Calorimetric Research into the Heat Capacity of Novel Nano-Sized Cobalt(Nickelite)-Cuprate-Manganites of LaBaMeCuMnO6 (MeII = Co, Ni) and their Thermodynamic Properties

The isobaric heat capacities of novel nano-sized cobalt-cuprate-manganite of lanthanum and barium LaBaCoCuMnO6 and nickel-cuprate-manganite of lanthanum and barium LaBaNiCuMnO6 were investigated by dynamic calorimetry over the temperature range of 298.15‒673 K. It is found that a λ-shaped effect is observed on the curve of the heat capacity dependence on temperature of LaBaCoCuMnO6 at 523 K, while LaBaNiCuMnO6 also has a similar effect at 473 K. Equations for the temperature dependence of the heat capacity of cobalt(nickelite)-cupratemanganite of lanthanum and barium are derived with allowance for the temperatures of phase transitions. Based on the experimental data, the fundamental constants ‒ the standard heat capacities of the compounds under study were found. Irrespective of the experimental data, we also calculated the standard heat capacities of the mentioned compounds using the Debye theory using the characteristic temperatures of the elements, their melting points, the Koref and Nernst-Lindemann equations. The obtained calculated data on 0 p C (298.15) of the compounds were in satisfactory agreement with the experimental data on the standard heat capacity. The standard entropies of LaBaCoCuMnO6 and LaBaNiCuMnO6 were calculated by the ion increment method. We calculated the temperature dependences of the enthalpy Ho(T)Ho(298.15), entropy ΔSo(T), and the reduced thermodynamic potential ΔФ**(Т). Article info Received: 11 January 2019 Received in revised form: 18 March 2019 Accepted: 24 May 2019


Introduction
Interest in the compounds (manganites, cuprates, nickelites, cobaltites, etc.) being formed from the oxides of transition (3d-and 4f-) and alkaline-earth metals is due to their unique multifunctional properties such as superconductivity, giant (GMR) and colossal magnetoresistance (CMR).
Manganites, having effects of GMR and CMR, can be used in magnetic field sensors, readout heads for high-density magnetic recording, temperature displacement transducers, etc. [7].
It should be noted that GMR has attracted great attention because it has had a significant impact on the development of magnetic storage devices. Since the implementation of GMR-type sensors, the memory capacity has increased by about 100 times [8].
At present, considerable attention is paid to nanocrystalline materials because a substance in a nanocrystalline state manifests special properties (magnetic, optical, etc.) not characteristic for bulk materials [7]. For this reason, producing and researching novel nanocrystalline materials is an important stage in creating materials for a new generation [9].
In view of the above, a certain theoretical and practical interest is in obtaining and researching into the physicochemical properties of novel nano-sized compounds in which manganites, cobaltites, nickelites, and cuprates are represented as single phases like cobalt-cuprate-manganites and nickelite-cuprate-manganites of rare-earth and alkaline earth metals. This paper, based on the above data, presents the results of calorimetric studies of the heat capacity and calculation of the thermodynamic functions of novel nano-sized cobalt-cuprate-manganite and nickelite-cuprate-manganite of lanthanum and barium LaBaCoCuMnO 6 and LaBaNiCuMnO 6 .

