Thermodynamic Properties of Stoichiometric Non-Superconducting Phase Y2BaCuO5

Y2BaCuO5 often occurs as an accompanying phase of the well-known high-temperature superconductor YBa2Cu3O7 (also known as YBCO). Y2BaCuO5, easily identifiable due to its characteristic green coloration, is often referred to as ‘green phase’ or ‘Y-211’. In this contribution, Y2BaCuO5 phase was studied in detail with a focus on its thermal and thermodynamic properties. Energy dispersive spectroscopy (EDS), X-ray diffraction (XRD), and scanning electron microscopy (SEM) were employed in the study of sample’s morphology and chemical composition. XRD data were further analyzed and lattice parameters refined by Rietveld analysis. Simultaneous thermal analysis was employed to study thermal stability. Particle size distribution was analyzed by laser diffraction. Finally, thermodynamic properties, namely heat capacity and relative enthalpy, were measured by drop calorimetry, differential scanning calorimetry (DSC), and physical properties measurement system (PPMS). Enthalpy of formation was assessed from ab-initio DFT calculations.


Introduction
Transition metal (TM) oxides constitute a large family of oxides, which possess a variety of interesting properties [1][2][3][4]. Cobalt mixed oxides with misfit structure are thermoelectric materials for the recovery of waste heat, and misfit cobaltites also show unique catalytic properties [5][6][7]. Mixed oxides containing lithium found a crucial application in accumulator industry [8]. Nano-sized oxides are widely used in catalysis, electrochemistry, and solar cells [9][10][11][12][13]. Among TM oxides, the high-temperature superconductors (HTS) revealing critical temperature close to the temperature of liquid nitrogen have been attracting permanent attention since their discovery in 1986 [14]. Although enhanced critical temperatures and intriguing superconducting behavior have been later reported in several systems, for example in layered ternary and quaternary arsenide systems [15,16], the HTS cuprates became the most wide-spread group of high-temperature superconductors, still being at the forefront of both theoretical and applied research in the field of superconductivity.
Their discovery in the Ba-La-Cu-O system [14] was immediately followed by an intensive search for novel HTS phases in congeners systems such as Y-Ba-Cu-O, Bi-Sr-Ca-Cu-O, Tl-Ba-Ca-Cu-O, and Hg-Ba-Ca-Cu-O [17][18][19][20][21][22][23][24][25]. Superconducting phases in these systems are usually derived from perovskites by inserting other structural motifs such as rock-salt type blocks, and thus forming layered structures. In general, perovskites and similar layered oxides exhibit a wide variety of

Materials and Methods
We used the following chemicals for the synthesis of Y 2 BaCuO 5 : Barium carbonate (Sigma-Aldrich, Prague, Czech Republic; 99 + %), yttrium (III) oxide (Chemapol, Prague, Czech Republic; 99.99%), and copper (II) oxide (Sigma-Aldrich; 99.99%). Powders were homogenized in the ratio corresponding to Y 2 BaCuO x stoichiometry and repeatedly calcined in corundum crucible at 1123 K for 12 h, then at temperatures of 1138 K, 1153 K, and 1163 K for 24 h with a homogenization between each step. Finally, the sample was pressed into pellets and calcined for additional 24 h at 1173 K. The sample was slowly cooled in order to obtain a thermodynamically stable phase fully saturated with oxygen. The sample with the stoichiometry Y 2 BaCuO 5 is termed Y-211 hereinafter.
The microstructure was analyzed using scanning electron microscopy (SEM). The elemental composition was studied using energy-dispersive spectroscopy (EDS) analyzer X-Max N with 20 mm 2 silicon drift detector from Oxford instruments (Abingdon, UK) and software package Aztec Energy v. 3 (Asylum Research-Nanoanalysis, Wycombe, UK) using a Tescan Lyra dual beam microscope (Tescan, Brno, Czech Republic) with a field emission gun electron source.
