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

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-TiO2 melts in this region.

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

#### **Figure 5.**

*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].*

should be close to 1. The second composition was in the region of "Ca4Ti3O10 + liquid," according to the information presented in [7, 18], or in the region of "Ca3Ti2O7 + liquid," as follows from the data presented by Tulgar [11]. However, the calculated values are quite close (**Figure 5**), which contradicts the CaO-TiO2 phase diagram (**Figure 1**). A possible reason for the discrepancies seems to be a significant error in the measurements of CaO activities in the melt, which may be, in our opinion, more than 50%.

Shornikov [64] investigated the evaporation from molybdenum containers of more than 200 compositions of the CaO-TiO2 system containing from 34 to 98 mol % TiO2 at 2241–2441 K. The studied compositions were the CaO-TiO2-SiO2 residual melts containing up to 1 mol% SiO2 that was lost during high-temperature evaporation. The determined composition of the gas phase over the CaO-TiO2 melts allowed to conclude that evaporation reactions are typical for individual oxides predominate.

The oxide activities in the CaO-TiO2 melts were calculated according to Lewis equations [65]:

$$a\_i = p\_i / p\_i^\circ,\tag{5}$$

Δ*G<sup>m</sup>*

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

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

Δ*G<sup>m</sup>*

and are represented in **Figure 6**.

**Figure 6.**

**123**

*heterogeneous areas).*

*<sup>T</sup>* <sup>¼</sup> <sup>X</sup> *i*

*i*

The results presented by Banon et al. [52] correlate with the data found in [64]. Some difference in values, as mentioned above, is probably due to the procedures for extrapolating information obtained by Banon et al. [52] for compositions of the CaTiO3-Ti2O3-TiO2 triple system, which could reduce their accuracy. The observed behavior of TiO2 activity in melts in the concentration region close to rutile may indicate some immiscibility of the melt, which follows from the observed inflection of the concentration dependence (**Figure 5**, line 3). However, in our opinion, the behavior of TiO2 and CaTiO3 activities (**Figure 5**, lines 4 and 6) are close to the ideal. The maximum value corresponds to the area of compositions close to

*The thermodynamic properties of the CaO-TiO2 melts at 2278 K [64] (the chemical potentials of oxides and the mixing energy (a), the partial enthalpies of oxides and the enthalpy of formation (b), and the partial entropies of oxides and the entropy of formation (c)); symbols: (1) CaO, (2) TiO2, (3) integral*

*thermodynamic characteristics (mixing energy, enthalpy, and entropy of formation of the melts, respectively; the vertical dashed line marks the boundary of the "CaO + liquid" region and the melt) and the comparison of mixing energies (d) in the CaO-TiO2 (4), CaO-SiO2 (5), and CaO-Al2O3 (6) melts determined by the Knudsen effusion mass spectrometric method in [64, 68, 69], respectively (the dashed lines correspond to*

<sup>Δ</sup>*HT* <sup>¼</sup> <sup>X</sup>

<sup>Δ</sup>*ST* <sup>¼</sup> <sup>X</sup> *i*

*xi*Δμ*<sup>i</sup>* (13)

*xi*Δ*Hi* (14)

*xi*Δ*Si* (15)

*<sup>T</sup>* ¼ Δ*HT* � *T*Δ*ST* (16)

where *p*<sup>∘</sup> *<sup>i</sup>* and *pi* are the partial pressures of vapor species over individual oxide and melt, respectively. However, it is preferable to calculate the values of oxide activities using the Belton-Fruehan approach [66] via the following equation:

$$
\ln a\_i = -\int \mathbf{x}\_j d\ln \left( a\_j / a\_i \right),
\tag{6}
$$

in which the ratio of the oxide activities in the melt could be easily converted to the ratio of the partial pressures, proportional to the ion currents (*Ii*):

$$\begin{split} \ln \mathfrak{a}\_{\text{TiO}\_2} &= -\int \mathfrak{x}\_{\text{CaO}} d \ln \left( p\_{\text{CaO}} / p\_{\text{TiO}\_2} \right) = -\int \mathfrak{x}\_{\text{CaO}} d \ln \left( p\_{\text{Ca}} p\_{\text{O}} / p\_{\text{TiO}} p\_{\text{O}} \right) \\ &= -\int \mathfrak{x}\_{\text{CaO}} d \ln \left( I\_{\text{Ca}} / I\_{\text{TiO}} \right), \end{split} \tag{7}$$

and thus to evade the needs in additional thermochemical data, used in Eq. (5). The consistency of the values of TiO2 activities calculated by relation (7) was verified using the Gibbs-Duhem equation [67]:

$$
\ln a\_{\rm CaO} = -\int \frac{\varkappa\_{\rm TiO\_2}}{\varkappa\_{\rm CaO}} d \ln a\_{\rm TiO\_2},\tag{8}
$$

Values of chemical potentials (Δμ*i*), partial enthalpy (Δ*Hi*), and entropy (Δ*Si*) of oxides in the CaO-TiO2 melts were calculated by known equations [67]:

$$
\Delta \mu\_i = RT \ln a\_i \tag{9}
$$

$$
\Delta \mu\_i = \Delta H\_i - T \Delta S\_i \tag{10}
$$

$$
\Delta H\_i = \frac{d(\Delta \mu\_i/T)}{d(1/T)} = R \frac{d \ln a\_i}{d(1/T)} \tag{11}
$$

$$
\Delta \mathbf{S}\_i = -d \Delta \mu\_i / dT,\tag{12}
$$

which are related to the corresponding integral thermodynamic mixing functions:

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

$$
\Delta G\_T^m = \sum\_i \mathbf{x}\_i \Delta \mu\_i \tag{13}
$$

$$
\Delta H\_T = \sum\_i \mathbf{x}\_i \Delta H\_i \tag{14}
$$

$$
\Delta \mathbf{S}\_T = \sum\_i \mathbf{x}\_i \Delta \mathbf{S}\_i \tag{15}
$$

$$
\Delta G\_T^m = \Delta H\_T - T\Delta S\_T \tag{16}
$$

and are represented in **Figure 6**.

should be close to 1. The second composition was in the region of "Ca4Ti3O10 + liquid," according to the information presented in [7, 18], or in the region of "Ca3Ti2O7 + liquid," as follows from the data presented by Tulgar [11]. However, the calculated values are quite close (**Figure 5**), which contradicts the CaO-TiO2 phase diagram (**Figure 1**). A possible reason for the discrepancies seems to be a significant error in the measurements of CaO activities in the melt, which may be,

Shornikov [64] investigated the evaporation from molybdenum containers of more than 200 compositions of the CaO-TiO2 system containing from 34 to 98 mol % TiO2 at 2241–2441 K. The studied compositions were the CaO-TiO2-SiO2 residual melts containing up to 1 mol% SiO2 that was lost during high-temperature evaporation. The determined composition of the gas phase over the CaO-TiO2 melts allowed to conclude that evaporation reactions are typical for individual oxides

The oxide activities in the CaO-TiO2 melts were calculated according to Lewis

*=p*<sup>∘</sup> *i*

*<sup>i</sup>* and *pi* are the partial pressures of vapor species over individual oxide

*xjd* ln *aj=ai*

in which the ratio of the oxide activities in the melt could be easily converted to

¼ � ð

and thus to evade the needs in additional thermochemical data, used in Eq. (5). The consistency of the values of TiO2 activities calculated by relation (7) was

> ð *x*TiO2 *x*CaO

Values of chemical potentials (Δμ*i*), partial enthalpy (Δ*Hi*), and entropy (Δ*Si*) of

*<sup>d</sup>*ð Þ <sup>1</sup>*=<sup>T</sup>* <sup>¼</sup> *<sup>R</sup> <sup>d</sup>* ln *ai*

