72.
F. Aratani, Y. Omori, and K. Sanbongi: Tetsu-to-Hagane, 1968, vol. 54, pp. 143-51.
M. Iwase, H. Fujiwara, E. Ichise, H. Kitaguchi, and K. Ashida: Trans. Iron Steel Soc., 1989, vol. 10, pp. 45-52.
M. Iwase, H. Fujiwara, E. Ichise, H. Kitaguchi, and K. Ashida: Trans. Iron Steel Soc., 1990, vol. 11, pp. 31-38.
A. Tagaya, F. Tsukihashi, and N. Sano: Trans. Iron Steel Soc., 1991, vol. 18 (7), pp. 63-69.
A. Tagaya, F. Tsukihashi, and N. Sano: Iron Steelmaker 1992, vol. 13, pp. 59-65.
T. Nagai, M. Miyake, and M. Maeda: Metall. Mater. Trans. B, 2009, vol. 40, pp. 544-49.
E. Yamasue, K. Shimizu, and K. Nagata: ISIJ International, 2013, vol. 53, pp. 1828-35.
H. Sakao and K. Sano: Nippon Kinzoku Gakkaishi, 1959, vol. 23, pp. 671-74.
J.F. Elliott, M. Gleisser, and V. Ramakrishna: Thermochemistry for Steelmaking, vol. 2: Thermodynamic and Transport Properties, Addison-Wesley, Reading, 1963.
J. Wojciechowska, J. Berak, and W. Trzebiatowski: Rocz. Chem., 1956, vol. 30, pp. 743-56.
S. Ban-ya and M. Suzuki: Tetsu-to-Hagane, 1975, vol. 61, pp.2023-42.
M. Yamamoto, K. Yamada, L.L. Meshkov, and E. Kato: Tetsu-to-Hagane, 1980, vol. 66, pp. 2032-39.
B.A. Butylin, I.A. Rat’kovskii, V.A. Ershov, and G.I. Novikov: Dokl. Akad. Nauk BSSR, 1975, vol. 19(7), pp. 618-21.
P.V. Riboud: Ann. Chim., 1973, vol. 8, pp. 381-90.
Z.G. Smirnova, V.V. Illarionov, and S.I. Vol’fkovich: Russ. J. Inorg. Chem., 1962, vol. 7, pp. 920-22.
J.C. Southard and R.T. Milner: J. Am. Chem. Soc., 1935, vol. 57, pp. 983-84.
E.V. Britzke and B.K.Veselovskii: Bull. Akad. Sci. SSSR Otd. Teck., 1937, pp. 479–88.
K.K. Kelley: Bur. Mines Bull., 1960, vol. 584, pp. 1-232.
M. Berthelot: Ann. Chim. Phys., 1879, Series 5, vol. 17, pp. 132-37.
M. Berthelot: Ann. Chim. Phys., 1887, Series 6, vol. 11, pp. 350-62.
M. Berthelot: Thermochimie, données et lois numériques. vol. 2, Les lois expérimentales., pp. 237-238, Gauthier-Villard et fils, Paris, 1897.
C. Matignon and M. Séon: Compt. Rend. Acad. Sci. Paris, 1932, vol. 194, pp. 2184-87.
F.D. Richardson, J.H.E. Jeffes, and G. Withers: J. Iron Steel Inst., 1950, vol. 166, pp. 213-45.
T.R. Meadowcroft and F.D. Richardson: Trans. Faraday Soc., 1963, vol. 59, pp. 1564-71.
S. Ben Abdelkader, A. Ben Cherifa, I. Khattech, and M. Jemal: Thermochem. Acta, 1999, vol. 334, pp. 123-29.
N. Soga, K. Hirao, M. Matsuno, and R. Ota: Fiz. Khim. Stekla, 1985, vol. 11, pp. 356-62.
H. Yama-zoye, E. Ichise, H. Fujiwara, and M. Iwase: Iron Steelmak., 1991, vol. 18, pp. 75-80.
H. Yama-zoye, E. Ichise, H. Fujiwara, and M. Iwase: Trans. ISS AIME, 1992, vol. 13, pp. 41-46.
S.I. Lopatin: Izv. Akad. Nauk SSSR Neorg. Mater., 1990, vol. 26 (11), pp. 2435-36.
S.I. Lopatin: Russ. J. Gen. Chem., 1997, vol. 67 (2), pp.193-211.
E.P. Egan Jr. and Z.T. Wakefield: J. Am. Chem. Soc., 1957, vol. 79, pp. 558-61.
