The emergence of the cell-doubled (OII) and both cell-tripled (OIII and OII
I*) phases of YBa2Cu3O6+x are observed on oxygen-chain-equalized and order-
stabilized pair samples at an extended range of oxygen concentrations (0.28
<x<0.83), including the interval of x, which is characteristic of the onset
of superconductivity. The phase diagram for the asymmetric next-nearest-ne
ighbor interaction model, extended to include an additional longer-range in
teraction potential between oxygen atoms, is calculated and compared to two
experimental phase diagrams, obtained for intercalated as well as for dein
tercalated members of the pair samples. A fairly good agreement with experi
mental data on locations of the OII, OIII, and OIII* phases in the phase di
agram and on the average length of the O-Cu-O chains is obtained.