Phenomenological theory of the isostructural phase transition in H-bonded Sn${\mathrm{Cl}}_2$ · ${\left({\mathrm{H}}_2\mathrm{O}\right)}_2$ and $\mathrm{Sn}{\mathrm{Cl}}_2·{\left({\mathrm{H}}_2\mathrm{O}\right)}_x{\left({\mathrm{D}}_2\mathrm{O}\right)}_{2-x}$ with a pseudospin model

With the use of a statistical Green's-function technique and at the suggestion of Ishibashi [J. Phys. Soc. Jpn. 49, 613 (1980)] the two-sublattice pseudospin-phonon-coupled-mode (PLCM) model has been extended, for the first time, to explain the isostructural phase transitions in Sn${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O and its partially deuterated forms. The expressions for the transition temperature ($T_C$), Curie-Weiss constant ($C$), dielectric constant ($\epsilon$), and renormalized phonon spectrum have been derived and fitted with the available experimental data, and a single set of model parameters has been obtained. The experimental values of $\epsilon$ (for the pure salt) and the isotope dependences of $T_C$ have been found to agree well with our calculated values. Using Ishibashi's formula and the calculated parameters of our model a symmetrical thermal behavior (around $T_C$) of heat capacity has also been predicted. Our present model can explain simultaneously the thermal behavior of both dielectric constant and heat capacity which is, however, not possible with the well-known dimer model. The exponents of the "staggered polarization" obtained from our calculations are found to be 0.41 for $T<\mathrm{}{T}_0$ and 0.40 for $T>\mathrm{}{T}_0$. These values agree well with those obtained from recent neutron-diffraction results by Youngblood and Kjems [Phys. Rev. B 20, 3792 (1979)]. The two-sublattice pseudospin model may, therefore, be considered as a unified model applicable for Rochelle salt, K${\mathrm{H}}_2$P${\mathrm{O}}_4$, Sn${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O, and similar other H-bonded salts with suitable modifications. This also suggests the unified character of the PLCM model.