*x*CaO*d* ln ð Þ *I*Ca*=I*TiO , (7)

, (5)

� �, (6)

� �

*d* ln *a*TiO2 , (8)

*<sup>d</sup>*ð Þ <sup>1</sup>*=<sup>T</sup>* (11)

Δμ*<sup>i</sup>* ¼ *RT* ln *ai* (9) Δμ*<sup>i</sup>* ¼ Δ*Hi* � *T*Δ*Si* (10)

Δ*Si* ¼ �*d*Δμ*i=dT*, (12)

*x*CaO*d* ln *p*Ca*p*O*=p*TiO*p*<sup>O</sup>

*ai* ¼ *pi*

and melt, respectively. However, it is preferable to calculate the values of oxide activities using the Belton-Fruehan approach [66] via the following equation:

ð

ln *ai* ¼ �

the ratio of the partial pressures, proportional to the ion currents (*Ii*):

� �

ln *a*CaO ¼ �

oxides in the CaO-TiO2 melts were calculated by known equations [67]:

<sup>Δ</sup>*Hi* <sup>¼</sup> *<sup>d</sup>*ð Þ Δμ*i=<sup>T</sup>*

which are related to the corresponding integral thermodynamic mixing

*x*CaO*d* ln *p*CaO*=p*TiO2

in our opinion, more than 50%.

*Perovskite and Piezoelectric Materials*

predominate.

equations [65]:

where *p*<sup>∘</sup>

ln *a*TiO2 ¼ �

functions:

**122**

ð

verified using the Gibbs-Duhem equation [67]:

¼ � ð

The results presented by Banon et al. [52] correlate with the data found in [64]. Some difference in values, as mentioned above, is probably due to the procedures for extrapolating information obtained by Banon et al. [52] for compositions of the CaTiO3-Ti2O3-TiO2 triple system, which could reduce their accuracy. The observed behavior of TiO2 activity in melts in the concentration region close to rutile may indicate some immiscibility of the melt, which follows from the observed inflection of the concentration dependence (**Figure 5**, line 3). However, in our opinion, the behavior of TiO2 and CaTiO3 activities (**Figure 5**, lines 4 and 6) are close to the ideal. The maximum value corresponds to the area of compositions close to

#### **Figure 6.**

*The thermodynamic properties of the CaO-TiO2 melts at 2278 K [64] (the chemical potentials of oxides and the mixing energy (a), the partial enthalpies of oxides and the enthalpy of formation (b), and the partial entropies of oxides and the entropy of formation (c)); symbols: (1) CaO, (2) TiO2, (3) integral thermodynamic characteristics (mixing energy, enthalpy, and entropy of formation of the melts, respectively; the vertical dashed line marks the boundary of the "CaO + liquid" region and the melt) and the comparison of mixing energies (d) in the CaO-TiO2 (4), CaO-SiO2 (5), and CaO-Al2O3 (6) melts determined by the Knudsen effusion mass spectrometric method in [64, 68, 69], respectively (the dashed lines correspond to heterogeneous areas).*

perovskite (**Figure 5**, lines 5 and 6). Differences with values obtained by Stolyarova et al. [63] (**Figure 5**, points 1), are caused, apparently, by the low accuracy of the latter.

The partial and integral thermodynamic regularities presented in **Figure 6** characterizing the CaO-TiO2 melts are symbate. The enthalpy and entropy of melt formation are positive. The extreme values of the integral thermodynamic properties of the melts are in the concentration ranges close to perovskite, which confirms its stability in the melt. Some displacement of the extremum of integral thermodynamic functions can be caused by the presence of oxide compounds with a large amount of CaO in comparison with perovskite CaTiO3 in the melt. A comparison of mixing energies in the CaO-TiO2 melts at 2300 K with those for the CaO-SiO2 [68] and CaO-Al2O3 [69] melts (**Figure 6d**) indicates a stronger chemical interaction in the CaO-TiO2 melts than the CaO-Al2O3 melts, but smaller than in the CaO-SiO2 melts. It manifests in more positive values of the mixing energy of the melts.

#### **5. The gas phase over perovskite**

The evaporation processes and the thermodynamic properties of simple oxides CaO and TiO2 were considered in detail in reference books [23, 24, 57, 70, 71].

The gas phase over calcium oxide consists of the molecular components (O), (O2), (O3), (O4), (Ca), (Ca2), and (CaO) possibly formed by the following reactions:

$$\left[\mathbf{CaO}\right] = \left(\mathbf{CaO}\right) \tag{17}$$

Note that the predominant components of the gas phase over these oxides are (Ca), (CaO), (TiO), (TiO2), (O), and (O2); the content of other vapor species does

The properties of the gas phase over perovskite were studied in less detail. The experimental conditions and results of high-temperature studies of perovskite

, Ca+

ð Þþ Сa ð Þ¼ TiO ð Þþ CaO ð Þ Ti (30)

<sup>+</sup> molecular ion into Ti<sup>+</sup> and TiO<sup>+</sup>

<sup>+</sup> ion or because this was not the

, TiO<sup>+</sup>

. The energies of ion appearance in the mass spectra allowed the

, CaO+

, CaO+

, TiO2 + , and

, Ti<sup>+</sup>

, TiO+ ,

<sup>+</sup> ion,

, CaO+

, Ti<sup>+</sup>

, TiO+

<sup>+</sup> ion was not

) in the

Zakharov and Protas [73] studied ion emission from the perovskite surface under the action of laser radiation and identified the ion of a complex molecule

mass spectra of the vapor. They explained the presence of this ion by the similarity of high-temperature evaporation of alkaline-earth oxide titanates, which is confirmed by the composition of the observed condensates (BaTiO3, SrTiO3, and CaTiO3) formed under similar conditions [74, 75]. The intensity ratio of ion currents in the mass spectra of vapor over perovskite obtained at laser pulse duration of 800–1000 μs at a wavelength of 6943 Å and energy of 3–5 J was as follows: *I*O:*I*Ca:

observed in the mass spectrum of vapor over both perovskite CaTiO3 and rutile TiO2. This is explained by the peculiarity of the mass spectrometric experiment using a laser, in which the easily ionizable molecular species dominate the mass spectra of vapor and the not readily ionizable molecules are discriminated. This selectivity of detected ions in the mass spectra of vapor significantly limits the accuracy and applicability of this method [76]. According to the data of [57], the estimated temperature of heating of perovskite under the action of laser radiation

is 4890 � 70 K, which is approximate, but does not contradict the conditions of similar laser-impact mass spectrometry experiments in the range 4000–6000 K. Banon et al. [52] studied the evaporation of the CaTiO3-Ti2O3-TiO2 melts from molybdenum Knudsen effusion cells at 1900–2200 K by differential mass spectrometry. The mass spectra were recorded at a low ionizing voltage of 13 eV in order

Atomic calcium was the dominant component of the gas phase over the composites. The complex gaseous oxide (CaTiO3) was not detected. The partial pressures of the (Ca), (TiO), (TiO2), and (O) vapor over perovskite at 2150 K were calculated using the thermochemical data of [57] and are shown in **Figure 7** as a function of the inverse temperature (for easily understanding, the temperature

Gaseous perovskite was also not detected in the mass spectrometric studies of high-temperature evaporation of various compositions of the CaO-TiO2-SiO2 system from molybdenum and tungsten Knudsen effusion cells at 1700–2500 K [53, 63, 82, 83] presumably because the sensitivity of the equipment used in [63, 83]

Lopatin and Semenov [84] studied the evaporation of a mixture of calcium carbonate and titanium dioxide from tungsten cells by the Knudsen effusion mass spectrometry method in the temperature range 2100–2500 K. The following ions

<sup>+</sup> ions. The TiO<sup>+</sup> ion also contained a fragment component of the TiO2

were detected in the mass spectra of vapor over the mixture: Ca+

authors to determine the molecular origin of the Ca+

*I*CaO:*I*Ti:*I*TiO:*I*CaTiO3 = 0.41:100:0.17:4.32:0.54:0.05. Note that the TiO2

not exceed 1% of the total concentration at 1700–2200 K.