The thermal stability Y 2 BaCuO 5 was analyzed by simultaneous thermal analysis (STA) using Setaram Setsys Evolution (Setaram, Lyon, France). The heating rate during the measurement performed in dynamic air atmosphere (50 cm 3 min −1 ) was 10 K min −1 .
The particle size distribution was analyzed by the laser diffraction method; Malvern Panalytical Mastersizer 3000 device (Malvern, UK) with 4 mW He-Ne 632.8 nm Red light source and 10 mW LED 470 nm Blue light source was used. The range of measurement was set from 0.1 to 1000 µm. The measurement was done using dispersion (1 g/100 mL) of the material in isopropyl alcohol. Y-211 sample was measured 5 times (5 scans) and distribution was created as an average value.
The heat capacity in the low-temperature region was measured using the physical properties measurement system (PPMS) equipment, Evercool-II 9 T-type (Quantum Design, San Diego, CA, USA). The heat capacity was obtained by the relaxation method under high vacuum.
A Tian-Calvet-type calorimeter µDSC IIIa (Setaram, Lyon, France) was used for the measurement of heat capacities in the temperature range 262 to 358 K, employing NIST Standard reference material No. 720 as a reference material. Performance of the calorimeter is regularly checked by measurement of compounds with well-established C pm data (naphthalene, benzophenone, benzoic acid). Based on these checking experiments, the combined expanded uncertainty of the heat capacity measurements is estimated to be U c (C pm ) = 0.01 C pm . More details can be found in paper [38]. Data obtained from this calorimeter are referred as DSC data.
Multi HTC 96 (Setaram, Lyon, France) high-temperature calorimeter (operated in a static air atmosphere) was used to measure enthalpy increments. The measurement was performed by dropping of the reference material (synthetic sapphire, NIST No. 720) and the sample in the sequence standard-sample-standard-sample-standard. The delays between two subsequent drops were 25 min in order to stabilize the heat flow. The estimated combined expanded uncertainty of the heat capacity measurements is estimated to be U c (C pm ) = 0.03 C pm .
Enthalpy of formation was assessed from ab-initio density functional theory (DFT)-based calculations. The electronic structure and total energies of Y 2 BaCuO 5 and the constituent oxides, Y 2 O 3 , BaO, and CuO, were calculated by means MedeA-VASP [39] program using projector augmented plane waves basis set and generalized gradient approximation (GGA-PBE0 [40]) to exchange-correlation functional combined with additional local orbital specific coulomb potential U = 3 eV acting on Cu-3d states [41]. An antiferromagnetic ground state was considered for both CuO [42] and Y 2 BaCuO 5 [37]. The basis set with a cut-off energy of 400 eV was applied. The k-point mesh was constructed inside the first Brillouin zone with k-point spacing smaller than 0.25 Å −1 . A tetrahedron integration scheme was applied for electron density of states calculation.  SEM micrographs of the sample show that the Y 2 BaCuO 5 particle size lies mostly between 1 and 5 µm; the particle size remained very homogeneous across the sample, as can be seen from Figure 2a. This is in good agreement with the microstructures typically observed in polycrystalline cuprates. Elemental distribution maps were obtained by EDS and can be seen in Figure 2b. The sample appears to be homogenous and pure from a chemical point of view. Only Y, Ba, Cu, and O were detected. These results correspond with the results obtained by X-ray diffraction and confirm purity and phase composition of the prepared sample.  In order to confirm the sizes of grains obtained from SEM, the powder was also analyzed by laser diffraction. Particle size distribution is shown in Figure 3, revealing that the grains are mainly of the size between 1 and 10 μm, dx(50) = 5.2 μm, dx(10) = 2.8 μm and dx(90) = 10.3 μm. These data are in good agreement with SEM. In order to confirm the sizes of grains obtained from SEM, the powder was also analyzed by laser diffraction. Particle size distribution is shown in Figure 3, revealing that the grains are mainly of the size between 1 and 10 µm, dx(50) = 5.2 µm, dx(10) = 2.8 µm and dx(90) = 10.3 µm. These data are in good agreement with SEM.

