Since thermal properties such as entropy and enthalpy of materials are important for their applications in heat-related devices, it is important to study the specific heat capacities of materials. Specific heat capacity is an intrinsic property of a material. So, it can also be used to characterize a compound. Thus, an attempt has been made for a comparative study of the specific heat capacities of A₂FeCoO_6−δ (A = Ca or Sr) at 40˚C. They are oxygen-deficient perovskites. Because of their unique properties, oxygen-deficient perovskite oxides can be used in a variety of devices including gas diffusion membranes, [1] oxygen separation ceramic membranes [2] , solid oxide fuel cells (SOFCs), [3] electrodes, [4] sensors, [5] superconductors, and colossal magnetoresistance. [6]

Oxygen-deficient perovskites are the oxides with lanthanides or alkali metals in their A site and 3d and 4d-transition metal in their B site in the general formula ABO_3−x or A₂B₂O_6−δ. Here, X and δ are the oxygen vacancies in the compound. The arrangement of Oxygen vacancies can be ordered or disordered. The different arrangements and numbers of vacancies result in insignificant variation and diversity in the structure and properties. The different arrangements of the vacancies can also lead to different coordination geometries such as square pyramidal or tetrahedral geometry around B cation. When the vacancies are ordered and tetrahedral geometries are formed, brownmillerite structures are formed with the tetrahedra sharing corners and forming chains. These chains are arranged alternating with octahedral chains as layers. Thus, tetrahedral layers are sandwiched between the octahedral layers above and below connecting through their apexes. The ordered vacancy arrangement can also form square pyramids as in Sr₂Fe₂O_6−δ. [7] [8]

When A or B site cations are replaced in oxygen-deficient perovskites, it can lead to a variation in the structure and properties of materials, for example, the compounds Sr₂Fe₂O_6−δ and Sr₂FeMnO_6−δ. Here, Sr₂Fe₂O_6−δ has a tetragonal crystal structure but Sr₂FeMnO_6−δ has a cubic crystal structure. The different crystal structures are the result of the B-site cation replacement. Here, Fe in Sr₂Fe₂O_6−δ is substituted by Mn to get Sr₂FeMnO_6−δ. This leads to the variation of their properties. The magnetic moments of Sr₂Fe₂O_6−δ are in the spin-density wave state and that of Sr₂FeMnO_6−δ in an inhomogeneous magnetic ground state, where most of the sample at 4 K contains fluctuating spins with a magnetically ordered small fraction [9] . A site cation substitution can also affect in the structures and properties of the compounds. [10] For example, CaSrFeGaO_6−δ has Ibm2 space group and Ca₂FeGaO_6−δ has Pnma space group. [11] The tetrahedral arrangements change in these materials. The crystal structure of Ca₂FeGaO_6−δ (Pnma) has tetrahedral chains oriented in opposite directions in alternating tetrahedral layers, whereas CaSrFeGaO_6−δ (Ibm2) has all tetrahedra oriented in the same direction. As a result, their charge transport properties vary. [11]

The concept of the effect of A and B site substitution on the structure and properties inspired us to conduct a comparative study of specific heat capacities of the compounds A₂FeCoO_6−δ (A = Ca or Sr).

All the compounds were synthesized at 1200˚C and characterized by powder X-ray diffraction, SEM, and their thermal conductivities were measured at 40˚C. SrCO₃, CaCO₃, Co₃O₄ and Fe₂O₃ were the precursor compounds used for the formation of Ca₂FeCoO_6−δ CaSrFeCoO_6−δ and Sr₂FeCoO_6−δ materials. They were purchased from Alfa Aesar (99.9 %) pure. The powders were weighed and mixed in stoichiometric proportion in an agate mortar and a pestle. The uniform mixture was used to make pellets. The pellets are kept at 1000˚C for 24 hours for calcination. The calcined pellets were powdered and re-pressed at a pressure of 3 tons to make pellets. The circular pellets have dimensions of 3 mm radius and 0.6 mm thickness. The pellets were sintered at 1200˚C for 24 hours. The heating ramp for calcination and sintering was maintained at 100˚C/h. Powder X-ray diffractometer (PXRD) with Cu Kα1 radiation of wavelength, λ = 1.54056 Å was used for the phase purity test and structure determination of the materials at room temperature. The PXRD data were refined by Rietveld refinement using the GSAS2 software. The materials were investigated for their microstructures using scanning electron microscopy (SEM). The specific heat capacity of the materials was studied with the help of a computer-controlled heat flow meter (HFM 446 Lambda from NETZSCH). The circular samples with the dimensions mentioned before and a mass of 295 mg were used for the measurements.

