Analysis of Phase Diagram of CaO-CoO_x-ErO_y and Crystal Structure of Perovskite (Ca_3−xEr_x)Co₂O_6−z Solid Solution

Abstract

In this work, a series of compounds in the CaO-CoO_x-ErO_y ternary oxide system were synthesized in air at 885 °C, using a high temperature solid-phase synthesis method. The phase boundary of each solid solution region in the CaO-CoO_x-ErO_y system was determined by X-ray powder diffraction techniques. The phase diagram of the CaO-CoO_x-ErO_y system at 885 °C includes three series of ternary oxide solid solutions: (Ca_3−xEr_x)Co₄O_9−z (0 ≤ x ≤ 0.9), (Ca_3−xEr_x)Co₂O_6−z (0 ≤ x ≤ 1.25), and (Er_1−xCa_x)CoO_3−z (0 ≤ x ≤ 0.33). Four three-phase regions and five solid solution tie-line regions were obtained. The structure of the perovskite solid solution (Ca_3−xEr_x)Co₂O_6−z has been analyzed by Rietveld refinements. With the increase of Er content, the cell parameters of (Ca_3−xEr_x)Co₂O_6−z exhibit a decreasing trend in a and b directions and an increasing trend in c direction. A brief comparison of the phase diagrams of the CaO-CoO_x-RO_y (R = La, Dy, and Er) systems in air at 885 °C is provided.

1. Introduction

The increasing demand for energy in everyday life, coupled with concerns about climate change, has prompted the scientific community to explore materials for more efficient energy conversion and storage. Perovskite [1,2,3] is a type of outstanding materials, including metal halides and perovskite oxides, which have a good development prospect as energy materials and can effectively replace traditional materials. In 1839, Russian geologist Lev Perovski discovered the structure of ABO₃. Since that the perovskite structure was generated by the discovery of the special structure of CaTiO₃ in calcium titanate during the study of perovskite, the structure of ABO₃ is called the perovskite structure. The perovskite structure is also called the 113 structure, because the proportion of the elements in ABO₃ is A:B:O = 1:1:3. The spatial group of the standard perovskite structure is Pm3m [4]. In ABO₃, A is an alkaline earth metal or a rare earth ion with a relatively large ionic radius, B is a transition metal ion with a relatively small ionic radius, and O is the oxygen ion [4,5].

Examples of high quality thermoelectric materials are Bi₂Te₃-based alloys [6], MgAgSb alloys [7], Pb(Te,Se,S) [8], and SiGe [9], among others. In recent years, some perovskite-type thermoelectric materials have made breakthrough progress, such as ABX₃ (A = Cs⁺, CH₃NH³⁺, CH(NH₂)²⁺; B = Pb²⁺, Sn²⁺; X = Cl⁻, Br⁻, I⁻), but only a few of them have been found to have practical industrial applications due to their low efficiency [10]. To measure the performance of thermoelectric materials, the dimensionless figure of merit (zT), given by zT = S²σT/κ [11,12,13], where S is the Seebeck coefficient or thermopower, σ is the electrical conductivity (σ = 1/ρ, ρ is the electrical resistivity), κ is the thermal conductivity, and T is the absolute temperature, has been used. However, due to the correlation of S, ρ, and κ, the optimization of the zT value is a difficult task. High quality thermoelectric materials need to meet the following requirements: high electrical conductivity, high Seebeck coefficient, and low thermal conductivity.

Thermoelectric oxides have been considered possible candidates for waste heat conversion applications because of their stability at high temperatures [14]. Low-dimensional oxide thermoelectric materials, including chain oxides Ca₃Co₂O₆ [15,16,17], layered oxides Ca₃Co₄O₉ [18,19,20,21,22,23,24,25,26], NaCo₂O₄ [27], Bi₂Sr₂Co₂O_x [28], and natural superlattices (Bi,A)OCuSe (A = Pb, Ba, Sr, Ca) [29], are considered candidates for waste heat conversion applications. Among them, the 2D mismatched layered oxide Ca₃Co₄O₉ exhibited the highest zT value. Much work has been done to improve the thermoelectric properties of Ca₃Co₄O₉ by doping at Ca or Co sites [30,31,32,33].