Results and Discussion
Simultaneous thermal analysis (STA) was employed to study the thermal behavior of Y 2 BaCuO 5 ( Figure 4). The phase Y-211 decomposed in air atmosphere at 1551 K. Throughout the measurement, the mass was almost constant, i.e., the phase was stable up to temperatures of~1550 K and we did not detect any release of oxygen, suggesting the presence of the stoichiometric phase. The weight decrease related to the original mass of Y 2 BaCuO 5 was approximately 1 wt % suggesting formation of  Simultaneous thermal analysis (STA) was employed to study the thermal behavior of Y2BaCuO5 ( Figure 4). The phase Y-211 decomposed in air atmosphere at 1551 K. Throughout the measurement, the mass was almost constant, i.e., the phase was stable up to temperatures of ~1550 K and we did not detect any release of oxygen, suggesting the presence of the stoichiometric phase. The weight decrease related to the original mass of Y2BaCuO5 was approximately 1 wt % suggesting formation of Y2O3 (s), BaO (s), and Cu-O (l).  Figure 7).
For further analysis of low temperature heat capacity data, two sets of the Cpm data (relaxation time + DSC) were considered. Since the studied material is a magnetic insulator, only the lattice part of heat capacity is relevant for temperatures well above the Néel temperature, T = 16.2 K. For this reason, only the data above 30 K were considered for the analysis of phonon heat capacity, which was performed using the combination of the Debye and Einstein models according to the following Equation (1):  Simultaneous thermal analysis (STA) was employed to study the thermal behavior of Y2BaCuO5 ( Figure 4). The phase Y-211 decomposed in air atmosphere at 1551 K. Throughout the measurement, the mass was almost constant, i.e., the phase was stable up to temperatures of ~1550 K and we did not detect any release of oxygen, suggesting the presence of the stoichiometric phase. The weight decrease related to the original mass of Y2BaCuO5 was approximately 1 wt % suggesting formation of Y2O3 (s), BaO (s), and Cu-O (l).  Figure 7).
For further analysis of low temperature heat capacity data, two sets of the Cpm data (relaxation time + DSC) were considered. Since the studied material is a magnetic insulator, only the lattice part of heat capacity is relevant for temperatures well above the Néel temperature, T = 16.2 K. For this reason, only the data above 30 K were considered for the analysis of phonon heat capacity, which was performed using the combination of the Debye and Einstein models according to the following Equation (1):  Figure 7).
For further analysis of low temperature heat capacity data, two sets of the C pm data (relaxation time + DSC) were considered. Since the studied material is a magnetic insulator, only the lattice part of heat capacity is relevant for temperatures well above the Néel temperature, T = 16.2 K. For this reason, only the data above 30 K were considered for the analysis of phonon heat capacity, which was performed using the combination of the Debye and Einstein models according to the following Equation (1): Here R is the gas constant, θ D and θ Ei are the Debye and Einstein characteristic temperatures, and x D = θ D /T, x Ei = θ Ei /T, and w i refer to a degeneracy of the corresponding Einstein mode.
It is a well-known fact that the phonon spectrum of a mixed oxide contains 3n-3 optical branches and three acoustic branches (n is number of atoms per formula unit). In Y 2 BaCuO 5 , there are 9 atoms per formula unit representing 24 optical branches which were grouped into three 8-fold degenerate Einstein modes.
