Heat Capacity and Thermodynamic Functions of Titanium-Manganites of Lanthanum, Lithium and Sodium of LaLi2TiMnO6 and LaNa2TiMnO6

Titanium-manganites of LaLi2TiMnO6 and LaNa2TiMnO6 were synthesized by the methods of ceramic technology from the oxides of lanthanum, titanium (IV), manganese (III), and the carbonates of lithium and sodium. The types of their syngony and the parameters of their gratings were determined radiographically. The isobaric heat capacities of titanium-manganites were measured with experimental calorimetry in the range of 298.15–673 K. It was found that on the dependence curve of heat capacity versus temperature of C°p~f(T), for LaLi2TiMnO6 at 348 K and 598 K, and LaNa2TiMnO6 at 348 K, there are abnormal jumps in heat capacity, probably related to phase transitions of the second kind. Taking into account the temperatures of the phase transitions, the equations of the temperature dependence of the heat capacity of titanium-manganites were derived. Their standard entropies were calculated by the ion increments method. Temperature dependences of the thermodynamic functions of S°(T), H°(T)-H°(298.15), and Φxx(T) were calculated using the experimental data on heat capacities and the calculated values of the standard entropies. The standard heat capacities of the studied compounds were calculated by the independent methods of ion increments and Debye, the values of which were in satisfactory agreement with the experimental data. The standard enthalpy of the formation of LaLi2TiMnO6 and LaNa2TiMnO6 was calculated according to the methodology developed by the authors. The conducted electrophysical studies determined the nature of the second-order phase transition and the semiconductor features of their conductivity. Thus, all the above-mentioned data on the experimental and calculated studies of the temperature dependence of heat capacity, the thermodynamic functions to determine a standard enthalpy of formation of LaLi2TiMnO6 and LaNa2TiMnO6, and the investigation of their electrical properties are absolutely new, and they have no analogues.


Introduction
Ferroelectric materials are of interest in developing electrically controlled ultrahigh frequency devices [1]. They include manganites and compounds based on titanium dioxide and have unique physical and physical-chemical properties [2,3]. Manganites-perovskites, as representatives of strongly correlated systems, are currently the subject of intensive research; this is primarily due to the colossal magnetoresistance (CMS) observed in manganites. Such CMR values allow the use of manganites in the field of spin electronics: magnetic sensors, magnetoresistive reading heads, and magnetoresistive RAM [4]. Recently, manganites have been considered promising materials for creating magnetic refrigerators operating at room temperatures, which are compact, highly efficient, and environmentally safe [5].
It should be noted that the authors in [6] obtained substituted lanthanum-strontium manganites La 0.7 Sr 0.3 Mn 0. 9 Me 0.1 O 3 ± δ (Me = Ti, Cr, Fe, Cu) using standard ceramic and glycerin-nitrate technologies. Their crystal structure was studied by high-temperature X-ray powder diffraction, thermal expansion coefficients were calculated, and electrical conductivity was investigated. In [7], the structural, electrical, and magnetic properties of the La 0.7 Sr 0.3 Mn 1-x Ti x O 3 system, which is characterized by rhombohedral distortion of the structure, were considered. It was found that the substitution of manganese ions with titanium ions leads to a weakening of ferromagnetism and an increase in resistivity. The study [8], presents the results of a study of the electrochemical properties of perovskite-like solid solutions (La 0.5+x Sr 0.5−x ) 1-y Mn 0.5 Ti 0.5 O 3−δ (x = 0-0.25, y = 0-0.03), synthesized by the citrate method, and studied as an oxide anode materials for solid oxide fuel cells. The authors in [9] present the structural, magnetic, and electrical properties of mixed Ti-MnSr (1−x) La (x) Ti (0.5) Mn (0.5) O 3 (0 ≤ x ≤ 0.5). X-ray absorption spectroscopic measurements show that the addition of La 3+ is compensated by a partial reduction of Mn 4+ to Mn 3+ .