Phase equilibrium diagrams, which provide blue prints for processing and understanding phase relationships, are important for designing and understanding materials properties. The phase diagrams of the CaO-CoO_x-RO_y (R = lanthanide) systems are of interest to the thermoelectric research community. The phase diagrams of CaO-CoO_x-RO_y systems, with R = La [34], Nd [35], Sm [36], Eu [37], Gd [38], Dy [39], and Ho [40], at 885 °C, have been reported. The CaO-CoO_x-RO_y phase diagram of the lanthanide Er has not been drawn. In the CaO-CoO_x-RO_y system, there are Ca₃Co₄O₉, Ca₃Co₂O₆, and RCoO₃ phases, all of which have perovskite or its derivative structure and have excellent thermoelectric properties [34,35,36,37,38,39,40].

In this study, we have established the phase compatibility relationships, crystal chemistry, and crystallography of selected compounds in the CaO-CoO_x-RO_y systems at 885 °C (R = Er in this report), particularly to obtain subsolidus phase relationships in the vicinity of the Ca₃Co₄O₉ and Ca₃Co₂O₆ compounds. The possible formation of (Ca_3−xEr_x)Co₄O_9−z, (Er_1−xCa_x)CoO_3−z, and (Ca_3−xEr_x)Co₂O_6−z solid solutions and the effect of doping on the crystal structure are also discussed. In addition, the phase formation and phase relationships between CaO-CoO_x-LaO_y [34], CaO-CoO_x-DyO_y [39], and the CaO-CoO_x-ErO_y systems are compared. These reference patterns will be included in the ICDD Powder Diffraction File^TM (PDF^® [41]).

2. Materials and Methods

2.1. Sample Preparation

The commonly used solid phase synthesis methods with different powders are spark plasma sintering (SPS), hot isostatic pressing (HIP), cold isostatic pressing (CIP), and high temperature solid sintering [42,43,44]. The synthesis method chosen in this experiment is high temperature solid phase sintering. The samples were prepared by high temperature solid-state synthesis technique.

Table 1. Fifty-two samples (mole fraction, %) prepared for the phase equilibria study of the CaO-CoO_x-ErO_y system at 885 °C in air. In this table, Ca = CaO; Co = ⅓Co₃O₄; Er = ½Er₂O₃. The selection of sample proportions is based on the CaO-CoO_x-RO_y phase diagram of other lanthanide elements.

Sample #	Ca	Co	Er
#01	0.05	0	0.95
#02	0.08	0	0.92
#03	0.1	0	0.9
#04	0.95	0	0.05
#05	0.98	0	0.02
#06	0.05	0.2	0.75
#07	0.2	0.2	0.6
#08	0.55	0.24	0.21
#09	0.65	0.25	0.1
#10	0	0.3333	0.6667
#11	0.3	0.3333	0.3667
#12	0.31	0.3333	0.3567
#13	0.32	0.3333	0.3467
#14	0.3333	0.3333	0.3334
#15	0.35	0.3333	0.3167
#16	0.39	0.3333	0.2767
#17	0.4	0.3333	0.2667
#18	0.42	0.3333	0.2467
#19	0.43	0.3333	0.2367
#20	0.45	0.3333	0.2167
#21	0.5	0.3333	0.1667
#22	0.55	0.3333	0.1167
#23	0.4	0.4	0.2
#24	0.5	0.4	0.1
#25	0.55	0.4	0.05
#26	0.6	0.4	0
#27	0.2	0.425	0.375
#28	0	0.5	0.5
#29	0.1	0.5	0.4
#30	0.15	0.5	0.35
#31	0.16	0.5	0.34
#32	0.17	0.5	0.33
#33	0.18	0.5	0.32
#34	0.19	0.5	0.31
#35	0.2	0.5	0.3
#36	0.21	0.5	0.29
#37	0.22	0.5	0.28
#38	0.25	0.5	0.25
#39	0.28	0.5	0.22
#40	0.3	0.5	0.2
#41	0.25	0.5714	0.1786
#42	0.26	0.5714	0.1686
#43	0.27	0.5714	0.1586
#44	0.28	0.5714	0.1486
#45	0.29	0.5714	0.1386
#46	0.295	0.5714	0.1336
#47	0.3	0.5714	0.1286
#48	0.3572	0.5714	0.0714
#49	0.4143	0.5714	0.0143
#50	0.4286	0.5714	0
#51	0.02	0.6	0.38
#52	0.2	0.65	0.15

