Chemical bond and thermoelectric properties of Ca₃Co₂O₆ and Ca₃Co₄O₉

Min Xinmin, Xing Xueling, Hong Hanlie
(State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of  Technology, Wuhan 430070)

Received Nov. 22, 2003; Supported by the National Natural Science Foundation of China (20271040).

Abstract The relation between electronic structure, chemical bond and thermoelectric property of Ca₃Co₂O₆ and Ca₃Co₄O₉ is studied by using density function and discrete variation method(DFT-DVM). The gaps between the highest valence band (HVB) and the lowest conduction band(LCB) of Ca₃Co₂O₆ and Ca₃Co₄O₉ both show the semiconductor property, and the gap of Ca₃Co₄O₉ is less than that of Ca₃Co₂O₆. Co 3d and O 2p mainly contribute to HVB and LCB near Fermi level, but there is obvious difference between Ca₃Co₂O₆ and Ca₃Co₄O₉. The Co-O covalent and ionic bonds of Ca₃Co₄O₉ are both stronger than those of Ca₃Co₂O₆. Ca plays the role of connections between the chains of  ...... -Co(1)O₃-Co(2)O₃- ...... in Ca₃Co₂O₆, and between CoO₂ and Ca₂CoO₃ layers in Ca₃Co₄O₉. The component of Ca also can decrease ionic and covalent bond strength and prove the thermoelectric property.
Keywords cobaltite, electronic structure, chemical bond, thermoelectric property

1 INTRODUCTION
In general, the thermoelectric performance of oxide compounds is believed to be much lower than that of the semiconductor alloys because of their high ionic character that generally causes strong localization of electrons and thus lead to very low carrier mobility. However, it has recently reported that Na_xCo₂O₄ has a much large thermoelectric power^[1], which is almost comparable to that of the conventional thermoelectric materials. The conventional thermoelectric materials, such as Bi₂Te₃, PbTe and SiGe, have some inevitable shortages. For example, they are not stable in air at high temperature, toxic to environment and difficult to manufacture. Oxides can overcome the shortages as thermoelectric materials, so they have attracted much attention. Ca₃Co₂O₆ and Ca₃Co₄O₉ are the stable phases in the Ca-Co-O system. However, understanding of electronic structure of these technologically important cobaltite oxides has quite limited. Most recently, Asahi et al have calculated the band-structure of one of the cobaltite oxides, i.e., (Ca₂CoO₃)₄(CoO₂)₆^[2], but the other cobaltite oxides have not been reported. In this paper, the electronic structures of Ca₃Co₂O₆ and Ca₃Co₄O₉ are calculated using density function and discrete variation method(DFT-DVM). The relations between electronic structure, chemical bond and thermoelectric property are discussed.

2 CALCULATION DETAILS AND MODEL
DFT-DVM method^[3] is used to resolve the Kohn-Sham equation. A number of discrete sampling points in a three-dimensional grid are chosen. The parameter in the error function is varied to obtain all the minima for the points. Using the multi-dimensional numeral integer method, self-consistent process is carried out to obtain energy eigenvalue, wave function and others. DFT-DVM method can be used to calculate larger structure models of molecules, clusters and solids, so it has been widely used in chemistry, physics, material science an so on^[3,4].
    The crystal structure of Ca₃Co₂O₆ belongs to space group^[5]. Its crystal cell is shown in Fig.1. The cobalt atoms are divided into two types, Co(1) and Co(2). The framework of the cell is a cube(Fig.1 a). One Co(1) is in the center, and other eight Co(1)'s are at the corners. One Co(1) atom at the corner is computed as 1/8 based on the principle of corner-sharing in crystal theory. Therefore, there are two Co(1) atoms in the cell. A Co(1)-Co(2)-Co(1)-Co(2)-Co(1) chain is along the diagonal, so there are two Co(2) atoms in the cell. Co(1) in the center is coordinated by 6 O(1) atoms. The 6 O(1) atoms are divided into two classes, and they coordinate to two Co(2) atoms above and below the center Co(1) respectively. Therefore, the chain along the diagonal consist of alternating face-sharing [Co(1)O₆] octahedron and [Co(2)O₆] trigonal prisms and can be shown as -Co(1)O₃-Co(2)O₃- ... chain. Ca atoms are at the positions among the chains. There is a O(2) atom near to every Co(1) at the corner in the cell. 22 atoms, i.e. 4 Co, 6 Ca and 12 O, exit in the cell. To revolve the chain as the vertical axis, the hexagon projection of atoms in the cell is shown in Fig.1b. Atoms of Co(1)-Co(2)-Co(1)-Co(2)-Co(1) chain all are projected in the center. Other 6 Co(1) atoms are at the corner of the hexagon, but they are not in the same height. In reality, with the original point of Co(1) in the center, the 6 Co(1) atoms at the corner of the hexagon are with symmetry of D_3d point group. As the same, 6 Ca atoms, or 6 O(1) and 6 O(2), are also with symmetry of D_3d point group, respectively. The calculated model of Ca₃Co₂O₆ is expanded into 66 atoms, or [Ca₁₈Co₁₂O₃₆], which is three times as the cell. The 22 atoms discussed above are the insides of the model, and other 44 atoms are the outsides. These 66 atoms are divided into 26 classes with the symmetry operation of C₃ point group.

