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 $\alpha$-quartz structure, including Ge${\mathrm{O}}_2$, Si${\mathrm{O}}_2$, and AlP${\mathrm{O}}_4$; (5) the "improper ferroelectrics" ${\mathrm{Gd}}_2$ ${\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$ and ${\mathrm{Tb}}_2$ ${\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$; (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 ($\omega >{10}^{11}$ Hz) probed by ir, Raman, and neutron spectroscopy; (10) $\beta$-tungsten ($A-15\mathrm{}$) 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" $\beta$ differing from one-half in the temperature dependences of the order parameter $\varphi \mathrm{}\left(T\right)={\varphi }_0{(T-T_0)}^{\beta }$ and of the soft-mode frequency $\omega \mathrm{}\left(T\right)={\omega }_0{(T-T_0)}^{\beta }$; 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).