Along with manganites, semiconductor titanium oxides with transition metal impurities also attract attention as promising materials for their use in spin electronics and catalysis [10]. These include barium titanate, a traditional electro-ceramic material with properties of ferro-, ferroelectric, and paraelectric. It should be emphasized that the high values of the dielectric permittivity of ferroelectrics near the phase transition temperature allow them to be used in miniature capacitors [11]. The solid electrolytes of Li 0.35 La 0.55 TiO 3x wt.% LiF (LLTO-FX, x = 0.2, 4 and 6) were synthesized by the solid-phase reaction, as described in [12]; all samples formed a perovskite structure and the grain size gradually enlarged with increasing LiF content. The LLTO-F2 electrolyte showed high conductivity at a low activation energy of 0.26 eV; therefore, it is suitable to use in solid-state batteries. Titanates of Bi 2 Pr 2 Ti 3 O 12 and Bi 2 Nd 2 Ti 3 O 12 were obtained with solid-phase synthesis and sintered in air at temperatures of 1003-1323 K of the stoichiometric mixtures of Bi 2 O 3 , Nd 2 O 3 , Pr 6 O 11 , and TiO 2 . Their crystal structure was detected by X-ray diffraction. The high-temperature heat capacity was determined by differential scanning calorimetry. Based on the experimental data of C p = f(T), the basic thermodynamic functions were calculated [13]. The heat capacities and thermodynamic characteristics of K 2 La 2 Ti 3 O 10 , K 2 Nd 2 Ti 3 O 10 , ErGaTi 2 O 7, DyGaTi 2 O 7 , and EuGaTi 2 O 7 were studied by the experimental and calculated methods described in [14][15][16]. The research of the thermodynamic properties of double and ternary substituted manganites of the compositions of LaMe I Mn 2 O 5 , LnMe II Mn 2 O 5.5 , LnMe I 3 Mn 2 O 6 , and LnMe II 3 Mn 4 O 12 (Me I -alkali, Me II -alkaline earth, Lnrare-earth metals), was generalized in [17]. The above results demonstrate that the data available in the literature describe the thermodynamic properties of the individually substituted titanates and the individual manganites of the rare earth, alkali, and alkaline earth metals.
The study of the thermodynamic properties of substances is important for the directed synthesis of new compounds and materials. The thermodynamic functions in a wide temperature range are calculated during the study of heat capacity. Data on heat capacity allow the exploration of various ordering processes, determining the magnetic ferroelectric and superconductivity properties, etc. [18]. It should be stated that it is not possible to calculate the temperature dependences of enthalpy and entropy without heat capacity, i.e., the thermodynamic functions determining the direction of a chemical reaction such as Gibbs energy (∆G) and the reduced thermodynamic potential (Φ**(T)) are calculated on their basis. However, the above data shows that there is no information in the literature about the synthesis and thermodynamic properties of combined double titanium-manganites of rare earth and alkali metals.
As a result of the above, the purpose of this study is a calorimetric investigation of heat capacity; calculations of the thermodynamic functions of the new titanium-manganites of LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 ; calculation of the fundamental thermodynamic constants of the studied compounds; the standard heat capacity, standard entropy, standard enthalpy of formation by the independent methods; and also the study of the temperature dependence of their electrophysical characteristics. This study is a continuation of our investigations; our results were summarized in [17]. The results obtained are of importance to predict the directed synthesis of the studied and analogous compounds, to analyze the heterogeneous equilibria according to II and III laws of thermodynamics involving titanium-manganites, and to discover their valuable physical and chemical properties. The new thermochemical constants of titanium-manganites are an initial data store to be included in fundamental reference books and information databanks.

Results and Discussion
Results of the calorimetric studies in Figure 5 and Table 7 describe that LaLi 2 TiMnO 6 (at 348 K, 598 K) and LaNa 2 TiMnO 6 (at 348 K) had anomalous discontinuities of heat capacity on the C • p~f (T) curve; this is probably related to the second-order phase transition. These transitions can be caused by Schottky effects, changes in the magnetic resistance, the electrical conductivity, the dielectric permittivity, Curie points, and Néel points, etc. [19]. Based on temperatures of the second-order phase transition, the equations of the temperature dependence of the heat capacity of titanium-manganites were calculated. They are described by the following equations (Table 1). The resulting calculated curves and lines sufficiently describe the experimental data ( Figure 5).
