**2. The thermodynamic properties of perovskite solid phase**

Thermochemical data on perovskite [20–24] are based on calorimetric measurements of entropy of perovskite formation Δ*S*298(CaTiO3), obtained by Shomate [25], and high-temperature heat capacity of perovskite *Cp*(CaTiO3) in the temperature ranges of 15–398 K [26], 293–773 K [27], 376–1184 K [28], 383–1794 K [29], and 413–1825 K [30]. The differences between the data do not exceed 5 J/(mol K) up to a temperature of 1200 K, but they are quite contradictory at higher temperatures (**Figure 2**).

#### **Figure 1.**

*The phase diagram of the CaO-TiO2 system [7, 18, 19]: (1) CaO + liquid; (2) CaO + Ca3Ti2O7; (3) Ca3Ti2O7 + liquid; (4) Ca4Ti3O10 + liquid; (5) Ca3Ti2O7 + Ca4Ti3O10; (6) Ca4Ti3O10 + CaTiO3; (7, 8) CaTiO3 + liquid; (9) CaTiO3 + TiO2; (10) TiO2 + liquid; (11) liquid.*

temperature range of 296–1720 K, Yashima and Ali [31] concluded that the *Cmcm* phase does not exist and claimed that the first transition is the (*Pbnm*) ! (*I*4/*mcm*) at 1512 � 13 K, followed by the (*I*4/*mcm*) ! (*Pm*3*m*) transition at 1635 � 2 K. Panfilov and Fedos'ev [32] determined the enthalpy of the reaction with a calorimetric bomb by burning stoichiometric mixtures of rutile TiO2 and calcium carbonate CaCO3 (here and below, the square brackets denote the condensed phase;

*Enthalpy and entropy of perovskite formation from simple oxides (calculated per 1 mol of compound).*

**Experimental approach** *T***, K Δ***HT***, kJ/mol Δ***ST***, J/(mol K) Refs.** HF/HCl solution calorimetry 298 1.05 � 0.21 [25] HF/HCl solution calorimetry 298 �40.48 � 0.42 1.86 � 0.71 [33] Bomb calorimetry 298 �41.84 � 1.88 [32] Adiabatic calorimetry 298 �40.48 � 1.65 2.40 � 0.35 [26] Adiabatic calorimetry 298 �47.11 � 1.41 2.72 � 0.23 [28] Na6Mo4O15 solution calorimetry 298 �42.98 � 1.96 [34] EMF 888–972 �37.05 � 3.28 4.62 � 3.54 [35] EMF 900–1250 �40.07 � 0.05 3.15 � 0.05 [36] Pb2B2O5 solution calorimetry 973 �38.73 � 1.34 [37] Na6Mo4O15 solution calorimetry 975 �42.25 � 1.05 [38] Na6Mo4O15 solution calorimetry 975 �41.88 � 1.36 [39] Na6Mo4O15 solution calorimetry 976 �42.86 � 1.71 [40] Pb2B2O5 solution calorimetry 1046 �42.38 � 1.82 [37] (Li,Na)BO2 solution calorimetry 1068 � 2 �40.45 � 1.15 [41] Pb2B2O5 solution calorimetry 1073 �40.43 � 1.87 4.37 � 1.23 [42] Pb2B2O5 solution calorimetry 1074 �43.78 � 1.73 [43] Pb2B2O5 solution calorimetry 1078 �42.83 � 3.12 [44] EMF 1180–1290 �26.88 � 8.05 11.07 � 6.44 [45] Raman spectroscopy 1300 2.82 � 1.29 [46] Thermochemical calculations 1600–1800 �37.19 � 0.14 5.85 � 0.09 [22] Thermochemical calculations 1600–2100 �38.23 � 0.04 5.00 � 0.02 [23] Thermochemical calculations 1600–2100 �37.47 � 0.03 5.60 � 0.02 [24] DTA 1740 � 20 �37.55 � 3.76 [47] Knudsen mass spectrometry 1791–2241 �39.98 � 0.54 3.15 � 0.28 [48] Knudsen mass spectrometry 2241–2398 7.73 � 1.76 24.39 � 0.76 [48]

