Soft-mode spectroscopy: Experimental studies of structural phase transitions

Abstract

This paper reviews the experimental studies of displacive phase transitions in solids. Primary emphasis is upon inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized. Several prototype structures are considered in detail: (1) the rocksalt IV-VI semiconductors PbTe, SnTe, and GeTe; (2) the ferroelectric perovskites exemplified by PbTi${\mathrm{O}}_{3}$ and BaTi${\mathrm{O}}_{3}$; (3) perovskites which exhibit cell-doubling transitions, such as LaAl${\mathrm{O}}_{3}$, SrTi${\mathrm{O}}_{3}$, and KMn${\mathrm{F}}_{3}$; (4) crystals having the $\ensuremath{\alpha}$-quartz structure, including Ge${\mathrm{O}}_{2}$, Si${\mathrm{O}}_{2}$, and AlP${\mathrm{O}}_{4}$; (5) the "improper ferroelectrics" ${\mathrm{Gd}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$ and ${\mathrm{Tb}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$; (6) the V-VI-VII semiconductors typified by SbSI; (7) the hydrogen-bonded ferroelectrics of the K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ family; (8) Jahn-Teller systems such as DyV${\mathrm{O}}_{4}$ and RbCo${\mathrm{F}}_{3}$, in which structural distortions occur as secondary effects; (9) order-disorder systems such as NaN${\mathrm{O}}_{2}$ and the ammonium halides (N${\mathrm{H}}_{4}$Cl, N${\mathrm{H}}_{4}$Br), in which no "soft mode" occurs in the spectral region ($\ensuremath{\omega}>{10}^{11}$ Hz) probed by ir, Raman, and neutron spectroscopy; (10) $\ensuremath{\beta}$-tungsten ($A\ensuremath{-}15$) structures such as ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn, which exhibit high-temperature superconductivity. These crystal categories are used to illustrate several phenomena of current physical interest: Specifically, we discuss harmonic and anharmonic mode coupling; "critical exponents" $\ensuremath{\beta}$ differing from one-half in the temperature dependences of the order parameter $\ensuremath{\phi}(T)={\ensuremath{\phi}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$ and of the soft-mode frequency $\ensuremath{\omega}(T)={\ensuremath{\omega}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$; and the recently discovered "central" modes centered at zero frequency, which grow in intensity as the transition temperature ${T}_{0}$ is approached from above or below. The review covers the period 1940-1972. A few 1973 works are mentioned for which the author had preprints in 1972 or very early 1973. This review is in no sense a comprehensive survey of ferroelectricity. Readers are referred to the following earlier reviews on that subject: Silverman (1966, 1969), Cochran and Cowley (1967), Blinc (1968), Murzin et al. (1968), Nettleton (1970), and Blinc and Zaks (1972).