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

(CaTiO3) in addition to the ions of simple oxides (O+

based on the possible equilibrium in the gas phase.

to avoid possible fragmentation of the TiO2

was insufficient for determining the CaTiO3

+

scale was scaled appropriately).

purpose of the study [53, 82].

, and CaTiO3

TiO2 +

**125**

CaTiO3

fragmentation ions, which were also molecular ions.

evaporation we will consider below.

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

$$(\mathbf{CaO}) = (\mathbf{Ca}) + (\mathbf{O})\tag{18}$$

$$\mathbf{2(Ca)} = (\mathbf{Ca\_2})\tag{19}$$

$$\mathcal{Z}(\mathsf{O}) = (\mathsf{O}\_2) \tag{20}$$

$$\mathcal{B}(\mathcal{O}) = (\mathcal{O}\_3) \tag{21}$$

$$\mathsf{4}(\mathsf{O}) = (\mathsf{O}\_{\mathsf{4}}).\tag{22}$$

The gas phase over titanium oxide contains similar vapor molecular forms (O), (O2), (O3), (O4), (Ti), (Ti2), (Ti3), (TiO), and (TiO2) formed by similar reactions:

$$\left[\text{TiO}\_2\right] = \left(\text{TiO}\_2\right) \tag{23}$$

$$(\text{TiO}\_2) = (\text{TiO}) + (\text{O})\tag{24}$$

$$(\text{TiO}) = (\text{Ti}) + (\text{O}) \tag{25}$$

$$\mathbf{Z}(\mathbf{T}\mathbf{i}) = (\mathbf{T}\mathbf{i}\_2) \tag{26}$$

$$\mathbf{\dot{z}(Ti)} = (\text{Ti}\_3). \tag{27}$$

Balducci et al. [72] detected (Ti2O3) and (Ti2O4) molecules in the gas phase over cobalt titanate CoTiO3 at 2210–2393 K by the Knudsen effusion mass spectrometric method, which can be involved in the following equilibria:

$$\mathcal{Z}(\text{TiO}\_2) = (\text{Ti}\_2\text{O}\_4),\tag{28}$$

$$(\text{Ti}\_2\text{O}\_4) = (\text{Ti}\_2\text{O}\_3) + (\text{O}).\tag{29}$$

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

perovskite (**Figure 5**, lines 5 and 6). Differences with values obtained by Stolyarova et al. [63] (**Figure 5**, points 1), are caused, apparently, by the low accuracy of the

The partial and integral thermodynamic regularities presented in **Figure 6** char-

The evaporation processes and the thermodynamic properties of simple oxides CaO and TiO2 were considered in detail in reference books [23, 24, 57, 70, 71]. The gas phase over calcium oxide consists of the molecular components (O),

> ½ �¼ CaO ð Þ CaO (17) ð Þ¼ CaO ð Þþ Ca ð Þ O (18)

2 Ca ð Þ¼ ð Þ Ca2 (19) 2 Oð Þ¼ ð Þ O2 (20) 3 Oð Þ¼ ð Þ O3 (21) 4 Oð Þ¼ ð Þ O4 *:* (22)

½ �¼ TiO2 ð Þ TiO2 (23)

2 Ti ð Þ¼ ð Þ Ti2 (26) 3 Ti ð Þ¼ ð Þ Ti3 *:* (27)

2 TiO ð Þ¼ <sup>2</sup> ð Þ Ti2O4 , (28) ð Þ¼ Ti2O4 ð Þþ Ti2O3 ð Þ O *:* (29)

ð Þ¼ TiO2 ð Þþ TiO ð Þ O (24) ð Þ¼ TiO ð Þþ Ti ð Þ O (25)

(O2), (O3), (O4), (Ca), (Ca2), and (CaO) possibly formed by the following

The gas phase over titanium oxide contains similar vapor molecular forms (O), (O2), (O3), (O4), (Ti), (Ti2), (Ti3), (TiO), and (TiO2) formed by similar

Balducci et al. [72] detected (Ti2O3) and (Ti2O4) molecules in the gas phase over cobalt titanate CoTiO3 at 2210–2393 K by the Knudsen effusion mass spectrometric

method, which can be involved in the following equilibria:

acterizing the CaO-TiO2 melts are symbate. The enthalpy and entropy of melt formation are positive. The extreme values of the integral thermodynamic properties of the melts are in the concentration ranges close to perovskite, which confirms its stability in the melt. Some displacement of the extremum of integral thermodynamic functions can be caused by the presence of oxide compounds with a large amount of CaO in comparison with perovskite CaTiO3 in the melt. A comparison of mixing energies in the CaO-TiO2 melts at 2300 K with those for the CaO-SiO2 [68] and CaO-Al2O3 [69] melts (**Figure 6d**) indicates a stronger chemical interaction in the CaO-TiO2 melts than the CaO-Al2O3 melts, but smaller than in the CaO-SiO2 melts. It manifests in more positive values of the mixing energy of the melts.

latter.

reactions:

reactions:

**124**

**5. The gas phase over perovskite**

*Perovskite and Piezoelectric Materials*

Note that the predominant components of the gas phase over these oxides are (Ca), (CaO), (TiO), (TiO2), (O), and (O2); the content of other vapor species does not exceed 1% of the total concentration at 1700–2200 K.

The properties of the gas phase over perovskite were studied in less detail. The experimental conditions and results of high-temperature studies of perovskite evaporation we will consider below.

Zakharov and Protas [73] studied ion emission from the perovskite surface under the action of laser radiation and identified the ion of a complex molecule (CaTiO3) in addition to the ions of simple oxides (O+ , Ca+ , CaO+ , Ti<sup>+</sup> , TiO+ ) in the mass spectra of the vapor. They explained the presence of this ion by the similarity of high-temperature evaporation of alkaline-earth oxide titanates, which is confirmed by the composition of the observed condensates (BaTiO3, SrTiO3, and CaTiO3) formed under similar conditions [74, 75]. The intensity ratio of ion currents in the mass spectra of vapor over perovskite obtained at laser pulse duration of 800–1000 μs at a wavelength of 6943 Å and energy of 3–5 J was as follows: *I*O:*I*Ca: *I*CaO:*I*Ti:*I*TiO:*I*CaTiO3 = 0.41:100:0.17:4.32:0.54:0.05. Note that the TiO2 <sup>+</sup> ion was not observed in the mass spectrum of vapor over both perovskite CaTiO3 and rutile TiO2. This is explained by the peculiarity of the mass spectrometric experiment using a laser, in which the easily ionizable molecular species dominate the mass spectra of vapor and the not readily ionizable molecules are discriminated. This selectivity of detected ions in the mass spectra of vapor significantly limits the accuracy and applicability of this method [76]. According to the data of [57], the estimated temperature of heating of perovskite under the action of laser radiation based on the possible equilibrium in the gas phase.

$$(\mathbf{(Ca)} + (\mathbf{TiO}) = (\mathbf{CaO}) + (\mathbf{Ti})\tag{30}$$

is 4890 � 70 K, which is approximate, but does not contradict the conditions of similar laser-impact mass spectrometry experiments in the range 4000–6000 K.