*Thermodynamics of Perovskite: Solid, Liquid, and Gas Phases*

*DOI: http://dx.doi.org/10.5772/intechopen.91309*

They then calculated the enthalpy of perovskite formation Δ*H*298(CaTiO3): �41.84 � 1.88 kJ/mol (**Table 1**). Although the obtained value was determined with poor accuracy, due to the difficulty of determining the amounts of substances in the reaction products (1), it corresponded satisfactorily to the more accurate results of

Kelley et al. [33], who determined this value according to the reaction:

½ �þ CaCO3 ½ �¼ TiO2 ½ �þ CaTiO3 ð Þ CO2 *:* (1)

½ �þ CaO ½ �¼ TiO2 ½ � CaTiO3 (2)

the parentheses denote the gas phase):

**Table 1.**

**117**

**Figure 2.**

*Heat capacity of perovskite: (1–5) determined via high-temperature calorimetry [26–30], respectively, and (6) taken from [22].*

Naylor and Cook [29] determined the enthalpy of perovskite phase transition: 2.30 0.07 kJ/mol at 1530 1 K. The overlapping phase transitions in perovskite observed by Guyot et al. [30] (**Figure 2**) were explained as consequences of a structural change, i.e., a transition from orthorhombic (*Pbnm*) to orthorhombic (*Cmcm*) structure at 1384 10 K and the overlapping of transitions from orthorhombic to tetragonal (*I*4/*mcm*) and tetragonal to cubic phase (*Pm*3*m*) at 1520 10 K with heat effects of 1.0 0.5 and 5.5 0.5 kJ/mol, respectively. The considerable anomaly of perovskite heat capacity above 1520 K could be caused by strong disordering of the cubic phase up to the temperature of perovskite melting. However, based on diffraction data about perovskite structure obtained in the


#### *Thermodynamics of Perovskite: Solid, Liquid, and Gas Phases DOI: http://dx.doi.org/10.5772/intechopen.91309*

#### **Table 1.**

*Enthalpy and entropy of perovskite formation from simple oxides (calculated per 1 mol of compound).*

temperature range of 296–1720 K, Yashima and Ali [31] concluded that the *Cmcm* phase does not exist and claimed that the first transition is the (*Pbnm*) ! (*I*4/*mcm*) at 1512 � 13 K, followed by the (*I*4/*mcm*) ! (*Pm*3*m*) transition at 1635 � 2 K.

Panfilov and Fedos'ev [32] determined the enthalpy of the reaction with a calorimetric bomb by burning stoichiometric mixtures of rutile TiO2 and calcium carbonate CaCO3 (here and below, the square brackets denote the condensed phase; the parentheses denote the gas phase):

$$[\mathbf{[CaCO\_3]} + [\mathbf{TiO\_2}] = [\mathbf{CaTiO\_3}] + (\mathbf{CO\_2}).\tag{1}$$

They then calculated the enthalpy of perovskite formation Δ*H*298(CaTiO3): �41.84 � 1.88 kJ/mol (**Table 1**). Although the obtained value was determined with poor accuracy, due to the difficulty of determining the amounts of substances in the reaction products (1), it corresponded satisfactorily to the more accurate results of Kelley et al. [33], who determined this value according to the reaction:

$$[\mathbf{[CaO]} + [\mathbf{TiO\_2}] = [\mathbf{CaTiO\_3}]] \tag{2}$$

Naylor and Cook [29] determined the enthalpy of perovskite phase transition: 2.30 0.07 kJ/mol at 1530 1 K. The overlapping phase transitions in perovskite observed by Guyot et al. [30] (**Figure 2**) were explained as consequences of a structural change, i.e., a transition from orthorhombic (*Pbnm*) to orthorhombic (*Cmcm*) structure at 1384 10 K and the overlapping of transitions from orthorhombic to tetragonal (*I*4/*mcm*) and tetragonal to cubic phase (*Pm*3*m*) at

