Oscillation electron model of mixed copper-lanthanum oxide crystals

Abstract

The crystal is represented in the form of individual molecule sublattices. Within oscillation electronic model, a superconducting phase transition in an ABCD crystal is possible when the square plasma energy of the resulting molecular sublattices is equal (or larger) to the square plasma energy of the initial crystal. Lanthanum cuprate crystal is La2CuO4 considered. An elementary cell with two molecules z = 2 is considered, number of sublattices is n = 4. The square plasma energies of the initial crystal A B C D and its individual molecules A2, B2, C2, D2 were calculated. The phase transition curve of a superconductor is described by the quadratic function equation, where Tc is the temperature of the superconducting phase transition, q is the interaction parameter. From the equation of the phase transition curve in pure ideal mixed oxides of lanthanum and copper, a superconducting phase transition is not detected. When Lanthanum La is replaced by Strontium Sr, the superconducting transition temperature Tc reaches a value of up to 40K according to the literature data. Interaction parameter and order parameter are given. The influence of zinc and nickel impurities on the superconductivity of mixed copper and lanthanum oxides is calculated. The superconducting phase transition in a crystal proceeds as follows antiferromagnetic state - spin glass - phase separation - superconducting state. It should be noted that when the transition to the superconducting state of the base crystal, the dopants pass into the antiferromagnetic state. Superconducting - antiferromagnetic - paramagnetic state La, Superconducting - antiferromagnetic - paramagnetic - diamagnetic state Cu, Superconducting - antiferromagnetic - paramagnetic state Sr, Superconducting - antiferromagnetic - paramagnetic - diamagnetic state Zn, Superconducting - antiferromagnetic - paramagnetic - ferromagnetic state Nι. When calculating the temperature of the superconducting transition Tc for a crystal, it is necessary to consider the balance criterion of the square plasma energies, established for each temperature with allowance for thermodynamic equilibrium. Doping causes a violation of thermodynamic equilibrium at a certain temperature. This leads to the formation of valence bonds ―Cu ― О― with the release of energy with decreasing temperature, then a balance of energies is observed at a lower temperature, valence bonds are formed ―Cu ― Cu―, the released energy is spent on breaking the bonds ―Cu ― O― and so on.