The Debye-Einstein model is based on a harmonic crystal approximation describing the heat capacity at constant volume. As can be seen Figure 6, the experimentally obtained heat capacity exceeded the Dulong-Petit limit valid for C V at~670 K. It was previously described [43] that a multiplication factor 1/(1−αT) can be introduced to any vibration mode (in order to take into account the anharmonic effects) and to describe the C p -C V difference using a semi-empirical approach. Hence, in our analysis, we used such an anharmonicity parameter that was combined only with the Debye mode in Equation (1). The analysis of the phonon heat capacity is shown in Table 1. The fitted curve based on PPMS and DSC data corresponding to LT-fit in Figure 5 describes the low temperature data satisfactorily above 60 K. Below this temperature, a substantial excess term due to magnetic ordering is clearly visible (see the inset in Figure 5). The absolute entropy at the reference temperature (T = 298.15 K) was obtained by integrating the experimental data of the heat capacity divided by the thermodynamic temperature from 2 K up to ambient temperature as S m (298.15) = 209.47 J mol −1 K −1 . This experimental value can be decomposed into a lattice vibrations contribution, S lat (298.15) = 206.9 J mol −1 K −1 , and an excess entropy due to magnetic ordering disruption S lat (298.15) = 2.8 J mol −1 K −1 , which is about two times lower than the theoretical value R ln2 corresponding to spin 1 2 of Cu(+II) and also lower than the experimental value reported by Knafo et al. [43] who, however, derived the phonon contribution by scaling the C p data of YBa 2 Cu 3 O 7 .
Materials 2019, 12, x FOR PEER REVIEW 6 of 11 Here R is the gas constant, θD and θEi are the Debye and Einstein characteristic temperatures, and xD = θD/T, xEi = θEi/T, and wi refer to a degeneracy of the corresponding Einstein mode.
It is a well-known fact that the phonon spectrum of a mixed oxide contains 3n-3 optical branches and three acoustic branches (n is number of atoms per formula unit). In Y2BaCuO5, there are 9 atoms per formula unit representing 24 optical branches which were grouped into three 8-fold degenerate Einstein modes.
The Debye-Einstein model is based on a harmonic crystal approximation describing the heat capacity at constant volume. As can be seen Figure 6, the experimentally obtained heat capacity exceeded the Dulong-Petit limit valid for CV at ~670 K. It was previously described [43] that a multiplication factor 1/(1−αT) can be introduced to any vibration mode (in order to take into account the anharmonic effects) and to describe the Cp-CV difference using a semi-empirical approach. Hence, in our analysis, we used such an anharmonicity parameter that was combined only with the Debye mode in Equation (1). The analysis of the phonon heat capacity is shown in Table 1. The fitted curve based on PPMS and DSC data corresponding to LT-fit in Figure 5 describes the low temperature data satisfactorily above 60 K. Below this temperature, a substantial excess term due to magnetic ordering is clearly visible (see the inset in Figure 5). The absolute entropy at the reference temperature (T = 298.15 K) was obtained by integrating the experimental data of the heat capacity divided by the thermodynamic temperature from 2 K up to ambient temperature as Sm(298.15) = 209.47 J mol −1 K −1 . This experimental value can be decomposed into a lattice vibrations contribution, Slat(298.15) = 206.9 J mol −1 K −1 , and an excess entropy due to magnetic ordering disruption Slat(298.15) = 2.8 J mol −1 K −1 , which is about two times lower than the theoretical value R ln2 corresponding to spin ½ of Cu(+II) and also lower than the experimental value reported by Knafo et al. [43] who, however, derived the phonon contribution by scaling the Cp data of YBa2Cu3O7.  Above room temperature, dependence of the heat capacity was also determined. The linear least-squares method was used for treatment of the heat capacity data from DSC and the enthalpy increment data from drop calorimetry. The temperature dependence of C pm was obtained in Equation (2):  Above room temperature, dependence of the heat capacity was also determined. The linear leastsquares method was used for treatment of the heat capacity data from DSC and the enthalpy increment data from drop calorimetry. The temperature dependence of Cpm was obtained in Equation  Above room temperature, dependence of the heat capacity was also determined. The linear leastsquares method was used for treatment of the heat capacity data from DSC and the enthalpy increment data from drop calorimetry. The temperature dependence of Cpm was obtained in Equation Let us note that the related temperature function of enthalpy, ∆H m (T) = H m (T) − H m (T 0 ), is given by the following Equation (3): The sum of squares was applied on both functions, Equations (2) and (3), and both sets of data were simultaneously minimized. Different weights w i were assigned to the individual points (calculated as w i = 1/δ i , where δ i is the absolute error bar). The obtained temperature dependence of heat capacity can be expressed as (valid between 298 and 1400 K) Equation (4): We compared obtained data with the curve calculated using the Neumann-Kopp rule (NKR), where the heat capacity of Y 2 BaCuO 5 was evaluated by the following Equation (5): As can be seen from Figure 6, our data are in good agreement with the calculated NKR curve, suggesting that the lattice dynamics-including the anharmonic effects-are comparable in Y 2 BaCuO 5 and the constituent binary oxides.