*Heat capacity of perovskite: (1–5) determined via high-temperature calorimetry [26–30], respectively, and*

*The phase diagram of the CaO-TiO2 system [7, 18, 19]: (1) CaO + liquid; (2) CaO + Ca3Ti2O7; (3) Ca3Ti2O7 + liquid; (4) Ca4Ti3O10 + liquid; (5) Ca3Ti2O7 + Ca4Ti3O10; (6) Ca4Ti3O10 + CaTiO3;*

*(7, 8) CaTiO3 + liquid; (9) CaTiO3 + TiO2; (10) TiO2 + liquid; (11) liquid.*

**Figure 1.**

*Perovskite and Piezoelectric Materials*

**Figure 2.**

**116**

*(6) taken from [22].*

1520 10 K with heat effects of 1.0 0.5 and 5.5 0.5 kJ/mol, respectively. The considerable anomaly of perovskite heat capacity above 1520 K could be caused by strong disordering of the cubic phase up to the temperature of perovskite melting. However, based on diffraction data about perovskite structure obtained in the

by solution calorimetry in a mixture of hydrofluoric and hydrochloric acids. The reactions of dissolution were more complete than combustion reaction (1).

Navrotsky et al. [19, 26, 34, 37–43] performed a number of studies by various calorimetric methods, using adiabatic calorimetry [26] and solution calorimetry in the (Li, Na)BO2 [41], Pb2B2O5 [37, 42, 43], and Na6Mo4O15 [19, 34, 38–40] salts in the temperature range 973–1074 K. They determined the value of Δ*HT*(CaTiO3), which lies in the range of �44 to �39 kJ/mol; the accuracy of measurements was 2 kJ/mol (**Table 1**). The differences could be due to the properties of the solvents that were used. Perovskite and its oxides are poorly soluble in oxide solvent Pb2B2O5; Na6Mo4O15 liquid alloy is quite volatile and cannot be used at temperatures above 1000 K; (Li,Na)BO2 solution is hygroscopic, which creates difficulties in synthesizing [49]. The Δ*H*1078(CaTiO3) value determined by Koito et al. [44] by similar method (solution calorimetry in Pb2B2O5 salt) is less accurate but close to the results obtained by Navrotsky et al. [19, 34, 37–43].

The data obtained by Sato et al. [28] using adiabatic calorimetry deviate negligibly (by as much as 7 kJ/mol) in the enthalpy values of (*HT*–*H*298) in the temperature range above 1000 K. Approximately the same systematic deviation is observed in determination of enthalpy of perovskite formation from oxides (per 1 mole of the compound) due to its use in calculations of the rough semiempirical approximation proposed in [50]. At the same time, the entropy of perovskite formation determined by Sato et al. [28] is in satisfactory agreement with the results obtained by Kelley and Mah [20], Woodfield et al. [26], and Prasanna and Navrotsky [42] and calculated by Gillet et al. [46] based on information obtained on Raman spectra (**Table 1**).

Golubenko and Rezukhina [45] studied the heterogeneous reaction using a solid electrolyte galvanic cell (EMF method) in the temperature range of 1180–1290 K:

$$[\mathbf{[CaO]}] + \mathbb{V}[\mathbf{Ti\_2O}] + \mathbb{V}(\mathbf{O\_2}) = [\mathbf{CaTiO\_3}].\tag{3}$$

A mixture of FeO and Fe (or NbO and Nb) was used as the reference electrode, and a mixture of La2O3-ThO2 crystals was used as the solid electrolyte. The Gibbs energy of perovskite Δ*GT*(CaTiO3) was calculated based on a compilation of fairly approximate literature data and their own estimates of the thermodynamic properties of the [Ti2O] compound. This produced a considerable error in determining this value (**Figure 3**). Rezukhina et al. [35] later made more precise measurements of Δ*GT*(CaTiO3) in the temperature range of 888–972 K, inside a galvanic cell with CaF2 as the electrolyte (**Figure 3**). However, the non-systematic errors in determining Δ*HT*(CaTiO3) and Δ*ST*(CaTiO3) values were considerable (**Table 1**).