Banon et al. [52] studied the evaporation of the CaTiO3-Ti2O3-TiO2 melts from molybdenum Knudsen effusion cells at 1900–2200 K by differential mass spectrometry. The mass spectra were recorded at a low ionizing voltage of 13 eV in order to avoid possible fragmentation of the TiO2 <sup>+</sup> molecular ion into Ti<sup>+</sup> and TiO<sup>+</sup> fragmentation ions, which were also molecular ions.

Atomic calcium was the dominant component of the gas phase over the composites. The complex gaseous oxide (CaTiO3) was not detected. The partial pressures of the (Ca), (TiO), (TiO2), and (O) vapor over perovskite at 2150 K were calculated using the thermochemical data of [57] and are shown in **Figure 7** as a function of the inverse temperature (for easily understanding, the temperature scale was scaled appropriately).

Gaseous perovskite was also not detected in the mass spectrometric studies of high-temperature evaporation of various compositions of the CaO-TiO2-SiO2 system from molybdenum and tungsten Knudsen effusion cells at 1700–2500 K [53, 63, 82, 83] presumably because the sensitivity of the equipment used in [63, 83] was insufficient for determining the CaTiO3 <sup>+</sup> ion or because this was not the purpose of the study [53, 82].

Lopatin and Semenov [84] studied the evaporation of a mixture of calcium carbonate and titanium dioxide from tungsten cells by the Knudsen effusion mass spectrometry method in the temperature range 2100–2500 K. The following ions were detected in the mass spectra of vapor over the mixture: Ca+ , CaO+ , Ti<sup>+</sup> , TiO+ , TiO2 + , and CaTiO3 + . The energies of ion appearance in the mass spectra allowed the authors to determine the molecular origin of the Ca+ , CaO+ , TiO<sup>+</sup> , TiO2 + , and CaTiO3 <sup>+</sup> ions. The TiO<sup>+</sup> ion also contained a fragment component of the TiO2 <sup>+</sup> ion,

#### **Figure 7.**

*The partial pressure of Ca (a),TiO (b),TiO2 (c), and O (d) over perovskite (1–3) and oxides of calcium (4, 5, 9) and titanium (6–8, 10) vs. the inverse temperature, determined via Knudsen mass spectrometry: (1) in [77], (2) in [52], (4) in [78], (5) in [79], (6) in [80], (7) in [81], and (8) in [71]; using the vacuum furnace (according to Langmuir), (3) in [4]; and calculated, (9) and (10), according to the thermochemical data [57]; the vertical dashed lines (11) and (12) indicate melting points of titanium oxide and perovskite, respectively.*

and the Ti<sup>+</sup> ion was completely fragmentary. The energy of appearance of the CaTiO3 <sup>+</sup> molecular ion was determined to be 9 � 1 eV (the energy of appearance of the gold ion was used as a standard). The partial pressures of vapor species (*pi*) were calculated by comparison with the accepted partial vapor pressures of gold taken as standard pressures (*ps*) by the equation:

$$p\_i = \frac{I\_i T\_i}{I\_s T\_s} p\_s \times \frac{\sigma\_i \eta\_s \eta\_s}{\sigma\_i \eta\_i \eta\_i},\tag{31}$$

and subsequently calculate the enthalpies of formation (Δ*fH*298) and atomization

**kJ/mol**

(CaTiO3) = (CaO) + (TiO2) 2287–2466 545 � 8 284 � 44 28 � 19 [84]

(CaTiO3) = (Ca) + (Ti) + 3(O) 2287–2466 2225 � 26 — — [84]

[CaTiO3] = (CaTiO3) 2000 — 1030 � 22 — [85]

**Δ***rHT***, kJ/mol**

2000 — 298 � 30 — [85] 1956–2182 — 287 � 12 18 � 6 [77]

2287–2466 �826 � 26 — — [84]

1956–2182 — �760 � 10 �242 � 5 [77]

2000 — 1983 � 81 — [85] 1956–2182 — 1993 � 15 396 � 7 [77]

1956–2182 — 1027 � 10 297 � 5 [77]

**Δ***rST***, J/(mol K)** **Refs.**

Zhang et al. [4] studied the isotope fractionation of calcium and titanium during the evaporation of a perovskite melt suspended on an iridium wire in a vacuum furnace at a temperature of 2278 K (according to Langmuir method). The change in the composition of the residual perovskite melt during evaporation suggested that the component that evaporated predominantly from the melt was its calcium component. The total vapor pressure over perovskite could be evaluated from the data

Shornikov [64, 77] investigated the evaporation of perovskite at 1791–2182 K and its melts at 2241–2441 K from molybdenum Knudsen effusion cells by high-

perovskite and its melts at the ionizing electron energy of 20 eV, as well as other ions characteristic of the mass spectra over individual oxides [57, 58, 71]. A small

current intensities in the mass spectra of vapor over perovskite at 2182 K was the following: *I*Ca:*I*CaO:*I*Ti:*I*TiO:*I*TiO2:*I*CaTiO3:*I*O:*I*O2 = 80:0.04:0.1:75:100:0.02:40:0.3. It corresponded to that observed by Samoilova and Kazenas [78] in the same temperature range at evaporation of CaO from alundum cell and by Semenov [86] at

The ratio of the ion current intensities in the mass spectra of vapor over perovskite melt containing 57.81 � 0.15 mol% TiO2 at 2278 K was the following: *I*Ca:*I*CaO: *I*Ti:*I*TiO:*I*TiO2:*I*CaTiO3:*I*O:*I*O2 = 25:0.02:0.1:56:100:0.13:0.44:0.012, which is different

as well as the interaction of perovskite with the cell material (*I*TiO2:*I*Mo:*I*MoO:*I*MoO2: *I*MoO3 = 100:0.8:2.6:7.3:0.6) that was detected according to the following equilibria:

skite was due to the evaporation of molybdenum cell at high temperature:

<sup>+</sup> ion was observed, which was fragmented into CaTi+

<sup>+</sup> ions (*I*CaTi:*I*CaTiO:*I*CaTiO2:*I*CaTiO3 = 6:10:13:100). The ratio of the ion

, and O+ ions prevailed in the mass spectra of vapor over

<sup>+</sup> (*i* = 0–3) ions in the mass spectra of vapor over perov-

½ �¼ Mo ð Þ Mo , (33)

, CaTiO<sup>+</sup>

,

(Δ*atH*298) of the CaTiO3 molecule (**Table 3**).

*Enthalpies and entropies of the reactions involving the CaTiO3 molecule.*

**Reaction** *T***, K Δ***rH***298,**

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

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

temperature mass spectrometric method.

evaporation of TiO2 from a tungsten cell.

from that for the case of perovskite [77].

The presence of MoO*<sup>i</sup>*

, TiO<sup>+</sup>

obtained (**Figure 7**).

[Ca] + [Ti] + 3/2 (O2) = (CaTiO3)

**Table 3.**

+ , Ca<sup>+</sup>

The TiO2

amount of CaTiO3

and CaTiO2

**127**

where *Ii* (*Is*) is the intensity of the ion current of the *i*th component of vapor (standard substance) recorded at a temperature *Ti* (*Ts*). The calculation should also include the ratios of the effective ionization cross sections of the *i*th molecular form and the standard substance (σ*i*/σ*s*), isotope distributions (η*i*/η*s*), and individual ion efficiencies (γ*i*/γ*s*), which depend on various parameters of ion current recording devices. The pressures *p*CaO , *p*TiO2 , and *p*CaTiO3 calculated by (31) were used to determine the temperature dependence of the equilibrium constant in the gas phase:

$$(\text{CaTiO}\_3) = (\text{CaO}) + (\text{TiO}\_2) \tag{32}$$


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

#### **Table 3.**

*Enthalpies and entropies of the reactions involving the CaTiO3 molecule.*

and subsequently calculate the enthalpies of formation (Δ*fH*298) and atomization (Δ*atH*298) of the CaTiO3 molecule (**Table 3**).