reports the 52 samples prepared by stoichiometric mixtures of CaCO₃, Co₃O₄, and Er₂O₃ (all with purity greater than 99%). The samples were mixed and sintered in a muffle furnace at 850 °C in air for 6 h, at the rate of 10 °C/min, with the purpose of calcinating CaCO₃ at high temperature and transforming CaCO₃ into CaO. Samples were ground until grainless. Ethanol was added during grinding, so that the sample was evenly mixed. A diffusion effect during the sintering process was also applied, to ensure that the sample was evenly mixed. Samples were then sintered at 885 °C for 6–9 days, with grinding, and the heat treatment process repeated until the X-ray powder diffraction (XRPD) pattern showed no further change.

2.2. X-ray Powder Diffraction

XRPD analysis of the samples was carried out at room temperature using a Rigaku SmartLab (Rigaku Corporation, Tokyo, Japan) 9 kw diffractometer with Cu K_α radiation (40 kV, 200 mA) and a graphite monochromator, at the China University of Geosciences Beijing. A step scan mode was employed, with a step width of 2θ = 0.02° and a sampling time of 1 s in the range of 15 ≤ 2θ ≤ 70°. The compositions in the CaO-CoO_x-ErO_y system were analyzed by using the Powder Diffraction File^TM (PDF^®) [31].

2.3. Rietveld Refinements

The structural changes of the samples in the solid solution region (Ca_3−xEr_x)Co₂O_6−z were analyzed by Rietveld refinements [45,46]. XRPD analysis of these perovskite crystals has been carried out at room temperature using a Rigaku SmartLab diffractometer with Cu K_α radiation (40 kV, 200 mA) and a graphite monochromator, as mentioned above. A step scan mode was employed, with a step width of 2θ = 0.02° and a sampling time of 1 s, in the range of 15 ≤ 2θ ≤ 120°.

3. Results

Figure 1 shows the phase diagram of the CaO-CoO_x-ErO_y system that was determined at 885 °C. The phase relations between the solid solution and other phases are represented by tie-lines. The phase diagram of CaO-CoO_x-ErO_y ternary system at 885 °C has five two-phase zones, four three-phase zones, eight two-phase contact lines, and three solid solution zones. The phase diagram of CaO-CoO_x-ErO_y ternary system at 885 °C shows three solid solution distinctions: (Ca_3−xEr_x)Co₄O_9−z (0 ≤ x ≤ 0.9), (Ca_3−xEr_x)Co₂O_6−z (0 ≤ x ≤ 1.25), and (Er_1−xCa_x)CoO_3−z (0 ≤ x ≤ 0.33). The crystal chemistry and crystallography of the phases in binary and ternary oxide systems are discussed below.

3.1. Binary Oxide Systems

3.1.1. CaO-CoO_x

Binary CaO-CoO_x oxide systems have been studied extensively. In this system, two single-phase structures have been identified: Ca₃Co₂O₆ (Co:Ca = 40:60) and Ca₃Co₄O₉ (Co:Ca = 57.14:42.86) [18,30]. Both Ca₃Co₂O₆ and Ca₃Co₄O₉ have perovskite-derived structures. It was also confirmed that there are only two single-phase Ca₃Co₂O₆ and Ca₃Co₄O₉ in the binary system under the current high temperature solid-phase synthesis conditions.

