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

Introduction

Study of physico-chemical properties of ferrites formed Bi₂O₃ – Me^IIО – Fe₂O₃ (Me^II – alkaline earth metals) systems is of certain scientific and practical interest for directed synthesis of compounds with desired properties. Analysis of the published data shows that among ferrites, the most studied ones are orthoferrites BiFeO3, the so-called multiferroics having both electric polarization and magnetic ordering. In recent years interest to these classes of compounds has significantly increased due to perspective of their use as a working environment in information storage and processing devices. On the basis of the most known multiferroic, new materials with ferroelectric properties of the specific electronic and magnetic structures were searched for. Substituted perovskites based on bismuth ferrite often combine ferromagnetic and weak ferroelectric properties under the dominant anti-ferromagnetic ordering [1-6].

The purpose of this work is a calorimetric study of Bі₂СаFe₄O₁₀, BіMgFe₂O_5,5 , Bі₂MgFe₄O₁₀ ferrites. The tested ferrites have been synthesized by solid phase interaction of stoichiometrically matching oxide mixtures Bi2O3, Fe2O3 of chemically pure grade, and carbonates of alkaline-earth metals of essential purity. Formation of equilibrium phases of ferrites was detected by X-ray diffraction method and types of their symmetry and lattice constants [7,8] were identified. It has been determined that ferrites crystallize into a tetragonal and cubic structure with the following lattice cell parameters: Bі₂СаFe₄O₁₀ –а=5.56, с=8.12 Å, V_el.cell.=251.0 Å3, Z=1, ρ_rent.=6.56, ρ_pikn.=6.93g/cm³: BіMgFe2O5,5  –  а=11,1 Å, V_el.cell= 1382 Å3, Z=8, ρ_rent.= 6,02, ρ_pikn.=3,03 g/ cm³: Bі2MgFe4O10–   а=11,1 Å, V_el.cell= 1364 Å3, Z=16, ρ_rent.= 9,66, ρ_pikn.=9,60 g/ cm³[9].

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 pre-calibrated, 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, t^–_TM. is the average lag time at the heat meter in experiments with copper sample in seconds, t^-o_T  is the average lag time at the heat meter in experiments with an empty vial.

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, τt is the time lag of temperature at the heat meter in secondsτT⁰, and  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 ( ^–δ, J/(g·K)), average values for molar heat capacities, and random error components (Δ º, J/(mol K)) were calculated [10].

Results and Discussion

Calibration of the instrument was made by measuring standard heat capacity ɑ-A12O3. The obtained value of C⁰_p (298.15) A12O3 [76.0 J/mol K] satisfactorily aggrees with the recommended one – [79.0 J/mol K] [11].

Table 1 shows results of calorimetric definition of the BіSaFe₄O₁₀ ferrite heat capacities.

Table 1. Experimental values of heat capacity

T, K	Bі2СаFe4O10
	С0р + δ(J/g·К)	С0р + ∆º( J/mol К)
298.15	0,429±0,02	360,81±11,9
323	0,439±0,01	369,73±5,86
348	0,450±0,01	378,92±5,71
373	0,464±0,01	390,25±5,41
398	0,469±0,01	394,63±5,48
423	0,486±0,02	408,71±10,5
448	0.491±0.01	412,99±5,24
473	0,505±0,02	425,31±10,1
498	0,512±0,02	430,45±10,0
523	0,524±0,01	441,12±4,9
548	0,535±0,02	450,83±9,61
573	0,544±0,02	458,06±9,45
598	0,552±0,01	464,86±4,66
623	0,549±0,01	360,81±11,9
648	0,557±0,01	369,73±5,86
673	0,592±0,01	378,92±5,71

 

In studying the heat capacity of BіСаFe₄O₁₀ ferrite within the limits between 598 K and 648 K, 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 (Table 2) [12,13].

Table 2. Equation of temperature dependence ferrites hear capacity.