Zhang et al. [4] studied the isotope fractionation of calcium and titanium during the evaporation of a perovskite melt suspended on an iridium wire in a vacuum furnace at a temperature of 2278 K (according to Langmuir method). The change in the composition of the residual perovskite melt during evaporation suggested that the component that evaporated predominantly from the melt was its calcium component. The total vapor pressure over perovskite could be evaluated from the data obtained (**Figure 7**).

Shornikov [64, 77] investigated the evaporation of perovskite at 1791–2182 K and its melts at 2241–2441 K from molybdenum Knudsen effusion cells by hightemperature mass spectrometric method.

The TiO2 + , Ca<sup>+</sup> , TiO<sup>+</sup> , and O+ ions prevailed in the mass spectra of vapor over perovskite and its melts at the ionizing electron energy of 20 eV, as well as other ions characteristic of the mass spectra over individual oxides [57, 58, 71]. A small amount of CaTiO3 <sup>+</sup> ion was observed, which was fragmented into CaTi+ , CaTiO<sup>+</sup> , and CaTiO2 <sup>+</sup> ions (*I*CaTi:*I*CaTiO:*I*CaTiO2:*I*CaTiO3 = 6:10:13:100). The ratio of the ion current intensities in the mass spectra of vapor over perovskite at 2182 K was the following: *I*Ca:*I*CaO:*I*Ti:*I*TiO:*I*TiO2:*I*CaTiO3:*I*O:*I*O2 = 80:0.04:0.1:75:100:0.02:40:0.3. It corresponded to that observed by Samoilova and Kazenas [78] in the same temperature range at evaporation of CaO from alundum cell and by Semenov [86] at evaporation of TiO2 from a tungsten cell.

The ratio of the ion current intensities in the mass spectra of vapor over perovskite melt containing 57.81 � 0.15 mol% TiO2 at 2278 K was the following: *I*Ca:*I*CaO: *I*Ti:*I*TiO:*I*TiO2:*I*CaTiO3:*I*O:*I*O2 = 25:0.02:0.1:56:100:0.13:0.44:0.012, which is different from that for the case of perovskite [77].

The presence of MoO*<sup>i</sup>* <sup>+</sup> (*i* = 0–3) ions in the mass spectra of vapor over perovskite was due to the evaporation of molybdenum cell at high temperature:

$$[\mathbf{M}\mathbf{o}] = (\mathbf{M}\mathbf{o}),\tag{33}$$

as well as the interaction of perovskite with the cell material (*I*TiO2:*I*Mo:*I*MoO:*I*MoO2: *I*MoO3 = 100:0.8:2.6:7.3:0.6) that was detected according to the following equilibria:

and the Ti<sup>+</sup> ion was completely fragmentary. The energy of appearance of the

*The partial pressure of Ca (a),TiO (b),TiO2 (c), and O (d) over perovskite (1–3) and oxides of calcium (4, 5, 9) and titanium (6–8, 10) vs. the inverse temperature, determined via Knudsen mass spectrometry: (1) in [77], (2) in [52], (4) in [78], (5) in [79], (6) in [80], (7) in [81], and (8) in [71]; using the vacuum furnace (according to Langmuir), (3) in [4]; and calculated, (9) and (10), according to the thermochemical data [57]; the vertical dashed lines (11) and (12) indicate melting points of titanium oxide and perovskite,*

the gold ion was used as a standard). The partial pressures of vapor species (*pi*) were calculated by comparison with the accepted partial vapor pressures of gold

where *Ii* (*Is*) is the intensity of the ion current of the *i*th component of vapor (standard substance) recorded at a temperature *Ti* (*Ts*). The calculation should also include the ratios of the effective ionization cross sections of the *i*th molecular form and the standard substance (σ*i*/σ*s*), isotope distributions (η*i*/η*s*), and individual ion efficiencies (γ*i*/γ*s*), which depend on various parameters of ion current recording devices. The pressures *p*CaO , *p*TiO2 , and *p*CaTiO3 calculated by (31) were used to determine the temperature dependence of the equilibrium constant in the gas

*pi* <sup>¼</sup> *IiTi IsTs ps* �

taken as standard pressures (*ps*) by the equation:

<sup>+</sup> molecular ion was determined to be 9 � 1 eV (the energy of appearance of

σ*s*γ*s*η*<sup>s</sup>* σ*i*γ*i*η*<sup>i</sup>*

ð Þ¼ CaTiO3 ð Þþ CaO ð Þ TiO2 (32)

, (31)

CaTiO3

*respectively.*

**Figure 7.**

*Perovskite and Piezoelectric Materials*

phase:

**126**

$$(\mathbf{M}\mathbf{o}) + (\mathbf{O}) = (\mathbf{M}\mathbf{o}\mathbf{O})\tag{34}$$

Taking into account predominance of typical for CaO and TiO2 vapor species in the gas phase over perovskite and small amounts of CaTiO3, the α*<sup>i</sup>* values were used

The partial pressures of vapor species over perovskite at 1791–2182 K and its melts at 2278 K calculated using the relationships (38) and (39) with an error not

The partial pressure of atomic oxygen determined using the relationships (38) and (39) agrees satisfactorily with those calculated using the thermochemical data [57] on *Kr*(*T*) equilibrium constants of possible reactions (18), (20), (24), (25), and

*K*18ð Þ *T* (40)

*K*24ð Þ *T* (41)

*K*25ð Þ *T* (42)

*K*36ð Þ *T :* (44)

lg*pi* ¼ *ai=T* þ *bi:* (45)

*<sup>T</sup>* <sup>þ</sup> <sup>Δ</sup>*rST*, (46)

(43)

*<sup>p</sup>*<sup>O</sup> <sup>¼</sup> *<sup>p</sup>*CaO *p*Ca

*<sup>p</sup>*<sup>O</sup> <sup>¼</sup> *<sup>p</sup>*TiO2 *p*TiO

*<sup>p</sup>*<sup>O</sup> <sup>¼</sup> *<sup>p</sup>*TiO *p*Ti

s

It should be noted that the *p*<sup>O</sup> values calculated according to the independent reactions in the gas phase over perovskite (40)–(45) were the same. It confirmed the assumption about the molecular origin of the identified ions in the mass spec-

As it follows from **Figure 8a**, the defined partial pressures of vapor species over

perovskite can be represented as linear logarithmic dependence vs. the inverse

Note that the relationship (45) is the same as the expression for the reaction

which allows to determine the enthalpy (Δ*rHT*) and entropy (Δ*rST*) of a

The partial pressures of the predominant vapor species of the gas phase over perovskite (Ca, TiO, TiO2 and O) are compared in **Figure 7** with the results on evaporation of simple oxides (CaO and TiO2) under similar redox conditions caused by the interaction of oxygen with molybdenum [79, 81], tungsten [71], and tantalum [80] effusion cells or in chemically neutral conditions (in the absence of this

We used the TiO and TiO2 activities as well as the Gibbs energy of perovskite obtained by Banon et al. [52] and thermochemical data [52] on equilibriums (17), (18), (23), and (24) to estimate the partial pressure of vapor species over the perovskite at 2150 K. Therefore, the obtained values characterized by the evaporation of perovskite were not under reducing conditions (from molybdenum cell),

*<sup>T</sup>* ¼ � <sup>Δ</sup>*rHT*

*<sup>R</sup>* ln *Kr*ð Þ¼� *<sup>T</sup>* <sup>Δ</sup>*rGT*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *p*2 O2 *K*20ð Þ *T*

*p*<sup>O</sup> ¼

*<sup>p</sup>*<sup>O</sup> <sup>¼</sup> *<sup>p</sup>*MoO3 *p*MoO2

(36) in the gas phase over perovskite in the following relations:

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

from [91].

exceeding 8% are shown in **Figure 8**.