Ca₃Co₄O₉ is a mismatched layered oxide with two monocline subsystems, with the same a, c, but different b values. There are two different Co-O layers stacked regularly along the direction of the c-axis, one of which is the CoO₂ layer. The CoO₂ layer has a CdI₂-type structure and can be regarded as a Co ion in the center, with six O ions around the central Co ion; the center of the octahedron is the Co ion, the apex of the octahedron is the O ion. Adjacent octahedrons are connected in the form of common edges. The other layer is Ca₂CoO₃, formed by Ca-Co-O, which has a halite structure. The CoO₂ layer can provide charge carriers (holes) needed for conducting electricity, and the Co ions in the CoO₂ layer include Co³⁺ and Co⁴⁺, located at the adjacent O²⁻ midpoint. There is strong interaction between adjacent positive ions. The change of valence of the Co ion makes it easy to shift from the center of the octahedron, resulting in a difference in the length of the Co-O bond. The bonding mode between ions in the Ca₂CoO₃ layer is ionic bond, and there is no change of valence, so the Ca₂CoO₃ layer does not conduct electricity, and the presence of Ca₂CoO₃ reduces the thermal conductivity of the material. Higher conductivity σ and lower thermal conductivity κ will make the material have a higher thermoelectric value. Therefore, the phase exhibits strong anisotropic thermoelectric properties in the ab plane [39].

Ca₃Co₂O₆ (R-3c, a = 9.0793 (7) Å, c = 10.381 (1) Å) is a member of the n = 1 of the perovskite-derived series A_n+2B_nB′O_3n+3, where the A positions are alkaline earth metals, such as Ca, Sr, and Ba, and the B and B′ positions are usually transition metal elements. In Ca₃Co₂O₆, the A site is the Ca ion, the B site is the Co ion in the center of the octahedron, and the B′ site is the Co ion in the center of the distorted trigonal prism [40]. Figure 2 shows the structure of Ca₃Co₂O₆. Ca₃Co₂O₆ has a one-dimensional Co-O chain structure. This unique structure gives Ca₃Co₂O₆ excellent thermoelectric properties, magnetic properties, and chemical stability. Ca₃Co₂O₆ is suitable for use in moderate and relatively harsh environmental conditions. The Seebeck coefficient of Ca₃Co₂O₆ increases with the increase of temperature, the conductivity of Ca₃Co₂O₆ is semiconductor, and the thermal conductivity of Ca₃Co₂O₆ is relatively low. Therefore, Ca₃Co₂O₆ is a highly efficient thermoelectric material with potential to be developed.

3.1.2. CaO-ErO_y

Five samples were prepared in the CaO-ErO_y binary system to determine the phases form. There is no single phase in the CaO-ErO_y binary system, indicating that there is no solid solution near CaO and Er₂O₃, that is, there is no solid solution zone in the CaO-ErO_y binary system.

3.1.3. CoO_x-ErO_y

At 885 °C, the only phase found in the ErO_x-CoO_y system is the ErCoO₃ phase, which has the Pnma space group perovskite structure. In the CoO_x-LaO_y binary system of the CaO-CoO_x-LaO_y [34] phase diagram, La₂CoO₄ phase was determined, but, in this study, the Er₂CoO₄ phase could not be obtained under the present conditions.

3.2. Ternary Oxide Systems

Three series of ternary solid solutions were found at 885 °C, which were (Ca_3−xEr_x)Co₂O_6−z (0 ≤ x ≤ 1.25), (Er_1−xCa_x)CoO_3−z (0 ≤ x ≤ 0.33), and (Ca_3−xEr_x)Co₄O_9−z (0 ≤ x ≤ 0.9). We found that the solid solution region (Ca_3−xEr_x)Co₄O_9−z near Ca₃Co₄O₉ and the solid solution region (Er_1−xCa_x)CoO_3−z near ErCoO₃ are close to the previously reported range in the other CaO-RO_x-CoO_y systems. The solution region (Ca_3−xEr_x)Co₂O_6−z was found near Ca₃Co₂O₆, while the solid solution of other lanthanides did not occur at (Ca,R)₃Co₂O₆. Different from what previously reported for the CaO-CoO_x-RO_y (R = Eu, Gd, Sm) systems, the solid solution region of (Er_2−xCa_x)CoO_4−z did not exist in the CaO-CoO_x-ErO_y system at 885 °C. The phase relationship of each solid solution zone will be discussed in detail below.