The graphs in Figure 5 are based on the experimental data and equations in Table 1, using the KOMPAS-3D LT software. For the reliability and correctness of the obtained straight lines and curves of the dependences of C • p~f (T), the calculated values of the heat capacities are also shown in Figure 5 between the experimental ones. Then, after the thermodynamic studies, we demonstrated the results of the electrophysical investigations to determine the nature of the mentioned second-order phase transitions.
In order to compare the phase transitions on the dependence curve C • p~f (T) of titanium-manganites, the temperature dependence of the heat capacity on the IT-S-400 of the standard substance of barium titanate (BaTiO 3 ) was investigated. BaTiO 3 ("p.a.") corresponding to TU 6-09-3963-84 (purity of BaTiO 3 -99.8448%) was chosen to explore. It was analyzed by X-ray phase analysis using DRON-2.0 to compare with the reference data.
All the diffraction maxima on the X-ray photograph of BaTiO 3 were equal to 4.04, 2.87, 2.35, 2.05, 1.83, and 1.66; 1.44 Å corresponded to data in the ASTM database [20]. Figure 1 and Table 2 show the research results of BaTiO 3 heat capacity in the range of 298.15-673 K.  It should be stated that the experimental value of the standard heat capacity of BaTiO3 was equal to 101 ± 7 J/(mol·K), which is in good agreement with its reference data of 102.
The experimental value of C°p(298.15) for BaTiO3 also corresponds well with its calculated value equal to 100.3 J/(mol·K). It was calculated by the method of the ionic entropic increments [2] under the formula: where S i Ba 2+ and S i TiO3 2− -ionic entropic increments equal 28.4 and 71.9 J/(mol·K), respectively [22]. Figure 1 illustrates the dependence diagram of C°p~f(T) for BaTiO3 in the interval of 298.15-673 K.
The data in Figure 1 and Table 2 demonstrate that the phase transition was observed in BaTiO3 at 398 K (125 °C). Referring to the literature data [23], this transition is observed at 393 K (120 °C) with a transition of its tetragonal modification to a cubic one with the appearance of the Curie point. The temperature dependence of the heat capacity of BaTiO3  It should be stated that the experimental value of the standard heat capacity of BaTiO3 was equal to 101 ± 7 J/(mol·K), which is in good agreement with its reference data of 102.45 J/(mol·K), derived on the basis of the equation of the temperature dependence of the heat capacity (J/(mol·K)) [21]: The experimental value of C°p(298.15) for BaTiO3 also corresponds well with its calculated value equal to 100.3 J/(mol·K). It was calculated by the method of the ionic entropic increments [2] under the formula: where S i Ba 2+ and S i TiO3 2− -ionic entropic increments equal 28.4 and 71.9 J/(mol·K), respectively [22]. Figure 1 illustrates the dependence diagram of C°p~f(T) for BaTiO3 in the interval of 298.15-673 K.
The data in Figure 1 and Table 2 demonstrate that the phase transition was observed in BaTiO3 at 398 K (125 °C). Referring to the literature data [23], this transition is observed at 393 K (120 °C) with a transition of its tetragonal modification to a cubic one with the appearance of the Curie point. The temperature dependence of the heat capacity of BaTiO3 -experimental data, •-calculated data.  It should be stated that the experimental value of the standard heat capacity of BaTiO 3 was equal to 101 ± 7 J/(mol·K), which is in good agreement with its reference data of 102.45 J/(mol·K), derived on the basis of the equation of the temperature dependence of the heat capacity (J/(mol·K)) [21]: The experimental value of C • p (298.15) for BaTiO 3 also corresponds well with its calculated value equal to 100.3 J/(mol·K). It was calculated by the method of the ionic entropic increments [2] under the formula: where S i Ba 2+ and S i TiO 3 2− -ionic entropic increments equal 28.4 and 71.9 J/(mol·K), respectively [22]. Figure 1 illustrates the dependence diagram of C • p~f (T) for BaTiO 3 in the interval of 298.15-673 K.