Fig.1 Crystal cell of Ca₃Co₂O₆. (a) The cube framework; (b) the projection of hexagon

    Ca₃Co₄O₉ is with symmetry of space group C_m^[6]. Ca₃Co₄O₉ has two layers structure, Ca₂CoO₃ in the center and CoO₂ at the top and below as shown in Fig.2. The cobalt atoms are also divided into two types, Co(1) in the CoO₂ layer and Co(2) in the Ca₂CoO₃ layer. The oxygen atoms are divided into two types and belong to the two layers respectively, too. The character structure of CoO₂ layer is edge-sharing [Co(1)O₆] octahedron. Ca₂CoO₃ layer is similar to structure of NaCl. There are normal a and c constants of Ca₃Co₄O₉. However, there is different cell constant along b axis (right and left direction in Fig.2), b₁(CoO₂)=0.28238nm and b₂(Ca₂CoO₃)=0.45582nm. CoO₂ or Ca₂CoO₃ layer is alone with space group C_m. In the symmetry meaning, Ca₃Co₄O₉ is much like a mixture compound. The calculated model consists of the atoms of the right plane in Fig.2 as the center part and the neighboring atoms. Therefore, the model is with 68 atoms, or [Ca₁₄Co₁₅O₃₉] and divided into 46 classes with symmetry operation of C_s point group.

Fig.2 Structure of Ca₃Co₄O₉

3 RESULTS AND DISCUSSION
The average values of the covalent bond orders between inside atoms are in Table 1. The covalent bond of Co(1)-O is stronger than that of Co(2)-O in both of Ca₃Co₂O₆ and Ca₃Co₄O₉, but the strength difference between Co(1)-O and Co(2)-O bonds in Ca₃Co₄O₉ is more obvious than that in Ca₃Co₂O₆. On the other hand, the covalent bond of Co-O in Ca₃Co₄O₉ is stronger than that in Ca₃Co₂O₆.
    The average values of net charge of the inside atoms are also in Table 1. The charge of Co(1) is higher than that of Co(2) in both of Ca₃Co₂O₆ and Ca₃Co₄O₉, but the charge difference between Co(1) and Co(2) atoms in Ca₃Co₄O₉ is also more obvious than that in Ca₃Co₂O₆. On the other hand, the average value of charge of Co(1) and Co(2) in Ca₃Co₄O₉ is slightly higher than that in Ca₃Co₂O₆. The charge of Ca in Ca₃Co₄O₉ is also higher than that in Ca₃Co₂O₆. There are more oxygen atoms with larger electronegtivity in Ca₃Co₄O₉ than in Ca₃Co₂O₆, which lead to the higher charge of metal atoms in Ca₃Co₄O₉. As there are less differences of the distance between atoms between Ca₃Co₄O₉ and Ca₃Co₂O₆, the Co-O ionic bonds of Ca₃Co₄O₉ are also stronger than those of Ca₃Co₂O₆.