Experimental part
Using ceramic technology we obtained nano-sized LaBaCoCuMnO 6 and LaBaNiCuMnO 6 which were subjected to a calorimetric study.
Polycrystalline samples of these compounds were obtained by solid-phase interaction of La 2 O 3 , NiO, CoO, CuO, Mn 2 O 3 , and BaCO 3 over the range of 800-1200 °C.
Calorimetric study of the heat capacity of the synthesized nano-sized LaBaCoCuMnO 6 and LaBaNiCuMnO 6 was carried out on an IT-S-400 calorimeter over the range of 298.15-673 K. The device operation principle is based on the comparative method of a dynamic c-calorimeter with a heat meter. The measuring circuit of the device provides the measurement of a temperature level from "minus" 100 to "plus" 400 °C at the fixed points in each 25 °C intervals by means of a builtin DC potentiometer and a switch.
The volume range is minimum of 1·10 6 J/K·m 3 . The time of measuring over the entire temperature range together with the experimental data processing is about 2.5 h. Measurement uncertainties on an IT-S-400 device do not exceed ± 10%. Liquid nitrogen was used as a cooling agent.
The device was calibrated by determining the thermal conductivity of the heat meter K Т [11,12]. This required several experiments with a copper where С c.s. the total specific heat of a copper sample, J/(mol·K); ῑ TM is a mean value of the lag time on the heat meter in the experiments with a copper sample, s; is a mean value of the lag time in the experiments with an empty ampoule, s.
The total heat capacity of the copper sample was calculated by the Eq. 2: where C c is a tabulated value of the specific heat capacity of copper, J/(mol·K); m s is a copper sample mass, kg. The specific heat value of a substance was calculated by the Eq. 3: , n where n is the number of experiments, C i is the measured value of the specific heat, is the arithmetic mean of the measured values of the specific heat.
For the averaged values of the molar heat capacity according to [12,13], a random error component was calculated: sample and an empty ampoule. The thermal conductivity of the heat meter was determined by the Eq. 1: where is a random error component, %, t p is the Student coefficient (for n = 5, t p = 2.75 with p = 0.95 of the confidence interval).
A systematic error component was calculated by the formula: where K T is heat conductivity of the heat meter; m 0 is the mass of the test substance; τ T is the temperature lag time on the heat meter, 0 T τ is the temperature lag time on the heat meter in the experiments with an empty ampoule, s.
From the specific heat capacity, we calculated the molar heat capacity taking into account the molar mass. Five parallel experiments were performed for each temperature; the results were averaged and processed by the methods of mathematical statistics.
At each temperature for the specific heat averaged values we calculated the root-mean-square deviation ( ) by [13]: where Δ c is systematic error component in %, C 0 is the heat capacity value of the standard measure taken at the temperature at which the heat capacity was determined.
The maximum permissible error was calculated by the formula: The systematic error and uncertainties in measuring temperature were not considered in our research since they were negligible compared to the random component.
According to the theory of errors, if a random error is significantly greater than the sum of the systematic error of an instrument scale error, then the measurement accuracy of the instrument will be determined by a random error [12,13], that is, instead of a limiting error, a random error is used.
The reliability of the obtained heat capacity values can be indicated by the fact that the experimental value of the standard heat capacity of sodium arsenate Na 3 AsO 4 , previously determined on the same IT-C-400 calorimeter [14] and equal to 169.1 J/(mol·K), is in satisfactory agreement with its recommended value (170.3 J/(mol·K)) given in the reference book [15].
The work of the calorimeter was additionally tested in determining the heat capacity of α-Al 2 O 3 . The obtained value of (298.15) α-Al 2 O 3 , equal to 76.0 J/(mol·K), is in satisfactory agreement with its recommended value of 79.0 J/(mol·K) [16]. These data also prove the correctness and reliability of the results.
It should be noted, that we carried out studies on the heat capacity of similar compounds on the same calorimeter [17][18][19]. Table 1 and figure given below present the results of a calorimetric study of the heat capacities of LaBaCoCuMnO 6 and LaBaNiCuMnO 6 .
The measurement results show that the studied compounds on 0 p C~f(Т) curves ( Fig.) have second-order phase transitions at 523 K (LaBaCo-CuMnO 6 ) and at 473 K (LaBaNiCuMnO 6 ) which can be associated with the Schottky effects, the Curie, points and the Néel points, changes in electrical resistance, dielectric constant, etc.
It should be noted that the formation of a ferromagnetic (the Curie point) or an antiferromagnetic (the Néel point) relates to second order magnetic phase transitions. Apart from magnetic transitions, there are electrical ones. When cooling paraelectric, the cases of second-order phase transitions into the ferroelectric state and antiferroelectric state are observed [20]. We observed the same phase   transitions in studying the heat capacity of similar manganites, which were further confirmed by the electrophysical methods, i.e., a second-order phase transition, we revealed in manganites transitions from the semiconductor conductivity to the metallic one and vice versa [21].
Taking into account the temperature of phase transitions, the equations of the temperature dependence of the compounds under study are derived ( Table 2).
The standard heat capacities of LaBaCoCuMnO 6 and LaBaNiCuMnO 6 were also calculated according to Debye [22,23]. The necessary data for the calculation were the Debye characteristic temperatures (Q d , K) of the elements constituting a chemical compound and their melting points (T melt. , K) [22,23]. The characteristic temperatures of the elements for the compounds under study were found using the Koref formula [22,23]: the isochoric heat capacity of the elements using the Debye function and sum them.
The transition from the isochoric heat capacity to the isobaric one is carried out by the Nernst-Lindemann equation: The following data were used for the calculation: Based on the above data, the standard heat capacities of LaBaNiCuMnO 6 and LaBaCoCuMnO 6 were calculated. They are equal to 252.3 and 252.0 J/(mol K), respectively, and agree with the experimental data within an accuracy of 1.5 and 5.1%.
, where and Т melt. are melting points of a compound and an element. We take the synthesis temperature (1473 K) at which the compound is stable as of the compounds under study. Then we find . melt T Eurasian Chemico-Technological Journal 22 (2020) 27-33 Table 3 Thermodynamic functions of nano-sized cobalt(nickelite)-cuprate-manganites   [24] were used.
The values of S о (298.15) of the compounds under study calculated according to the scheme are presented in Table 3.  Table 3.
It should be emphasized that the function of the reduced thermodynamic potential is very convenient for calculating the standard thermal effect of chemical reactions, as well as for calculating chemical equilibria according to the third law of thermodynamics, starting at 298.15 K.
When estimating the errors of the functions ΔS o (T) and ΔФ ** (Т) the estimation errors of S o (298.15) (~3.0%) were taken into account.

Conclusions
1. For the first time, the isobaric heat capacities of nano-sized cobalt-cuprate-manganite LaBaCoCuMnO 6 and nickel-cuprate-manganite LaBaNiCuMnO 6 were studied by experimental calorimetry over the range of 298.15-673 K.
2. The temperatures of second-order phase transitions were established on the curves of 0 p C~ f(Т) dependencies of the compounds under study and, taking them into account, the equations of the temperature dependence of the heat capacity were derived.
3. Based on the experimental data on the heat capacities and the estimated value of the standard entropies, the temperature dependences of the thermodynamic functions were calculated.
4. According to Debye, the standard heat capacities of LaBaCoCuMnO 6 and LaBaNiCuMnO 6 were calculated using the Koref and Nernst-Linde- Due to the technical limitations of an IT-S-400 calorimeter, which do not allow calculating the standard enthalpy of the compounds directly from the experimental data on the heat capacities, we estimated them using the ion increment method [24] according to the scheme: mann equations. Their values agree well with the experimental data.
5. The research results are of interest for the directed synthesis of similar compounds, prediction of promising physical and physicochemical properties of cobalt(nickelite)-cuprate-manganites and similar phases.