The data in Figure 1 and Table 2 demonstrate that the phase transition was observed in BaTiO 3 at 398 K (125 • C). Referring to the literature data [23], this transition is observed at 393 K (120 • C) with a transition of its tetragonal modification to a cubic one with the appearance of the Curie point. The temperature dependence of the heat capacity of BaTiO 3 was studied, and it depended on the heating rate of 1, 3, and 5 K/min, as described in [24]. This phase transition was observed at 395 K, 394.1 K, and 390.9 K, respectively. The technical capabilities of the IT-C-400 calorimeter can measure the heat capacities only per 25 K (in this interval of 373-398 K); thus, the temperature of this observed phase transition at 398 K is quite correct. Based on the temperature of the phase transition (398 K), we derived the equations describing this temperature dependence (J/(mol·K)): The technical capabilities of the calorimeter made it possible to calculate the standard entropies of compounds by using a system of ionic entropy increments [22]. These were equal to 203 ± 6 and 244 ± 7 J/(mol . K), respectively, for LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 .
The temperature dependences of C • p (T) and the thermodynamic functions of S • (T), H • (T)-H • (298.15), and Φ xx (T) ( Table 3, Figure 2), in the interval of 298.15-675 K, were calculated by equations [25]:   It should be stated that the experimental value of the standard heat capacity of BaTiO3 was equal to 101 ± 7 J/(mol·K), which is in good agreement with its reference data of 102.45 J/(mol·K), derived on the basis of the equation of the temperature dependence of the heat capacity (J/(mol·K)) [21]: The experimental value of C°p(298.15) for BaTiO3 also corresponds well with its calculated value equal to 100.3 J/(mol·K). It was calculated by the method of the ionic entropic increments [2] under the formula: where S i Ba 2+ and S i TiO3 2− -ionic entropic increments equal 28.4 and 71.9 J/(mol·K), respectively [22]. Figure 1 illustrates the dependence diagram of C°p~f(T) for BaTiO3 in the interval of 298.15-673 K.
The data in Figure 1 and Table 2 demonstrate that the phase transition was observed in BaTiO3 at 398 K (125 °C). Referring to the literature data [23], this transition is observed at 393 K (120 °C) with a transition of its tetragonal modification to a cubic one with the appearance of the Curie point. The temperature dependence of the heat capacity of BaTiO3  Table 1). This temperature range was chosen using the fact that the Φ xx (T) function is only calculated from 298.15 K. It should be pointed out that the mentioned thermodynamic potential of Φ xx (T) is an important thermodynamic function necessary to calculate the chemical equilibria under the third law of thermodynamics. The errors of functions S • (T) and Φ xx (T) were calculated using the errors of S • (298.15) (±3.0%) [22] and the experimental data on C • p (T).
As a result, temperature dependences of the heat capacities of LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 in the range of 298.15-673 K were first studied.
To compare the values of the experimental data of the standard heat capacities of LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 , they were calculated by independent calculation methods. According to [22] 15) LaNa 2 TiMnO 6 , the Debaev characteristic temperatures of the elements (Q D , K) that make up this titanium-manganite and their melting temperatures (T melt. , K) were used. For T melt. LaNa 2 TiMnO 6 , was 1473 K. The characteristic temperatures of the elements for LaNa 2 TiMnO 6 (Q D ) were determined by the Korefan equation [26]: where T melt. and T melt. are the melting temperatures of the compound and element, respectively. Then we calculate the isochoric heat capacities of the elements using Debye functions, and by summing them, we found the isochoric heat capacity of LaNa 2 TiMnO 6 . The transition from isochoric heat capacity to isobaric was carried out according to the Nernst-Lindeman equation: Table 3. The thermodynamic functions of the compounds. Taking the above into account, the following data were used to calculate the standard heat capacity of LaNa 2 TiMnO 6 : T melt. Then by the equation: we calculated the isochoric heat capacity of LaNa 2 TiMnO 6 , equal to 185.62 J/(mol·K). Further, according to the Nernst-Lindeman Equation (11), we calculated the standard isobaric heat capacity of C o p (298.15) LaNa 2 TiMnO 6 , equal to 250.3 J/(mol·K). This calculated value was in satisfactory agreement with the experimental value of the C o p (298.15) LaNa 2 TiMnO 6 (240 ± 11 250.3 J/(mol·K)), with an accuracy of 4.1%. Thus, it shows the correctness of our experimental data. Therefore, values of the calculated standard heat capacity of titanium manganites calculated by the independent methods confirmed the correctness and reliability of their experimental values.