Table 1 Calculated covalent bond orders and atomic net charges

    The bonding model and strength are further studied by the contour map of one electron wave function, or molecular orbital. The maps of the representative orbitals of Co(1) and Co(2) of Ca₃Co₂O₆ are shown in Fig.3 a and b respectively. Solid and dash lines express positive and negative values of the molecular wave functions attributed from the atoms, respectively. It has been pointed out that the original point of Co(1) is in the center, and its first-neighboring 6 atoms of O(1) are with symmetry of D_3d point group. Therefore, the section of the Fig.3 a can be chosen to pass through the O(1)-Co(1)-O(1) straight line in the center. On the other hand, with the original point of Co(2) in the center, the first-neighboring atoms are 3 O(1) and 3 O(2) and only with symmetry of D₃ point group. Therefore, O(1)-Co(2)-O(2) is not a straight line. The values of the out contour lines between Co and O are indicated, and the values of Fig.3 a are larger than that of b. Therefore, the strength of covalent bond of Co(1)-O is stronger than that of Co(2)-O in Ca₃Co₂O₆.
    The maps of the representative orbitals of Co(1) and Co(2) of Ca₃Co₄O₉ are shown in Fig.4 a and b respectively. Oxygen at below is in the section but that at the top is above the section, so the O-Co-O from top to below is not a real straight line. It is shown from comparing the values of the out contour lines between Co and O that the strength of covalent bond of Co(1)-O is stronger than that of Co(2)-O in Ca₃Co₄O₉. Comparing Fig.3 and 4, it is indicated that Co-O covalent bonds of Ca₃Co₄O₉ are stronger than those of Ca₃Co₂O₆, which is consistent with the above numeral results.

Fig.3 A pair of contour maps of the representative orbitals of Ca₃Co₂O₆


Fig.4 A pair of contour maps of the representative orbitals of Ca₃Co₄O₉

    The total density of state (DOS), Co(1) 3d, Co(2) 3d, O(1) 2p and O(2) 2p partial DOS of Ca₃Co₂O₆ are in Fig.5 a to e, respectively. The partial DOS is that of inside atoms (Co(1) is only one in the center). Fermi level is at the zero point in the cross axis. The maximum of total DOS is 100(%), and the contribution of partial DOS to the total DOS can be seen from the vertical axis. DOS of other valent orbital, such as Co 4s, Ca 4s or O 2s, is rather small in this energy field and not shown. In the total DOS, the gap between the highest valence band (HVB) and the lowest conduction band (LCB) shows the semiconductor characteristics. It is indicated from comparing the partial DOS that the contribution of Co(1) 3d to HVB is larger than that of Co(2) 3d, but the contribution of Co(1) 3d to LCB is less than that of Co(2) 3d. O 2p mainly contributes to HVB, and the peaks exist in the wider field. There is less difference between O(1) and O(2) 2p contribution to HVB, but the contribution of O(1) 2p to LCB is obviously nearer to Fermi level than that of O(2) 2p. The contributions of Co 3d to HVB and LCB nearer to Fermi level are larger than those of O 2p, which is in agreement with Asahi et al.'s conclusion in the calculation of (Ca₂CoO₃)₄(CoO₂)₆^[2]. The n-type transport is primarily through Co(2) 3d orbitals (contributing to LCB) and p-type transport through Co(1) 3d orbitals (contributing to HVB).
    The total, Co(1) 3d, Co(2) 3d, O(1) 2p and O(2) 2p partial DOS of Ca₃Co₄O₉ are also shown in Fig.6 a to e, respectively. Co 4s, Ca 4s or O 2s, is also rather small in this energy field and not shown. The gap between HVB and LCB of total DOS of [Ca₁₈Ni₃Co₉O₃₆] also shows the semiconductor characteristics. The gap of Ca₃Co₄O₉ is less than that of Ca₃Co₂O₆, and it results from the obvious difference between the electron structures of two systems and should affect electrical conductivity and thermoelectric property. It is indicated from comparing the partial DOS that the main peaks of Co(1) 3d states exist in both of HVB and LCB, but the peaks are some far away from Fermi level. Co(2) 3d states are mainly contribution to LCB and near to Fermi level. The main peaks of O(1) 2p states also exist in both of HVB and LCB, but the peaks are further away from Fermi level. The HVB near Fermi level is mainly the contribution from O(2) 2p states.