R.E. Mesmer and R.R. Irani: J. Chem. Eng. Data, 1963, vol. 8 (4), pp. 530-32.
S. Jacob, M.L. Schmitt, and M.E. Schlesinger: J. Therm. Anal. Calorim., 2010, vol. 100, pp. 897-900.
H. Hoshino, M. Iwase, and A. McLean: High-Temp. Mater. Process., 2004, vol. 23, pp. 377-82.
M.H. Sandström, D. Boström, and E. Rosén: J. Chem. Thermodynamics, 2006, vol. 38, pp. 1371-76.
I.A. Rat’kovskii, B.A. Butylin, and G.I. Novikov: Izv. Akad. Nauk SSSR Neorg. Mater., 1975, vol. 11 (1), 112-16.
I.A. Rat’kovskii, B.A. Butylin, and G.I. Novikov: Dokl. Akad. Nauk BSSR, 1975, vol. 19 (2), pp. 139-40.
E.P. Egan Jr. and Z.T. Wakefield: J. Am. Chem. Soc., 1956, vol. 78, pp. 4245-49.
V.N. Yaglov and A.I. Volkov: Khim. Khim. Tekh., 1977, vol. 12, pp. 26-32.
A.I. Volkov, O.N. Komshilova, G.I. Novikov, and V.N. Yaglov: Khim. Khim. Tekh. 1982, vol. 14, pp. 34-42.
S.V. Golubchenko: Ph.D. Thesis, Moscow State University, Moscow, 1986.
K. Schwerdtfeger and H.J. Engell: Arch. Eisenhuettenwes., 1963, 34 (9), 647-52.
A. Pelton, S. Degterov, G. Eriksson, C. Robelin, and Y. Dessureault: Metall. Mater. Trans. B, 2000, vol. 31, pp. 651–59.
G. Eriksson, P. Wu, M. Blander, and A.D. Pelton: Can. Metall. Q., 1994, vol. 33 (1), pp. 13-21.
D. Manara, R. Böhler, L. Capriotti, A. Quaini, Z. Bao, K. Boboridis, L. Luzzi, A. Janssen, P. Pöml, R. Eloirdi, and R.J.M. Konings: J. Eur. Ceram. Soc., 2014, vol. 34 (6), pp. 1623-36.
M. Foex: Sol. Energy, 1965, vol. 9, pp. 61-7.
J.P. Traverse and M. Foex: High Temp. High Pressures, 1969, vol. 1 (4), pp. 409-27.
T. Yamada, M. Yoshimura, and S. Somiya: J. Am. Ceram. Soc., 1986, vol. 69, pp. C243-5.
M.W. Chase Jr.: NIST-JANAF Thermochemical Tables, 4th ed. Part II, Monograph no. 9, The American Institute of Physics, Woodburry, NY, 1998, p. 729.
T. Noguchi, M. Mizuno, and W.M. Conn: Sol. Energy, 1967, vol. 11, pp. 145-52.
Z. Panek: Silikaty (Prague), 1979, vol. 23 (2), pp. 97-102.
V. Shevchenko, L.M. Lopato, A.I. Stegny, G.I. Gerasimyuk, V.S. Dvernyakov, and V.V. Pasichnys: Dokl. Akad. Nauk SSSR, Ser. A, 1979, vol. 8, pp. 682-85.
J. Hlaváč: Pure Appl. Chem., 1982, vol. 54, pp. 681-8.
D.J.M. Bevan and F.D. Richardson: Proc. Australian Atomic Energy Symp. Peaceful Uses of Atomic Energy, Melbourne University Press, Melbourne, Australia, 1959, pp. 586–87.
H. Fischbach: Steel Res., 1985, vol. 56, pp. 365-8.
A.I. Zaitsev and B.M. Mogutnov: Metall. Mater. Trans. B, 2001, vol. 32, pp. 305-11.
A.D. Pelton and M. Blander: Metall. Trans. B., 1986, vol. 17, pp. 805-15.
P. Wu, G. Eriksson, and A.D. Pelton: J. Am. Ceram. Soc., 1993, vol. 76, pp. 2065-75.
D. Lindberg and P. Chartrand: J. Chem. Thermodyn., 2009, vol. 41, pp. 1111-24.
P. Termier and A. Richard: Bull. Soc. Franc. Mineral., 1895, vol. 18 (7), pp. 391-95.
M.A. Bredig, H.H. Franck, and H. Füldner: Z. Elektrochem., 1932, vol. 38, pp. 158-64.
P.D.S. St. Pierre: Canada Department of Mines and Technical Surveys Mines Branch, 1953, Technical Paper No. 2, 107 pp.
