Rochelle salt - a structural reinvestigation with improved tools. I. The high-temperature para-electric phase at 308 K

Unusual features of lattice dynamics in lawsonite near its phase transitions

Lattice dynamics of a single crystal of lawsonite were studied over a broad range of frequencies (1 Hz to 20 THz) using impedance, THz time-domain and infrared spectroscopies. Based on polarized spectra of complex permittivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\varepsilon }$$\end{document}ε^ measured as a function of temperature between 10 K and 500 K, we analyzed the properties of the two known phase transitions—an antiferrodistortive one near \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}1}=270\,\mathrm{K}$$\end{document}Tc1=270K and a ferroelectric one, occurring at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}2}=124\,\mathrm{K}$$\end{document}Tc2=124K. The former one is accompanied by a flat maximum in the THz-range permittivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\varepsilon }_{\mathrm{c}}$$\end{document}ε^c near \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}1}$$\end{document}Tc1, which is due to an overdamped polar excitation in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {E} \parallel c$$\end{document}E‖c spectra reflecting the dynamics of water and hydroxyl groups. The strength of this mode decreases on cooling below \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}1}$$\end{document}Tc1, and the mode vanishes below \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}2}$$\end{document}Tc2 due to hydrogen ordering. At the pseudoproper ferroelectric phase transition, two independent anomalies in permittivity were observed. First, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\varepsilon }_a$$\end{document}ε^a exhibits a peak at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}2}=124\,\mathrm{K}$$\end{document}Tc2=124K due to critical slowing down of a relaxation in the GHz range. Second, infrared and THz spectra revealed an optical phonon softening towards \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}2}$$\end{document}Tc2 which causes a smaller but pronounced maximum in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\varepsilon }_b$$\end{document}ε^b. Such anomaly, consisting in a soft mode polarized perpendicularly to the ferroelectric axis, is unusual in ferroelectrics.

Assessment of phase transition and thermal expansion coefficients by means of secondary multiple reflections of Renninger scans

This paper reports the successful extension of the basis of the X-ray multiple diffraction phenomenon in the assessment of structural phase transitions and the determination of thermal expansion coefficients along three crystallographic directions, using synchrotron radiation Renninger scans. Suitable simultaneous four-beam cases have accurately resolved the lattice-parameter variation in a nearly perfect single-crystal Rochelle salt using a high-stability temperature apparatus. Secondary reflections observed in the Renninger patterns, chosen by their sensitivity to the shifts in angular position as a function of temperature, have allowed the detection of a monoclinic to orthorhombic phase transition, as well as subtle expansions of all the basic lattice parameters, i.e. without having to carry out measurements on each crystal axis. The thermal expansion coefficients have been estimated from the linear fit of the temperature dependence of the lattice parameters, and are in agreement with those reported in the literature.