Structural phase transitions in the perovskite-type layer compounds N${\mathrm{H}}_3$${\left(\mathrm{C}{\mathrm{H}}_2\right)}_3$N${\mathrm{H}}_3$Cd${\mathrm{Cl}}_4$, N${\mathrm{H}}_3$${\left(\mathrm{C}{\mathrm{H}}_2\right)}_4$N${\mathrm{H}}_3$Mn${\mathrm{Cl}}_4$, and N${\mathrm{H}}_3$${\left(\mathrm{C}{\mathrm{H}}_2\right)}_5$N${\mathrm{H}}_3$Cd${\mathrm{Cl}}_4$

The structural phase transitions in the perovskite-type layer-structure compounds [N${\mathrm{H}}_3$ ${\left(\mathrm{C}{\mathrm{H}}_2\right)}_3$N${\mathrm{H}}_3$]Cd${\mathrm{Cl}}_4$ ($T_c=375\mathrm{} \mathrm{K}$), [N${\mathrm{H}}_3$ ${\left(\mathrm{C}{\mathrm{H}}_2\right)}_4$N${\mathrm{H}}_3$]Mn${\mathrm{Cl}}_4$ ($T_c=382\mathrm{} \mathrm{K}$), and [N${\mathrm{H}}_3$ ${\left(\mathrm{C}{\mathrm{H}}_2\right)}_5$N${\mathrm{H}}_3$]Cd${\mathrm{Cl}}_4$ ($T_c=338\mathrm{} \mathrm{K}$) have been studied by ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ and deuteron quadrupole resonance spectroscopy, birefringence, and dilatation measurements, optical-domain investigations and group-theoretical considerations. The results show that this transition, which is for all three compounds of second order, is basically a dynamic order-disorder transition of the alkylenediammonium chains, each of which can take on four different states (two all-trans states and two twisted states). The high-temperature phase is characterized by a dynamical disorder of the chains between the four possible states, the twisted states being less populated because of their higher potential energy. In the low-temperature phase, well below the phase transition, the chains are completely ordered in one of the two all-trans states. A strong even-odd effect, concerning the number of carbon atoms in the alkylene chains, has been observed in the temperature dependence of the static dielectric constant and in the critical exponent $\beta$ of the order parameter. This is connected with the symmetry of the chains in the all-trans state which is $\mathrm{mm}2\mathrm{}$ for "odd" chains and $\frac{2}{m}$ for "even" chains. In contrast to the "even" chains the "odd" chains can thus carry a permanent electric dipole moment. As a consequence the phase transition in the two Cd compounds is of antiferrodistortive nature and leads from a paraelectric phase to an antiferroelectric phase, whereas the Mn compound undergoes a proper ferroelastic transition, although the microscopic mechanism is the same for both types. It is shown that the order-disorder transition in these compounds can be described adequately with a microscopic rigid-lattice model in the mean-field approximation.