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

trum of vapor over perovskite.

interaction) for alundum cell [78].

temperature:

constant [57]:

reaction.

**129**

$$(\mathbf{MoO}) + (\mathbf{O}) = (\mathbf{MoO}\_2) \tag{35}$$

$$(\mathbf{M}\mathbf{O}\mathbf{O}\_2) + (\mathbf{O}) = (\mathbf{M}\mathbf{O}\mathbf{O}\_3). \tag{36}$$

Note that Berkowitz et al. [81] found that during evaporation of titanium oxide from a molybdenum liner inserted into a tantalum crucible at 1881 K, *p*MoO2 was initially 10–10<sup>2</sup> times higher than *<sup>p</sup>*TiO2 . The *<sup>p</sup>*MoO2 value gradually decreased and became comparable with the *p*TiO2 value, which is significantly different from the other results [52, 53, 56, 64, 77, 82]. The high *p*MoO2 observed in [81] probably was due to poor quality of the molybdenum liner material (or its alloy). Possibly it was made using powder technology from MoO3 reduced to metal molybdenum at �1300 K. It could lead to such an excess of partial pressure of (MoO3) and its decrease as it evaporates from the surface layers of the liner material.

The appearance energies of ions in the mass spectra of vapor over perovskite were determined by the Warren method [87] and corresponded to the accepted values of the ionization energies of atoms and molecules [88]. The appearance energy of CaTiO3 <sup>+</sup> ion in the mass spectra of vapor over perovskite was equal to 8.5 � 0.6 eV (the appearance energy of silver ion was used as a standard) and corresponded to obtained by Lopatin and Semenov [84].

The established molecular composition of the gas phase over perovskite allowed us to draw a conclusion on the predominant evaporation of perovskite according to the reactions (17), (18), (20), (23), (24), and (25), typical for evaporation of simple oxides [57, 71, 78, 86]. The presence of a small amount of (CaTiO3) molecules in the gas phase over perovskite is probably due to the reaction:

$$[\mathbf{[\mathbf{\bar{a}TiO\_3}]} = (\mathbf{\bar{a}TiO\_3}).\tag{37}$$

The partial pressure values of vapor species in the gas phase over perovskite were determined by the Hertz-Knudsen equation, written in the following form [89]:

$$p\_i = K\_a \frac{q\_i}{s\_{or} C\_{or} t} \sqrt{\frac{2\pi RT}{\mathcal{M}\_i}},\tag{38}$$

where *qi* is the amount of *i*th substance component evaporated from the effusion cell, *Mi* is the molecular weight, *t* is time of evaporation,*T* is temperature, *Cor* is the Clausing coefficient characterized the effusion hole, and *sor* is the hole area.

The *K*<sup>α</sup> constant value was calculated taking into account the evaporation coefficient (α*i*) of substance component associated with the molecule changing during its transition to the gas phase from the surface with an *Sv* area, using the Komlev equation [90]:

$$K\_a = \frac{1}{C\_{or}} + s\_{or} \frac{1 - C\_c \alpha\_i}{S\_v \alpha\_i C\_c},\tag{39}$$

where *Cc* is the Clausing coefficient characterized effusion cell.

The Clausing coefficient is associated with the collision of vapor species inside the effusion orifice channel of effusion cell and their reverse reflection from the channel walls. Its value does not exceed 1 and depends on the ratio of the diameter of the effusion hole to its thickness.

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

ð Þþ Mo ð Þ¼ O ð Þ MoO (34)

ð Þþ MoO ð Þ¼ O ð Þ MoO2 (35) ð Þþ MoO2 ð Þ¼ O ð Þ MoO3 *:* (36)

Note that Berkowitz et al. [81] found that during evaporation of titanium oxide from a molybdenum liner inserted into a tantalum crucible at 1881 K, *p*MoO2 was initially 10–10<sup>2</sup> times higher than *<sup>p</sup>*TiO2 . The *<sup>p</sup>*MoO2 value gradually decreased and became comparable with the *p*TiO2 value, which is significantly different from the other results [52, 53, 56, 64, 77, 82]. The high *p*MoO2 observed in [81] probably was due to poor quality of the molybdenum liner material (or its alloy). Possibly it was made using powder technology from MoO3 reduced to metal molybdenum at �1300 K. It could lead to such an excess of partial pressure of (MoO3) and its decrease as it evaporates from the surface layers of the liner

The appearance energies of ions in the mass spectra of vapor over perovskite were determined by the Warren method [87] and corresponded to the accepted values of the ionization energies of atoms and molecules [88]. The appearance

The established molecular composition of the gas phase over perovskite allowed us to draw a conclusion on the predominant evaporation of perovskite according to the reactions (17), (18), (20), (23), (24), and (25), typical for evaporation of simple oxides [57, 71, 78, 86]. The presence of a small amount of (CaTiO3) molecules in the gas phase over perovskite is probably due to the reaction:

The partial pressure values of vapor species in the gas phase over perovskite

*qi sorCort*

The *K*<sup>α</sup> constant value was calculated taking into account the evaporation coefficient (α*i*) of substance component associated with the molecule changing during its transition to the gas phase from the surface with an *Sv* area, using the Komlev

The Clausing coefficient is associated with the collision of vapor species inside the effusion orifice channel of effusion cell and their reverse reflection from the channel walls. Its value does not exceed 1 and depends on the ratio of the diameter

1 � *Cc*α*<sup>i</sup> S*vα*iCc*

where *qi* is the amount of *i*th substance component evaporated from the effusion cell, *Mi* is the molecular weight, *t* is time of evaporation,*T* is temperature, *Cor* is the Clausing coefficient characterized the effusion hole, and *sor* is the hole

ffiffiffiffiffiffiffiffiffiffiffi 2π*RT Mi*

r

were determined by the Hertz-Knudsen equation, written in the following

*pi* ¼ *K<sup>α</sup>*

*<sup>K</sup>*<sup>α</sup> <sup>¼</sup> <sup>1</sup> *Cor* þ *sor*

where *Cc* is the Clausing coefficient characterized effusion cell.

8.5 � 0.6 eV (the appearance energy of silver ion was used as a standard) and

corresponded to obtained by Lopatin and Semenov [84].

<sup>+</sup> ion in the mass spectra of vapor over perovskite was equal to

½ �¼ CaTiO3 ð Þ CaTiO3 *:* (37)

, (38)

, (39)

material.

form [89]:

area.

**128**

equation [90]:

of the effusion hole to its thickness.

energy of CaTiO3

*Perovskite and Piezoelectric Materials*

Taking into account predominance of typical for CaO and TiO2 vapor species in the gas phase over perovskite and small amounts of CaTiO3, the α*<sup>i</sup>* values were used from [91].

The partial pressures of vapor species over perovskite at 1791–2182 K and its melts at 2278 K calculated using the relationships (38) and (39) with an error not exceeding 8% are shown in **Figure 8**.

