J. Phys. Chew. Solids Vol. 52. No. 5. pp. 659-663, Printed in Great Britain.
0022-3697/91 S3.00 + 0.00 Q 1991 Pergamon Press plc
COORDINATION CHEMISTRY AND SUPERCONDUCTIVITY ZENG ZUOTAO Changchun Institute of Applied Chemistry, Academia Sinica, Changchun 130022,P.R. China (Received
1990; accepted 31 October
Abstract-Analysing the coordination state of copper ions in cuprate superconductors, it is found that the larger the energy splitting between dx2_,2 and $ orbitals of Cu or the higher the energy of the cf,,_, orbital, the higher the Tc. Thus, appropriate coordination structures and strong-field ligands must be chosen for expanding the energy splitting and increasing the energy of the d,, _p orbital when searching for new high-Tc superconductors. Summarizing the experimental results of ESR and XPS, it is considered that the [Cu2+ - Ok - Cu3+] resonance exists in cuprate superconductors and the electron field breathing mode is present. Analysing the mechanism and the relationship between the coordination state of Cu and Tc, we consider that the two dimensional Cu-0 planes are responsible for the superconductivity of YBa,Cu,O,_,. Keyword: Cuprate superconductors, electron field breathing mode.
INTRODUCTION Since Bednorz and Muller [I] discovered the La-Ba-Cu-0 superconductor, a series of cuprate superconductors have been discovered. So far, 20 types of cuprate superconductors have been obtained. Comparing with Bi-K-Baa  and Bi-PbBa-O  superconductors, the structures of cuprate superconductors also are of the perovskite type, but the Tc of cuprate superconductors generally is higher than of the others. This may be caused by the special electron configuration of the copper ion. Cu*+ is the only ion
with the d9 electron configuration. Its Jahn-Teller distortions raise special questions in crystallography and coordination chemistry. Comparing the coordination state of copper ion in superconductors can help us to recognize the nature of high-Tc superconductors and to search for new high-Tc superconductors. Bok  considered that the larger the number of CuO, layers, the higher the Tc. But the Tc values of TlBa,Ca, Cu,O,, _~ with four CuO, layers and TlBa,Ca,Cu,O,,_, with five Cu02 layers are all lower than the Tc of Tl, BazCa,Cu,O,,+,, with only three CuO, layers. So the view of Bok is questionable and the essentials of the question seem not to have been considered. In this paper, we present some relationship among Tc and the coordination structure of copper ion and the energy of the d,,_,,, orbital. From this, we can understand easily why Tc increases with the number, n, of adjacent CuO, layers in Tl-base superconductors for n < 3 and that Tc does not change significantly for n > 3. THE COORDINATION STATE OF COPPER ION IN CUPRATE SUPERCONDUCTORS
Table 1 shows the relations between Tc and the coordination state of Cu in cuprate superconductors. PCS 5215-B
crystal-field splitting, Cu2+-02--Cu3+
All cuprate superconductors which have been found so far can be divided into three classes according to the value of Tc: (i) the superconductors with Tc lower than 30 K are La*_ ,M,CuO, (M = Ba, Sr, Ca, Na) [1,5-q, Bi2Sr,Cu0,+,, , TlBa,CuO,_, [9-lo], TlzBazCuOs+, [ll] and Nd,_,Ce,CuO, ; (ii) the superconductors with Tc between liquid nitrogen temperature and 100 K are LnBa,Cu,O, _y  (Ln = rare earth element) YBa,Cu,O,+, , [ll], Bi, Sr, CaCu, O8+ x [IS, 161, TlBa2CaCu,07_,, Tlz Ba, CaCu, 0s +x , Pb2Sr2LnCu,0t,+, [18, 191, Pb,,5Sr2.5Y,_,Ca,Cu,O,_, , TlCa, _,Ln,Sr2Cu,0,_, [21,22] and Tlo,5Pbo,5SrZCaCu20,+,  and (iii) the superconductors with Tc higher than 100 K are Bi2Sr2Ca2Cu,0,,+, , TlBazCazCu,09_, 19,241, Tl,Ba,Ca,Cu,O,,+,, TlBa,Ca,Cu,O,,_, [9, 101, TlBa,Ca,Cu,O,,_, [9,24], T1,,I,Pbo.~SrzCa2Cu,0,+, 1231.
The transition temperatures of superconductors with octahedral structures in their unit cell are all lower than 30 K. The transition temperatures of superconductors with pyramidal structure are higher than liquid nitrogen temperature. Except for Nd2 _ .Ce,CuO,, the transition temperatures of superconductors with square planar structures are higher than 100 K. Nd, _ XCeXCuO.,is the only n-type cuprate superconductor found so far. As its carrier type is different from the others, its properties and mechanism deserve to be studied further. However, in this paper, we will not compare it with other p-type superconductors. There is a rhombic planar structure in the Cu-0 chain of LnBa2Cu,0, _y. The distance between the copper and oxygen ions on the c axis is longer than the distance between copper and the two oxygen ions on the a axis. There is much to argue about the effect of the Cu-0 plane and Cua 659
ZENGZUOTAO :N -
Table 1. The Tc and the coordination state of copper ion in cuprate superconductors Coordination structures
. 49 I
La2-xMxCu04+y (M = Ba, Sr,Ca and Na)
chain [25-281. The question will be discussed later. There are two kinds of coordinate structures of Cu in Pb,Sr,LnCu,OB+,,. Its structure is shown in Fig. 1. The Cu-0 plane with pyramidal coordinate structure extends continuously along the two dimensional plane. The Cu-0 chain with linear coordination structure is isolated and discontinuous. Thus, the Cu-0 chains are not responsible for the superconductivity.
