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 ($\ensuremath{\omega}g{10}^{11}$ 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).

Soft-mode spectroscopy: Experimental studies of structural phase transitions

Structural phase transitions can be studied by a variety of techniques; macroscopic fields, X-ray, light and neutron diffraction, and resonance methods. The information which can be obtained by these different techniques about the order parameter and susceptibility at structural phase transitions is described and compared. Landau theory coupled with the ‘soft mode’ concept provides a simple picture of many structural phase transitions in terms of relatively few phenomenological constants. A review is given of the application of this type of theory to the wide variety of different phenomena which can occur at structural phase transitions. In particular, emphasis is placed on the nature of the fluctuations within Landau-Ginzburg theory and on the role of secondary order parameters. The nature of incommensurate phases and of lock-in phase transitions are discussed using both the conventional lattice dynamical approach and the soft soliton theories. The parameters of the Landau theory can, in princip...

Structural phase transitions I. Landau theory

Imidazolium periodate (IPI) is found to be an improper ferroelectric. It shows bistable properties simultaneously in three channels of dielectricity, piezoelectricity, and second-harmonic generation within the temperature window 300-310 K.

Switchable dielectric, piezoelectric, and second-harmonic generation bistability in a new improper ferroelectric above room temperature.

REVIEWS OF TOPICAL PROBLEMS: Improper ferroelectrics

Beta‐gadolinium molybdate, β‐Gd2(MoO4)3, is ferroelectric and ferroelastic with a Curie temperature of about 160°C and is paramagnetic with a moment of 7.98 μB. β‐Gd2(MoO4)3 crystallizes in the orthorhombic system with space group Pba2 and four formulas in the unit cell. The lattice constants at 298°K are a = 10.38582 ± 0.00014, b = 10.41861 ± 0.00010, and c = 10.70039 ± 0.00004 A. The integrated intensities of 14 490 reflections were measured with PEXRAD, within a hemisphere of reciprocal space of radius (sinθ) / λ = 1.02 A−1. The crystal structure was solved by interpretation of Patterson and Fourier series and refined by the method of least squares, using a total of 2545 symmetry independent Fmeas. The final agreement factor R is 0.089, based on isotropic thermal vibrations for all atoms. X‐radiation exposure introduces appreciable nonrandom error in the Fmeas. The structure consists of three crystallographically independent discrete sets of (MoO4)2− tetrahedra; one set is oriented with apex oxygen ato...

Ferroelectric Ferroelastic Paramagnetic Beta‐Gd2(MoO4)3 Crystal Structure of the Transition‐Metal Molybdates and Tungstates. VI

Results of a number of electrical, optical and mechanical measurements on ferroelectric Gd2(MoO4)3, are presented Based on these results it is concluded that the symmetry in the paraelectric phase above 159°C is tetragonal 42m, and the symmetry below the transition is orthorhombic mm2. Twin walls are shown to be ferroelectric domain walls with the relationship between the polarity of the spontaneous polarization P, and the relative positions of the orthorhombic a and b axes being dictated by the piezoelectric effect in the paraelectric phase. A large mechanical dimension change and large optical effects accompanying ferroelectric switching are discussed and possible applications of these effects are considered briefly.

S. E. Cummins

Papers

Electrical, optical, and mechanical behavior of ferroelectric Gd2(MoO4)3