3.2.1. (Ca_3−xEr_x)Co₂O_6−z

Ca₃Co₂O₆ was found in the CaO-CoO_x boundary binary system, the corresponding Co content is 40 at.%. Ca₃Co₂O₆ showed the perovskite-derived structure. Ca₃Co₂O₆ is a good thermoelectric material and has a splendid prospect in the field of energy. The solid solution region (Ca_3−xEr_x)Co₂O_6−z forms with the addition of the doping element Er. Moreover, the solid solution formation appears for (Ca_3−xEr_x)Co₂O_6−z, with the value of x ranging from 0 to 1.25. The XRPD patterns of the sample with 40 at.% Co content, as well as results of MDI Jade, show that the peak shifts systematically with the Er content. As shown in Figure 3, the peaks shift according to the amount of Er content in (Ca_3−xEr_x)Co₂O_6−z, but the directions of the peak shifts are not the same. In Figure 3, it is shown that the crystal plane (113) moves towards a low angle direction, while the crystal plane (300) moves toward a high angle direction, probably due to anisotropic expansion of the unit cell.

At 885 °C, a solid solution was found near Ca₃Co₂O₆. The samples of (Ca_3−xEr_x)Co₂O_6−z (x = 0, 0.25, 0.5, 1) were slowly scanned with XRPD, followed by Rietveld finishing. The diffraction patterns were analyzed by the Rietveld refinement technique using the FullProf program. Figure 4 shows the refinement results of (Ca₂Er₁)Co₂O_6−z and Ca₃Co₂O₆, respectively, with χ² of 2.47 and 2.22.

Table 2. Refinement parameters of (Ca_3−xEr_x)Co₂O_6−z (x = 0, 0.25, 0.5, 1). The bracketed values represent standard deviations.

x	a&b (Å)	c (Å)	Rwp (%)	χ2
0	9.07628 (8)	10.38005 (12)	11.0	2.22
0.25	9.05344 (21)	10.44059 (28)	10.8	3.53
0.5	9.02907 (22)	10.50383 (28)	9.57	3.43
1	8.98770 (12)	10.58704 (17)	6.79	2.47

and

Table 3. Atomic coordinates and displacement parameters for (Ca_3−xEr_x)Co₂O_6−z. The bracketed values represent standard deviation. The numerical error of B_ios obtained by XRPD is relatively large, so the neutron diffraction B_ios [47] is used in the finishing.

	x	y	z	Biso [47]
Ca3Co2O6
Ca	0.36986 (2)	0	0.25	0.39
Co1	0	0	0	0.37
Co2	0	0	0.25	0.48
O	0.17804 (6)	0.02561 (8)	0.11402 (5)	0.53
(Ca2.75Er0.25)Co2O6−z
Ca/Er	0.36834 (3)	0	0.25	0.39
Co1	0	0	0	0.37
Co2	0	0	0.25	0.48
O	0.17787 (11)	0.02463 (13)	0.11268 (7)	0.53
(Ca2.5Er0.5)Co2O6−z
Ca/Er	0.36773 (3)	0	0.25	0.39
Co1	0	0	0	0.37
Co2	0	0	0.25	0.48
O	0.17959 (12)	0.02464 (14)	0.11238 (8)	0.53
(Ca2Er1)Co2O6−z
Ca/Er	0.36688 (2)	0	0.25	0.39
Co1	0	0	0	0.37
Co2	0	0	0.25	0.48
O	0.18265 (12)	0.02475 (13)	0.11010 (7)	0.53

provide the refinement parameters and the atomic coordinates of (Ca_3−xEr_x)Co₂O_6−z (x = 0, 0.25, 0.5, 1), respectively. Figure 5 shows the changes of the cell parameters of (Ca_3−xEr_x)Co₂O_6−z (x = 0, 0.25, 0.5, 1). With the increase of x, a and b become smaller, while c becomes larger, confirming the previous conjecture.