P.D.S. St. Pierre: J. Am. Ceram. Soc., 1954, vol. 37 (6), pp. 243-58.
H. Guérin, J. Masson, and A. Artur: Bull. Soc. Chim. Fr., 1957, pp. 545–47.
W. Bobrownicki and K. Slawski: Rocz. Chem., 1959, vol. 33, pp. 251-54.
R.W. Nurse, J.H. Welch, and W.H. Gutt: J. Chem. Soc., 1959, vol. 3, pp. 1077-83.
J. Berak: Rocz. Chem., 1961, vol. 35, pp. 23-30.
W. Fix, H. Heymann, and R. Heinke: J. Am. Ceram. Soc., 1969, vol. 52 (6), pp. 346-47.
A.K. Shirvinskaya and I.A. Bondar: Dokl. Akad. Nauk SSSR [Chem], 1975, vol. 225 (1), pp. 95–98.
R.W. Nurse, J.H. Welch, and W.H. Gutt: Nature, 1958, vol. 182, p. 1230.
J. Berak: Rocz. Chem., 1961, vol. 35, pp. 69–77.
J. Ando and S. Matsuno: Bull. Chem. Soc. Japan, 1968, vol. 41, pp. 342-47.
E.R. Kreidler: J. Electrochem. Soc., 1971, vol. 118 (6), 923-29.
W.A. Fisher, D. Janke, and K. Zielinski: Radex Rundschau, 1972, vol. 2, pp. 98-110.
K. Cieśla and R. Rudnicki: Polish J. Chem., 1991, vol. 65, pp. 1585-95.
J. Zhou, J. Chen, X. Zhang, and P.A. Zhou: in Polymers and Biomaterials, H. Feng, Y. Han, and L. Huang, eds., C-MRS Int. Symp. Proc., Elsevier Science, Amsterdam, 1991, pp. 325–30.
H. Aoki: Science and medical applications of hydroxyapatite, Takayama Press System Center Co. Japan, Tokyo, 1994.
P.N. De Aza, F. Guitián, and S. De Aza: J. Amer. Ceram. Soc., 1995, vol. 78 (6), pp. 1653-56.
R.G. Carrodeguas, A.H. De Aza I. Garcia-Páez, S. De Aza, and P. Pena: J. Am. Ceram. Soc., 2010, vol. 93 (2), pp. 561-69.
I.M. Martínez, P.A. Velásquez, and P.N. De Aza: Mater. Charact., 2010, vol. 61, pp. 761-67.
W.L. Hill, D.S. Reynolds, S.B. Hendricks, and K.D. Jacob: J. Assoc. Off. Agric. Chem., 1945, vol. 28, pp. 105-18.
G. Trömel, H.I. Harkcort, and W. Hotop: Z. Anorg. Chem., 1948, vol. 256 (5-6), pp. 253-72.
J. Ando: Bull. Chem. Soc. Japan, 1958, vol. 31, pp. 201-5.
J.F. Sarver, M.V. Hoffman, and F.A. Hummel: J. Electrochem. Soc., 1961, vol. 108 (12), pp. 1103-8.
H. Bauer: N. Jb. Miner. Abh., 1964, vol. 102 (1), pp. 68-88.
J. Kubicki: Chem. Stosowana A, 1966, vol. 3, pp. 287-303.
G.R. Boell, A.J. Majumdar, and J.A. Watts: J. Aust. Ceram. Soc., 1978, vol. 14 (2), pp. 29-30.
H. Monma and M. Goto: Yogyo Kyokai-Shi, 1983, vol. 91 (10), pp. 473-75.
K. Cieśla and R. Rudnicki: Prace Naukowe Akademii Ekonomicznej imienia Oskara Langego we Wroclawiu, 1986, vol. 338, pp. 213-14.
R. Famery, N. Richard, and P. Boch: Ceram. Int., 1994, vol. 20, pp. 327-36.
I.R. Gibson, I. Rehman, S.M. Best, and W. Bonfield: J. Mater. Sci. Mater. Med., 2000, vol 12, pp. 799-804.
N. Jinlong, Z. Zhenxi, and J. Dazong: J. Mater. Synthesis Processing, 2001, vol. 9 (5), pp. 235-40.
H.S. Ryu, H.J. Youn, K.S. Hong, B.S. Chang, C.K. Lee, and S.S. Chung: Biomaterials, 2002, vol. 23, pp. 909-14.