Fig.5 DOS of Ca₃Co₂O₆



Fig.6 DOS of Ca₃Co₄O₉

    The contributions to HVB and LCB near Fermi level in Ca₃Co₂O₆ are mainly from O(1) and O(2) 2p, and Co(1) and Co(2) 3d, but those in Ca₃Co₄O₉ are only mainly from O(2) 2p and Co(2) 3d, which is also an obvious difference of partial DOS between Ca₃Co₂O₆ and Ca₃Co₄O₉. Therefore, the semiconductor, or thermoelectric property of Ca₃Co₄O₉ should be mainly from Ca₂CoO₃ layer, but it seems to have no direct relation to the CoO₂ layer. It is well known that binary oxides (such as Co₂O₃) hardly have thermoelectric property, but trinary oxide compounds (such as Ca₃Co₂O₆ and Ca₃Co₄O₉) have quite good thermoelectric property, which is consistent with our conclusion. Binary oxides often have high ionic or covalent character, such CoO₂ layer in Ca₃Co₄O₉ (Table 1), so hardly have good thermoelectric property. Co-O ionic and covalent bonds of Ca₃Co₂O₆ and Ca₂CoO₃ layer in Ca₃Co₄O₉ are all weaker than those of CoO₂ layer in Ca₃Co₄O₉, and the component Ca can decrease ionic and covalent bond strength.
    In Ca₃Co₄O₉ the first-neighboring 6 oxygen atoms to Co(1) are all in the CoO₂ layer, and the first-neighboring 8 oxygen atoms to Co(2) are all in the Ca₂CoO₃ layer. In other word, there is no direct interaction between Co and O in the different layers. On the other hand, the first-neighboring 8 oxygen atoms to Ca are in both of CoO₂ and Ca₂CoO₃ layers. Therefore, Ca plays a role to connect interaction between CoO₂ and Ca₂CoO₃ layers. In Ca₃Co₂O₆ the first-neighboring 6 oxygen atoms to Co(1) are all O(1), and those to Co(2) are 3 O(1) and 3 O(2). The oxygen atoms coordinate to both Co(1) and Co(2) that neighbors each other are in the same -Co(1)O₃-Co(2)O₃- ... chain. Therefore, there is no direct interaction between Co and O in the different chains. The first-neighboring 8 oxygen atoms to Ca are O(1) and O(2), and these oxygen atoms coordinate several cobalt atoms in the different chains. Ca also plays a role to connect interaction among  ... -Co(1)O₃-Co(2)O₃- ... chains.

4 CONCLUSIONS
The gaps between the highest valence band (HVB) and the lowest conduction band(LCB) of density of state of Ca₃Co₂O₆ and Ca₃Co₄O₉ both show the semiconductor property, and the gap of Ca₃Co₄O₉ is less than that of Ca₃Co₂O₆.
    The contributions to HVB and LCB near Fermi level in Ca₃Co₂O₆ are mainly from O(1) and O(2) 2p, and Co(1) and Co(2) 3d, but those in Ca₃Co₄O₉ are only mainly from O(2) 2p and Co(2) 3d in Ca₂CoO₃ layer. Therefore, the semiconductor, or thermoelectric property of Ca₃Co₄O₉ should be mainly from Ca₂CoO₃ layer, which is consistent with that binary oxides hardly have thermoelectric property, but trinary oxide compounds have quite good thermoelectric property.
    CoO₂ layer in Ca₃Co₄O₉ has high ionic and covalent character. Ionic and covalent bonds of Ca₃Co₂O₆ and Ca₂CoO₃ layer in Ca₃Co₄O₉ are all weaker than those of CoO₂ layer in Ca₃Co₄O₉. The Co-O covalent and ionic bonds of Ca₃Co₄O₉ are both stronger than those of Ca₃Co₂O₆.
    Ca plays the role to connect the interaction among ...-Co(1)O₃-Co(2)O₃- ... chains in Ca₃Co₂O₆, and to connect the interaction between CoO₂ and Ca₂CoO₃ layers in Ca₃Co₄O₉. The component of Ca also can decrease ionic and covalent bond strength and prove the thermoelectric property.

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