The partial pressure of atomic oxygen determined using the relationships (38) and (39) agrees satisfactorily with those calculated using the thermochemical data [57] on *Kr*(*T*) equilibrium constants of possible reactions (18), (20), (24), (25), and (36) in the gas phase over perovskite in the following relations:

$$p\_{\rm O} = \frac{p\_{\rm CaO}}{p\_{\rm Ca}} K\_{\rm 18}(T) \tag{40}$$

$$p\_{\rm O} = \frac{p\_{\rm TiO\_2}}{p\_{\rm TiO}} K\_{24}(T) \tag{41}$$

$$p\_{\rm O} = \frac{p\_{\rm TiO}}{p\_{\rm Ti}} K\_{\rm 25}(T) \tag{42}$$

$$p\_{\mathcal{O}} = \sqrt{\frac{p\_{\mathcal{O}\_2}^2}{K\_{20}(T)}}\tag{43}$$

$$p\_{\rm O} = \frac{p\_{\rm MoO\_3}}{p\_{\rm MoO\_2}} K\_{\rm 36}(T). \tag{44}$$

It should be noted that the *p*<sup>O</sup> values calculated according to the independent reactions in the gas phase over perovskite (40)–(45) were the same. It confirmed the assumption about the molecular origin of the identified ions in the mass spectrum of vapor over perovskite.

As it follows from **Figure 8a**, the defined partial pressures of vapor species over perovskite can be represented as linear logarithmic dependence vs. the inverse temperature:

$$\mathbf{l}\mathbf{g}p\_i = a\_i/T + b\_i.\tag{45}$$

Note that the relationship (45) is the same as the expression for the reaction constant [57]:

$$R\ln K\_r(T) = -\frac{\Delta\_r G\_T}{T} = -\frac{\Delta\_r H\_T}{T} + \Delta\_r \mathbf{S}\_T,\tag{46}$$

which allows to determine the enthalpy (Δ*rHT*) and entropy (Δ*rST*) of a reaction.

The partial pressures of the predominant vapor species of the gas phase over perovskite (Ca, TiO, TiO2 and O) are compared in **Figure 7** with the results on evaporation of simple oxides (CaO and TiO2) under similar redox conditions caused by the interaction of oxygen with molybdenum [79, 81], tungsten [71], and tantalum [80] effusion cells or in chemically neutral conditions (in the absence of this interaction) for alundum cell [78].

We used the TiO and TiO2 activities as well as the Gibbs energy of perovskite obtained by Banon et al. [52] and thermochemical data [52] on equilibriums (17), (18), (23), and (24) to estimate the partial pressure of vapor species over the perovskite at 2150 K. Therefore, the obtained values characterized by the evaporation of perovskite were not under reducing conditions (from molybdenum cell),

The total vapor pressure over the perovskite melt at 2278 K obtained by Zhang

Similar slopes of lg *p*Ca and lg *p*<sup>O</sup> vs. the inverse temperature for calcium oxide and perovskite in **Figure 7a** and **d** (lines 1, 5 and 9, respectively) indicate a predominant effect of calcium component on evaporation of calcium from perovskite. This also can explain the difference in the slope of lg *p*TiO in **Figure 7b** in the case of perovskite (line 1) and rutile (line 10) according to the equilibriums (18) and (24). The enthalpy and entropy of reactions involving CaTiO3 gaseous complex oxide calculated by the relationship (46) are given in **Table 3**. They are in a good agreement with those found by Lopatin and Semenov [84] and our earlier estimates [85]. The concentration dependences of partial pressures of vapor species over perovskite melts show a sharp decrease in *p*Ca and *p*CaO (**Figure 8b**, lines 1 and 2) with increasing of TiO2 content in the melt. The vapor species containing titanium —(Ti), (TiO), and (TiO2)—are increased with increasing TiO2 concentration up to 65–70 mol% TiO2, and further they are almost constant in the region of 75– 100 mol% TiO2 (**Figure 8b**, lines 3–5), which may indicate the immiscibility of the melt observed by Banon et al. [52]. The partial pressures of (O) and (O2) slightly vary throughout the concentration range under consideration, showing a minimum in the perovskite concentration (**Figure 8b**, lines 6 and 7). The (CaTiO3) partial pressures have maximum values in the melt region with a high calcium content compared to the perovskite concentration (**Figure 8b**, line 8), as it was

The thermodynamic properties of perovskite determined by different calorimetric approaches and EMF method agree with the results obtained via Knudsen effusion mass spectrometry at high temperatures. The resulting values of oxide activities in perovskite, as well as the Gibbs energy, the entropy and enthalpy of the formation of perovskite from simple oxides, and the melting enthalpy of perovskite are consistent with each other. The enthalpy of perovskite formation is constant throughout the temperature range, and the entropy of perovskite formation tends

The oxide activities in perovskite melts were determined by mass spectrometric

The evaporation of perovskite and its melts from a molybdenum cell at high temperature was studied by the Knudsen effusion mass spectrometric method. The molecular components typical of simple oxides and the (CaTiO3) gaseous complex

Knudsen effusion method. The thermodynamic properties of melts (chemical potentials of oxides and mixing energies, as well as partial and integral enthalpies and entropies of melt's formation) were calculated based on the experimental data. The obtained experimental information testifies to the symbate behavior of thermodynamic functions characterizing the melts. The extreme values of the integral thermodynamic properties of melts are in the concentration region close to perovskite, which confirms its stability in the melt. The displacement of the extremum of the integral thermodynamic functions in the CaO-TiO2 melts can be caused by the presence in the melt of oxide compounds with a large amount of CaO compared to perovskite. A comparison of mixing energies in the CaO-TiO2 melts with those for the CaO-SiO2 and CaO-Al2O3 melts indicates a stronger chemical interaction in the CaO-TiO2 melts than the similar CaO-Al2O3 melts, but smaller than in the

et al. [4] is consistent with the extrapolated values of partial pressures of the predominant vapor species of the gas phase—atomic calcium and titanium dioxide

(**Figure 7a** and **c**) found in [77].

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

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

noted earlier.

**6. Conclusions**

to increase slightly.

CaO-SiO2 melts.

**131**

#### **Figure 8.**

*The partial pressure values of vapor species over perovskite (a) [77] and over the CaO-TiO2 melts at 2278 K (b) [64]: (1) Ca, (2) CaO, (3) Ti, (4) TiO, (5) TiO2, (6) O, (7) O2, and (8) CaTiO3.*

but, in contrary, under chemically neutral conditions (in the absence of interaction of perovskite with the cell material).

**Figure 7** also shows the partial pressures of vapor species over calcium and titanium oxides calculated using thermochemical data [57]. By comparison of the experimental data obtained in [71, 77–81] and the calculated results, we can see the effect of reducing properties of cell materials on gas phase composition: tantalum [80], molybdenum [79, 81], tungsten [71], and alundum [78]. As we noted earlier [85], the greatest effect of cell materials on the vapor composition are observed with the oxygen-"deficient" species such as atomic calcium (**Figure 7a**), titanium monoxide (**Figure 7b**), and atomic oxygen itself (**Figure 7d**). There are no differences in the partial pressure of gaseous titanium dioxide (**Figure 7c**) determined in evaporation experiments using molybdenum [81] and tungsten [71] cells.

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

The total vapor pressure over the perovskite melt at 2278 K obtained by Zhang et al. [4] is consistent with the extrapolated values of partial pressures of the predominant vapor species of the gas phase—atomic calcium and titanium dioxide (**Figure 7a** and **c**) found in [77].

Similar slopes of lg *p*Ca and lg *p*<sup>O</sup> vs. the inverse temperature for calcium oxide and perovskite in **Figure 7a** and **d** (lines 1, 5 and 9, respectively) indicate a predominant effect of calcium component on evaporation of calcium from perovskite. This also can explain the difference in the slope of lg *p*TiO in **Figure 7b** in the case of perovskite (line 1) and rutile (line 10) according to the equilibriums (18) and (24).

