A CLUSTER MODEL OF QUASI-ONE-DIMENSIONAL H(D)-ORDERING PHASE-TRANSITIONS

Basing on the previous study on Isotope effect in hydrogen bonded crys tals, the equation for the critical temperature T(c) is presented in a cluster approximation. The obtained T(c) includes the information of hydrogen bond lengths (oxygen-oxygen distance R(O-O), hydrogen-hydroge n distance R(H-H) etc.), and has an extended form of that in pseudo-sp in model which gives the exact solution in the one-dimensional hydroge n bonded systems. From theoretical viewpoint, experimental data of T(c )-R(O-O) and T(c)-R(H-H) relations are analyzed. It is pointed out tha t the quantum effect of H(D) atoms leads to the isotope effect in thes e geometric values, but this isotope effect contributes to T(c) in a q uite different manner depending on R(O-O).