All the three materials, Ca₂FeCOO_6−δ, CaSrFeCoO_6−δ and Sr₂FeCoO_6−δ were previously reported. [3] PXRD was used to investigate the crystal structure and phase purity of our materials. All the three compounds revealed crystal structures and space groups as reported before. Note that the A cations are different which vary the average radius of the A cations in these compounds. This cation size difference can cause structural variation. Ca₂FeCoO_6−δ compound possesses a large unit cell double the size of a typical brownmillerite. The tetrahedral chains are ordered, and each chain is oriented opposite to all of its nearest neighbors. Figure 1 shows Rietveld refinement parameters and crystal structure of

Ca₂FeCoO_6−δ. The Rietveld refinements reveal the orthorhombic structure with Pbcm space group. Table 1 lists the refined atomic parameters for Ca₂FeCoO_6−δ.

CaSrFeCoO_6−δ compound also possesses a typical brownmillerite structure with ordered tetrahedral chains. Unlike in Ca₂FeCOO_6−δ all the tetrahedral chains are oriented in the same direction. Figure 2 shows Rietveld refinement parameters and crystal structure of CaSrFeCoO_6−δ. The Rietveld refinements reveal the orthorhombic structure with Ibm2 space group. Table 2 lists the refined atomic parameters for CaSrFeCoO_6−δ.

Space group Pbcm, a = 5.368540 Å, b = 11.106282 c = 14.807982 Rp = 0.0168, and wRp = 0.0216, χ² = 1.356.

Space group Ibm2, a = 5.557669 Å, b = 15.165850 Å, c = 5.414111 Å Rp = 0.0165, wRp = 0.0220 and χ² = 1.834.

In Sr₂FeCoO_6−δ (inset of Figure 3), the vacancies are distributed randomly, and the crystal structure resembles the cubic structure of parent perovskite where there are no oxygen vacancies. Table 3 shows the Rietveld refinement parameters for Sr₂FeCoO_6−δ.

Rietveld refinements were accomplished for the structural analysis of all three compounds. (Figure 1 inset) In Ca₂FeCoO_6−δ, the oxygen-vacancies are present in every other layer with the formation of (Fe/Co)O₄ tetrahedral units and the remaining layers (green polyhedra in Figure 1 inset) with no oxygen vacancies of typical perovskite octahedra. Thus, the oxygen-vacancies occur in alternating layers of tetrahedral units and octahedral units. The tetrahedral (Fe/Co)O₄ units are corner shared forming chains that are sandwiched between the octahedral layers. CaSrFeCoO_6−δ has also vacancy ordered structure with alternating octahedral and tetrahedral layers (Figure 2 inset), but the tetrahedral chain-order is one less, due to all identical orientation, than that of Ca₂FeCoO_6−δ where the tetrahedral chains have alternating orientations forming an R-L-R-L-… arrangement (R = righthanded; L = left handed). The structure of Sr₂FeCoO_6−δ resembles the typical perovskite oxide structure with octahedral coordination around transition metals (Figure 3) with the vacant oxygen sites distributed randomly.

Space group Pm3̅m, a = 3.864689 Å, Rp = 0.0142, and wRp = 0.0192, χ² = 0.9485.

Scanning electron microscopy (SEM) was used to investigate the surface structure of Ca₂FeCOO_6−δ, CaSrFeCoO_6−δ and Sr₂FeCoO_6−δ. Figure 4 illustrates the surface microstructure of Ca₂FeCOO_6−δ, CaSrFeCoO_6−δ and Sr₂FeCoO_6−δ. The effect of unit cell crystal structure variation can be observed in SEM micrograph. Though less porous or nonporous nature of Ca₂FeCoO_6−δ was observed, the number of pores can be seen increasing after Sr incorporation in the material. The SEM images demonstrate the porosity for Sr₂FeCoO_6−δ. The grains are interconnected like a diffused one in Sr₂FeCoO_6−δ, while there are explicit separations of grains in Ca₂FeCoO_6−δ, and CaSrFeCoO_6−δ. The grains seem to have compact arrangement without pores in Ca₂FeCoO_6−δ, and CaSrFeCoO_6−δ. However, the grain growths are irregular in Ca₂FeCoO_6−δ. The microstructure variation between these materials (as seen in the SEM images i.e.) are expected as the crystal structures between these materials are different.