In order to determine the nature of the second-order phase transition on the curves of dependences (C • p~f (T)) of LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 in the interval of 293-483 K per 10 K step, their electrical properties were studied, as described in [27] on an LCR-781 serial device (Taiwan) operating at a frequency of 1 kHz. The accuracy of measurements of the electric capacity, relative dielectric permittivity (ε), and electrical resistivity (R), according to the datasheet, is ±0.05% [27]. The research technique was described in detail in [28] and in our similar study [29]. The dielectric permittivity of a standard substance of barium titanate (BaTiO 3 ) was measured at 1 kHz to confirm the validity of the obtained data. We have described before the purity of the used BaTiO 3 in our thermodynamic studies.
The obtained value of the dielectric permittivity of BaTiO 3 at 293 K is 1296, which conforms satisfactorily to its recommended value of 1400 ± 250 [30][31][32]. Table 4 and Figure 3 below demonstrate the results of the electrophysical measurements.    The data in Table 4 and Figure 3 demonstrate that LaLi 2 TiMnO 6 in the range of 293-363 K had semiconductor conductivity. It had metallic conductivity at 363-413 K, and it had semiconductor conductivity again at 413-483 K. LaNa 2 TiMnO 6 in the range of 293-363 K shows the semiconductor conductivity. Then, it had the metallic conductivity at 363-433 K, and the semiconductor conductivity was again observed at 433-483 K. The above-mentioned changes from the semiconductor to metallic conductivity indicate the nature of the second-order phase transition on the dependence curves of LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 at 348 K. It should also be stated that LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 at 363 K have the maximum values of the dielectric permittivity equal to 53,224 and 2,182,878 respectively and, thus, this also explains the nature of phase transitions.
These experiments demonstrated that the phase transitions of LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 on the dependence curves of thermal capacity versus temperature at 348 K correspond in the tested temperature range of 293-363 K (maximum at 363 K) to a transition from the semiconductor to metallic conductivity. They are characterized by the maximum values of the dielectric permittivity. The high values of the dielectric permittivity of ferroelectrics near a temperature of the phase transition are described in [11]. The activation energies of conductivity were calculated for LaLi 2 TiMnO 6 (21.44 kJ/mol) and LaNa 2 TiMnO 6 (75.49 kJ/mol).
The widths of band gaps for LaLi 2 TiMnO 6 in the range of 293-363 K and 413-483 K were equal to 0.69 and 2.31 eV, respectively. The widths of band gaps for LaNa 2 TiMnO 6 between 293-363 K and 433-483 K were equal to 1.02 and 1.83 eV. Thus, they can be classified as narrow-band semiconductors.
In order to calculate the values of the standard enthalpies of formation of the test titanium-manganites, our developed method was used to calculate the standard enthalpy of formation of the double and triple manganites of the rare earth, alkali, and alkaline earth metals of the composition of LnMeI 3 MeII 3 Mn 4 O 12 (MeI-alkali, MeII-alkaline earth, Ln-rare earth metals) [33,34].
The calculation method is as follows: the similarity coefficient K 1 was calculated from the ratio of where Then the similarity coefficient K 2 was calculated under the equation of where ∆ ok H • (298.15)MeIMnO 4 -a standard enthalpy of formation of permanganate of alkali metal from oxides is equal to The similarity coefficient K 3 was calculated from the ratio of where ∆ ok H • (298.15)MeII(MnO 4 ) 2 is a standard enthalpy of formation of permanganate of the alkaline earth metal from oxides is equal to The average similarity coefficient K was calculated from Similar to Equations (13), (15) and (19), the ratio can be described as: Based on the above and taking the ratios of (24,25) for the titanium-manganites of lanthanum, the alkali, and alkaline earth metals, the following ratios can be demonstrated as:  Table 5 below shows the initial data for calculating the standard enthalpies of titaniummanganites formation, which are borrowed from [17,[29][30][31]. It should be noted that the K coefficient for calculating ∆ ƒ H • (298.15) LaLi 2 TiMnO 6 will be equal to 1.2375, and for LaNa 2 TiMnO 6 − 1.3084.