The Co-O chain in the Ca₃Co₂O₆ crystal structure is part of a polyhedron chain parallel to the c-axis. Figure 6 shows the projection of the regular octahedrons and distorted trigonal prisms of the Co-O chain along the b-axis. Various planes can be constructed using neighboring O ions in the Co-O chain; among these planes, the one perpendicular to the c-axis was found to move most significantly with the doping of Er.

Table 4. Structural parameters of (Ca_3−xEr_x)Co₂O_6−z. In this table, h1 and h2 represent the distance between the planes of the oxygen ion perpendicular to the c-axis (Figure 6). Columns Occ_Ca and Occ_Er represent the occupancy of Ca and Er ions, which are in the position of 18e. θ1 and θ2 are the angles in the projection of Figure 7, with the bracketed values representing the standard deviation.

x	h1 (Å)	h2 (Å)	h1 + h2 (Å)	OccCa	OccEr	θ1 (°)	θ2 (°)
0	2.367	2.823	5.19	1	0	60.000 (44)	15.290 (39)
0.25	2.3529	2.8674	5.2203	0.916	0.076	60.000 (53)	14.683 (52)
0.5	2.3608	2.8911	5.2519	0.834	0.16	60.000 (51)	14.540 (52)
1	2.3312	2.9623	5.2935	0.666	0.298	60.000 (45)	14.349 (38)

reports the structural parameters of (Ca_3−xEr_x)Co₂O_6−z. With the increase of Er content, the Ca₃Co₂O₆ structure is lengthened in the c-axis direction, mainly due to the lengthening of h2 (shown in Figure 6); alternatively, the distorted trigonal prism in the Co-O chain is elongated.

The Ca ion is replaced by an Er ion in (Ca_3−xEr_x)Co₂O_6−z crystal structure. Since the Er ion is positive trivalent and the Ca ion is positive bivalent, Er³⁺ entering (Ca_3−xEr_x)Co₂O_6−z structure would be lower than Ca²⁺, causing site vacancy. In Table 4, Occ_Ca and Occ_Er represent the occupancy of Ca and Er sites, which are in the position of 18e. Moreover, the radius of Er³⁺ is smaller than that of Ca²⁺ [48], so that the entry of the Er ion is expected to lead the shortening of the crystal structure of (Ca_3−xEr_x)Co₂O_6−z in the directions of a&b.

In Figure 3, the crystal plane (300) can be used to represent the a&b directions, and the crystal plane (113) can approximately represent the c direction. With the increase of x, the crystal plane (300) moves towards the higher angle direction, which means the crystal structure becomes shorter in the a&b directions, and the crystal plane (113) shifts towards the lower angle direction, which means the crystal structure becomes longer in the c direction.

Figure 7 shows the c-axis projection of the regular octahedron and the distorted trigonal prism in the Co-O chain, and Table 4 shows the angle of θ in Figure 7. The angle θ1 of the regular octahedron is 60°, while the angle θ2 of the distorted trigonal prism is much less than 60°. With the increase of x, angle θ2 tends to become even smaller. This is the reason why the distorted trigonal prism becomes elongated in the direction of the c-axis.

In conclusion, with the increase of the x value in (Ca_3−xEr_x)Co₂O_6−z, the diffraction peak migration direction of Ca₃Co₂O₆ in the XRPD pattern is inconsistent. The structural analysis of the (Ca_3−xEr_x)Co₂O_6−z series samples shows that with the increase of the x value, Er ions in the structure of (Ca_3−xEr_x)Co₂O_6−z increase, and the radius of the Er ion is smaller than that of the Ca ion [48], because the Er ion is +3 valence and the Ca ion is +2 valence. The valence equilibrium makes the number of incoming Er ions lower than the number of replaced Ca ions, so the structure of (Ca_3−xEr_x)Co₂O_6−z is shortened in the a&b directions. As the x value increases, the Co-O chain becomes longer, therefore, the structure of (Ca_3−xEr_x)Co₂O_6−z becomes longer in the c direction.