Taylor and Schmalzried [51] (at 873 K) and Jacob and Abraham [36] (at 900– 1250 K) also determined the perovskite Gibbs energy via EMF using the same solid electrolyte. The obtained Δ*GT*(CaTiO3) values were close to the results of Rezukhina et al. [35].

Klimm et al. [47] used differential thermal analysis (DTA) to determine the enthalpy of reaction (2) at 1740 � 20 K. The obtained value is consistent with the results of thermochemical calculations, although it has a significant error.

Suito et al. [54, 55] has studied the equilibrium at 1873 K:

$$\text{[Ti]} + \text{2(O)} = \text{[TiO\_2]} \tag{4}$$

Banon et al. [52] (at 2150 K) and Shornikov et al. [48, 53, 56] (at 1791–2398 K) determined the values of CaO and TiO2 activities (**Figure 4**) and Δ*GT*(CaTiO3) via Knudsen effusion mass spectrometric method. The resulting values correlated with

*Activities of CaO (1–3) and TiO2 (4–8) in perovskite, determined (1–3, 6–8) via Knudsen effusion mass spectrometry [48, 52, 53] and (4, 5) in studying the heterogeneous equilibria of multicomponent melts*

*The Gibbs energy of the formation of perovskite, determined via (1, 2) calorimetry [28, 42], respectively; (3–6) EMF [35, 36, 45, 51], respectively; (7–9) Knudsen effusion mass spectrometric method in [48, 52, 53],*

*respectively; (10, 11) calculated from thermochemical data in [24, 26], respectively.*

*Thermodynamics of Perovskite: Solid, Liquid, and Gas Phases*

*DOI: http://dx.doi.org/10.5772/intechopen.91309*

one another within the experimental error (up to 2.5 kJ/mol); however, the Δ*GT*(CaTiO3) was obtained at a temperature 1000 K higher than in the earlier

results (**Figure 3**).

*[54, 55], respectively.*

**Figure 4.**

**119**

**Figure 3.**

in CaO-TiO*<sup>x</sup>* (or CaO-TiO*x*-Al2O3) slags with liquid nickel, relative to oxygen and nitrogen, depending on the content of Ti (or Al) in the metal. Crucibles made of CaO or Al2O3 were used. The activity (*ai*) of titanium oxide was estimated indirectly, depending on the content of Al, Ti, and O in the slag, and using data on the Gibbs energies of oxide formation (**Figure 4**).

#### **Figure 3.**

by solution calorimetry in a mixture of hydrofluoric and hydrochloric acids. The reactions of dissolution were more complete than combustion reaction (1). Navrotsky et al. [19, 26, 34, 37–43] performed a number of studies by various calorimetric methods, using adiabatic calorimetry [26] and solution calorimetry in the (Li, Na)BO2 [41], Pb2B2O5 [37, 42, 43], and Na6Mo4O15 [19, 34, 38–40] salts in the temperature range 973–1074 K. They determined the value of Δ*HT*(CaTiO3), which lies in the range of �44 to �39 kJ/mol; the accuracy of measurements was 2 kJ/mol (**Table 1**). The differences could be due to the properties of the solvents that were used. Perovskite and its oxides are poorly soluble in oxide solvent Pb2B2O5; Na6Mo4O15 liquid alloy is quite volatile and cannot be used at temperatures above 1000 K; (Li,Na)BO2 solution is hygroscopic, which creates difficulties in synthesizing [49]. The Δ*H*1078(CaTiO3) value determined by Koito et al. [44] by similar method (solution calorimetry in Pb2B2O5 salt) is less accurate but close to

The data obtained by Sato et al. [28] using adiabatic calorimetry deviate negligibly

