Note on the Theory of the Ih-XI Transition in Ice

Abstract

The lattice structure possible in the low-temperature phase of the Ih-XI transition in ice is studied from a statistical mechanical viewpoint. The entropy is calculated as a function of order parameters to clarify the role of the ice constraint within the Bragg-Williams approximation. The internal energy is introduced only in the quadratic form of order parameters. The order parameter is proved to show the jump between 1 and 0 at the Ih(P6₃⁄mmc)-Cmc2₁ transition in analytical manner. The Ih-P6₃mc transition was recently proposed on the basis of experimental results of neutron diffraction, but is proved to be of second order contrary to the experimental results indicating the first order transition accompanied with the anomalously large thermal relaxation time.