THE d ORBITAL23 OF Cu SPLITTING IN VARIOUS COORDINATION STRUCTURES
Figure 2 shows the d orbitals of Cu splitting in octahedral, pyramidal and square planar coordination structures. The d orbitals split into e,(dx2_,2) and tzp(dxy, d,, , d,,) orbitals in octahedral coordination structures; owing to the J-T effect, the ee
orbital of copper ion splits again. The distance from the copper ion to the four oxygen ions on the ab plane is shorter than the distance between the two oxygen ions on the c axis and, therefore, the energy of the dr2_+ orbital is higher than that of the dz2orbital after distortion. In going from a distorted octahedron to a pyramidal structure, the change amounts to the removal of one oxygen ligand on the z axis from the distorted octahedron. Consequently, the dz2orbital experiences a smaller repulsion from the ligand than in an octahedral structure. This results in a larger energy splitting between the dr2 and dx2_,,2 orbitals. The square planar structure corresponds to the structure with two oxygen ligands on the z axis in the octahedral structure having been removed. This results in a larger decrease in energy for the dz2orbital than for the pyramidal structure.
chemistry and superconductivity
Fig. 3. The 3d orbital energy splitting in planar rhombi and
linear coordination structures.
l oJ 00
Fig. 1. The structure of Pb,Sr,LnCu,O,+,. The strong CF splitting results in an increase of energy for the dx2_v2 orbital. The loss of the electron in dx2_yl orbital becomes easier. Thus, the copper ion in cuprate superconductors can be oxidized easily to a high oxidation state. The energy splitting in various coordination structures expands in the order: octahedral < pyramidal < square planar. At the same time, the energy of the dx2_+ orbital and the Tc of the superconductors increase in the same order. The electrons in the dx2_,,2 orbital, which is the highest energy orbital of the copper ion, take part in the process of superconducting current transportation and the change of the &_,,2 orbital energy should affect the energy band in the Cu-0 layers, and there must be some relationship between superconductivity and the energy of the dx2_,,2 orbital. The higher the energy of the dx2_,,2 orbital, the higher the Tc. For the TlBa, Ca, _ , Ct1.0~ + r system, the coordination structures are octahedral (n = l), pyramidal (n = 2) and square planar (n = 3), respectively. The energy of the dx2_-ylorbital and the Tc of the super-
conductors increase successively when n increases from 1 to 3. However, the coordination structures are still square planar when n increases from 3 to 5, so that Tc remains at around 120 K, and does not increase again. There are four oxygen ligands around the copper ion in both Cu-0 chains in LnBarCu,O,_, and But there is an essential differBi,SrrCa2Cu,0,,,+,. ence between the coordination states in the two compounds. The distance. from the copper ion to the two oxygen ligands on the c axis is shorter than the distance between the two oxygen ligands on the a axis in the Cu-0 chain of LnBarC&O,_,. In contrast the distances are the same from the copper ion to the four oxygen ligands in Bi2Sr2Ca2Cu,0k,+,. The coordination structure corresponds to the structure in which the two oxygen ligands on the y axis, rather than on the z axis, in the octahedral structure have been removed. This results in a decrease in the energy of the dx2_+ orbital. The dz2 orbital is the highest energy orbital in this coordination structure. Figure 3 shows the d orbitals splitting into rhombic planar and linear coordination structures. As the energy of the dz2 orbital is the highest among the d orbitals of Cu in the Cu-0 chain, the d electron configuration of Cu2+ is d&,d~zd$d~2_pdf2. However, the d electron configurations of Cu*+ for other coordination structures are d~zd&d&d:id~2_, or d&d&dfid!&dl _+. There are isolated Cu-0 chains in Pb, Sr, LnCu, 0, +Y. The distance between the G_yz
Fig. 2. The 3d orbital energy splitting in octahedral, pyramidal and square planar coordination structures.