Golubenko and Rezukhina [45] studied the heterogeneous reaction using a solid electrolyte galvanic cell (EMF method) in the temperature range of 1180–1290 K:

A mixture of FeO and Fe (or NbO and Nb) was used as the reference electrode, and a mixture of La2O3-ThO2 crystals was used as the solid electrolyte. The Gibbs energy of perovskite Δ*GT*(CaTiO3) was calculated based on a compilation of fairly approximate literature data and their own estimates of the thermodynamic properties of the [Ti2O] compound. This produced a considerable error in determining this value (**Figure 3**). Rezukhina et al. [35] later made more precise measurements of Δ*GT*(CaTiO3) in the temperature range of 888–972 K, inside a galvanic cell with CaF2 as the electrolyte (**Figure 3**). However, the non-systematic errors in determining Δ*HT*(CaTiO3) and Δ*ST*(CaTiO3) values were considerable (**Table 1**).

Taylor and Schmalzried [51] (at 873 K) and Jacob and Abraham [36] (at 900– 1250 K) also determined the perovskite Gibbs energy via EMF using the same solid

Klimm et al. [47] used differential thermal analysis (DTA) to determine the enthalpy of reaction (2) at 1740 � 20 K. The obtained value is consistent with the

in CaO-TiO*<sup>x</sup>* (or CaO-TiO*x*-Al2O3) slags with liquid nickel, relative to oxygen and nitrogen, depending on the content of Ti (or Al) in the metal. Crucibles made of CaO or Al2O3 were used. The activity (*ai*) of titanium oxide was estimated indirectly, depending on the content of Al, Ti, and O in the slag, and using data on the

electrolyte. The obtained Δ*GT*(CaTiO3) values were close to the results of

results of thermochemical calculations, although it has a significant error.

Suito et al. [54, 55] has studied the equilibrium at 1873 K:

Gibbs energies of oxide formation (**Figure 4**).

Rezukhina et al. [35].

**118**

½ �þ CaO ½ Ti ½ �þ 2O ¾ Oð Þ¼ <sup>2</sup> ½ � CaTiO3 *:* (3)

½ �þ Ti 2 Oð Þ¼ ½ � TiO2 (4)

(by as much as 7 kJ/mol) in the enthalpy values of (*HT*–*H*298) in the temperature range above 1000 K. Approximately the same systematic deviation is observed in determination of enthalpy of perovskite formation from oxides (per 1 mole of the compound) due to its use in calculations of the rough semiempirical approximation proposed in [50]. At the same time, the entropy of perovskite formation determined by Sato et al. [28] is in satisfactory agreement with the results obtained by Kelley and Mah [20], Woodfield et al. [26], and Prasanna and Navrotsky [42] and calculated by Gillet et al. [46] based on information obtained on Raman spectra (**Table 1**).

the results obtained by Navrotsky et al. [19, 34, 37–43].

*Perovskite and Piezoelectric Materials*

*The Gibbs energy of the formation of perovskite, determined via (1, 2) calorimetry [28, 42], respectively; (3–6) EMF [35, 36, 45, 51], respectively; (7–9) Knudsen effusion mass spectrometric method in [48, 52, 53], respectively; (10, 11) calculated from thermochemical data in [24, 26], respectively.*

#### **Figure 4.**

*Activities of CaO (1–3) and TiO2 (4–8) in perovskite, determined (1–3, 6–8) via Knudsen effusion mass spectrometry [48, 52, 53] and (4, 5) in studying the heterogeneous equilibria of multicomponent melts [54, 55], respectively.*

Banon et al. [52] (at 2150 K) and Shornikov et al. [48, 53, 56] (at 1791–2398 K) determined the values of CaO and TiO2 activities (**Figure 4**) and Δ*GT*(CaTiO3) via Knudsen effusion mass spectrometric method. The resulting values correlated with one another within the experimental error (up to 2.5 kJ/mol); however, the Δ*GT*(CaTiO3) was obtained at a temperature 1000 K higher than in the earlier results (**Figure 3**).