Compound	Сr =a+bT+cT-2			ΔT, K
	a	b 10-3	c·106
Bі2СаFe4O10	266,36±18	334±0,02	0,293±0,02	298,15 – 673
BiMgFe2O5,5	148,77±10	198±0/01	0,101±0,01	298,15 – 673
Bi2MgFe4O10	255,19±18	403±0,03	0,565±0,04	298,15 – 673

 

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 C⁰_p~f(T) and the calculated values of S°(298.15), the temperature dependencies of the thermodynamic functions C⁰_p(T), H⁰(T) – H⁰298. 15), C⁰(T), F **(T) (Table 3) were calculated.

Table 3. Thermodynamic functions of ferrites in temperature range between 298.15 and 673 K.

T, K		CP0 (T), J/mol K	S0 (T) J/mol K		Fhh(T), J/mol K	H0 (T) H0 (298.15)kJ/mol
Bі2СаFe4O10
1		2	3		4	5
300		206,10	413,96		269,80	413,06
325		216,42	423,93		3516,63	413,11
350		228,07	432,52		6530,50	413,87
375		235,25	439,92		9311,38	415,09
400		237,05	446,28		11859,24	416,63
425		246,41	451,71		14174,04	418,36
450		257,73	456,31		16255,79	420,19
475		268.28	460,18		18104,46	422,07
500		273,67	463,38		19720,05	423,94
525		288,58	465,98		21102,54	425,79
550		290,70	468,04		22251,93	427,58
575		270,19	469,59		23168,21	429,31
600		292,93	470,70		23851,39	430,94
625		302,34	471,38		24301,47	432,49
650		310,86	471,67		24518,43	433,94
675		320,77	471,60		24502,28	435,30
BiMgFe2O5,5
1		2	3		4	5
300		319,63	234,39		534,82	323,62
325		322,36	255,49		7189,14	233,37
350		325,00	274.87		13786,05	235,49
375		327,58	292,78		20325,53	238,59
400		330,10	309,41		26807,55	242,39
425		332,58	324,89		33232,11	246.71
450		335,04	339,38		39599,21	251,38
475		337,48	352,96		45908,82	256,31
500		339,89	365,73		52160,96	261,41
525		342,29	377,77		58355,62	266,62
550		344,67	389,15		64492,78	271,89
575		347,05	399,92		70572,46	277,19
600		349,41	410,14		76594,65	282,49
625		351,76	419,85		82559,34	287,76
650		354,11	429,09		88466,54	292,99
675		356,46	437,91		94316,24	298,18
Bi2MgFe4O10
1	2			3	4	5
300	275,42			222,18	169,94	221,62
325	283,69			228,51	2181,83	221,80
350	291,92			233,78	3993,44	222,37
375	300,10			238,15	5604,47	223,21
400	308,26			241,73	7014,90	224,20
425	316,39			244,61	8224,73	225,26
450	324,50			246,88	9233,95	226,36
475	332,61			248,59	10042,56	227,45
500	340,70			249,81	10650,56	228,51
525	348,78			250,58	11057,94	229,51
550	356,86			250,94	11264,70	230,46
575	364,93			250,93	11270,85	231,33
600	372,99			250,58	11076,37	232,12
625	381,05			249,92	10381,28	232,83
650	389,10			248,97	10085,55	233,46
675	397,15			247,76	9289,22	233,99

 

Conclusion

Thus, for the first time, in the temperature range 298.15 – 673 K, the isobaric heat capacities of Bі₂СаFe₄O₁₀, BіMgFe₂O_5,5, Bі₂MgFe₄O₁₀ ferrites were experimentally determined. Equations that describe their dependence on temperature have been made. In course of changing the heat capacity of Bі₂СаFe₄O₁₀ at 625 K, heat capacity jumps were discovered, probably related to phase transitions of II kind. Values of thermodynamic functions С⁰_p(Т), H⁰(T) – H⁰(298,15), S°(T), F^hh(Т) have been defined. The results obtained increase thermodynamic database about complex inorganic crystalline compounds.

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