3.2.2. (Er_1−xCa_x)CoO_3−z

ErCoO₃ was found in the CoO_x-ErO_y boundary binary system. ErCoO₃ has a perovskite structure, it is a perovskite-type oxide, and it has thermoelectric properties. The solid solution region (Er_1−xCa_x)CoO_3−z forms with the addition of the doping element Ca. Thirteen samples were selected near ErCoO₃ to explore the boundary of the solid solution region (Er_1−xCa_x)CoO_3−z, and the range of x in the solution region (Er_1−xCa_x)CoO_3−z is from 0 to 0.33.

3.2.3. (Ca_3−xEr_x)Co₄O_9−z

Ca₃Co₄O₉, which is a mismatched layered oxide, was found in the CaO-CoO_x boundary binary system. Ca₃Co₄O₉ has the perovskite-derived structure. Ca₃Co₄O₉ is a good thermoelectric material and has a splendid prospect in the field of energy. The solid solution region (Ca_3−xEr_x)Co₄O_9−z forms with the addition of the doping element Er. Ten samples were selected near Ca₃Co₄O₉ to explore the boundary of the solid solution region (Ca_3−xEr_x)Co₄O_9−z; with the dopant Er, the content of x in the solid solution (Ca_3−xEr_x)Co₄O_9−z was found to be from 0 to 0.9.

The conductivity of (Ca_3−xEr_x)Co₄O_9−z was measured. Figure 8 shows the conductivity of (Ca_3−xEr_x)Co₄O_9−z (x = 0, 0.1, 0.5) from 100 K to 300 K. As can be seen from the figure, the conductivity of (Ca_3−xEr_x)Co₄O_9−z decreases with the increase of x. The electrical conductivity of Ca₃Co₄O_9−z is higher than all the Er containing samples. The curves show that the conductivity of Ca₃Co₄O_9−z and (Ca_2.9Er_0.1)Co₄O_9−z samples decreases with the increase of the temperature, exhibiting metallic behavior from 100 K to room temperature. On the contrary, the conductivity of (Ca_2.5Er_0.5)Co₄O_9−z increases with the increase of the temperature, exhibiting semiconducting behavior from 100 K to room temperature. The ${\rho }_{ab}{}^{(300\mathrm{K})}$ value measured for Ca₃Co₄O_9−z is found to be about 6 $\mathrm{m}\mathsf{\Omega }\mathrm{c}\mathrm{m}$, which is lower than that previously reported [18]. The crystal structure of Ca₃Co₄O₉ is composed of alternating layers of Ca₂CoO₃ and CoO₂ subsystems, stacked along the c-axis. The Ca₂CoO₃ subsystem is insulating in character, acts as a charge reservoir, and introduces hole carriers into CoO₂ planes, which in turn act as conduction sheets [18]. Since that the electrical conductivity is related to the carrier concentration (n) and the carrier mobility (u) by the relation $\sigma =neu$, our results imply that Er doping Ca₃Co₄O_9−z increases the carrier concentration, with Er that is trivalent and Ca that is divalent. However, Er³⁺ replacing Ca²⁺ will introduce vacancy and distortion of the crystal structure, decreasing the mobility of the carriers.

4. Discussion

It appears that the ionic size of the alkaline-earth and lanthanide ions governs the trend of phase formation, the extent of solid solutions formation of (R_1−xCa_x)CoO_3−z, (R_1−xCa_x)₂O_3−z, (Ca_3−xR_x)Co₄O_9−z, and (Ca_3−xR_x)Co₂O₆, as well as the tie-line relationships in the CaO-CoO_x-RO_y systems. Due to the different phase formation and different range of solid solutions in the La, Dy, and the Er systems, the tie-line relationships are substantially different, leading to different appearances of the diagrams.