We took advantage of this similarity in chemical bonding and used the binary oxides as a reference for evaluating the enthalpy of formation from GGA+U ab-initio calculations. Hence, the ground state enthalpy of formation from oxides, ∆ ox H = −32.2 kJ mol −1 , is the primary value derived from DFT while the enthalpy of formation from elements, ∆ f H = −2640.9 kJ mol −1 , was obtained from ∆ ox H and the tabulated ∆ f H values of the binary oxides. The enthalpy of formation is underestimated compared to dissolution calorimetry results ∆ f H = −2656 kJ mol −1 [44] and −2660 kJ mol −1 [45]. A part of this discrepancy can by accounted for by the negative integral of ∆ ox C p used to recalculate the ab-initio value from 0 to 298 K, for which the experimental data are reported.
Let us note that the magnetic structure has a substantial effect on the resulting value of ∆ ox H. Here, we present the results for A-type spin arrangement (two spins + 1 2 and two spins − 1 2 within the chemical unit cell) and no magnetic superstructure. The resulting density of states for both spin channels is shown in Figure 8. The spin polarization on copper sites clearly visible on Cu(1)-3d projection in Figure 8 amounts to 0.59 Bohr magnetons, which is in nice agreement with the neutron diffraction data (0.55 µB) [37]. If we considered the F type arrangement (all four spins aligned parallel) in the chemical unit cell and a magnetic superstructure with the wave vector k = [0, 1 2 , 1 2 ], which has been reported as an alternative ordering, the calculation converged to a non-spin polarized state and ∆ ox H = −0.5 kJ mol −1 . Interestingly, a similar result (zero spin and low stabilization) was obtained for A-type ordering and k = [0, 1 2 , 1 2 ] superstructure. Hence, the magnetic superstructure reported in [37] was not confirmed.

Conclusions
In our contribution, we prepared a polycrystalline cuprate Y2BaCuO5 by conventional solid-state reaction. The sample was thoroughly analyzed in order to ensure its purity. Morphology and thermal properties were further studied in detail. Using X-ray diffraction, we confirmed the presence of pure Y2BaCuO5 without any detectable impurities. Very high thermal stability (up to ~1550 K) of Y2BaCuO5 (compared to phase YBa2Cu3O7) is important for its inert behavior during the manufacturing of YBCO

Conclusions
In our contribution, we prepared a polycrystalline cuprate Y 2 BaCuO 5 by conventional solid-state reaction. The sample was thoroughly analyzed in order to ensure its purity. Morphology and thermal properties were further studied in detail. Using X-ray diffraction, we confirmed the presence of pure Y 2 BaCuO 5 without any detectable impurities. Very high thermal stability (up to~1550 K) of Y 2 BaCuO 5 (compared to phase YBa 2 Cu 3 O 7 ) is important for its inert behavior during the manufacturing of YBCO bulk ceramics. Moreover, the obtained calorimetry data are important for thermodynamic modeling of high temperature material processing, which can underpin future development of high-temperature superconductors and their possible applications in superconducting bearings, transport, or superconducting transmission lines.