As it is seen in **Figure 4**, the values of oxide activities in perovskite determined via Knudsen effusion mass spectrometric method agree with one another in the investigated temperature range. As the temperature grows, there is a slight trend toward the higher activities of calcium and titanium oxides in the crystalline perovskite phase. This trend is less noticeable in the area of the liquid phase. The activities of titanium oxide calculated based on studying of equilibria in slags [54, 55] are fairly approximate but not inconsistent with the results in [48, 52, 53].

estimates made by Bale et al. [24]. The enthalpy of perovskite melting estimated using Walden's empirical rule [62] is also close to the result obtained by Shornikov

Thermodynamic information about the CaO-TiO2 melts is quite scarce and limited by the results of only a few experimental studies. Consider the available experimental data, obtained by the Knudsen effusion mass spectrometry.

Banon et al. [52] investigated the evaporation of 24 compositions of the CaTiO3- Ti2O3-TiO2 system from molybdenum containers at 1900–2200 K. The synthesized compositions contained up to 90.2 mol% Ti2O3 and up to 42 mol% TiO2 as well as CaTiO3 compound. Based on the partial vapor pressures (Ca), (TiO), and (TiO2) over melts at 2150 K, the authors calculated the Ti, TiO, Ti2O3, TiO2, and CaTiO3 activities, as well as mixing energies in the melts. In the case of the CaTiO3-TiO2 melts, the TiO2 and CaTiO3 activities were calculated by extrapolation from the data relating to the CaTiO3-Ti2O3-TiO2 system and thus had, according to the authors themselves, low accuracy, which apparently was caused by inconsistency with different versions of the CaO-TiO2 phase diagram [7, 9, 11, 18]. Nevertheless Banon et al. [52], interpreting the obtained high values of TiO2 activities in the region close to titanium dioxide (**Figure 5**), assumed the presence of immiscibility of the CaO-

Stolyarova et al. [63] investigated the properties of the gas phase over 14 compositions of the CaO-TiO2-SiO2 system and also determined the values of oxide activity and melt mixing energy by high-temperature mass spectrometry during the evaporation of melts from tungsten effusion containers at 1800–2200 K. The synthesized compositions contained up to 70 mol% CaO, up to 69 mol% SiO2, and up to 40 mol% TiO2. As it is shown in **Figure 5**, one of the two studied compositions of the CaO-TiO2 system at 2057 K was in the "CaO + liquid" region, and thus its value

*The activities of CaO (1, 2),TiO2 (3, 4), and CaTiO3 (5, 6) in the CaO-TiO2 melts, determined at 2057 K*

*(1) in [63], at 2150 K (3, 5) in [52], and at 2250 K (2, 4, 6) in [64].*

[48]: Δ*Hmelt* = 8.8 [J/(g-at K)] *Tmelt* = 49.39 kJ/mol.

*Thermodynamics of Perovskite: Solid, Liquid, and Gas Phases*

*DOI: http://dx.doi.org/10.5772/intechopen.91309*

TiO2 melts in this region.

**Figure 5.**

**121**

**4. The thermodynamic properties of perovskite melts**

The values of Gibbs energy of perovskite formation determined at 800–1200 K via EMF [35, 36, 51] and solution calorimetry [42] correlate satisfactorily with the obtained via Knudsen effusion mass spectrometric method [48, 52, 53, 56]. **Figure 3** shows a good agreement between these data and the results from thermochemical calculations performed by Woodfield et al. [26]. The difference between our findings and the thermochemical data calculated by Bale et al. [24] is large in the perovskite melting area, but is still less than 3 kJ/mol.

The Δ*HT*(CaTiO3) and Δ*ST*(CaTiO3) values determined in [48] correlate with the results from studies performed via solution calorimetry [37, 41, 42, 44] and EMF [35, 36] at lower temperatures and by Raman spectroscopy [46] and DTA [47] at similar temperatures (**Table 1**).