The specific heat capacity (Cp) of materials is an important intrinsic property. Cp is also used to calculate the entropy and enthalpy of a material. [12] Investigation of specific heat capacity for perovskite oxide is not uncommon. [13] Specific heat capacities of the vacancy-ordered perovskite oxides, Ca₂FeCoO_6−δ, CaSrFeCoO_6−δ and Sr₂FeCoO_6−δ were investigated on their circular pellets at 40˚C using computer-controlled heat flow meter. The Cp values for Ca₂FeCoO_6−δ, CaSrFeCoO_6−δ, and Sr₂FeCoO_6−δ are 1.53, 1.62 and 1.94 J/(g·K), respectively. The comparison of Cp is shown in Figure 5.

Specific heat capacity (Cp) depends on different factors such as degree of freedom, physical state, molar mass, crystallinity, and temperature. Increasing the degree of freedom will lead to an increase of specific heat capacity. Cp for the amorphous phase is larger than that of the crystalline phase. [14] Note all our three materials are synthesized at the same temperature and environment with the same physical state. Ca₂FeCoO_6−δ, CaSrFeCoO_6−δ, and Sr₂FeCoO_6−δ, all have crystalline structures. So, the effect of the degree of freedom of the atoms and physical states is ignored here. The specific heat capacity increases with increasing the molar mass. [14] [15] Sr₂FeCoO_6−δ has the highest Cp values while Ca₂FeCoO_6−δ has the lowest Cp values while that of CaSrFeCoO_6−δ has an intermediate value. Sr₂FeCoO_6−δ has the highest molar mass and Ca₂FCoO_6−δ has the lowest molar mass. Thus, the molar mass may have impacted the Cp values of these materials. The same material can demonstrate the specific heat capacity variation with the phase or geometry change. [16] As discussed before, Ca₂FeCoO_6−δ, CaSrFeCoO_6−δ, and Sr₂FeCoO_6−δ have different crystal structures with different types of oxygen vacancy arrangements after A-site cation substitution. So, the variation of specific heat capacities is expected. Note that Ca is smaller in size than Sr. When Ca in Ca₂Fe₂O_6−δ is substituted by Sr, the specific heat capacity is increased. The high heat capacity value of Sr₂FeCoO_6−δ is due to bigger A-cation size, higher molar mass, different crystal structure. One report discussed the effect of particle size on the specific heat capacity of carbon nanotubes. [17] Our SEM micrographs show the different grain structures and sizes for the materials. Thus, grain size may have contributed to the variation of the Cp values. An

article discussed the effects of defects on the Cp variation. [18] Defects can be generated from impurities, broken bonds, or vacancies resulting in the interruption in the regular or natural structure. The report mentions that the presence of the defects, characterized by the absence of broken C–C bonds generates the graphene blocks of various sizes [18] which in turn affected the Cp values. Ca₂FeCoO_6−δ, CaSrFeCoO_6−δ and Sr₂FeCoO_6−δ are compounds with different concentrations of oxygen vacancies, i.e. oxygen defects. We have already reported the oxygen vacancy concentration of these materials in the previous article. [19] The values are δ = 0.9 for Ca₂FeCOO_6−δ, δ = 0.9 for CaSrFeCoO_6−δ and Sr₂FeCoO_6−δ has δ = 0.5. [19] There are differences not only in the concentration of the oxygen defects but also in the patterns in which they are distributed.

Thus, this comparative study demonstrated that the A site cation substitution in oxygen-deficient perovskite can lead to the variation of Cp values in oxygen-deficient perovskite. The fact that the Cp value decreases as both the average A-site ionic radius and molar mass decrease clearly indicates the direct relationship of the Cp with the average A-site ionic radius as well as molar mass.

This work is supported in part by the National Science Foundation Tribal College and University Program Instructional Capacity Excellence in TCUP Institutions (ICE-TI) award # 1561004, and we express gratitude to the program managers and review panels for project support. A part of this work is also supported by NSF grant no. HRD 1839895. Additional support for the work came from ND EPSCOR STEM grants for research. The authors also acknowledge the support of North Dakota EPSCoR for the purchase of thermal conductivity equipment, potentiostat and X-ray diffractometer. Permission was granted by United Tribes Technical Colleges (UTTC) Environmental Science Department to publish this information. The views expressed are those of the authors and do not necessarily represent those of United Tribes Technical College.

The authors declare no conflicts of interest regarding the publication of this paper.

Sanchez, S., Guinn, M., Phuyal, U.S., Dhaliwal, G.S. and Hona, R.K. (2023) Specific Heat Capacity of A₂FeCoO_6−δ (A = Ca or Sr). Journal of Materials Science and Chemical Engineering, 11, 1-10. https://doi.org/10.4236/msce.2023.114001