F. Goetz-Neunhoeffet, J. Neubauer, R. Enderle, and M. Göbbels: Z. Kristallogr. Suppl., 2007, vol. 26, pp. 375-80.
P.E. Stone, E.P. Egan Jr., and J.R. Lehr: J. Am. Ceram. Soc., 1956, vol. 39 (3), pp. 89-98.
H. Monma: Gypsum & Lime, 1990, vol. 225, pp. 17-81.
J.J. Bian, D.W. Kim, and K.S. Hong: Mater. Lett., 2004, vol. 58, pp. 347-51.
E.J. Fox and K.G. Clark: Ind. Eng. Chem., 1943, vol. 35, pp. 1264-8.
B.I. Lazoryak, B.N. Viting, S.V. Golubchenko, V.V. Men’shikov, and R.G. Aziev: Vestn. Mosk. Univ. Ser. 2: Khim., 1987, vol. 28 (1), pp. 93-95.
A. Boullé: Ann. Chim., 1942, vol. 17, pp. 213-67.
E. Thilo and I. Grunze: Z. Anorg. Allg. Chem., 1957, vol. 290, pp. 209-22.
I.D. Sokolova, E.L. Krivovyazov, and N.K. Voskresenskaya: Russ. J. Inorg. Chem., 1963, vol. 8 (12), pp. 1375-78.
R. Andrieux and R. Diament: Compt. Rend. Acad. Sci. Paris, Série C, 1963, vol. 259, pp. 4708-11.
A.B. Bekturov, Y.A. Kushnikov, D.Z. Serazetdinov, E.V. Poletaev, and M.A. Dykanbaev: Izv. Akad. Nauk SSSR Neorg. Mater. 1969, vol. 5 (10), pp. 1812-14.
Y. Henry and A. Durif: Bull. Soc. Fr. Mineral. Cristallogr., 1969, vol. 92, pp. 484-86.
J.C. Grenier, C. Martin, and A. Durif: Bull. Soc. Fr. Mineral. Cristallogr., 1970, vol. 93, pp. 52-55.
Y. Henry and A. Durif: Compt. Rend. Acad. Sci. Paris Série C, 1970, vol. 270, pp. 423-25.
Y. Henry and A. Durif: Compt. Rend. Acad. Sci. Paris, Série C, 1970, vol. 270, pp. 1984-90.
E. Rakotomahanina-Rolaisoa, Y. Henry, A. Durif, and C. Raholison: Bull. Soc. Fr. Miner. Crist., 1970, vol. 93, pp. 43-51.
D.Z. Serazetdinv, A.D. Kruchinina, and E.V. Poletaev: Khim. Tekhnol. Kondens. Fosfatov, Tr. Vses. Soveshch. 2nd, Meeting date 1968, 1970, pp. 30–36.
I.A. Tokman and G.A. Bukhalova: Russ. J. Inorg. Chem., 1970, 15 (3), pp. 448-49.
G.A. Bukhalova, I.A. Tokman, and V.M. Shpakova: Russ. J. Inorg. Chem., 1970, vol. 15 (6), pp. 865-66.
M. Hattori, T. Tsubaki, F. Murata, and M. Tanaka: Yogyo Kyokai-Shi, 1971, vol. 79 (2), pp. 49-55.
M.I. Kuźmenkov, S.V. Plyshevskii, and V.V. Pechkovski: Izv. Akad. Nauk SSSR Neorg. Mater., 1974, vol. 10 (10), pp. 1842-45.
G.A. Bukhalova, I.V. Mardirosova, N.P. Ocheret, and V.A. Ma’rosova: Neorg. Mater., 1992, vol. 25 (5), pp. 1053-56.
W. Szuszkiewicz: Mater. Chem. Phys., 1992, vol. 30, pp. 217-19.
N.P. Vassel, I.V. Mardirosova, M.A. Savenkova, and N.S. Kosobakova: Zh. Neorg. Khim., 1993, vol. 38 (7), pp. 1212-14.
C. Morin: Bull. Soc. Chim. Fr., 1961, pp. 1726–34.
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Financial supports from Tata Steel Europe, Posco, RIST, Hyundai Steel, Nucor Steel, RTIT, Nippon Steel and Sumitomo Metals Corp., JFE Steel, Voestalpine Stahl, RHI, and the Natural Sciences and Engineering Research Council of Canada are gratefully acknowledged.
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Hudon, P., Jung, IH. Critical Evaluation and Thermodynamic Optimization of the CaO-P2O5 System. Metall Mater Trans B 46, 494–522 (2015). https://doi.org/10.1007/s11663-014-0193-x
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DOI: https://doi.org/10.1007/s11663-014-0193-x