Since the doped element R in the CaO-CoO_x-RO_y series are lanthanide elements, these diagrams are expected to be related. Therefore, the next step of our present study is to compare the ternary phase diagrams of R = La [34], Dy [39], and Er, at 885 °C. The phase diagrams of La and Dy are reported in refs. [34,39].

La is the first element in the lanthanide series, and the phase diagram of CaO-CoO_x-LaO_y is the first phase diagram drawn in the series, so the phase diagram of CaO-CoO_x-LaO_y at 885 °C provides guidance for the phase diagram of the whole series. The phase diagrams of CaO-CoO_x-LaO_y and CaO-CoO_x-ErO_y were compared. The solid solution regions of (Ca_3−xR_x)Co₄O_9−z and (R_1−xCa_x)CoO_3−z existed in both systems. Although both systems contain perovskite RCoO₃ phase, LaCoO₃ and ErCoO₃ have different structures. The LaCoO₃ phase is rhombohedral and with a space group of R-3c [34], while the ErCoO₃ phase is orthorhombic with space group Pnma. The difference in ionic radius (r_La3+ > r_Ca2+ > r_Er3+) [48] results in the structural differences between LaCoO₃ and ErCoO₃. The solid solution region (La_2−xCa_x)O_3−z exists in the R = La system, which is different from the R = Er system. In the R = Er system, there is a solid solution region (Ca_3−xEr_x)Co₂O_6−z, which is absent in the R = La system.

In the phase diagram of the CaO-CoO_x-DyO_y and CaO-CoO_x-ErO_y systems, only one solid solution region is the same, namely (Ca_3−xR_x)Co₄O_9−z, but the range of the two solid solution regions is different when R = Dy, 0 ≤ x ≤ 0.6, and R = Er, 0 ≤ x ≤ 0.9. (Ca_3−xEr_x)Co₂O_6−z is a new solid solution region, and other CaO-CoO_x-RO_y (R is a lanthanide element) phase diagrams do not show solid solution phenomena at Ca₃Co₂O₆ at 885 °C.

Because of the different phase formation of these three systems, the tie-line relationships are also very different. In the La system, there are four three-phase regions and four two-phase connecting tie-line bundles [34]. In the Dy system, there are four three-phase regions and three two-phase connecting the tie-line bundles [39]. In the Er system, however, due to the addition of the (Ca_3−xEr_x)Co₂O_6−z phase, there are four three-phase regions and five solid solution tie-line regions.

5. Conclusions

The phase diagram of the CaO-CoO_x-ErO_y system at 885 °C has been drawn. This phase diagram shows the phase relationships between the phases in the CaO-CoO_x-ErO_y ternary system, which is crucial for knowing and understanding the properties and properties of the materials in the system. There are four three-phase zones and five solid solution contact zones in the system. Three series of solid solutions have been found in the CaO-CoO_x-ErO_y system at 885 °C, which are respectively (Er_1−xCa_x)CoO_3−z (0 ≤ x ≤ 0.33), with simple perovskite structure, and (Ca_3−xEr_x)Co₄O_9−z (0 ≤ x ≤ 0.9) and (Ca_3−xEr_x)Co₂O_6−z (0 ≤ x ≤ 1.25), with perovskite-derived structures. The solid solution phenomenon will lead to changes in the structure of materials, which will lead to changes in the properties of materials. The solid solution of perovskite and its derived structure in the system will affect the properties of materials. Studying the structure of materials will help to understand the changes in material properties and help to explore the acquisition of materials with more efficient energy conversion and storage. The solid solution is formed near Ca₃Co₂O₆. With the increase of the x value in (Ca_3−xEr_x)Co₂O_6−z, the diffraction peak migration direction of Ca₃Co₂O₆ in the XRPD pattern is inconsistent. The structural analysis of (Ca_3−xEr_x)Co₂O_6−z series samples concludes that this difference is the anisotropic expansion of the unit cell.