## **3. Melting of perovskite**

The data characterizing the melting of simple oxides [23, 24, 57–60] are quite rough (**Table 2**). According to different thermochemical data, perovskite's melting temperature lies in the range of 2188 to 2243 K.

Klimm et al. [47] estimated the perovskite melting enthalpy as 56.65 11.33 kJ/mol at 2220 20 K (**Table 2**) which is close to earlier thermochemical estimates [24, 59].

Shornikov [48] based on his own data (**Table 1**) has obtained more accurate values, characterizing the perovskite melting (**Table 2**). They coincide satisfactorily with the experimental data obtained by Klimm et al. [47] and the thermochemical


#### **Table 2.**

*Temperatures, enthalpies, and entropies of the melting of compounds in the CaO-TiO2 system (calculated for 1 mol of compound)*

As it is seen in **Figure 4**, the values of oxide activities in perovskite determined via Knudsen effusion mass spectrometric method agree with one another in the investigated temperature range. As the temperature grows, there is a slight trend toward the higher activities of calcium and titanium oxides in the crystalline perovskite phase. This trend is less noticeable in the area of the liquid phase. The activities of titanium oxide calculated based on studying of equilibria in slags [54, 55] are

The values of Gibbs energy of perovskite formation determined at 800–1200 K via EMF [35, 36, 51] and solution calorimetry [42] correlate satisfactorily with the obtained via Knudsen effusion mass spectrometric method [48, 52, 53, 56]. **Figure 3** shows a good agreement between these data and the results from thermochemical calculations performed by Woodfield et al. [26]. The difference between our findings and the thermochemical data calculated by Bale et al. [24] is large in the

The Δ*HT*(CaTiO3) and Δ*ST*(CaTiO3) values determined in [48] correlate with the results from studies performed via solution calorimetry [37, 41, 42, 44] and EMF [35, 36] at lower temperatures and by Raman spectroscopy [46] and DTA [47]

The data characterizing the melting of simple oxides [23, 24, 57–60] are quite rough (**Table 2**). According to different thermochemical data, perovskite's melting

Klimm et al. [47] estimated the perovskite melting enthalpy as 56.65 11.33 kJ/mol at 2220 20 K (**Table 2**) which is close to earlier thermochemical estimates [24, 59]. Shornikov [48] based on his own data (**Table 1**) has obtained more accurate values, characterizing the perovskite melting (**Table 2**). They coincide satisfactorily with the experimental data obtained by Klimm et al. [47] and the thermochemical

**Compound** *T***, K Δ***Hmelt***, kJ/mol Δ***Smelt***, J/(mol K) References** CaO 2843 52.00 18.29 [59]

CaTiO3 2188 41.84 19.12 [61]

TiO2 2103 66.90 31.81 [59]

*Temperatures, enthalpies, and entropies of the melting of compounds in the CaO-TiO2 system (calculated for 1*

2845 79.50 27.94 [24] 3200 50 79.50 24.84 [58] 3210 10 55.20 17.20 [60]

 20 56.65 11.33 25.52 5.10 [47] 53.32 23.88 [24] 10 47.61 1.84 21.24 0.81 [48] 63.65 28.38 [59]

2130 20 66.94 16.70 31.43 7.84 [23, 58] 2130 46.02 21.61 [24] 2185 10 68.00 8.00 31.12 3.66 [57]

fairly approximate but not inconsistent with the results in [48, 52, 53].

perovskite melting area, but is still less than 3 kJ/mol.

temperature lies in the range of 2188 to 2243 K.

at similar temperatures (**Table 1**).

*Perovskite and Piezoelectric Materials*

**3. Melting of perovskite**

**Table 2.**

**120**

*mol of compound)*

estimates made by Bale et al. [24]. The enthalpy of perovskite melting estimated using Walden's empirical rule [62] is also close to the result obtained by Shornikov [48]: Δ*Hmelt* = 8.8 [J/(g-at K)] *Tmelt* = 49.39 kJ/mol.