The calculated values based on the above data ∆ f H • (298.15) will be equal to −3607.0 kJ/mol for LaLi 2 TiMnO 6 and −3579.3 kJ/mol for LaNa 2 TiMnO 6 , respectively.

Experimental Part
Titanium-manganites of LaMe I 2 TiMnO 6 (Me I -Li, Na) were obtained by high-temperature synthesis using ceramic technology. Oxides of lanthanum (III) ("puriss. spec."), titanium (IV), manganese (III), and carbonates of lithium and sodium ("p.a.") were applied to synthesize the titanium-manganites. These substances were pre-annealed at 300 • C to remove adsorption moisture. The calculated mole ratios of the starting reagents to obtain the final compound were thoroughly mixed and ground in an agate mortar. Synthesis was performed in stages in a SNOL laboratory furnace. The first stage was at 600 • C for 5 h, and the second step was to raise the temperature of the synthesis to 800 • C for 5 h. The third stage had a temperature at 1000 • C for 10 h and was repeated twice. The fourth stage was at 1200 • C for 4 h. After each temperature rise, the mixture was cooled down and milled. The final process had a low-temperature annealing at 400 • C for 10 h to obtain the low-temperature equilibrium phases. The formation of the equilibrium composition of the studied phases was monitored by X-ray diffraction analysis on the DRON-2.0 apparatus.
The indexing of X-ray photographs demonstrated that compounds were crystallized in the cubic syngony with the lattice parameters as follows: LaLi 2 TiMnO 6 -a = 13.48 ± 0.02 Å, V • = 2449.46 ± 0.06 Å 3 , Z = 4, V o el.cell = 612.87 ± 0.02 Å 3 , ρ roent. = 3.81; ρ pick. = 3.78 ± 0.03 g/cm 3 ; LaNa 2 TiMnO 6 -a = 14.06 ± 0.02 Å, V • = 2779.43 ± 0.06 Å 3 , Z = 4, V • el.cell = 694.96 ± 0.02 Å 3 , ρ roent. = 3.67; ρ pick. = 3.65 ± 0.01 g/cm 3 [38]. A pycnometric density was determined by using toluene as an indifferent liquid according to a well-known method [39]. Figure 4 (below) illustrates the diffractograms of the studied titanium-manganites. It should be pointed out that we present in detail the results of the indexing of X-ray photographs of the above compounds, and their correctness and reliability were confirmed by good conformity between the experimental and calculated values of 10 4 /d 2 , and the pycnometric and X-ray densities of the theoretical and experimental values of their unit cells, as described in [38]. These compounds can be assigned to the perovskite structure according to the information below. The above-mentioned compounds can be represented as derivatives of lanthanum titanate (LaTiO 3 ) and lanthanum manganate (LaMnO 3 ), and they belong to a perovskite structure [40]. Secondly, in order to assign these compounds to the perovskite structure, we calculated the tolerance factor (t) by the formula [23]: where τ A, τ B, τ O -ion radii of A, B, and O 2 . In our case, A is a sum of ions of La 3+ , Li + , Ti 4+ or La 3+ , Na + , Ti 4+ , and B-ion Mn 3+ . The radii of ions of La 3+ , Li + , Na + , Ti 4+ , Mn 3+ , and O 2− at a coordination number equal to 6 according to the Goldschmidt system were used, according to [41]. The Goldschmidt system was preferred, i.e., the Pauling system has no ion radius of Mn 3+ . The tolerance factors (t) for LaLi 2 TiMnO 6 (t = 0.97) and LaNa 2 TiMnO 6 (t = 0.94) were calculated by Equation (24). Additionally, we calculated the "tolerance factor" t, based on the system of ion radii according to Shannon and Previtt, for LaLi 2 TiMnO 6 0.94 and for LaNa 2 TiMnO 6 -0.90. The tolerance factor (t) is approximately in the range of 0.80 ÷ 1.00 for all perovskite-type compounds and t > 0.89 for an ideal cubic structure, as described in [41]. The parameter increment of "a" and the volume increase of the unit cells were observed during the elevating ionic radii from Li to Na.