The enthalpy and entropy of reactions involving CaTiO3 gaseous complex oxide calculated by the relationship (46) are given in **Table 3**. They are in a good agreement with those found by Lopatin and Semenov [84] and our earlier estimates [85].

The concentration dependences of partial pressures of vapor species over perovskite melts show a sharp decrease in *p*Ca and *p*CaO (**Figure 8b**, lines 1 and 2) with increasing of TiO2 content in the melt. The vapor species containing titanium —(Ti), (TiO), and (TiO2)—are increased with increasing TiO2 concentration up to 65–70 mol% TiO2, and further they are almost constant in the region of 75– 100 mol% TiO2 (**Figure 8b**, lines 3–5), which may indicate the immiscibility of the melt observed by Banon et al. [52]. The partial pressures of (O) and (O2) slightly vary throughout the concentration range under consideration, showing a minimum in the perovskite concentration (**Figure 8b**, lines 6 and 7). The (CaTiO3) partial pressures have maximum values in the melt region with a high calcium content compared to the perovskite concentration (**Figure 8b**, line 8), as it was noted earlier.

## **6. Conclusions**

The thermodynamic properties of perovskite determined by different calorimetric approaches and EMF method agree with the results obtained via Knudsen effusion mass spectrometry at high temperatures. The resulting values of oxide activities in perovskite, as well as the Gibbs energy, the entropy and enthalpy of the formation of perovskite from simple oxides, and the melting enthalpy of perovskite are consistent with each other. The enthalpy of perovskite formation is constant throughout the temperature range, and the entropy of perovskite formation tends to increase slightly.

The oxide activities in perovskite melts were determined by mass spectrometric Knudsen effusion method. The thermodynamic properties of melts (chemical potentials of oxides and mixing energies, as well as partial and integral enthalpies and entropies of melt's formation) were calculated based on the experimental data. The obtained experimental information testifies to the symbate behavior of thermodynamic functions characterizing the melts. The extreme values of the integral thermodynamic properties of melts are in the concentration region close to perovskite, which confirms its stability in the melt. The displacement of the extremum of the integral thermodynamic functions in the CaO-TiO2 melts can be caused by the presence in the melt of oxide compounds with a large amount of CaO compared to perovskite. A comparison of mixing energies in the CaO-TiO2 melts with those for the CaO-SiO2 and CaO-Al2O3 melts indicates a stronger chemical interaction in the CaO-TiO2 melts than the similar CaO-Al2O3 melts, but smaller than in the CaO-SiO2 melts.

The evaporation of perovskite and its melts from a molybdenum cell at high temperature was studied by the Knudsen effusion mass spectrometric method. The molecular components typical of simple oxides and the (CaTiO3) gaseous complex

but, in contrary, under chemically neutral conditions (in the absence of interaction

*The partial pressure values of vapor species over perovskite (a) [77] and over the CaO-TiO2 melts at 2278 K*

*(b) [64]: (1) Ca, (2) CaO, (3) Ti, (4) TiO, (5) TiO2, (6) O, (7) O2, and (8) CaTiO3.*

**Figure 7** also shows the partial pressures of vapor species over calcium and titanium oxides calculated using thermochemical data [57]. By comparison of the experimental data obtained in [71, 77–81] and the calculated results, we can see the effect of reducing properties of cell materials on gas phase composition: tantalum [80], molybdenum [79, 81], tungsten [71], and alundum [78]. As we noted earlier [85], the greatest effect of cell materials on the vapor composition are observed with the oxygen-"deficient" species such as atomic calcium (**Figure 7a**), titanium monoxide (**Figure 7b**), and atomic oxygen itself (**Figure 7d**). There are no differences in the partial pressure of gaseous titanium dioxide (**Figure 7c**) determined in evapo-

ration experiments using molybdenum [81] and tungsten [71] cells.

of perovskite with the cell material).

*Perovskite and Piezoelectric Materials*

**Figure 8.**

**130**

oxide were identified in the gas phase over perovskite. The partial vapor pressures of the molecular components of the gas phase over perovskite were determined. A comparison of these values with the available experimental data and with the values corresponding to simple oxides showed that the character of perovskite evaporation is mainly affected by the calcium component of perovskite. The observed concentration dependences of the partial pressures of vapor species over the perovskite melts correspond to those characterizing the condensed phase.

**References**

[1] Rose G. Uber einige neue mineralien des Urals. Journal für Praktische Chemie. 1840;**19**:459-468

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

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

Anorganische und Allgemeine Chemie.

[10] Pontes FM, Pinheiro CD, Longo E, Leite ER, Lazaro SR, Varela JA, et al. The role of network modifiers in the creation of photoluminescence in CaTiO3. Materials Chemistry and

[11] Tulgar HE. Solid state relationships in the system calcium oxide—Titanium dioxide. Istanbul Teknik Üniversitesi

[13] Pfaff G. Peroxide route to synthesize calcium titanate powders of different composition. Journal of the European Ceramic Society. 1992;**9**:293-299

[14] Seko A, Hayashi H, Kashima H, Tanaka I. Matrix- and tensor-based recommender systems for the discovery

of currently unknown inorganic compounds. Physical Review Materials.

[15] Savenko VG, Sakharov VV.

Formation of calcium titanate Ca2Ti5O12 on thermolysis of mixed titanium and calcium hydroxides. Russian Journal of Inorganic Chemistry. 1979;**24**:1389-1391

Cherednichenko IF, Savos'kina AI. On calcium tetratitanate. Russian Journal of Inorganic Chemistry. 1972;**17**:559-561

[17] Oganov AR, Ma Y, Lyakhov AO, Valle M, Gatti C. Evolutionary crystal structure prediction as a method for the discovery of minerals and materials.

2018;**2**:13805-1-13805-9

[16] Limar TF, Kisel NG,

Reviews in Mineralogy and Geochemistry. 2010;**71**:271-298

1937;**230**:257-276

Physics. 2003;**78**:227-233

Bülteni. 1976;**29**:111-129

[12] Kisel NG, Limar TF,

1782-1785

Cherednichenko IF. On calcium dititanate. Russian Journal of Inorganic Chemistry. 1972;**8**:

[2] Stefanovsky SV, Yudintsev SV. Titanates, zirconates, aluminates and ferrites as waste forms for actinide immobilization. Russian Chemical

Reviews. 2016;**85**:962-994

[3] Wark D, Boynton WV. The formation of rims on calcium-

heating. Meteoritics & Planetary Science. 2001;**36**:1135-1166

[4] Zhang J, Huang S, Davis AM, Dauphas N, Hashimoto A, Jacobsen SB.

[5] Ivanova MA. Ca-Al-rich inclusions in carbonaceous chondrites: The oldest solar system objects.

Geochemistry International. 2016;**54**:

[6] Parga Pondal I, Bergt K. Sobre la combinacion de la cal en los sistemas CaO–TiO2 y CaO–SiO2–TiO2. Anales de la Sociedad Española de Física y Química. 1933;**31**:623-637

[7] Roth RS. Revision of the phase equilibrium diagram of the binary system calcia–titania, showing the compound Ca4Ti3O10. Journal of Research of NBS. 1958;**61**:437-440

[8] Lazaro SR. Estudo teoricoexperimental do titanato de

de Quimica; 2002. p. 57

Schmelzpunktsdiagramme

**133**

calcio—CaTiO3 [thesis]. Sao Carlos: Universidade Estadual Paulista, Intituto

[9] Wartenberg HV, Reusch HJ, Saran E.

hochstfeuerfester oxyde. VII. Systeme mit CaO und BeO. Zeitschrift für

Calcium and titanium isotopic fractionations during evaporation. Geochimica et Cosmochimica Acta.

2014;**140**:365-380

387-402

aluminum-rich inclusions: Step I—Flash
