The fixed triangle chemical bond and its effect in the y _1-xCa_xBa_2-yla_yCu₃O _z system from underdoped to overdoped

Samples of Y_1-x:Ca_x:Ba_2-y,La _yCu₃O_z (YCBLCO) were synthesized by the standard solid-state reaction with both x and y taking values from 0 to 0.5. Structural and superconducting properties have been investigated by x-ray diffraction, Rietveld refinement and dc magnetization measurement. The threedimensional phase diagram in the YCBLCO system is obtained, describing the dependence of T_c on the content of two dopants simultaneously. By careful study of the chemical bond lengths related to the Cu(2)O₂ plane and the Cu(1) - O chain, it is found that T_c has opposite dependences on the bond lengths of Cu(1) - O(4) or Cu(2) - O(4) in the underdoped (x < y) and overdoped (x > y) regions. In addition, calculation of the bond angles for the optimal-doped samples indicates that T_c is closely related to four pairs of bond angles, all of which characterize the curvature of the CuO₂ plane. It is demonstrated that the interaction between the perovskite block and the rock salt block in a unit cell has a close relationship with the superconductivity. The calculation of bond lengths and angles indicates that Cu(2), O(2) and O(3) on the CuO₂ plane form a 'fixed triangle', independent of the doping level in the system. It is suggested that the collective behavior of the fixed angle might result in a particular phonon mode, which may induce a special kind of electron - phonon coupling, different from that appearing in conventional superconductors. This may be of great importance for uncovering the elusive mechanism of high-temperature superconductivity.