Thermodynamic Properties of Complex Ferrite BiCa₃Fe₅O₁₂

Introduction

Investigation of the physico-chemical properties of ferrites formedin the Bi₂O₃-Me^IIO-Fe₂O₃ (Me^II-alkaline-land metal) systems is of definite scientific and practical interest for the directed synthesis of compounds with specified properties.The analysis of literature data shows that the most studied of ferrites arethe BiFeO₃orthoferrites, so-called multiferroics, which possess both electric polarization and magnetic ordering, recently there has been a significant increase in interest in these classes of compounds, their connection with promising applications as a working medium in devices of storage and information processing. On the basis of the most famous multiferroics, a wide search for new materials with ferroelectric properties is carried out by specific electronic and magnetic structures. The mixed result is based on bismuth ferrite which often combines ferroelectric and weakly ferromagnetic properties with the dominant antiferromagnetic ordering [1-2].Experimental studies, as a rule, are time-consuming, expensive and do not always yield reliable results. An alternative source of obtaining new information and revising the availableis the use of computational methods, which are based on the idea of thermodynamic similarity connecting the physicochemical properties of the system with its composition [3].

In this paper, semiempirical calculations of the thermodynamic properties and the temperature dependence of the heat capacity of complex ferrite BiCa₃Fe₅O₁₂werecarried out. The thermodynamic characteristics obtained are compared with the experimental data.

Experimental part

The complex ferrite was obtained by the solid-phase synthesis method in an alundum crucible from pre-annealed and thoroughly grindedfor 56 hours powders Fe₂O₃ (hp), CaCO₃ (bp) and Bi₂O₃ (bp).The composition of the obtained compound was confirmed by X-ray diffraction analysis using a RigakuMinilex 600 diffractometer.

The heat capacity of ferrites was studied by the method of dynamic calorimeter on a serial IT-S-400 instrument in the temperature range 298-673 K. The experiments were carried out in a monotonic regime, close to linear heating of the sample with an average rate of about 0.1 K per second. The maximum error in measuring the heat capacity on the S-400 IT device, according to the passport data, is ± 10% [9].

Results

The compound BiCa₃Fe₅O₁₂ was synthesized by the solid-phase reaction method and for the first time, the thermodynamic properties were calculated using semiempirical methods.All the calculated properties of the compound are shown in Table 1.

Table 1: Thermodynamic properties of BiCa₃Fe₅O₁₂ obtainedby semiempirical methods

	BiСа3Fe5O12
ΔH0298(ox), kJ / mol	-192.582±61.74
ΔH0298, kJ / mol	-4443.5 ± 61.74
S0298, kJ / mol	371.6±8
С0Р,298, kJ / mol	397.95 ±88.7
G0298, kJ / mol	– 3,684.94
а	82
b, 10-3	775· 103T
c, 105	122 ·10-5T-2

 

Discussions

Semiempirical calculation of thermodynamic properties:Information on the properties of simple oxides and Bi₂O₃ and Fe₂O₃, CaO was taken in [3].

Standard Enthalpy of Formation, Н⁰298

The standard enthalpy of formation is calculated by the formula used to estimate the heat of the compounds, which can be represented as pseudobinary or pseudotraic [4]

H° 298 (j) = Σ ni ΔH° 298 (i) + ΔH° 298(ox),

where ΔH⁰ 298, n_i is the standard heat of formation and the number of moles of the i-th compound in the j-th complex; ΔH⁰298 (ox) – SEO of a compound of simpler compounds.

In accordance with this formula, we can write

H° 298 (BiCa₃ Fe₅O₁₂) = 0,5. ΔH° 298 (Bi₂O₃) + 3. ΔH° 298 (CaO) + 2,5. ΔH° 298 (Fe₂O₃) + ΔH° 298(ox)

To estimate the value of ΔH⁰298 (ox) complex oxides, the empirical dependence was used [4].

H° 298(ox) ≈ (-16,0485) ± 5,145.m_o,

where m₀ is the number of oxygen atoms in the compound formula.