Temperature dependence of the heat capacity of synthesized compounds of LaLi 2 TiMnO 6 and LaNa 2 TiMnO 6 was explored in the temperature range of 298.15-673 K by dynamic calorimetry using an IT-C-400 calorimeter. The device is based on the comparative method of a dynamic calorimeter with a heat meter and an adiabatic shell. During the experiment of heating (per 25 • C), the time lag of the ampoule temperature in relation to the base temperature was measured on an F136 device and stopwatch. Based on the specifications of the calorimeter, the heat capacity was measured per 25 K, and the limit temperature measurement was 673 K. The initial temperature for the measurement of heat capacity was 298.15 K and permitted to obtain the fundamental constant-standard heat capacity of the compound.
The measuring range of the volumetric heat capacity was not less than 1 × 10 6 J/K·m 3 . The time for the full temperature range with the experimental data processing was no more than 2.5 h. The measurement errors on the IT-C-400 device did not exceed ±10%. The device was calibrated using a calculation of the thermal conductivity of the heat meter (K T ) [42,43].
A value of the molar heat capacity was calculated from the specific heat capacity using the molar mass. At each temperature after 25 K, five parallel experiments were conducted, the results of which were averaged and processed by methods of mathematical statistics.
For the averaged values of the specific heat capacity at each temperature, the standard deviation (δ) was estimated according to [43]: where n-number of experiments, C i -a measured value of specific heat capacity, and C-an arithmetic average of measured values of the specific heat capacity. A random error was calculated for averaged values of the molar heat capacity as described in [43]: where • ∆-a random error in % and t p -Student coefficient (for n = 5, t p = 2.75 at p = 0.95 of the confidence range).
Operation of the device was verified with a calculation of the heat capacity of α-Al 2 O 3 ("p.a.", TU 6.09-426-75). The repeated (parallel) measurements in the range of 173-673 K (at 25 K, 5 times) were performed for calibration and verification. Therefore, five parallel measurements were made at each temperature at 25 K. The results were averaged and processed using mathematical statistics. Liquid nitrogen served as the refrigerant.
Our results, with the new literature data in [44], were compared for the accuracy of the heat capacity measurements of α-Al 2 O 3 ( Table 6). Table 6. Comparison of the heat capacity of α-Al 2 O 3 with the literature data in [44] to verify the calorimeter operation.

T, K C • p (T), J/(mol·K)
Our Data Data in [ The data in Table 6 demonstrates that our results for the temperature dependence of the heat capacity of -Al 2 O 3 , in the range of 173-673 K, satisfactorily conformed to the results in [44] within the operating accuracy of the IT-C-400 calorimeter.
It should be stated that in order to compare our values of the heat capacities of Al 2 O 3 with the data in [44], our experimental values were used at 10 and 50 K based on equations of C • p~f (T) calculated from the experimental data because the data in [44] for C • p~f (T) were used at 10 and 50 K, while our experimental data were measured at ∆T = 25 K. It should be noted that the real errors of the experimental data on heat capacities calculated with Equations (25) and (26) were lower than a limiting accuracy of the device, i.e., it was less than 10%. Table 7 and Figure 5 demonstrate the results of the calorimetric studies.

Funding:
The work was carried out within the framework of program-targeted financing under the program 057 "Applied scientific research of a technological nature in the field of industry" of the Committee for Industrial Development of the Ministry of Industry and Infrastructure Development of the Republic of Kazakhstan within the framework of the scientific and technical project "Creation of new composite materials with high performance properties based on rare and rare earth elements" for 2021-2023.