Structural phase transformation in K 2 Se O 4

摘要: Successive phase transformations in ${\mathrm{K}}_{2}$Se${\mathrm{O}}_{4}$ at ${T}_{i}=130$ K and ${T}_{c}=93$ were studied by the neutron-scattering technique. The superlattice reflections intermediate found to be incommensurate with lattice periodicity. wave vector characterizing is ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}}=\frac{(1\ensuremath{-}\ensuremath{\delta}){\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}}^{*}}{3}$ $\ensuremath{\delta}=0.07$ 122.5 K. deviation \ensuremath{\delta} decreases decreasing temperature an apparently discontinuous jump zero ${T}_{c}$. Below this temperature, crystal remains commensurate known ferroelectric. incommensurate-commensurate transition simultaneous occurrence of spontaneous polarization are discussed using a Landau-type expansion free energy which term proportional ${Q}^{3}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}}){P}_{z}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{3\ensuremath{\delta}})$ plays essential role driving transformation inducing polarization. Here, $Q({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}})$ amplitude primary atomic displacements ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}}$ ${P}_{z}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{3\ensuremath{\delta}})$ ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{3\ensuremath{\delta}}=3\ensuremath{\delta}(\frac{{\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}}^{*}}{3})$ becomes macroscopic below Above ${T}_{i}$, ${\ensuremath{\Sigma}}_{2}$ optic-phonon branch along ($\ensuremath{\xi},0,0$) shows striking softening ${\ensuremath{\omega}}_{j}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\sim}(\frac{1}{3},0,0)$ tends ${T}_{i}$. results from temperature-dependent decrease interlayer forces ranges $\frac{a}{2}$ $a$ ($a$ one unit-cell length axis) presence strong persisting range $\frac{3a}{2}$. intensities soft phonon measured about different reciprocal-lattice points used determine nature soft-phonon mode suggest coupled translation potassium ions rotational motion Se${\mathrm{O}}_{4}$ groups origin instability.