As a result, we received:

H° 298(ox) ≈ 192,582 ± 61,74kJ/ mol

and

H° 298 (BiCa₃ Fe₅O₁₂) ≈ 4443,5+61,74kJ/ mol

Standard entropy of formation, S⁰298

The standard entropy of the formation of S⁰298 is calculated by three methods: additively by the Kopp-Neumann rule using S⁰298 simple oxides [5], the Latimer method [4] and the Kumok increments method [4]. The additive method for calculating S⁰298 is based on the addition of S⁰298 simple oxides that make up the compound in the molar ratio:

S° 298 = n. S° 298 (Bi₂ O₃) +m. S°298 (CaO)+ r. S° 298(Fe₂O₃)

S° 298 =(BiCa₃ Fe₅O₁₂)=419,2J (mol.K)

The Kumok increments method assumes the computation by equation

S° 298 =SK.nk+ Sa.na+Sl.nl,

where Sk and Sa, Sl are increments of cations and anions, respectively (values are taken in [4]), nk and na, nl is the number of cation and anion compounds making up a compound.

For BiСa₃Fe₅O₁₂ S⁰298, the Kumok increments method was 427.2 J/(mol∙K). Using the Latimer method, it was 268.4 J/(mol∙K). The average arithmetic value of the standard entropy of formation is 371.6 ± 8J/(Kmol).

Standard heat Capacity, С⁰_Р, 298

The standard heat capacity was calculated according to the Kopp-Neumann rule [5]:

C° P, 298=n. C° P, 298 (CaO) +k. C° P,298(Bi₂O₃)+1. C°P, 298 (Fe₂O₃)

and equaled 353.6 J/(mol∙K), according to the dependence [5].

As per the Kumok increments method:

C °P, 298 = C° P, 298 K.nk + C° P,298a.nc,

where C⁰ p, 298K and C⁰ p, 298a, C⁰ p, 298a ∙ nc cation and anion increments, respectively, n·k and n·a, n·c is the number of cation and anion compounds making up the compound, the heat capacity is equal to 442.3J/(mol∙K).

The average value of 397.95 ± 88.7 is listed in Table 1.

Standard Gibbs Energy, G⁰298

The standard Gibbs energy is calculated by the method of ion increments. Standard Gibbs energy of a solid salt according to this method is calculated according to the following formula:

Where Mⁿ⁺ is a cation, X^m– is an anion, m, n^– are indices of cations and anions. Using the alkaline, alkaline earth, transition, and rare-earth metal cations in standard aqueous solution and anions (ΔG⁰298), the standard Gibbs energies of the salts of the s, d, f elements in the solid state can be calculated [6-7].

Received

Temperature Dependence of the Heat Capacity, Cp (T)

The temperature dependence of the heat capacity was calculated in the following ways: an additive method using data on simple oxides [5].

Received

C (T) = 82 +775.10³ T-122.10^-5 T^-2

Experimental Findingof Heat Capacity

Calorimetric methods for studying the thermodynamic properties of solids were used to measure the dependence of the heat capacity of solids on temperature and the change in energy during cation exchange. On anIT-S-400 calorimeter at the temperature interval 298.15-650 K, the comparative heat capacities of the synthesized BiСa₃Fe₅O₁₂ compounds were foundexperimentally. Figure 1 shows that the heat capacity of substances increases with increasing temperature. One of the reasons for the increase in heat capacity with increasing temperature is the energy expenditure on the formation of a vacancy upon the transition of the nodes of crystal lattices to intermediate sites [8-9].

For BiСa₃Fe₅O₁₂, the temperature dependence of the heat capacity has the form shown in Fig. 1.

Figure 1: Temperature dependence of heat capacity of complex ferrite: 1 (black line) – calculated values; 2 (blue line) – experimental data; Click here to View figure

 

Conclusion

The results of calculations of the thermodynamic properties of complex ferrite, carried out using semiempirical methods, are in satisfactory agreement with those values ​​that could be obtained experimentally. Thus, for the first time in the temperature range 298.15-673 K, the specific heats of the complex ferrite BiСa₃Fe₅O₁₂ were experimentally found, and the polynomial equation of the temperature dependence of the heat capacity was derived. A comparative analysis of the experimental and calculated values ​​of the specific heat wascarried out.

Acknowledgment

The article was prepared with the financial support of the grant of the Ministry of Education and Science of the Republic of Kazakhstan No. 3288 / GF4 “Synthesis and physical and chemical studies of new generation multifunctional magnetic materials” (under contract No. 249 of March6, 2017)

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