Geometric distribution of CuO chains in YBa2Cu3O6+x

The dependence of critical temperature on oxygen concentration in YBa2Cu3O6+x in terms of the fragmented chain model

“…The above length distributions hold for practically the whole ( T ) space of the phase diagram, in the case of the bare ASYNNNI model [24], and also for the fragmented chain model [25], with the only departure being detected in a narrow region around second order phase transition lines in accordance with theoretical predictions [36]. When (A1) is inserted into (1) the expression for doping (2) (A3) where the first term gives the doping α1 ( ) that originates from CuO chains on the α 1 sublattice, while the second term is the contribution to doping, α2 ( ), from the chains residing on α 2 sites.…”

Chain length probability distribution — equivalence of ASYNNNI and 1d Ising model

“…This result was derived, in the case of low temperatures, by studying the structure of low energy levels and was confirmed in Monte Carlo numerical simulations for Ortho I and II structural phases. The result was confirmed for the Ortho II structural phase at a temperature of T ≈ 450 K, where T is the oxygen equilibrium temperature [18], and in the case of the Ortho I phase for temperatures as high as T ≈ 1800 K [17]. Furthermore, it was concluded that this specific form of the chain probability distribution should be valid for all oxygen concentrations, and all temperatures where the orthorhombic structures are stable, except in the close vicinity of the line of the critical points [18].…”

“…The result was confirmed for the Ortho II structural phase at a temperature of T ≈ 450 K, where T is the oxygen equilibrium temperature [18], and in the case of the Ortho I phase for temperatures as high as T ≈ 1800 K [17]. Furthermore, it was concluded that this specific form of the chain probability distribution should be valid for all oxygen concentrations, and all temperatures where the orthorhombic structures are stable, except in the close vicinity of the line of the critical points [18]. Since the same geometric chain length probability distribution also applies in the case of the infinite one dimensional Ising model [19,20], the conclusion was made that the result obtained is another manifestation of the previously established low temperature equivalence between ASYNNNI and 1d Ising model, in which the role of the Ising chain NN coupling J is played by the NNN interaction V 2 of the ASYNNNI model [21].…”

“…Recently, the plain ASYNNNI model has been employed in extensive studies of the properties of the distribution of the CuO chains with respect to chain length [17,18]. It was found that the chain length probability distribution satisfies the simple geometrical law [17] i.e.…”

Charge transfer mechanism andTc(x) dependence in Y0.8(Ca)0.2Ba2Cu3O6+x

“…Such behavior of length distributions ensures a rapid convergence of summations in equation (2). Although theoretical study has shown that a certain departure from geometric-like behavior of f(l)s can be expected in narrow interval Δx≈0.07 around critical point of the OI-to-OII phase transition, due to increased fluctuations of energy of the ASYNNNI model [18], our extended analysis has inferred that such departures are nevertheless compensated by sums in (2) [26], so that the doping can be expressed in the following integrated form ( ) …”