copper and oxygen ion is 1.826 A. It approaches the Cu-0 distance on the c axis in the Cu-0 chain of LnBazCu, 0, _ y. So the d electron configuration is d~yd~2_y2d&d&d: also. Its structure corresponds to the structure in which the four oxygen ligands on the x and y axes in the octahedral structure have been removed. As the oxidation state of the copper ion in Cu-0 based superconductors is between +2 and + 3, the magnetic moment of Cu should be higher than Cuz+ if Cu3+ were in the high-spin state. But the experimental results  indicate that the magnetic moment is very small. So Cu3+ should be in the low-spin state if it existed in Cu-0 based superconductors. This means that the . d electronic configuration of Cu’+ in the Cu-0 chain should be d$.yd$_y2d;zd&d$ and the dx2_y2 orbital should be fully empty in other coordination structures. THE lCuz+-O~~u3+) RESONANCE STATE IN Cu-0 LAYERS Only a slight signal of Cu*+ has been observed in ESR experiments on YBa2Cu307_y and the signal may originate from the impurity phase . Thus, there are scarcely any independent divalent copper ions in YBa,Cu,O, _y. There is no Cu*+ signal in ESR experiments on BiSrCaCu,O, . We did not observe any CU*+ signals in our ESR experiment on Bi,,, Pb,, Sr, Ca,-Cu, 0, either. But the Cu’+ was not observed in the XPS experiment either. Summarizing the experimental results of ESR and XPS, we can conclude that the state of the copper ion in high-Tc superconductors is different from the ionic state in general mixed-valence compounds. The copper ion does not consist of independent Cu*+ and Cu3+ ions, but is in a complex state between +2 and +3 valence. Recently, the O:- ion was found in YBa,Cu30,_, . This indicates the existence of a 0, hole. So it may be considered that the resonance between Cu2+ and Cu’+ through oxygen bridges exists in cuprate superconductors. The copper ion is in the [Cu*+-O&-Cu’+] resonance state. The state is similar to the state in a benzene ring. The one which is in the highest energy d orbitals of Cu cruises over the whole Cu-0 layer through oxygen bridges and belongs to the whole Cu-0 layer rather than to only any one of the copper ions. There are neither independent Cu2+ nor independent Cu’+, SO that the Cu*+ signal cannot be observed in an ESR experiment and the Cu3+ signal cannot be observed in an XPS experiment either. The resonance of [Cu*+-O2,- - Cu’+ ] (IJ represents hole) makes the charge move freely in the Cu-0 layers. This supplies the carriers for the cuprate superconductors. DISCUSSIONS ABOUT SUPERCONDUCTING MECHANISM David et al.  considered that there is a disproportionateness of Cuz+ into Cu+ and Cd+ and this
Fig. 4. Schematic view of the proposed electron field breathing mode of the Cu-0 sheets.
leads to a breathing vibration in the Cu-0 sheets. But the breathing mode cannot explain why the isotope effect is not observed in YBa,Cu,O,_, . We consider that the breathing vibration can be produced in another way rather than the disproportionateness of Cu*+ into Cu+ and Cu’+. The oxidation state of the copper ion is between +2 and +3. The highest energy electron of Cu*+ is in the dx2_p orbital in the Cu-0 plane. When the valency fluctuation between Cu*+ and Cu3+ occurs, the emptying and filling of the dx2_y2orbital can lead to an attracting and repelling action on the surrounding electron cloud and the charge density waves will occur in the electron sea of the Cu-0 plane, as shown in Pig. 4. As the ionic polarizability of oxygen is large, the shape of its 2p electron cloud can be changed easily. The 3d electron clouds of the copper ions extend farther, so that its shape can also be changed easily. Thus, the vibration of electron clouds can be separated from the lattice vibrations when the vibration frequency is higher and an electron field breathing wave appears. When a hole is close to a copper ion, it will lead to the contraction of the 3dx2_,2 electron cloud and the electron cloud will expand when the hole leaves. Thus, the motion of the hole will couple with the electron field breathing wave and Cooper pairs will be generated by the interaction mediated by the electron field breathing wave. As the frequency of the electron cloud vibration can be much higher than the lattice vibration, the electron field breathing wave can be transmitted independently and not affected by the lattice vibration. Thus, isotope substitution does not affect the superconductivity. As the motion of the hole immediately leads to the breathing vibration of the dxl_yl electron cloud, it may be considered that there is a strong coupling
Coordination chemistry and superconductivity
between them. The frequency of the electron field breathing wave is higher than the lattice vibration. These two reasons lead to the cuprate superconductors having a higher Tc. The energy of the & orbital is the highest in the Cu-0 chain of YBa,Cu,O,_,. Carriers move through dr2orbitals. The valency fluctuation between Cu2+ and Cu3+ leads to the extension and contraction of the dz2 electron cloud. As this vibration direction is vertical to the Cu-0 chain, the transmission of the wave caused by the vibration of the dz2electron cloud is difficult. So it may be considered that the Cu-0 chain is not responsible for the superconductivity. For other cuprate superconductors, their highest energy orbitals are all dx2_-ylorbitals rather than dz2. There are only Cu-0 planes in which the coordination structures are pyramidal in Bi, Sr, CaCu, 0, +y, and TlBa,CaCu,O,_,, not in T12Ba2CaCu20,+, the CuO chain at all, but their superconducting transition temperatures are all about 90 K. Thus, the Cu-0 planes are responsible for the superconductivity of YBa, Cu, 0, _ y. CONCLUSIONS resonance exists in cuprate [cl?+ - O&-Cu3+] superconductors. The charge fluctuation in the electron field of Cu-0 layers can lead to the formation of an electron field breathing wave. The interaction
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