Calorimetric and Thermodynamic Studies of Complex Ferrites in the Temperature Range of 298 , 15-673 K

By method of dynamic calorimetry, in the temperature range between 298,15 and 673 K, isobaric heat capacity of polycrystalline ferrites Bi 2 CaFe 4 O 10 , BVMgFe 2 O 5.5 , BiMgFe 4 O 10 was experimentally studied. Mathematical processing of experimental data made it possible to derive polynomial equation of temperature dependence of ferrites heat capacity for respective temperature ranges, in dependencies C0 p ~f(T) of ferrite Bi 2 CaFe 4 O 10 a jump was detected in heat capacity at 625K associated with phase transitions of type II. The values of the thermodynamic functions C0 p (T), H0(T) – H0(298,15), C0(T), Fhh(T) have been calculated. Standard values of thermodynamic functions were determined using the method of ion increments. The results obtained broaden thermodynamic data bank for complex inorganic crystalline compounds.


MATERIALS AND METHODS
Heat capacity of ferrites was investigated by dynamic calorimetry method using a serial device IT-400 in the temperature range between 298 and 673 K. Experiments were performed in the mode of a monotonous close to linear heating of the sample at the average heating rate of about 0.1 K per second.The maximum error of measurement of specific heat capacity using the IT-400 device according to the datasheet is ± 10% [10,11].Principle of calorimeter operation is based on comparative method of a dynamic c-calorimeter with a heat meter.The tested sample placed in a metal vial of the measuring cell was heated up continuously by heat flow through a calorimeter.After every 25 °C of heating, time lag of the vial temperature was measured against temperature of the base, using a micro voltamperemeter -136 V and a stopwatch SEC-100.The meter had been precalibrated, i.e., thermal conduction of the K T calorimeter was defined.After that, specific heat of a standard copper sample was defined, as well as specific and molar heat capacities of the substance.Thermal conductivity of the heat meter was defined by the following formula: where C copper.sample is the total heat capacity of a copper sample in J/K,   The total heat capacity of the copper sample was calculated according to the following equation: where C m is the tabular value of specific heat capacity of copper in J/(kg•K), and M sample is the mass of the copper sample in kg.
The value of specific heat capacity of the substance tested was calculated by the following formula: where K T is the thermal conductivity of the heat meter, m0 is the mass of the tested substance in kg, Tt is the time lag of temperature at the heat meter in seconds, and 0 T  is the time lag of temperature at the heat meter in experiments with an empty vial in seconds.
Five experiments were made for each sample temperature range.The obtained results of the lag time at the heat meter were averaged and processed by methods of mathematical statistics.For the average values of specific heat capacities at each temperature, standard deviations (  , J/ (g•K)), average values for molar heat capacities, and random error components (°, J/(mol K)) were calculated 10 .

RESULTS AND DISCUSSION
Calibration of the instrument was made by measuring standard heat capacity Q-A12O3.The obtained value of C 0 p (298.15) A12O3 [76.0 J/mol K] satisfactorily aggrees with the recommended one -[79.0J/mol K] 11 .
Table 1 shows results of calorimetric definition of the BVSaFe 4 O 10 ferrite heat capacities.
In studying the heat capacity of BiCaFe 4 O 10 ferrite within the limits between 598K and 648K, jumps of value C°p~f(T) were found, probably related to phase transitions of II kind.These transitions may be caused by cationic rearrangements, changing coefficients of thermal expansion and changes of magnetic moments of synthesized ferrites.
Mathematical processing of experimental data was used to derive equations of temperature dependence of ferrites heat capacity for respective temperature ranges T (Table 2) 12,13 .
Due to the fact that specifications of IT-400 calorimeter do not allow calculation of values of the standard entropy of compounds from experimental data about heat capacity, they were assessed using the system of ion entropy increments 14 .Errors of temperature dependence of the thermodynamic functions were calculated basing on the average error of the heat capacity and accuracy of entropy calculation (~3%).Next, by the known relations of the experimental data on C 0 p ~f(T) and the calculated values of S°(298.15), the temperature dependencies of the thermodynamic functions C 0 p (T), H 0 (T) -H 0 298.15),C 0 (T), F **(T) (Table 3) were calculated.-CONCLUSIONThus, for the first time, in the temperature range 298.15 -673 K, the isobaric heat capacities of Bi 2 CaFe 4 O 10 , BiMgFe 2 O 5,5 , Bi 2 MgFe 4 O 10 ferrites were experimentally determined.Equations that describe their dependence on temperature have been made.In course of changing the heat capacity of Bi 2 CaFe 4 O 10 at 625 K, heat capacity jumps were discovered, probably related to phase transitions of II kind.Values of thermodynamic functions C 0 p (T), H 0 (T) -H 0 (298,15), S°(T), F hh (T) have been defined.The results obtained increase thermodynamic database about complex inorganic crystalline compounds.
lag time at the heat meter in experiments with copper sample in seconds, 0 Т  is the average lag time at the heat meter in experiments with an empty vial.